--- /dev/null
+/**
+ * @file ed448goldilocks/decaf.c
+ * @author Mike Hamburg
+ *
+ * @copyright
+ * Copyright (c) 2015-2016 Cryptography Research, Inc. \n
+ * Released under the MIT License. See LICENSE.txt for license information.
+ *
+ * @brief Decaf high-level functions.
+ *
+ * @warning This file was automatically generated in Python.
+ * Please do not edit it.
+ */
+#define _XOPEN_SOURCE 600 /* for posix_memalign */
+#include "word.h"
+#include "field.h"
+
+#include <decaf.h>
+#include <decaf/ed448.h>
+
+/* Template stuff */
+#define API_NS(_id) decaf_448_##_id
+#define SCALAR_BITS DECAF_448_SCALAR_BITS
+#define SCALAR_SER_BYTES DECAF_448_SCALAR_BYTES
+#define SCALAR_LIMBS DECAF_448_SCALAR_LIMBS
+#define scalar_t API_NS(scalar_t)
+#define point_t API_NS(point_t)
+#define precomputed_s API_NS(precomputed_s)
+#define IMAGINE_TWIST 0
+#define COFACTOR 4
+
+/* Comb config: number of combs, n, t, s. */
+#define COMBS_N 5
+#define COMBS_T 5
+#define COMBS_S 18
+#define DECAF_WINDOW_BITS 5
+#define DECAF_WNAF_FIXED_TABLE_BITS 5
+#define DECAF_WNAF_VAR_TABLE_BITS 3
+
+#define EDDSA_USE_SIGMA_ISOGENY 0
+
+static const int EDWARDS_D = -39081;
+static const scalar_t point_scalarmul_adjustment = {{{
+ SC_LIMB(0xc873d6d54a7bb0cf), SC_LIMB(0xe933d8d723a70aad), SC_LIMB(0xbb124b65129c96fd), SC_LIMB(0x00000008335dc163)
+}}}, precomputed_scalarmul_adjustment = {{{
+ SC_LIMB(0xc873d6d54a7bb0cf), SC_LIMB(0xe933d8d723a70aad), SC_LIMB(0xbb124b65129c96fd), SC_LIMB(0x00000008335dc163)
+}}};
+
+const uint8_t decaf_x448_base_point[DECAF_X448_PUBLIC_BYTES] = { 0x05 };
+
+#define RISTRETTO_FACTOR DECAF_448_RISTRETTO_FACTOR
+const gf RISTRETTO_FACTOR = {{{
+ 0x42ef0f45572736, 0x7bf6aa20ce5296, 0xf4fd6eded26033, 0x968c14ba839a66, 0xb8d54b64a2d780, 0x6aa0a1f1a7b8a5, 0x683bf68d722fa2, 0x22d962fbeb24f7
+}}};
+
+#if IMAGINE_TWIST
+#define TWISTED_D (-(EDWARDS_D))
+#else
+#define TWISTED_D ((EDWARDS_D)-1)
+#endif
+
+#if TWISTED_D < 0
+#define EFF_D (-(TWISTED_D))
+#define NEG_D 1
+#else
+#define EFF_D TWISTED_D
+#define NEG_D 0
+#endif
+
+/* End of template stuff */
+
+/* Sanity */
+#if (COFACTOR == 8) && !IMAGINE_TWIST && !UNSAFE_CURVE_HAS_POINTS_AT_INFINITY
+/* FUTURE MAGIC: Curve41417 doesn't have these properties. */
+#error "Currently require IMAGINE_TWIST (and thus p=5 mod 8) for cofactor 8"
+ /* OK, but why?
+ * Two reasons: #1: There are bugs when COFACTOR == && IMAGINE_TWIST
+ # #2:
+ */
+#endif
+
+#if IMAGINE_TWIST && (P_MOD_8 != 5)
+ #error "Cannot use IMAGINE_TWIST except for p == 5 mod 8"
+#endif
+
+#if (COFACTOR != 8) && (COFACTOR != 4)
+ #error "COFACTOR must be 4 or 8"
+#endif
+
+#if IMAGINE_TWIST
+ extern const gf SQRT_MINUS_ONE;
+#endif
+
+#define WBITS DECAF_WORD_BITS /* NB this may be different from ARCH_WORD_BITS */
+
+extern const point_t API_NS(point_base);
+
+/* Projective Niels coordinates */
+typedef struct { gf a, b, c; } niels_s, niels_t[1];
+typedef struct { niels_t n; gf z; } VECTOR_ALIGNED pniels_s, pniels_t[1];
+
+/* Precomputed base */
+struct precomputed_s { niels_t table [COMBS_N<<(COMBS_T-1)]; };
+
+extern const gf API_NS(precomputed_base_as_fe)[];
+const precomputed_s *API_NS(precomputed_base) =
+ (const precomputed_s *) &API_NS(precomputed_base_as_fe);
+
+const size_t API_NS(sizeof_precomputed_s) = sizeof(precomputed_s);
+const size_t API_NS(alignof_precomputed_s) = sizeof(big_register_t);
+
+/** Inverse. */
+static void
+gf_invert(gf y, const gf x, int assert_nonzero) {
+ gf t1, t2;
+ gf_sqr(t1, x); // o^2
+ mask_t ret = gf_isr(t2, t1); // +-1/sqrt(o^2) = +-1/o
+ (void)ret;
+ if (assert_nonzero) assert(ret);
+ gf_sqr(t1, t2);
+ gf_mul(t2, t1, x); // not direct to y in case of alias.
+ gf_copy(y, t2);
+}
+
+/** identity = (0,1) */
+const point_t API_NS(point_identity) = {{{{{0}}},{{{1}}},{{{1}}},{{{0}}}}};
+
+/* Predeclare because not static: called by elligator */
+void API_NS(deisogenize) (
+ gf_s *__restrict__ s,
+ gf_s *__restrict__ inv_el_sum,
+ gf_s *__restrict__ inv_el_m1,
+ const point_t p,
+ mask_t toggle_s,
+ mask_t toggle_altx,
+ mask_t toggle_rotation
+);
+
+void API_NS(deisogenize) (
+ gf_s *__restrict__ s,
+ gf_s *__restrict__ inv_el_sum,
+ gf_s *__restrict__ inv_el_m1,
+ const point_t p,
+ mask_t toggle_s,
+ mask_t toggle_altx,
+ mask_t toggle_rotation
+) {
+#if COFACTOR == 4 && !IMAGINE_TWIST
+ (void)toggle_rotation; /* Only applies to cofactor 8 */
+ gf t1;
+ gf_s *t2 = s, *t3=inv_el_sum, *t4=inv_el_m1;
+
+ gf_add(t1,p->x,p->t);
+ gf_sub(t2,p->x,p->t);
+ gf_mul(t3,t1,t2); /* t3 = num */
+ gf_sqr(t2,p->x);
+ gf_mul(t1,t2,t3);
+ gf_mulw(t2,t1,-1-TWISTED_D); /* -x^2 * (a-d) * num */
+ gf_isr(t1,t2); /* t1 = isr */
+ gf_mul(t2,t1,t3); /* t2 = ratio */
+ gf_mul(t4,t2,RISTRETTO_FACTOR);
+ mask_t negx = gf_lobit(t4) ^ toggle_altx;
+ gf_cond_neg(t2, negx);
+ gf_mul(t3,t2,p->z);
+ gf_sub(t3,t3,p->t);
+ gf_mul(t2,t3,p->x);
+ gf_mulw(t4,t2,-1-TWISTED_D);
+ gf_mul(s,t4,t1);
+ mask_t lobs = gf_lobit(s);
+ gf_cond_neg(s,lobs);
+ gf_copy(inv_el_m1,p->x);
+ gf_cond_neg(inv_el_m1,~lobs^negx^toggle_s);
+ gf_add(inv_el_m1,inv_el_m1,p->t);
+
+#elif COFACTOR == 8 && IMAGINE_TWIST
+ /* More complicated because of rotation */
+ gf t1,t2,t3,t4,t5;
+ gf_add(t1,p->z,p->y);
+ gf_sub(t2,p->z,p->y);
+ gf_mul(t3,t1,t2); /* t3 = num */
+ gf_mul(t2,p->x,p->y); /* t2 = den */
+ gf_sqr(t1,t2);
+ gf_mul(t4,t1,t3);
+ gf_mulw(t1,t4,-1-TWISTED_D);
+ gf_isr(t4,t1); /* isqrt(num*(a-d)*den^2) */
+ gf_mul(t1,t2,t4);
+ gf_mul(t2,t1,RISTRETTO_FACTOR); /* t2 = "iden" in ristretto.sage */
+ gf_mul(t1,t3,t4); /* t1 = "inum" in ristretto.sage */
+
+ /* Calculate altxy = iden*inum*i*t^2*(d-a) */
+ gf_mul(t3,t1,t2);
+ gf_mul_i(t4,t3);
+ gf_mul(t3,t4,p->t);
+ gf_mul(t4,t3,p->t);
+ gf_mulw(t3,t4,TWISTED_D+1); /* iden*inum*i*t^2*(d-1) */
+ mask_t rotate = toggle_rotation ^ gf_lobit(t3);
+
+ /* Rotate if altxy is negative */
+ gf_cond_swap(t1,t2,rotate);
+ gf_mul_i(t4,p->x);
+ gf_cond_sel(t4,p->y,t4,rotate); /* t4 = "fac" = ix if rotate, else y */
+
+ gf_mul_i(t5,RISTRETTO_FACTOR); /* t5 = imi */
+ gf_mul(t3,t5,t2); /* iden * imi */
+ gf_mul(t2,t5,t1);
+ gf_mul(t5,t2,p->t); /* "altx" = iden*imi*t */
+ mask_t negx = gf_lobit(t5) ^ toggle_altx;
+
+ gf_cond_neg(t1,negx^rotate);
+ gf_mul(t2,t1,p->z);
+ gf_add(t2,t2,ONE);
+ gf_mul(inv_el_sum,t2,t4);
+ gf_mul(s,inv_el_sum,t3);
+
+ mask_t negs = gf_lobit(s);
+ gf_cond_neg(s,negs);
+
+ mask_t negz = ~negs ^ toggle_s ^ negx;
+ gf_copy(inv_el_m1,p->z);
+ gf_cond_neg(inv_el_m1,negz);
+ gf_sub(inv_el_m1,inv_el_m1,t4);
+#else
+#error "Cofactor must be 4 (with no IMAGINE_TWIST) or 8 (with IMAGINE_TWIST)"
+#endif
+}
+
+void API_NS(point_encode)( unsigned char ser[SER_BYTES], const point_t p ) {
+ gf s,ie1,ie2;
+ API_NS(deisogenize)(s,ie1,ie2,p,0,0,0);
+ gf_serialize(ser,s,1);
+}
+
+decaf_error_t API_NS(point_decode) (
+ point_t p,
+ const unsigned char ser[SER_BYTES],
+ decaf_bool_t allow_identity
+) {
+ gf s, s2, num, tmp;
+ gf_s *tmp2=s2, *ynum=p->z, *isr=p->x, *den=p->t;
+
+ mask_t succ = gf_deserialize(s, ser, 1, 0);
+ succ &= bool_to_mask(allow_identity) | ~gf_eq(s, ZERO);
+ succ &= ~gf_lobit(s);
+
+ gf_sqr(s2,s); /* s^2 = -as^2 */
+#if IMAGINE_TWIST
+ gf_sub(s2,ZERO,s2); /* -as^2 */
+#endif
+ gf_sub(den,ONE,s2); /* 1+as^2 */
+ gf_add(ynum,ONE,s2); /* 1-as^2 */
+ gf_mulw(num,s2,-4*TWISTED_D);
+ gf_sqr(tmp,den); /* tmp = den^2 */
+ gf_add(num,tmp,num); /* num = den^2 - 4*d*s^2 */
+ gf_mul(tmp2,num,tmp); /* tmp2 = num*den^2 */
+ succ &= gf_isr(isr,tmp2); /* isr = 1/sqrt(num*den^2) */
+ gf_mul(tmp,isr,den); /* isr*den */
+ gf_mul(p->y,tmp,ynum); /* isr*den*(1-as^2) */
+ gf_mul(tmp2,tmp,s); /* s*isr*den */
+ gf_add(tmp2,tmp2,tmp2); /* 2*s*isr*den */
+ gf_mul(tmp,tmp2,isr); /* 2*s*isr^2*den */
+ gf_mul(p->x,tmp,num); /* 2*s*isr^2*den*num */
+ gf_mul(tmp,tmp2,RISTRETTO_FACTOR); /* 2*s*isr*den*magic */
+ gf_cond_neg(p->x,gf_lobit(tmp)); /* flip x */
+
+#if COFACTOR==8
+ /* Additionally check y != 0 and x*y*isomagic nonegative */
+ succ &= ~gf_eq(p->y,ZERO);
+ gf_mul(tmp,p->x,p->y);
+ gf_mul(tmp2,tmp,RISTRETTO_FACTOR);
+ succ &= ~gf_lobit(tmp2);
+#endif
+
+#if IMAGINE_TWIST
+ gf_copy(tmp,p->x);
+ gf_mul_i(p->x,tmp);
+#endif
+
+ /* Fill in z and t */
+ gf_copy(p->z,ONE);
+ gf_mul(p->t,p->x,p->y);
+
+ assert(API_NS(point_valid)(p) | ~succ);
+ return decaf_succeed_if(mask_to_bool(succ));
+}
+
+void API_NS(point_sub) (
+ point_t p,
+ const point_t q,
+ const point_t r
+) {
+ gf a, b, c, d;
+ gf_sub_nr ( b, q->y, q->x ); /* 3+e */
+ gf_sub_nr ( d, r->y, r->x ); /* 3+e */
+ gf_add_nr ( c, r->y, r->x ); /* 2+e */
+ gf_mul ( a, c, b );
+ gf_add_nr ( b, q->y, q->x ); /* 2+e */
+ gf_mul ( p->y, d, b );
+ gf_mul ( b, r->t, q->t );
+ gf_mulw ( p->x, b, 2*EFF_D );
+ gf_add_nr ( b, a, p->y ); /* 2+e */
+ gf_sub_nr ( c, p->y, a ); /* 3+e */
+ gf_mul ( a, q->z, r->z );
+ gf_add_nr ( a, a, a ); /* 2+e */
+ if (GF_HEADROOM <= 3) gf_weak_reduce(a); /* or 1+e */
+#if NEG_D
+ gf_sub_nr ( p->y, a, p->x ); /* 4+e or 3+e */
+ gf_add_nr ( a, a, p->x ); /* 3+e or 2+e */
+#else
+ gf_add_nr ( p->y, a, p->x ); /* 3+e or 2+e */
+ gf_sub_nr ( a, a, p->x ); /* 4+e or 3+e */
+#endif
+ gf_mul ( p->z, a, p->y );
+ gf_mul ( p->x, p->y, c );
+ gf_mul ( p->y, a, b );
+ gf_mul ( p->t, b, c );
+}
+
+void API_NS(point_add) (
+ point_t p,
+ const point_t q,
+ const point_t r
+) {
+ gf a, b, c, d;
+ gf_sub_nr ( b, q->y, q->x ); /* 3+e */
+ gf_sub_nr ( c, r->y, r->x ); /* 3+e */
+ gf_add_nr ( d, r->y, r->x ); /* 2+e */
+ gf_mul ( a, c, b );
+ gf_add_nr ( b, q->y, q->x ); /* 2+e */
+ gf_mul ( p->y, d, b );
+ gf_mul ( b, r->t, q->t );
+ gf_mulw ( p->x, b, 2*EFF_D );
+ gf_add_nr ( b, a, p->y ); /* 2+e */
+ gf_sub_nr ( c, p->y, a ); /* 3+e */
+ gf_mul ( a, q->z, r->z );
+ gf_add_nr ( a, a, a ); /* 2+e */
+ if (GF_HEADROOM <= 3) gf_weak_reduce(a); /* or 1+e */
+#if NEG_D
+ gf_add_nr ( p->y, a, p->x ); /* 3+e or 2+e */
+ gf_sub_nr ( a, a, p->x ); /* 4+e or 3+e */
+#else
+ gf_sub_nr ( p->y, a, p->x ); /* 4+e or 3+e */
+ gf_add_nr ( a, a, p->x ); /* 3+e or 2+e */
+#endif
+ gf_mul ( p->z, a, p->y );
+ gf_mul ( p->x, p->y, c );
+ gf_mul ( p->y, a, b );
+ gf_mul ( p->t, b, c );
+}
+
+static DECAF_NOINLINE void
+point_double_internal (
+ point_t p,
+ const point_t q,
+ int before_double
+) {
+ gf a, b, c, d;
+ gf_sqr ( c, q->x );
+ gf_sqr ( a, q->y );
+ gf_add_nr ( d, c, a ); /* 2+e */
+ gf_add_nr ( p->t, q->y, q->x ); /* 2+e */
+ gf_sqr ( b, p->t );
+ gf_subx_nr ( b, b, d, 3 ); /* 4+e */
+ gf_sub_nr ( p->t, a, c ); /* 3+e */
+ gf_sqr ( p->x, q->z );
+ gf_add_nr ( p->z, p->x, p->x ); /* 2+e */
+ gf_subx_nr ( a, p->z, p->t, 4 ); /* 6+e */
+ if (GF_HEADROOM == 5) gf_weak_reduce(a); /* or 1+e */
+ gf_mul ( p->x, a, b );
+ gf_mul ( p->z, p->t, a );
+ gf_mul ( p->y, p->t, d );
+ if (!before_double) gf_mul ( p->t, b, d );
+}
+
+void API_NS(point_double)(point_t p, const point_t q) {
+ point_double_internal(p,q,0);
+}
+
+void API_NS(point_negate) (
+ point_t nega,
+ const point_t a
+) {
+ gf_sub(nega->x, ZERO, a->x);
+ gf_copy(nega->y, a->y);
+ gf_copy(nega->z, a->z);
+ gf_sub(nega->t, ZERO, a->t);
+}
+
+/* Operations on [p]niels */
+static DECAF_INLINE void
+cond_neg_niels (
+ niels_t n,
+ mask_t neg
+) {
+ gf_cond_swap(n->a, n->b, neg);
+ gf_cond_neg(n->c, neg);
+}
+
+static DECAF_NOINLINE void pt_to_pniels (
+ pniels_t b,
+ const point_t a
+) {
+ gf_sub ( b->n->a, a->y, a->x );
+ gf_add ( b->n->b, a->x, a->y );
+ gf_mulw ( b->n->c, a->t, 2*TWISTED_D );
+ gf_add ( b->z, a->z, a->z );
+}
+
+static DECAF_NOINLINE void pniels_to_pt (
+ point_t e,
+ const pniels_t d
+) {
+ gf eu;
+ gf_add ( eu, d->n->b, d->n->a );
+ gf_sub ( e->y, d->n->b, d->n->a );
+ gf_mul ( e->t, e->y, eu);
+ gf_mul ( e->x, d->z, e->y );
+ gf_mul ( e->y, d->z, eu );
+ gf_sqr ( e->z, d->z );
+}
+
+static DECAF_NOINLINE void
+niels_to_pt (
+ point_t e,
+ const niels_t n
+) {
+ gf_add ( e->y, n->b, n->a );
+ gf_sub ( e->x, n->b, n->a );
+ gf_mul ( e->t, e->y, e->x );
+ gf_copy ( e->z, ONE );
+}
+
+static DECAF_NOINLINE void
+add_niels_to_pt (
+ point_t d,
+ const niels_t e,
+ int before_double
+) {
+ gf a, b, c;
+ gf_sub_nr ( b, d->y, d->x ); /* 3+e */
+ gf_mul ( a, e->a, b );
+ gf_add_nr ( b, d->x, d->y ); /* 2+e */
+ gf_mul ( d->y, e->b, b );
+ gf_mul ( d->x, e->c, d->t );
+ gf_add_nr ( c, a, d->y ); /* 2+e */
+ gf_sub_nr ( b, d->y, a ); /* 3+e */
+ gf_sub_nr ( d->y, d->z, d->x ); /* 3+e */
+ gf_add_nr ( a, d->x, d->z ); /* 2+e */
+ gf_mul ( d->z, a, d->y );
+ gf_mul ( d->x, d->y, b );
+ gf_mul ( d->y, a, c );
+ if (!before_double) gf_mul ( d->t, b, c );
+}
+
+static DECAF_NOINLINE void
+sub_niels_from_pt (
+ point_t d,
+ const niels_t e,
+ int before_double
+) {
+ gf a, b, c;
+ gf_sub_nr ( b, d->y, d->x ); /* 3+e */
+ gf_mul ( a, e->b, b );
+ gf_add_nr ( b, d->x, d->y ); /* 2+e */
+ gf_mul ( d->y, e->a, b );
+ gf_mul ( d->x, e->c, d->t );
+ gf_add_nr ( c, a, d->y ); /* 2+e */
+ gf_sub_nr ( b, d->y, a ); /* 3+e */
+ gf_add_nr ( d->y, d->z, d->x ); /* 2+e */
+ gf_sub_nr ( a, d->z, d->x ); /* 3+e */
+ gf_mul ( d->z, a, d->y );
+ gf_mul ( d->x, d->y, b );
+ gf_mul ( d->y, a, c );
+ if (!before_double) gf_mul ( d->t, b, c );
+}
+
+static void
+add_pniels_to_pt (
+ point_t p,
+ const pniels_t pn,
+ int before_double
+) {
+ gf L0;
+ gf_mul ( L0, p->z, pn->z );
+ gf_copy ( p->z, L0 );
+ add_niels_to_pt( p, pn->n, before_double );
+}
+
+static void
+sub_pniels_from_pt (
+ point_t p,
+ const pniels_t pn,
+ int before_double
+) {
+ gf L0;
+ gf_mul ( L0, p->z, pn->z );
+ gf_copy ( p->z, L0 );
+ sub_niels_from_pt( p, pn->n, before_double );
+}
+
+static DECAF_NOINLINE void
+prepare_fixed_window(
+ pniels_t *multiples,
+ const point_t b,
+ int ntable
+) {
+ point_t tmp;
+ pniels_t pn;
+ int i;
+
+ point_double_internal(tmp, b, 0);
+ pt_to_pniels(pn, tmp);
+ pt_to_pniels(multiples[0], b);
+ API_NS(point_copy)(tmp, b);
+ for (i=1; i<ntable; i++) {
+ add_pniels_to_pt(tmp, pn, 0);
+ pt_to_pniels(multiples[i], tmp);
+ }
+
+ decaf_bzero(pn,sizeof(pn));
+ decaf_bzero(tmp,sizeof(tmp));
+}
+
+void API_NS(point_scalarmul) (
+ point_t a,
+ const point_t b,
+ const scalar_t scalar
+) {
+ const int WINDOW = DECAF_WINDOW_BITS,
+ WINDOW_MASK = (1<<WINDOW)-1,
+ WINDOW_T_MASK = WINDOW_MASK >> 1,
+ NTABLE = 1<<(WINDOW-1);
+
+ scalar_t scalar1x;
+ API_NS(scalar_add)(scalar1x, scalar, point_scalarmul_adjustment);
+ API_NS(scalar_halve)(scalar1x,scalar1x);
+
+ /* Set up a precomputed table with odd multiples of b. */
+ pniels_t pn, multiples[NTABLE];
+ point_t tmp;
+ prepare_fixed_window(multiples, b, NTABLE);
+
+ /* Initialize. */
+ int i,j,first=1;
+ i = SCALAR_BITS - ((SCALAR_BITS-1) % WINDOW) - 1;
+
+ for (; i>=0; i-=WINDOW) {
+ /* Fetch another block of bits */
+ word_t bits = scalar1x->limb[i/WBITS] >> (i%WBITS);
+ if (i%WBITS >= WBITS-WINDOW && i/WBITS<SCALAR_LIMBS-1) {
+ bits ^= scalar1x->limb[i/WBITS+1] << (WBITS - (i%WBITS));
+ }
+ bits &= WINDOW_MASK;
+ mask_t inv = (bits>>(WINDOW-1))-1;
+ bits ^= inv;
+
+ /* Add in from table. Compute t only on last iteration. */
+ constant_time_lookup(pn, multiples, sizeof(pn), NTABLE, bits & WINDOW_T_MASK);
+ cond_neg_niels(pn->n, inv);
+ if (first) {
+ pniels_to_pt(tmp, pn);
+ first = 0;
+ } else {
+ /* Using Hisil et al's lookahead method instead of extensible here
+ * for no particular reason. Double WINDOW times, but only compute t on
+ * the last one.
+ */
+ for (j=0; j<WINDOW-1; j++)
+ point_double_internal(tmp, tmp, -1);
+ point_double_internal(tmp, tmp, 0);
+ add_pniels_to_pt(tmp, pn, i ? -1 : 0);
+ }
+ }
+
+ /* Write out the answer */
+ API_NS(point_copy)(a,tmp);
+
+ decaf_bzero(scalar1x,sizeof(scalar1x));
+ decaf_bzero(pn,sizeof(pn));
+ decaf_bzero(multiples,sizeof(multiples));
+ decaf_bzero(tmp,sizeof(tmp));
+}
+
+void API_NS(point_double_scalarmul) (
+ point_t a,
+ const point_t b,
+ const scalar_t scalarb,
+ const point_t c,
+ const scalar_t scalarc
+) {
+ const int WINDOW = DECAF_WINDOW_BITS,
+ WINDOW_MASK = (1<<WINDOW)-1,
+ WINDOW_T_MASK = WINDOW_MASK >> 1,
+ NTABLE = 1<<(WINDOW-1);
+
+ scalar_t scalar1x, scalar2x;
+ API_NS(scalar_add)(scalar1x, scalarb, point_scalarmul_adjustment);
+ API_NS(scalar_halve)(scalar1x,scalar1x);
+ API_NS(scalar_add)(scalar2x, scalarc, point_scalarmul_adjustment);
+ API_NS(scalar_halve)(scalar2x,scalar2x);
+
+ /* Set up a precomputed table with odd multiples of b. */
+ pniels_t pn, multiples1[NTABLE], multiples2[NTABLE];
+ point_t tmp;
+ prepare_fixed_window(multiples1, b, NTABLE);
+ prepare_fixed_window(multiples2, c, NTABLE);
+
+ /* Initialize. */
+ int i,j,first=1;
+ i = SCALAR_BITS - ((SCALAR_BITS-1) % WINDOW) - 1;
+
+ for (; i>=0; i-=WINDOW) {
+ /* Fetch another block of bits */
+ word_t bits1 = scalar1x->limb[i/WBITS] >> (i%WBITS),
+ bits2 = scalar2x->limb[i/WBITS] >> (i%WBITS);
+ if (i%WBITS >= WBITS-WINDOW && i/WBITS<SCALAR_LIMBS-1) {
+ bits1 ^= scalar1x->limb[i/WBITS+1] << (WBITS - (i%WBITS));
+ bits2 ^= scalar2x->limb[i/WBITS+1] << (WBITS - (i%WBITS));
+ }
+ bits1 &= WINDOW_MASK;
+ bits2 &= WINDOW_MASK;
+ mask_t inv1 = (bits1>>(WINDOW-1))-1;
+ mask_t inv2 = (bits2>>(WINDOW-1))-1;
+ bits1 ^= inv1;
+ bits2 ^= inv2;
+
+ /* Add in from table. Compute t only on last iteration. */
+ constant_time_lookup(pn, multiples1, sizeof(pn), NTABLE, bits1 & WINDOW_T_MASK);
+ cond_neg_niels(pn->n, inv1);
+ if (first) {
+ pniels_to_pt(tmp, pn);
+ first = 0;
+ } else {
+ /* Using Hisil et al's lookahead method instead of extensible here
+ * for no particular reason. Double WINDOW times, but only compute t on
+ * the last one.
+ */
+ for (j=0; j<WINDOW-1; j++)
+ point_double_internal(tmp, tmp, -1);
+ point_double_internal(tmp, tmp, 0);
+ add_pniels_to_pt(tmp, pn, 0);
+ }
+ constant_time_lookup(pn, multiples2, sizeof(pn), NTABLE, bits2 & WINDOW_T_MASK);
+ cond_neg_niels(pn->n, inv2);
+ add_pniels_to_pt(tmp, pn, i?-1:0);
+ }
+
+ /* Write out the answer */
+ API_NS(point_copy)(a,tmp);
+
+
+ decaf_bzero(scalar1x,sizeof(scalar1x));
+ decaf_bzero(scalar2x,sizeof(scalar2x));
+ decaf_bzero(pn,sizeof(pn));
+ decaf_bzero(multiples1,sizeof(multiples1));
+ decaf_bzero(multiples2,sizeof(multiples2));
+ decaf_bzero(tmp,sizeof(tmp));
+}
+
+void API_NS(point_dual_scalarmul) (
+ point_t a1,
+ point_t a2,
+ const point_t b,
+ const scalar_t scalar1,
+ const scalar_t scalar2
+) {
+ const int WINDOW = DECAF_WINDOW_BITS,
+ WINDOW_MASK = (1<<WINDOW)-1,
+ WINDOW_T_MASK = WINDOW_MASK >> 1,
+ NTABLE = 1<<(WINDOW-1);
+
+ scalar_t scalar1x, scalar2x;
+ API_NS(scalar_add)(scalar1x, scalar1, point_scalarmul_adjustment);
+ API_NS(scalar_halve)(scalar1x,scalar1x);
+ API_NS(scalar_add)(scalar2x, scalar2, point_scalarmul_adjustment);
+ API_NS(scalar_halve)(scalar2x,scalar2x);
+
+ /* Set up a precomputed table with odd multiples of b. */
+ point_t multiples1[NTABLE], multiples2[NTABLE], working, tmp;
+ pniels_t pn;
+
+ API_NS(point_copy)(working, b);
+
+ /* Initialize. */
+ int i,j;
+
+ for (i=0; i<NTABLE; i++) {
+ API_NS(point_copy)(multiples1[i], API_NS(point_identity));
+ API_NS(point_copy)(multiples2[i], API_NS(point_identity));
+ }
+
+ for (i=0; i<SCALAR_BITS; i+=WINDOW) {
+ if (i) {
+ for (j=0; j<WINDOW-1; j++)
+ point_double_internal(working, working, -1);
+ point_double_internal(working, working, 0);
+ }
+
+ /* Fetch another block of bits */
+ word_t bits1 = scalar1x->limb[i/WBITS] >> (i%WBITS),
+ bits2 = scalar2x->limb[i/WBITS] >> (i%WBITS);
+ if (i%WBITS >= WBITS-WINDOW && i/WBITS<SCALAR_LIMBS-1) {
+ bits1 ^= scalar1x->limb[i/WBITS+1] << (WBITS - (i%WBITS));
+ bits2 ^= scalar2x->limb[i/WBITS+1] << (WBITS - (i%WBITS));
+ }
+ bits1 &= WINDOW_MASK;
+ bits2 &= WINDOW_MASK;
+ mask_t inv1 = (bits1>>(WINDOW-1))-1;
+ mask_t inv2 = (bits2>>(WINDOW-1))-1;
+ bits1 ^= inv1;
+ bits2 ^= inv2;
+
+ pt_to_pniels(pn, working);
+
+ constant_time_lookup(tmp, multiples1, sizeof(tmp), NTABLE, bits1 & WINDOW_T_MASK);
+ cond_neg_niels(pn->n, inv1);
+ /* add_pniels_to_pt(multiples1[bits1 & WINDOW_T_MASK], pn, 0); */
+ add_pniels_to_pt(tmp, pn, 0);
+ constant_time_insert(multiples1, tmp, sizeof(tmp), NTABLE, bits1 & WINDOW_T_MASK);
+
+
+ constant_time_lookup(tmp, multiples2, sizeof(tmp), NTABLE, bits2 & WINDOW_T_MASK);
+ cond_neg_niels(pn->n, inv1^inv2);
+ /* add_pniels_to_pt(multiples2[bits2 & WINDOW_T_MASK], pn, 0); */
+ add_pniels_to_pt(tmp, pn, 0);
+ constant_time_insert(multiples2, tmp, sizeof(tmp), NTABLE, bits2 & WINDOW_T_MASK);
+ }
+
+ if (NTABLE > 1) {
+ API_NS(point_copy)(working, multiples1[NTABLE-1]);
+ API_NS(point_copy)(tmp , multiples2[NTABLE-1]);
+
+ for (i=NTABLE-1; i>1; i--) {
+ API_NS(point_add)(multiples1[i-1], multiples1[i-1], multiples1[i]);
+ API_NS(point_add)(multiples2[i-1], multiples2[i-1], multiples2[i]);
+ API_NS(point_add)(working, working, multiples1[i-1]);
+ API_NS(point_add)(tmp, tmp, multiples2[i-1]);
+ }
+
+ API_NS(point_add)(multiples1[0], multiples1[0], multiples1[1]);
+ API_NS(point_add)(multiples2[0], multiples2[0], multiples2[1]);
+ point_double_internal(working, working, 0);
+ point_double_internal(tmp, tmp, 0);
+ API_NS(point_add)(a1, working, multiples1[0]);
+ API_NS(point_add)(a2, tmp, multiples2[0]);
+ } else {
+ API_NS(point_copy)(a1, multiples1[0]);
+ API_NS(point_copy)(a2, multiples2[0]);
+ }
+
+ decaf_bzero(scalar1x,sizeof(scalar1x));
+ decaf_bzero(scalar2x,sizeof(scalar2x));
+ decaf_bzero(pn,sizeof(pn));
+ decaf_bzero(multiples1,sizeof(multiples1));
+ decaf_bzero(multiples2,sizeof(multiples2));
+ decaf_bzero(tmp,sizeof(tmp));
+ decaf_bzero(working,sizeof(working));
+}
+
+decaf_bool_t API_NS(point_eq) ( const point_t p, const point_t q ) {
+ /* equality mod 2-torsion compares x/y */
+ gf a, b;
+ gf_mul ( a, p->y, q->x );
+ gf_mul ( b, q->y, p->x );
+ mask_t succ = gf_eq(a,b);
+
+ #if (COFACTOR == 8) && IMAGINE_TWIST
+ gf_mul ( a, p->y, q->y );
+ gf_mul ( b, q->x, p->x );
+ #if !(IMAGINE_TWIST)
+ gf_sub ( a, ZERO, a );
+ #else
+ /* Interesting note: the 4tor would normally be rotation.
+ * But because of the *i twist, it's actually
+ * (x,y) <-> (iy,ix)
+ */
+
+ /* No code, just a comment. */
+ #endif
+ succ |= gf_eq(a,b);
+ #endif
+
+ return mask_to_bool(succ);
+}
+
+decaf_bool_t API_NS(point_valid) (
+ const point_t p
+) {
+ gf a,b,c;
+ gf_mul(a,p->x,p->y);
+ gf_mul(b,p->z,p->t);
+ mask_t out = gf_eq(a,b);
+ gf_sqr(a,p->x);
+ gf_sqr(b,p->y);
+ gf_sub(a,b,a);
+ gf_sqr(b,p->t);
+ gf_mulw(c,b,TWISTED_D);
+ gf_sqr(b,p->z);
+ gf_add(b,b,c);
+ out &= gf_eq(a,b);
+ out &= ~gf_eq(p->z,ZERO);
+ return mask_to_bool(out);
+}
+
+void API_NS(point_debugging_torque) (
+ point_t q,
+ const point_t p
+) {
+#if COFACTOR == 8 && IMAGINE_TWIST
+ gf tmp;
+ gf_mul(tmp,p->x,SQRT_MINUS_ONE);
+ gf_mul(q->x,p->y,SQRT_MINUS_ONE);
+ gf_copy(q->y,tmp);
+ gf_copy(q->z,p->z);
+ gf_sub(q->t,ZERO,p->t);
+#else
+ gf_sub(q->x,ZERO,p->x);
+ gf_sub(q->y,ZERO,p->y);
+ gf_copy(q->z,p->z);
+ gf_copy(q->t,p->t);
+#endif
+}
+
+void API_NS(point_debugging_pscale) (
+ point_t q,
+ const point_t p,
+ const uint8_t factor[SER_BYTES]
+) {
+ gf gfac,tmp;
+ /* NB this means you'll never pscale by negative numbers for p521 */
+ ignore_result(gf_deserialize(gfac,factor,0,0));
+ gf_cond_sel(gfac,gfac,ONE,gf_eq(gfac,ZERO));
+ gf_mul(tmp,p->x,gfac);
+ gf_copy(q->x,tmp);
+ gf_mul(tmp,p->y,gfac);
+ gf_copy(q->y,tmp);
+ gf_mul(tmp,p->z,gfac);
+ gf_copy(q->z,tmp);
+ gf_mul(tmp,p->t,gfac);
+ gf_copy(q->t,tmp);
+}
+
+static void gf_batch_invert (
+ gf *__restrict__ out,
+ const gf *in,
+ unsigned int n
+) {
+ gf t1;
+ assert(n>1);
+
+ gf_copy(out[1], in[0]);
+ int i;
+ for (i=1; i<(int) (n-1); i++) {
+ gf_mul(out[i+1], out[i], in[i]);
+ }
+ gf_mul(out[0], out[n-1], in[n-1]);
+
+ gf_invert(out[0], out[0], 1);
+
+ for (i=n-1; i>0; i--) {
+ gf_mul(t1, out[i], out[0]);
+ gf_copy(out[i], t1);
+ gf_mul(t1, out[0], in[i]);
+ gf_copy(out[0], t1);
+ }
+}
+
+static void batch_normalize_niels (
+ niels_t *table,
+ const gf *zs,
+ gf *__restrict__ zis,
+ int n
+) {
+ int i;
+ gf product;
+ gf_batch_invert(zis, zs, n);
+
+ for (i=0; i<n; i++) {
+ gf_mul(product, table[i]->a, zis[i]);
+ gf_strong_reduce(product);
+ gf_copy(table[i]->a, product);
+
+ gf_mul(product, table[i]->b, zis[i]);
+ gf_strong_reduce(product);
+ gf_copy(table[i]->b, product);
+
+ gf_mul(product, table[i]->c, zis[i]);
+ gf_strong_reduce(product);
+ gf_copy(table[i]->c, product);
+ }
+
+ decaf_bzero(product,sizeof(product));
+}
+
+void API_NS(precompute) (
+ precomputed_s *table,
+ const point_t base
+) {
+ const unsigned int n = COMBS_N, t = COMBS_T, s = COMBS_S;
+ assert(n*t*s >= SCALAR_BITS);
+
+ point_t working, start, doubles[t-1];
+ API_NS(point_copy)(working, base);
+ pniels_t pn_tmp;
+
+ gf zs[n<<(t-1)], zis[n<<(t-1)];
+
+ unsigned int i,j,k;
+
+ /* Compute n tables */
+ for (i=0; i<n; i++) {
+
+ /* Doubling phase */
+ for (j=0; j<t; j++) {
+ if (j) API_NS(point_add)(start, start, working);
+ else API_NS(point_copy)(start, working);
+
+ if (j==t-1 && i==n-1) break;
+
+ point_double_internal(working, working,0);
+ if (j<t-1) API_NS(point_copy)(doubles[j], working);
+
+ for (k=0; k<s-1; k++)
+ point_double_internal(working, working, k<s-2);
+ }
+
+ /* Gray-code phase */
+ for (j=0;; j++) {
+ int gray = j ^ (j>>1);
+ int idx = (((i+1)<<(t-1))-1) ^ gray;
+
+ pt_to_pniels(pn_tmp, start);
+ memcpy(table->table[idx], pn_tmp->n, sizeof(pn_tmp->n));
+ gf_copy(zs[idx], pn_tmp->z);
+
+ if (j >= (1u<<(t-1)) - 1) break;
+ int delta = (j+1) ^ ((j+1)>>1) ^ gray;
+
+ for (k=0; delta>1; k++)
+ delta >>=1;
+
+ if (gray & (1<<k)) {
+ API_NS(point_add)(start, start, doubles[k]);
+ } else {
+ API_NS(point_sub)(start, start, doubles[k]);
+ }
+ }
+ }
+
+ batch_normalize_niels(table->table,(const gf *)zs,zis,n<<(t-1));
+
+ decaf_bzero(zs,sizeof(zs));
+ decaf_bzero(zis,sizeof(zis));
+ decaf_bzero(pn_tmp,sizeof(pn_tmp));
+ decaf_bzero(working,sizeof(working));
+ decaf_bzero(start,sizeof(start));
+ decaf_bzero(doubles,sizeof(doubles));
+}
+
+static DECAF_INLINE void
+constant_time_lookup_niels (
+ niels_s *__restrict__ ni,
+ const niels_t *table,
+ int nelts,
+ int idx
+) {
+ constant_time_lookup(ni, table, sizeof(niels_s), nelts, idx);
+}
+
+void API_NS(precomputed_scalarmul) (
+ point_t out,
+ const precomputed_s *table,
+ const scalar_t scalar
+) {
+ int i;
+ unsigned j,k;
+ const unsigned int n = COMBS_N, t = COMBS_T, s = COMBS_S;
+
+ scalar_t scalar1x;
+ API_NS(scalar_add)(scalar1x, scalar, precomputed_scalarmul_adjustment);
+ API_NS(scalar_halve)(scalar1x,scalar1x);
+
+ niels_t ni;
+
+ for (i=s-1; i>=0; i--) {
+ if (i != (int)s-1) point_double_internal(out,out,0);
+
+ for (j=0; j<n; j++) {
+ int tab = 0;
+
+ for (k=0; k<t; k++) {
+ unsigned int bit = i + s*(k + j*t);
+ if (bit < SCALAR_BITS) {
+ tab |= (scalar1x->limb[bit/WBITS] >> (bit%WBITS) & 1) << k;
+ }
+ }
+
+ mask_t invert = (tab>>(t-1))-1;
+ tab ^= invert;
+ tab &= (1<<(t-1)) - 1;
+
+ constant_time_lookup_niels(ni, &table->table[j<<(t-1)], 1<<(t-1), tab);
+
+ cond_neg_niels(ni, invert);
+ if ((i!=(int)s-1)||j) {
+ add_niels_to_pt(out, ni, j==n-1 && i);
+ } else {
+ niels_to_pt(out, ni);
+ }
+ }
+ }
+
+ decaf_bzero(ni,sizeof(ni));
+ decaf_bzero(scalar1x,sizeof(scalar1x));
+}
+
+void API_NS(point_cond_sel) (
+ point_t out,
+ const point_t a,
+ const point_t b,
+ decaf_bool_t pick_b
+) {
+ constant_time_select(out,a,b,sizeof(point_t),bool_to_mask(pick_b),0);
+}
+
+/* FUTURE: restore Curve25519 Montgomery ladder? */
+decaf_error_t API_NS(direct_scalarmul) (
+ uint8_t scaled[SER_BYTES],
+ const uint8_t base[SER_BYTES],
+ const scalar_t scalar,
+ decaf_bool_t allow_identity,
+ decaf_bool_t short_circuit
+) {
+ point_t basep;
+ decaf_error_t succ = API_NS(point_decode)(basep, base, allow_identity);
+ if (short_circuit && succ != DECAF_SUCCESS) return succ;
+ API_NS(point_cond_sel)(basep, API_NS(point_base), basep, succ);
+ API_NS(point_scalarmul)(basep, basep, scalar);
+ API_NS(point_encode)(scaled, basep);
+ API_NS(point_destroy)(basep);
+ return succ;
+}
+
+void API_NS(point_mul_by_ratio_and_encode_like_eddsa) (
+ uint8_t enc[DECAF_EDDSA_448_PUBLIC_BYTES],
+ const point_t p
+) {
+
+ /* The point is now on the twisted curve. Move it to untwisted. */
+ gf x, y, z, t;
+ point_t q;
+#if COFACTOR == 8
+ API_NS(point_double)(q,p);
+#else
+ API_NS(point_copy)(q,p);
+#endif
+
+#if EDDSA_USE_SIGMA_ISOGENY
+ {
+ /* Use 4-isogeny like ed25519:
+ * 2*x*y*sqrt(d/a-1)/(ax^2 + y^2 - 2)
+ * (y^2 - ax^2)/(y^2 + ax^2)
+ * with a = -1, d = -EDWARDS_D:
+ * -2xysqrt(EDWARDS_D-1)/(2z^2-y^2+x^2)
+ * (y^2+x^2)/(y^2-x^2)
+ */
+ gf u;
+ gf_sqr ( x, q->x ); // x^2
+ gf_sqr ( t, q->y ); // y^2
+ gf_add( u, x, t ); // x^2 + y^2
+ gf_add( z, q->y, q->x );
+ gf_sqr ( y, z);
+ gf_sub ( y, u, y ); // -2xy
+ gf_sub ( z, t, x ); // y^2 - x^2
+ gf_sqr ( x, q->z );
+ gf_add ( t, x, x);
+ gf_sub ( t, t, z); // 2z^2 - y^2 + x^2
+ gf_mul ( x, y, z ); // 2xy(y^2-x^2)
+ gf_mul ( y, u, t ); // (x^2+y^2)(2z^2-y^2+x^2)
+ gf_mul ( u, z, t );
+ gf_copy( z, u );
+ gf_mul ( u, x, RISTRETTO_FACTOR );
+#if IMAGINE_TWIST
+ gf_mul_i( x, u );
+#else
+#error "... probably wrong"
+ gf_copy( x, u );
+#endif
+ decaf_bzero(u,sizeof(u));
+ }
+#elif IMAGINE_TWIST
+ {
+ API_NS(point_double)(q,q);
+ API_NS(point_double)(q,q);
+ gf_mul_i(x, q->x);
+ gf_copy(y, q->y);
+ gf_copy(z, q->z);
+ }
+#else
+ {
+ /* 4-isogeny: 2xy/(y^+x^2), (y^2-x^2)/(2z^2-y^2+x^2) */
+ gf u;
+ gf_sqr ( x, q->x );
+ gf_sqr ( t, q->y );
+ gf_add( u, x, t );
+ gf_add( z, q->y, q->x );
+ gf_sqr ( y, z);
+ gf_sub ( y, y, u );
+ gf_sub ( z, t, x );
+ gf_sqr ( x, q->z );
+ gf_add ( t, x, x);
+ gf_sub ( t, t, z);
+ gf_mul ( x, t, y );
+ gf_mul ( y, z, u );
+ gf_mul ( z, u, t );
+ decaf_bzero(u,sizeof(u));
+ }
+#endif
+ /* Affinize */
+ gf_invert(z,z,1);
+ gf_mul(t,x,z);
+ gf_mul(x,y,z);
+
+ /* Encode */
+ enc[DECAF_EDDSA_448_PRIVATE_BYTES-1] = 0;
+ gf_serialize(enc, x, 1);
+ enc[DECAF_EDDSA_448_PRIVATE_BYTES-1] |= 0x80 & gf_lobit(t);
+
+ decaf_bzero(x,sizeof(x));
+ decaf_bzero(y,sizeof(y));
+ decaf_bzero(z,sizeof(z));
+ decaf_bzero(t,sizeof(t));
+ API_NS(point_destroy)(q);
+}
+
+
+decaf_error_t API_NS(point_decode_like_eddsa_and_mul_by_ratio) (
+ point_t p,
+ const uint8_t enc[DECAF_EDDSA_448_PUBLIC_BYTES]
+) {
+ uint8_t enc2[DECAF_EDDSA_448_PUBLIC_BYTES];
+ memcpy(enc2,enc,sizeof(enc2));
+
+ mask_t low = ~word_is_zero(enc2[DECAF_EDDSA_448_PRIVATE_BYTES-1] & 0x80);
+ enc2[DECAF_EDDSA_448_PRIVATE_BYTES-1] &= ~0x80;
+
+ mask_t succ = gf_deserialize(p->y, enc2, 1, 0);
+#if 0 == 0
+ succ &= word_is_zero(enc2[DECAF_EDDSA_448_PRIVATE_BYTES-1]);
+#endif
+
+ gf_sqr(p->x,p->y);
+ gf_sub(p->z,ONE,p->x); /* num = 1-y^2 */
+ #if EDDSA_USE_SIGMA_ISOGENY
+ gf_mulw(p->t,p->z,EDWARDS_D); /* d-dy^2 */
+ gf_mulw(p->x,p->z,EDWARDS_D-1); /* num = (1-y^2)(d-1) */
+ gf_copy(p->z,p->x);
+ #else
+ gf_mulw(p->t,p->x,EDWARDS_D); /* dy^2 */
+ #endif
+ gf_sub(p->t,ONE,p->t); /* denom = 1-dy^2 or 1-d + dy^2 */
+
+ gf_mul(p->x,p->z,p->t);
+ succ &= gf_isr(p->t,p->x); /* 1/sqrt(num * denom) */
+
+ gf_mul(p->x,p->t,p->z); /* sqrt(num / denom) */
+ gf_cond_neg(p->x,gf_lobit(p->x)^low);
+ gf_copy(p->z,ONE);
+
+ #if EDDSA_USE_SIGMA_ISOGENY
+ {
+ /* Use 4-isogeny like ed25519:
+ * 2*x*y/sqrt(1-d/a)/(ax^2 + y^2 - 2)
+ * (y^2 - ax^2)/(y^2 + ax^2)
+ * (MAGIC: above formula may be off by a factor of -a
+ * or something somewhere; check it for other a)
+ *
+ * with a = -1, d = -EDWARDS_D:
+ * -2xy/sqrt(1-EDWARDS_D)/(2z^2-y^2+x^2)
+ * (y^2+x^2)/(y^2-x^2)
+ */
+ gf a, b, c, d;
+ gf_sqr ( c, p->x );
+ gf_sqr ( a, p->y );
+ gf_add ( d, c, a ); // x^2 + y^2
+ gf_add ( p->t, p->y, p->x );
+ gf_sqr ( b, p->t );
+ gf_sub ( b, b, d ); // 2xy
+ gf_sub ( p->t, a, c ); // y^2 - x^2
+ gf_sqr ( p->x, p->z );
+ gf_add ( p->z, p->x, p->x );
+ gf_sub ( c, p->z, p->t ); // 2z^2 - y^2 + x^2
+ gf_div_i ( a, c );
+ gf_mul ( c, a, RISTRETTO_FACTOR );
+ gf_mul ( p->x, b, p->t); // (2xy)(y^2-x^2)
+ gf_mul ( p->z, p->t, c ); // (y^2-x^2)sd(2z^2 - y^2 + x^2)
+ gf_mul ( p->y, d, c ); // (y^2+x^2)sd(2z^2 - y^2 + x^2)
+ gf_mul ( p->t, d, b );
+ decaf_bzero(a,sizeof(a));
+ decaf_bzero(b,sizeof(b));
+ decaf_bzero(c,sizeof(c));
+ decaf_bzero(d,sizeof(d));
+ }
+ #elif IMAGINE_TWIST
+ {
+ gf_mul(p->t,p->x,SQRT_MINUS_ONE);
+ gf_copy(p->x,p->t);
+ gf_mul(p->t,p->x,p->y);
+ }
+ #else
+ {
+ /* 4-isogeny 2xy/(y^2-ax^2), (y^2+ax^2)/(2-y^2-ax^2) */
+ gf a, b, c, d;
+ gf_sqr ( c, p->x );
+ gf_sqr ( a, p->y );
+ gf_add ( d, c, a );
+ gf_add ( p->t, p->y, p->x );
+ gf_sqr ( b, p->t );
+ gf_sub ( b, b, d );
+ gf_sub ( p->t, a, c );
+ gf_sqr ( p->x, p->z );
+ gf_add ( p->z, p->x, p->x );
+ gf_sub ( a, p->z, d );
+ gf_mul ( p->x, a, b );
+ gf_mul ( p->z, p->t, a );
+ gf_mul ( p->y, p->t, d );
+ gf_mul ( p->t, b, d );
+ decaf_bzero(a,sizeof(a));
+ decaf_bzero(b,sizeof(b));
+ decaf_bzero(c,sizeof(c));
+ decaf_bzero(d,sizeof(d));
+ }
+ #endif
+
+ decaf_bzero(enc2,sizeof(enc2));
+ assert(API_NS(point_valid)(p) || ~succ);
+
+ return decaf_succeed_if(mask_to_bool(succ));
+}
+
+decaf_error_t decaf_x448 (
+ uint8_t out[X_PUBLIC_BYTES],
+ const uint8_t base[X_PUBLIC_BYTES],
+ const uint8_t scalar[X_PRIVATE_BYTES]
+) {
+ gf x1, x2, z2, x3, z3, t1, t2;
+ ignore_result(gf_deserialize(x1,base,1,0));
+ gf_copy(x2,ONE);
+ gf_copy(z2,ZERO);
+ gf_copy(x3,x1);
+ gf_copy(z3,ONE);
+
+ int t;
+ mask_t swap = 0;
+
+ for (t = X_PRIVATE_BITS-1; t>=0; t--) {
+ uint8_t sb = scalar[t/8];
+
+ /* Scalar conditioning */
+ if (t/8==0) sb &= -(uint8_t)COFACTOR;
+ else if (t == X_PRIVATE_BITS-1) sb = -1;
+
+ mask_t k_t = (sb>>(t%8)) & 1;
+ k_t = -k_t; /* set to all 0s or all 1s */
+
+ swap ^= k_t;
+ gf_cond_swap(x2,x3,swap);
+ gf_cond_swap(z2,z3,swap);
+ swap = k_t;
+
+ gf_add_nr(t1,x2,z2); /* A = x2 + z2 */ /* 2+e */
+ gf_sub_nr(t2,x2,z2); /* B = x2 - z2 */ /* 3+e */
+ gf_sub_nr(z2,x3,z3); /* D = x3 - z3 */ /* 3+e */
+ gf_mul(x2,t1,z2); /* DA */
+ gf_add_nr(z2,z3,x3); /* C = x3 + z3 */ /* 2+e */
+ gf_mul(x3,t2,z2); /* CB */
+ gf_sub_nr(z3,x2,x3); /* DA-CB */ /* 3+e */
+ gf_sqr(z2,z3); /* (DA-CB)^2 */
+ gf_mul(z3,x1,z2); /* z3 = x1(DA-CB)^2 */
+ gf_add_nr(z2,x2,x3); /* (DA+CB) */ /* 2+e */
+ gf_sqr(x3,z2); /* x3 = (DA+CB)^2 */
+
+ gf_sqr(z2,t1); /* AA = A^2 */
+ gf_sqr(t1,t2); /* BB = B^2 */
+ gf_mul(x2,z2,t1); /* x2 = AA*BB */
+ gf_sub_nr(t2,z2,t1); /* E = AA-BB */ /* 3+e */
+
+ gf_mulw(t1,t2,-EDWARDS_D); /* E*-d = a24*E */
+ gf_add_nr(t1,t1,z2); /* AA + a24*E */ /* 2+e */
+ gf_mul(z2,t2,t1); /* z2 = E(AA+a24*E) */
+ }
+
+ /* Finish */
+ gf_cond_swap(x2,x3,swap);
+ gf_cond_swap(z2,z3,swap);
+ gf_invert(z2,z2,0);
+ gf_mul(x1,x2,z2);
+ gf_serialize(out,x1,1);
+ mask_t nz = ~gf_eq(x1,ZERO);
+
+ decaf_bzero(x1,sizeof(x1));
+ decaf_bzero(x2,sizeof(x2));
+ decaf_bzero(z2,sizeof(z2));
+ decaf_bzero(x3,sizeof(x3));
+ decaf_bzero(z3,sizeof(z3));
+ decaf_bzero(t1,sizeof(t1));
+ decaf_bzero(t2,sizeof(t2));
+
+ return decaf_succeed_if(mask_to_bool(nz));
+}
+
+/* Thanks Johan Pascal */
+void decaf_ed448_convert_public_key_to_x448 (
+ uint8_t x[DECAF_X448_PUBLIC_BYTES],
+ const uint8_t ed[DECAF_EDDSA_448_PUBLIC_BYTES]
+) {
+ gf y;
+ const uint8_t mask = (uint8_t)(0xFE<<(7));
+ ignore_result(gf_deserialize(y, ed, 1, mask));
+
+ {
+ gf n,d;
+
+#if EDDSA_USE_SIGMA_ISOGENY
+ /* u = (1+y)/(1-y)*/
+ gf_add(n, y, ONE); /* n = y+1 */
+ gf_sub(d, ONE, y); /* d = 1-y */
+ gf_invert(d, d, 0); /* d = 1/(1-y) */
+ gf_mul(y, n, d); /* u = (y+1)/(1-y) */
+ gf_serialize(x,y,1);
+#else /* EDDSA_USE_SIGMA_ISOGENY */
+ /* u = y^2 * (1-dy^2) / (1-y^2) */
+ gf_sqr(n,y); /* y^2*/
+ gf_sub(d,ONE,n); /* 1-y^2*/
+ gf_invert(d,d,0); /* 1/(1-y^2)*/
+ gf_mul(y,n,d); /* y^2 / (1-y^2) */
+ gf_mulw(d,n,EDWARDS_D); /* dy^2*/
+ gf_sub(d, ONE, d); /* 1-dy^2*/
+ gf_mul(n, y, d); /* y^2 * (1-dy^2) / (1-y^2) */
+ gf_serialize(x,n,1);
+#endif /* EDDSA_USE_SIGMA_ISOGENY */
+
+ decaf_bzero(y,sizeof(y));
+ decaf_bzero(n,sizeof(n));
+ decaf_bzero(d,sizeof(d));
+ }
+}
+
+void decaf_x448_generate_key (
+ uint8_t out[X_PUBLIC_BYTES],
+ const uint8_t scalar[X_PRIVATE_BYTES]
+) {
+ decaf_x448_derive_public_key(out,scalar);
+}
+
+void API_NS(point_mul_by_ratio_and_encode_like_x448) (
+ uint8_t out[X_PUBLIC_BYTES],
+ const point_t p
+) {
+ point_t q;
+#if COFACTOR == 8
+ point_double_internal(q,p,1);
+#else
+ API_NS(point_copy)(q,p);
+#endif
+ gf_invert(q->t,q->x,0); /* 1/x */
+ gf_mul(q->z,q->t,q->y); /* y/x */
+ gf_sqr(q->y,q->z); /* (y/x)^2 */
+#if IMAGINE_TWIST
+ gf_sub(q->y,ZERO,q->y);
+#endif
+ gf_serialize(out,q->y,1);
+ API_NS(point_destroy(q));
+}
+
+void decaf_x448_derive_public_key (
+ uint8_t out[X_PUBLIC_BYTES],
+ const uint8_t scalar[X_PRIVATE_BYTES]
+) {
+ /* Scalar conditioning */
+ uint8_t scalar2[X_PRIVATE_BYTES];
+ memcpy(scalar2,scalar,sizeof(scalar2));
+ scalar2[0] &= -(uint8_t)COFACTOR;
+
+ scalar2[X_PRIVATE_BYTES-1] &= ~(-1u<<((X_PRIVATE_BITS+7)%8));
+ scalar2[X_PRIVATE_BYTES-1] |= 1<<((X_PRIVATE_BITS+7)%8);
+
+ scalar_t the_scalar;
+ API_NS(scalar_decode_long)(the_scalar,scalar2,sizeof(scalar2));
+
+ /* Compensate for the encoding ratio */
+ for (unsigned i=1; i<DECAF_X448_ENCODE_RATIO; i<<=1) {
+ API_NS(scalar_halve)(the_scalar,the_scalar);
+ }
+ point_t p;
+ API_NS(precomputed_scalarmul)(p,API_NS(precomputed_base),the_scalar);
+ API_NS(point_mul_by_ratio_and_encode_like_x448)(out,p);
+ API_NS(point_destroy)(p);
+}
+
+/**
+ * @cond internal
+ * Control for variable-time scalar multiply algorithms.
+ */
+struct smvt_control {
+ int power, addend;
+};
+
+static int recode_wnaf (
+ struct smvt_control *control, /* [nbits/(table_bits+1) + 3] */
+ const scalar_t scalar,
+ unsigned int table_bits
+) {
+ unsigned int table_size = SCALAR_BITS/(table_bits+1) + 3;
+ int position = table_size - 1; /* at the end */
+
+ /* place the end marker */
+ control[position].power = -1;
+ control[position].addend = 0;
+ position--;
+
+ /* PERF: Could negate scalar if it's large. But then would need more cases
+ * in the actual code that uses it, all for an expected reduction of like 1/5 op.
+ * Probably not worth it.
+ */
+
+ uint64_t current = scalar->limb[0] & 0xFFFF;
+ uint32_t mask = (1<<(table_bits+1))-1;
+
+ unsigned int w;
+ const unsigned int B_OVER_16 = sizeof(scalar->limb[0]) / 2;
+ for (w = 1; w<(SCALAR_BITS-1)/16+3; w++) {
+ if (w < (SCALAR_BITS-1)/16+1) {
+ /* Refill the 16 high bits of current */
+ current += (uint32_t)((scalar->limb[w/B_OVER_16]>>(16*(w%B_OVER_16)))<<16);
+ }
+
+ while (current & 0xFFFF) {
+ assert(position >= 0);
+ uint32_t pos = __builtin_ctz((uint32_t)current), odd = (uint32_t)current >> pos;
+ int32_t delta = odd & mask;
+ if (odd & 1<<(table_bits+1)) delta -= (1<<(table_bits+1));
+ current -= delta << pos;
+ control[position].power = pos + 16*(w-1);
+ control[position].addend = delta;
+ position--;
+ }
+ current >>= 16;
+ }
+ assert(current==0);
+
+ position++;
+ unsigned int n = table_size - position;
+ unsigned int i;
+ for (i=0; i<n; i++) {
+ control[i] = control[i+position];
+ }
+ return n-1;
+}
+
+static void
+prepare_wnaf_table(
+ pniels_t *output,
+ const point_t working,
+ unsigned int tbits
+) {
+ point_t tmp;
+ int i;
+ pt_to_pniels(output[0], working);
+
+ if (tbits == 0) return;
+
+ API_NS(point_double)(tmp,working);
+ pniels_t twop;
+ pt_to_pniels(twop, tmp);
+
+ add_pniels_to_pt(tmp, output[0],0);
+ pt_to_pniels(output[1], tmp);
+
+ for (i=2; i < 1<<tbits; i++) {
+ add_pniels_to_pt(tmp, twop,0);
+ pt_to_pniels(output[i], tmp);
+ }
+
+ API_NS(point_destroy)(tmp);
+ decaf_bzero(twop,sizeof(twop));
+}
+
+extern const gf API_NS(precomputed_wnaf_as_fe)[];
+static const niels_t *API_NS(wnaf_base) = (const niels_t *)API_NS(precomputed_wnaf_as_fe);
+const size_t API_NS(sizeof_precomputed_wnafs) __attribute((visibility("hidden")))
+ = sizeof(niels_t)<<DECAF_WNAF_FIXED_TABLE_BITS;
+
+void API_NS(precompute_wnafs) (
+ niels_t out[1<<DECAF_WNAF_FIXED_TABLE_BITS],
+ const point_t base
+) __attribute__ ((visibility ("hidden")));
+
+void API_NS(precompute_wnafs) (
+ niels_t out[1<<DECAF_WNAF_FIXED_TABLE_BITS],
+ const point_t base
+) {
+ pniels_t tmp[1<<DECAF_WNAF_FIXED_TABLE_BITS];
+ gf zs[1<<DECAF_WNAF_FIXED_TABLE_BITS], zis[1<<DECAF_WNAF_FIXED_TABLE_BITS];
+ int i;
+ prepare_wnaf_table(tmp,base,DECAF_WNAF_FIXED_TABLE_BITS);
+ for (i=0; i<1<<DECAF_WNAF_FIXED_TABLE_BITS; i++) {
+ memcpy(out[i], tmp[i]->n, sizeof(niels_t));
+ gf_copy(zs[i], tmp[i]->z);
+ }
+ batch_normalize_niels(out, (const gf *)zs, zis, 1<<DECAF_WNAF_FIXED_TABLE_BITS);
+
+ decaf_bzero(tmp,sizeof(tmp));
+ decaf_bzero(zs,sizeof(zs));
+ decaf_bzero(zis,sizeof(zis));
+}
+
+void API_NS(base_double_scalarmul_non_secret) (
+ point_t combo,
+ const scalar_t scalar1,
+ const point_t base2,
+ const scalar_t scalar2
+) {
+ const int table_bits_var = DECAF_WNAF_VAR_TABLE_BITS,
+ table_bits_pre = DECAF_WNAF_FIXED_TABLE_BITS;
+ struct smvt_control control_var[SCALAR_BITS/(table_bits_var+1)+3];
+ struct smvt_control control_pre[SCALAR_BITS/(table_bits_pre+1)+3];
+
+ int ncb_pre = recode_wnaf(control_pre, scalar1, table_bits_pre);
+ int ncb_var = recode_wnaf(control_var, scalar2, table_bits_var);
+
+ pniels_t precmp_var[1<<table_bits_var];
+ prepare_wnaf_table(precmp_var, base2, table_bits_var);
+
+ int contp=0, contv=0, i = control_var[0].power;
+
+ if (i < 0) {
+ API_NS(point_copy)(combo, API_NS(point_identity));
+ return;
+ } else if (i > control_pre[0].power) {
+ pniels_to_pt(combo, precmp_var[control_var[0].addend >> 1]);
+ contv++;
+ } else if (i == control_pre[0].power && i >=0 ) {
+ pniels_to_pt(combo, precmp_var[control_var[0].addend >> 1]);
+ add_niels_to_pt(combo, API_NS(wnaf_base)[control_pre[0].addend >> 1], i);
+ contv++; contp++;
+ } else {
+ i = control_pre[0].power;
+ niels_to_pt(combo, API_NS(wnaf_base)[control_pre[0].addend >> 1]);
+ contp++;
+ }
+
+ for (i--; i >= 0; i--) {
+ int cv = (i==control_var[contv].power), cp = (i==control_pre[contp].power);
+ point_double_internal(combo,combo,i && !(cv||cp));
+
+ if (cv) {
+ assert(control_var[contv].addend);
+
+ if (control_var[contv].addend > 0) {
+ add_pniels_to_pt(combo, precmp_var[control_var[contv].addend >> 1], i&&!cp);
+ } else {
+ sub_pniels_from_pt(combo, precmp_var[(-control_var[contv].addend) >> 1], i&&!cp);
+ }
+ contv++;
+ }
+
+ if (cp) {
+ assert(control_pre[contp].addend);
+
+ if (control_pre[contp].addend > 0) {
+ add_niels_to_pt(combo, API_NS(wnaf_base)[control_pre[contp].addend >> 1], i);
+ } else {
+ sub_niels_from_pt(combo, API_NS(wnaf_base)[(-control_pre[contp].addend) >> 1], i);
+ }
+ contp++;
+ }
+ }
+
+ /* This function is non-secret, but whatever this is cheap. */
+ decaf_bzero(control_var,sizeof(control_var));
+ decaf_bzero(control_pre,sizeof(control_pre));
+ decaf_bzero(precmp_var,sizeof(precmp_var));
+
+ assert(contv == ncb_var); (void)ncb_var;
+ assert(contp == ncb_pre); (void)ncb_pre;
+}
+
+void API_NS(point_destroy) (
+ point_t point
+) {
+ decaf_bzero(point, sizeof(point_t));
+}
+
+void API_NS(precomputed_destroy) (
+ precomputed_s *pre
+) {
+ decaf_bzero(pre, API_NS(sizeof_precomputed_s));
+}
--- /dev/null
+/** @warning: this file was automatically generated. */
+#include "field.h"
+
+#include <decaf.h>
+
+#define API_NS(_id) decaf_448_##_id
+const API_NS(point_t) API_NS(point_base) = {{
+{FIELD_LITERAL(0x0000000000000000,0x0000000000000000,0x0000000000000000,0x0080000000000000,0x00fffffffffffffe,0x00ffffffffffffff,0x00ffffffffffffff,0x007fffffffffffff)},
+ {FIELD_LITERAL(0x006079b4dfdd4a64,0x000c1e3ab470a1c8,0x0044d73f48e5199b,0x0050452714141818,0x004c74c393d5242c,0x0024080526437050,0x00d48d06c13078ca,0x008508de14f04286)},
+ {FIELD_LITERAL(0x0000000000000001,0x0000000000000000,0x0000000000000000,0x0000000000000000,0x0000000000000000,0x0000000000000000,0x0000000000000000,0x0000000000000000)},
+ {FIELD_LITERAL(0x00e3c816dc198105,0x0062071833f4e093,0x004dde98e3421403,0x00a319b57519c985,0x00794be956382384,0x00e1ddc2b86da60f,0x0050e23d5682a9ff,0x006d3669e173c6a4)}
+}};
+const gf API_NS(precomputed_base_as_fe)[240]
+VECTOR_ALIGNED __attribute__((visibility("hidden"))) = {
+ {FIELD_LITERAL(0x00cc3b062366f4cc,0x003d6e34e314aa3c,0x00d51c0a7521774d,0x0094e060eec6ab8b,0x00d21291b4d80082,0x00befed12b55ef1e,0x00c3dd2df5c94518,0x00e0a7b112b8d4e6)},
+ {FIELD_LITERAL(0x0019eb5608d8723a,0x00d1bab52fb3aedb,0x00270a7311ebc90c,0x0037c12b91be7f13,0x005be16cd8b5c704,0x003e181acda888e1,0x00bc1f00fc3fc6d0,0x00d3839bfa319e20)},
+ {FIELD_LITERAL(0x003caeb88611909f,0x00ea8b378c4df3d4,0x00b3295b95a5a19a,0x00a65f97514bdfb5,0x00b39efba743cab1,0x0016ba98b862fd2d,0x0001508812ee71d7,0x000a75740eea114a)},
+ {FIELD_LITERAL(0x00ebcf0eb649f823,0x00166d332e98ea03,0x0059ddf64f5cd5f6,0x0047763123d9471b,0x00a64065c53ef62f,0x00978e44c480153d,0x000b5b2a0265f194,0x0046a24b9f32965a)},
+ {FIELD_LITERAL(0x00b9eef787034df0,0x0020bc24de3390cd,0x000022160bae99bb,0x00ae66e886e97946,0x0048d4bbe02cbb8b,0x0072ba97b34e38d4,0x00eae7ec8f03e85a,0x005ba92ecf808b2c)},
+ {FIELD_LITERAL(0x00c9cfbbe74258fd,0x00843a979ea9eaa7,0x000cbb4371cfbe90,0x0059bac8f7f0a628,0x004b3dff882ff530,0x0011869df4d90733,0x00595aa71f4abfc2,0x0070e2d38990c2e6)},
+ {FIELD_LITERAL(0x00de2010c0a01733,0x00c739a612e24297,0x00a7212643141d7c,0x00f88444f6b67c11,0x00484b7b16ec28f2,0x009c1b8856af9c68,0x00ff4669591fe9d6,0x0054974be08a32c8)},
+ {FIELD_LITERAL(0x0010de3fd682ceed,0x008c07642d83ca4e,0x0013bb064e00a1cc,0x009411ae27870e11,0x00ea8e5b4d531223,0x0032fe7d2aaece2e,0x00d989e243e7bb41,0x000fe79a508e9b8b)},
+ {FIELD_LITERAL(0x005e0426b9bfc5b1,0x0041a5b1d29ee4fa,0x0015b0def7774391,0x00bc164f1f51af01,0x00d543b0942797b9,0x003c129b6398099c,0x002b114c6e5adf18,0x00b4e630e4018a7b)},
+ {FIELD_LITERAL(0x00d490afc95f8420,0x00b096bf50c1d9b9,0x00799fd707679866,0x007c74d9334afbea,0x00efaa8be80ff4ed,0x0075c4943bb81694,0x00c21c2fca161f36,0x00e77035d492bfee)},
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+ {FIELD_LITERAL(0x00aa2261022d883f,0x00ebcca4548010ac,0x002528512e28a437,0x0070ca7676b66082,0x0084bda170f7c6d3,0x00581b4747c9b8bb,0x005c96a01061c7e2,0x00fb7c4a362b5273)},
+ {FIELD_LITERAL(0x00c30020eb512d02,0x0060f288283a4d26,0x00b7ed13becde260,0x0075ebb74220f6e9,0x00701079fcfe8a1f,0x001c28fcdff58938,0x002e4544b8f4df6b,0x0060c5bc4f1a7d73)},
+ {FIELD_LITERAL(0x00ae307cf069f701,0x005859f222dd618b,0x00212d6c46ec0b0d,0x00a0fe4642afb62d,0x00420d8e4a0a8903,0x00a80ff639bdf7b0,0x0019bee1490b5d8e,0x007439e4b9c27a86)},
+ {FIELD_LITERAL(0x00a94700032a093f,0x0076e96c225216e7,0x00a63a4316e45f91,0x007d8bbb4645d3b2,0x00340a6ff22793eb,0x006f935d4572aeb7,0x00b1fb69f00afa28,0x009e8f3423161ed3)},
+ {FIELD_LITERAL(0x009ef49c6b5ced17,0x00a555e6269e9f0a,0x007e6f1d79ec73b5,0x009ac78695a32ac4,0x0001d77fbbcd5682,0x008cea1fee0aaeed,0x00f42bea82a53462,0x002e46ab96cafcc9)},
+ {FIELD_LITERAL(0x0051cfcc5885377a,0x00dce566cb1803ca,0x00430c7643f2c7d4,0x00dce1a1337bdcc0,0x0010d5bd7283c128,0x003b1b547f9b46fe,0x000f245e37e770ab,0x007b72511f022b37)},
+ {FIELD_LITERAL(0x0060db815bc4786c,0x006fab25beedc434,0x00c610d06084797c,0x000c48f08537bec0,0x0031aba51c5b93da,0x007968fa6e01f347,0x0030070da52840c6,0x00c043c225a4837f)},
+ {FIELD_LITERAL(0x001bcfd00649ee93,0x006dceb47e2a0fd5,0x00f2cebda0cf8fd0,0x00b6b9d9d1fbdec3,0x00815262e6490611,0x00ef7f5ce3176760,0x00e49cd0c998d58b,0x005fc6cc269ba57c)},
+ {FIELD_LITERAL(0x008940211aa0d633,0x00addae28136571d,0x00d68fdbba20d673,0x003bc6129bc9e21a,0x000346cf184ebe9a,0x0068774d741ebc7f,0x0019d5e9e6966557,0x0003cbd7f981b651)},
+ {FIELD_LITERAL(0x004a2902926f8d3f,0x00ad79b42637ab75,0x0088f60b90f2d4e8,0x0030f54ef0e398c4,0x00021dc9bf99681e,0x007ebf66fde74ee3,0x004ade654386e9a4,0x00e7485066be4c27)},
+ {FIELD_LITERAL(0x00445f1263983be0,0x004cf371dda45e6a,0x00744a89d5a310e7,0x001f20ce4f904833,0x00e746edebe66e29,0x000912ab1f6c153d,0x00f61d77d9b2444c,0x0001499cd6647610)}
+};
+const gf API_NS(precomputed_wnaf_as_fe)[96]
+VECTOR_ALIGNED __attribute__((visibility("hidden"))) = {
+ {FIELD_LITERAL(0x00303cda6feea532,0x00860f1d5a3850e4,0x00226b9fa4728ccd,0x00e822938a0a0c0c,0x00263a61c9ea9216,0x001204029321b828,0x006a468360983c65,0x0002846f0a782143)},
+ {FIELD_LITERAL(0x00303cda6feea532,0x00860f1d5a3850e4,0x00226b9fa4728ccd,0x006822938a0a0c0c,0x00263a61c9ea9215,0x001204029321b828,0x006a468360983c65,0x0082846f0a782143)},
+ {FIELD_LITERAL(0x00ef8e22b275198d,0x00b0eb141a0b0e8b,0x001f6789da3cb38c,0x006d2ff8ed39073e,0x00610bdb69a167f3,0x00571f306c9689b4,0x00f557e6f84b2df8,0x002affd38b2c86db)},
+ {FIELD_LITERAL(0x00cea0fc8d2e88b5,0x00821612d69f1862,0x0074c283b3e67522,0x005a195ba05a876d,0x000cddfe557feea4,0x008046c795bcc5e5,0x00540969f4d6e119,0x00d27f96d6b143d5)},
+ {FIELD_LITERAL(0x000c3b1019d474e8,0x00e19533e4952284,0x00cc9810ba7c920a,0x00f103d2785945ac,0x00bfa5696cc69b34,0x00a8d3d51e9ca839,0x005623cb459586b9,0x00eae7ce1cd52e9e)},
+ {FIELD_LITERAL(0x0005a178751dd7d8,0x002cc3844c69c42f,0x00acbfe5efe10539,0x009c20f43431a65a,0x008435d96374a7b3,0x009ee57566877bd3,0x0044691725ed4757,0x001e87bb2fe2c6b2)},
+ {FIELD_LITERAL(0x000cedc4debf7a04,0x002ffa45000470ac,0x002e9f9678201915,0x0017da1208c4fe72,0x007d558cc7d656cb,0x0037a827287cf289,0x00142472d3441819,0x009c21f166cf8dd1)},
+ {FIELD_LITERAL(0x003ef83af164b2f2,0x000949a5a0525d0d,0x00f4498186cac051,0x00e77ac09ef126d2,0x0073ae0b2c9296e9,0x001c163f6922e3ed,0x0062946159321bea,0x00cfb79b22990b39)},
+ {FIELD_LITERAL(0x00b001431ca9e654,0x002d7e5eabcc9a3a,0x0052e8114c2f6747,0x0079ac4f94487f92,0x00bffd919b5d749c,0x00261f92ad15e620,0x00718397b7a97895,0x00c1443e6ebbc0c4)},
+ {FIELD_LITERAL(0x00eacd90c1e0a049,0x008977935b149fbe,0x0004cb9ba11c93dc,0x009fbd5b3470844d,0x004bc18c9bfc22cf,0x0057679a991839f3,0x00ef15b76fb4092e,0x0074a5173a225041)},
+ {FIELD_LITERAL(0x003f5f9d7ec4777b,0x00ab2e733c919c94,0x001bb6c035245ae5,0x00a325a49a883630,0x0033e9a9ea3cea2f,0x00e442a1eaa0e844,0x00b2116d5b0e71b8,0x00c16abed6d64047)},
+ {FIELD_LITERAL(0x00c560b5ed051165,0x001945adc5d65094,0x00e221865710f910,0x00cc12bc9e9b8ceb,0x004faa9518914e35,0x0017476d89d42f6d,0x00b8f637c8fa1c8b,0x0088c7d2790864b8)},
+ {FIELD_LITERAL(0x00ef7eafc1c69be6,0x0085d3855778fbea,0x002c8d5b450cb6f5,0x004e77de5e1e7fec,0x0047c057893abded,0x001b430b85d51e16,0x00965c7b45640c3c,0x00487b2bb1162b97)},
+ {FIELD_LITERAL(0x0099c73a311beec2,0x00a3eff38d8912ad,0x002efa9d1d7e8972,0x00f717ae1e14d126,0x002833f795850c8b,0x0066c12ad71486bd,0x00ae9889da4820eb,0x00d6044309555c08)},
+ {FIELD_LITERAL(0x004b1c5283d15e41,0x00669d8ea308ff75,0x0004390233f762a1,0x00e1d67b83cb6cec,0x003eebaa964c78b1,0x006b0aff965eb664,0x00b313d4470bdc37,0x008814ffcb3cb9d8)},
+ {FIELD_LITERAL(0x009724b8ce68db70,0x007678b5ed006f3d,0x00bdf4b89c0abd73,0x00299748e04c7c6d,0x00ddd86492c3c977,0x00c5a7febfa30a99,0x00ed84715b4b02bb,0x00319568adf70486)},
+ {FIELD_LITERAL(0x0070ff2d864de5bb,0x005a37eeb637ee95,0x0033741c258de160,0x00e6ca5cb1988f46,0x001ceabd92a24661,0x0030957bd500fe40,0x001c3362afe912c5,0x005187889f678bd2)},
+ {FIELD_LITERAL(0x0086835fc62bbdc7,0x009c3516ca4910a1,0x00956c71f8d00783,0x0095c78fcf63235f,0x00fc7ff6ba05c222,0x00cdd8b3f8d74a52,0x00ac5ae16de8256e,0x00e9d4be8ed48624)},
+ {FIELD_LITERAL(0x00c0ce11405df2d8,0x004e3f37b293d7b6,0x002410172e1ac6db,0x00b8dbff4bf8143d,0x003a7b409d56eb66,0x003e0f6a0dfef9af,0x0081c4e4d3645be1,0x00ce76076b127623)},
+ {FIELD_LITERAL(0x00f6ee0f98974239,0x0042d89af07d3a4f,0x00846b7fe84346b5,0x006a21fc6a8d39a1,0x00ac8bc2541ff2d9,0x006d4e2a77732732,0x009a39b694cc3f2f,0x0085c0aa2a404c8f)},
+ {FIELD_LITERAL(0x00b261101a218548,0x00c1cae96424277b,0x00869da0a77dd268,0x00bc0b09f8ec83ea,0x00d61027f8e82ba9,0x00aa4c85999dce67,0x00eac3132b9f3fe1,0x00fb9b0cf1c695d2)},
+ {FIELD_LITERAL(0x0043079295512f0d,0x0046a009861758e0,0x003ee2842a807378,0x0034cc9d1298e4fa,0x009744eb4d31b3ee,0x00afacec96650cd0,0x00ac891b313761ae,0x00e864d6d26e708a)},
+ {FIELD_LITERAL(0x00a84d7c8a23b491,0x0088e19aa868b27f,0x0005986d43e78ce9,0x00f28012f0606d28,0x0017ded7e10249b3,0x005ed4084b23af9b,0x00b9b0a940564472,0x00ad9056cceeb1f4)},
+ {FIELD_LITERAL(0x00db91b357fe755e,0x00a1aa544b15359c,0x00af4931a0195574,0x007686124fe11aef,0x00d1ead3c7b9ef7e,0x00aaf5fc580f8c15,0x00e727be147ee1ec,0x003c61c1e1577b86)},
+ {FIELD_LITERAL(0x009d3fca983220cf,0x00cd11acbc853dc4,0x0017590409d27f1d,0x00d2176698082802,0x00fa01251b2838c8,0x00dd297a0d9b51c6,0x00d76c92c045820a,0x00534bc7c46c9033)},
+ {FIELD_LITERAL(0x0080ed9bc9b07338,0x00fceac7745d2652,0x008a9d55f5f2cc69,0x0096ce72df301ac5,0x00f53232e7974d87,0x0071728c7ae73947,0x0090507602570778,0x00cb81cfd883b1b2)},
+ {FIELD_LITERAL(0x005011aadea373da,0x003a8578ec896034,0x00f20a6535fa6d71,0x005152d31e5a87cf,0x002bac1c8e68ca31,0x00b0e323db4c1381,0x00f1d596b7d5ae25,0x00eae458097cb4e0)},
+ {FIELD_LITERAL(0x00920ac80f9b0d21,0x00f80f7f73401246,0x0086d37849b557d6,0x0002bd4b317b752e,0x00b26463993a42bb,0x002070422a73b129,0x00341acaa0380cb3,0x00541914dd66a1b2)},
+ {FIELD_LITERAL(0x00c1513cd66abe8c,0x000139e01118944d,0x0064abbcb8080bbb,0x00b3b08202473142,0x00c629ef25da2403,0x00f0aec3310d9b7f,0x0050b2227472d8cd,0x00f6c8a922d41fb4)},
+ {FIELD_LITERAL(0x001075ccf26b7b1f,0x00bb6bb213170433,0x00e9491ad262da79,0x009ef4f48d2d384c,0x008992770766f09d,0x001584396b6b1101,0x00af3f8676c9feef,0x0024603c40269118)},
+ {FIELD_LITERAL(0x009dd7b31319527c,0x001e7ac948d873a9,0x00fa54b46ef9673a,0x0066efb8d5b02fe6,0x00754b1d3928aeae,0x0004262ac72a6f6b,0x0079b7d49a6eb026,0x003126a753540102)},
+ {FIELD_LITERAL(0x009666e24f693947,0x00f714311269d45f,0x0010ffac1d0c851c,0x0066e80c37363497,0x00f1f4ad010c60b0,0x0015c87408470ff7,0x00651d5e9c7766a4,0x008138819d7116de)},
+ {FIELD_LITERAL(0x003934b11c57253b,0x00ef308edf21f46e,0x00e54e99c7a16198,0x0080d57135764e63,0x00751c27b946bc24,0x00dd389ce4e9e129,0x00a1a2bfd1cd84dc,0x002fae73e5149b32)},
+ {FIELD_LITERAL(0x00911657dffb4cdd,0x00c100b7cc553d06,0x00449d075ec467cc,0x007062100bc64e70,0x0043cf86f7bd21e7,0x00f401dc4b797dea,0x005224afb2f62e65,0x00d1ede3fb5a42be)},
+ {FIELD_LITERAL(0x00f2ba36a41aa144,0x00a0c22d946ee18f,0x008aae8ef9a14f99,0x00eef4d79b19bb36,0x008e75ce3d27b1fc,0x00a65daa03b29a27,0x00d9cc83684eb145,0x009e1ed80cc2ed74)},
+ {FIELD_LITERAL(0x00bed953d1997988,0x00b93ed175a24128,0x00871c5963fb6365,0x00ca2df20014a787,0x00f5d9c1d0b34322,0x00f6f5942818db0a,0x004cc091f49c9906,0x00e8a188a60bff9f)},
+ {FIELD_LITERAL(0x0032c7762032fae8,0x00e4087232e0bc21,0x00f767344b6e8d85,0x00bbf369b76c2aa2,0x008a1f46c6e1570c,0x001368cd9780369f,0x007359a39d079430,0x0003646512921434)},
+ {FIELD_LITERAL(0x007c4b47ca7c73e7,0x005396221039734b,0x008b64ddf0e45d7e,0x00bfad5af285e6c2,0x008ec711c5b1a1a8,0x00cf663301237f98,0x00917ee3f1655126,0x004152f337efedd8)},
+ {FIELD_LITERAL(0x0007c7edc9305daa,0x000a6664f273701c,0x00f6e78795e200b1,0x005d05b9ecd2473e,0x0014f5f17c865786,0x00c7fd2d166fa995,0x004939a2d8eb80e0,0x002244ba0942c199)},
+ {FIELD_LITERAL(0x00321e767f0262cf,0x002e57d776caf68e,0x00bf2c94814f0437,0x00c339196acd622f,0x001db4cce71e2770,0x001ded5ddba6eee2,0x0078608ab1554c8d,0x00067fe0ab76365b)},
+ {FIELD_LITERAL(0x00f09758e11e3985,0x00169efdbd64fad3,0x00e8889b7d6dacd6,0x0035cdd58ea88209,0x00bcda47586d7f49,0x003cdddcb2879088,0x0016da70187e954b,0x009556ea2e92aacd)},
+ {FIELD_LITERAL(0x008cab16bd1ff897,0x00b389972cdf753f,0x00ea8ed1e46dfdc0,0x004fe7ef94c589f4,0x002b8ae9b805ecf3,0x0025c08d892874a5,0x0023938e98d44c4c,0x00f759134cabf69c)},
+ {FIELD_LITERAL(0x006c2a84678e4b3b,0x007a194aacd1868f,0x00ed0225af424761,0x00da0a6f293c64b8,0x001062ac5c6a7a18,0x0030f5775a8aeef4,0x0002acaad76b7af0,0x00410b8fd63a579f)},
+ {FIELD_LITERAL(0x001ec59db3d9590e,0x001e9e3f1c3f182d,0x0045a9c3ec2cab14,0x0008198572aeb673,0x00773b74068bd167,0x0012535eaa395434,0x0044dba9e3bbb74a,0x002fba4d3c74bd0e)},
+ {FIELD_LITERAL(0x0042bf08fe66922c,0x003318b8fbb49e8c,0x00d75946004aa14c,0x00f601586b42bf1c,0x00c74cf1d912fe66,0x00abcb36974b30ad,0x007eb78720c9d2b8,0x009f54ab7bd4df85)},
+ {FIELD_LITERAL(0x00db9fc948f73826,0x00fa8b3746ed8ee9,0x00132cb65aafbeb2,0x00c36ff3fe7925b8,0x00837daed353d2fe,0x00ec661be0667cf4,0x005beb8ed2e90204,0x00d77dd69e564967)},
+ {FIELD_LITERAL(0x0042e6268b861751,0x0008dd0469500c16,0x00b51b57c338a3fd,0x00cc4497d85cff6b,0x002f13d6b57c34a4,0x0083652eaf301105,0x00cc344294cc93a8,0x0060f4d02810e270)},
+ {FIELD_LITERAL(0x00a8954363cd518b,0x00ad171124bccb7b,0x0065f46a4adaae00,0x001b1a5b2a96e500,0x0043fe24f8233285,0x0066996d8ae1f2c3,0x00c530f3264169f9,0x00c0f92d07cf6a57)},
+ {FIELD_LITERAL(0x0036a55c6815d943,0x008c8d1def993db3,0x002e0e1e8ff7318f,0x00d883a4b92db00a,0x002f5e781ae33906,0x001a72adb235c06d,0x00f2e59e736e9caa,0x001a4b58e3031914)},
+ {FIELD_LITERAL(0x00d73bfae5e00844,0x00bf459766fb5f52,0x0061b4f5a5313cde,0x004392d4c3b95514,0x000d3551b1077523,0x0000998840ee5d71,0x006de6e340448b7b,0x00251aa504875d6e)},
+ {FIELD_LITERAL(0x003bf343427ac342,0x00adc0a78642b8c5,0x0003b893175a8314,0x0061a34ade5703bc,0x00ea3ea8bb71d632,0x00be0df9a1f198c2,0x0046dd8e7c1635fb,0x00f1523fdd25d5e5)},
+ {FIELD_LITERAL(0x00633f63fc9dd406,0x00e713ff80e04a43,0x0060c6e970f2d621,0x00a57cd7f0df1891,0x00f2406a550650bb,0x00b064290efdc684,0x001eab0144d17916,0x00cd15f863c293ab)},
+ {FIELD_LITERAL(0x0029cec55273f70d,0x007044ee275c6340,0x0040f637a93015e2,0x00338bb78db5aae9,0x001491b2a6132147,0x00a125d6cfe6bde3,0x005f7ac561ba8669,0x001d5eaea3fbaacf)},
+ {FIELD_LITERAL(0x00054e9635e3be31,0x000e43f31e2872be,0x00d05b1c9e339841,0x006fac50bd81fd98,0x00cdc7852eaebb09,0x004ff519b061991b,0x009099e8107d4c85,0x00273e24c36a4a61)},
+ {FIELD_LITERAL(0x00070b4441ef2c46,0x00efa5b02801a109,0x00bf0b8c3ee64adf,0x008a67e0b3452e98,0x001916b1f2fa7a74,0x00d781a78ff6cdc3,0x008682ce57e5c919,0x00cc1109dd210da3)},
+ {FIELD_LITERAL(0x00cae8aaff388663,0x005e983a35dda1c7,0x007ab1030d8e37f4,0x00e48940f5d032fe,0x006a36f9ef30b331,0x009be6f03958c757,0x0086231ceba91400,0x008bd0f7b823e7aa)},
+ {FIELD_LITERAL(0x00cf881ebef5a45a,0x004ebea78e7c6f2c,0x0090da9209cf26a0,0x00de2b2e4c775b84,0x0071d6031c3c15ae,0x00d9e927ef177d70,0x00894ee8c23896fd,0x00e3b3b401e41aad)},
+ {FIELD_LITERAL(0x00204fef26864170,0x00819269c5dee0f8,0x00bfb4713ec97966,0x0026339a6f34df78,0x001f26e64c761dc2,0x00effe3af313cb60,0x00e17b70138f601b,0x00f16e1ccd9ede5e)},
+ {FIELD_LITERAL(0x005d9a8353fdb2db,0x0055cc2048c698f0,0x00f6c4ac89657218,0x00525034d73faeb2,0x00435776fbda3c7d,0x0070ea5312323cbc,0x007a105d44d069fb,0x006dbc8d6dc786aa)},
+ {FIELD_LITERAL(0x0017cff19cd394ec,0x00fef7b810922587,0x00e6483970dff548,0x00ddf36ad6874264,0x00e61778523fcce2,0x0093a66c0c93b24a,0x00fd367114db7f86,0x007652d7ddce26dd)},
+ {FIELD_LITERAL(0x00d92ced7ba12843,0x00aea9c7771e86e7,0x0046639693354f7b,0x00a628dbb6a80c47,0x003a0b0507372953,0x00421113ab45c0d9,0x00e545f08362ab7a,0x0028ce087b4d6d96)},
+ {FIELD_LITERAL(0x00a67ee7cf9f99eb,0x005713b275f2ff68,0x00f1d536a841513d,0x00823b59b024712e,0x009c46b9d0d38cec,0x00cdb1595aa2d7d4,0x008375b3423d9af8,0x000ab0b516d978f7)},
+ {FIELD_LITERAL(0x00428dcb3c510b0f,0x00585607ea24bb4e,0x003736bf1603687a,0x00c47e568c4fe3c7,0x003cd00282848605,0x0043a487c3b91939,0x004ffc04e1095a06,0x00a4c989a3d4b918)},
+ {FIELD_LITERAL(0x00a8778d0e429f7a,0x004c02b059105a68,0x0016653b609da3ff,0x00d5107bd1a12d27,0x00b4708f9a771cab,0x00bb63b662033f69,0x0072f322240e7215,0x0019445b59c69222)},
+ {FIELD_LITERAL(0x00cf4f6069a658e6,0x0053ca52859436a6,0x0064b994d7e3e117,0x00cb469b9a07f534,0x00cfb68f399e9d47,0x00f0dcb8dac1c6e7,0x00f2ab67f538b3a5,0x0055544f178ab975)},
+ {FIELD_LITERAL(0x0099b7a2685d538c,0x00e2f1897b7c0018,0x003adac8ce48dae3,0x00089276d5c50c0c,0x00172fca07ad6717,0x00cb1a72f54069e5,0x004ee42f133545b3,0x00785f8651362f16)},
+ {FIELD_LITERAL(0x0049cbac38509e11,0x0015234505d42cdf,0x00794fb0b5840f1c,0x00496437344045a5,0x0031b6d944e4f9b0,0x00b207318ac1f5d8,0x0000c840da7f5c5d,0x00526f373a5c8814)},
+ {FIELD_LITERAL(0x002c7b7742d1dfd9,0x002cabeb18623c01,0x00055f5e3e044446,0x006c20f3b4ef54ba,0x00c600141ec6b35f,0x00354f437f1a32a3,0x00bac4624a3520f9,0x00c483f734a90691)},
+ {FIELD_LITERAL(0x0053a737d422918d,0x00f7fca1d8758625,0x00c360336dadb04c,0x00f38e3d9158a1b8,0x0069ce3b418e84c6,0x005d1697eca16ead,0x00f8bd6a35ece13d,0x007885dfc2b5afea)},
+ {FIELD_LITERAL(0x00c3617ae260776c,0x00b20dc3e96922d7,0x00a1a7802246706a,0x00ca6505a5240244,0x002246b62d919782,0x001439102d7aa9b3,0x00e8af1139e6422c,0x00c888d1b52f2b05)},
+ {FIELD_LITERAL(0x005b67690ffd41d9,0x005294f28df516f9,0x00a879272412fcb9,0x00098b629a6d1c8d,0x00fabd3c8050865a,0x00cd7e5b0a3879c5,0x00153238210f3423,0x00357cac101e9f42)},
+ {FIELD_LITERAL(0x008917b454444fb7,0x00f59247c97e441b,0x00a6200a6815152d,0x0009a4228601d254,0x001c0360559bd374,0x007563362039cb36,0x00bd75b48d74e32b,0x0017f515ac3499e8)},
+ {FIELD_LITERAL(0x001532a7ffe41c5a,0x00eb1edce358d6bf,0x00ddbacc7b678a7b,0x008a7b70f3c841a3,0x00f1923bf27d3f4c,0x000b2713ed8f7873,0x00aaf67e29047902,0x0044994a70b3976d)},
+ {FIELD_LITERAL(0x00d54e802082d42c,0x00a55aa0dce7cc6c,0x006477b96073f146,0x0082efe4ceb43594,0x00a922bcba026845,0x0077f19d1ab75182,0x00c2bb2737846e59,0x0004d7eec791dd33)},
+ {FIELD_LITERAL(0x0044588d1a81d680,0x00b0a9097208e4f8,0x00212605350dc57e,0x0028717cd2871123,0x00fb083c100fd979,0x0045a056ce063fdf,0x00a5d604b4dd6a41,0x001dabc08ba4e236)},
+ {FIELD_LITERAL(0x00c4887198d7a7fa,0x00244f98fb45784a,0x0045911e15a15d01,0x001d323d374c0966,0x00967c3915196562,0x0039373abd2f3c67,0x000d2c5614312423,0x0041cf2215442ce3)},
+ {FIELD_LITERAL(0x008ede889ada7f06,0x001611e91de2e135,0x00fdb9a458a471b9,0x00563484e03710d1,0x0031cc81925e3070,0x0062c97b3af80005,0x00fa733eea28edeb,0x00e82457e1ebbc88)},
+ {FIELD_LITERAL(0x006a0df5fe9b6f59,0x00a0d4ff46040d92,0x004a7cedb6f93250,0x00d1df8855b8c357,0x00e73a46086fd058,0x0048fb0add6dfe59,0x001e03a28f1b4e3d,0x00a871c993308d76)},
+ {FIELD_LITERAL(0x0030dbb2d1766ec8,0x00586c0ad138555e,0x00d1a34f9e91c77c,0x0063408ad0e89014,0x00d61231b05f6f5b,0x0009abf569f5fd8a,0x00aec67a110f1c43,0x0031d1a790938dd7)},
+ {FIELD_LITERAL(0x006cded841e2a862,0x00198d60af0ab6fb,0x0018f09db809e750,0x004e6ac676016263,0x00eafcd1620969cb,0x002c9784ca34917d,0x0054f00079796de7,0x00d9fab5c5972204)},
+ {FIELD_LITERAL(0x004bd0fee2438a83,0x00b571e62b0f83bd,0x0059287d7ce74800,0x00fb3631b645c3f0,0x00a018e977f78494,0x0091e27065c27b12,0x007696c1817165e0,0x008c40be7c45ba3a)},
+ {FIELD_LITERAL(0x00a0f326327cb684,0x001c7d0f672680ff,0x008c1c81ffb112d1,0x00f8f801674eddc8,0x00e926d5d48c2a9d,0x005bd6d954c6fe9a,0x004c6b24b4e33703,0x00d05eb5c09105cc)},
+ {FIELD_LITERAL(0x00d61731caacf2cf,0x002df0c7609e01c5,0x00306172208b1e2b,0x00b413fe4fb2b686,0x00826d360902a221,0x003f8d056e67e7f7,0x0065025b0175e989,0x00369add117865eb)},
+ {FIELD_LITERAL(0x00aaf895aec2fa11,0x000f892bc313eb52,0x005b1c794dad050b,0x003f8ec4864cec14,0x00af81058d0b90e5,0x00ebe43e183997bb,0x00a9d610f9f3e615,0x007acd8eec2e88d3)},
+ {FIELD_LITERAL(0x0049b2fab13812a3,0x00846db32cd60431,0x000177fa578c8d6c,0x00047d0e2ad4bc51,0x00b158ba38d1e588,0x006a45daad79e3f3,0x000997b93cab887b,0x00c47ea42fa23dc3)},
+ {FIELD_LITERAL(0x0012b6fef7aeb1ca,0x009412768194b6a7,0x00ff0d351f23ab93,0x007e8a14c1aff71b,0x006c1c0170c512bc,0x0016243ea02ab2e5,0x007bb6865b303f3e,0x0015ce6b29b159f4)},
+ {FIELD_LITERAL(0x009961cd02e68108,0x00e2035d3a1d0836,0x005d51f69b5e1a1d,0x004bccb4ea36edcd,0x0069be6a7aeef268,0x0063f4dd9de8d5a7,0x006283783092ca35,0x0075a31af2c35409)},
+ {FIELD_LITERAL(0x00c412365162e8cf,0x00012283fb34388a,0x003e6543babf39e2,0x00eead6b3a804978,0x0099c0314e8b326f,0x00e98e0a8d477a4f,0x00d2eb96b127a687,0x00ed8d7df87571bb)},
+ {FIELD_LITERAL(0x00777463e308cacf,0x00c8acb93950132d,0x00ebddbf4ca48b2c,0x0026ad7ca0795a0a,0x00f99a3d9a715064,0x000d60bcf9d4dfcc,0x005e65a73a437a06,0x0019d536a8db56c8)},
+ {FIELD_LITERAL(0x00192d7dd558d135,0x0027cd6a8323ffa7,0x00239f1a412dc1e7,0x0046b4b3be74fc5c,0x0020c47a2bef5bce,0x00aa17e48f43862b,0x00f7e26c96342e5f,0x0008011c530f39a9)},
+ {FIELD_LITERAL(0x00aad4ac569bf0f1,0x00a67adc90b27740,0x0048551369a5751a,0x0031252584a3306a,0x0084e15df770e6fc,0x00d7bba1c74b5805,0x00a80ef223af1012,0x0089c85ceb843a34)},
+ {FIELD_LITERAL(0x00c4545be4a54004,0x0099e11f60357e6c,0x001f3936d19515a6,0x007793df84341a6e,0x0051061886717ffa,0x00e9b0a660b28f85,0x0044ea685892de0d,0x000257d2a1fda9d9)},
+ {FIELD_LITERAL(0x007e8b01b24ac8a8,0x006cf3b0b5ca1337,0x00f1607d3e36a570,0x0039b7fab82991a1,0x00231777065840c5,0x00998e5afdd346f9,0x00b7dc3e64acc85f,0x00baacc748013ad6)},
+ {FIELD_LITERAL(0x008ea6a4177580bf,0x005fa1953e3f0378,0x005fe409ac74d614,0x00452327f477e047,0x00a4018507fb6073,0x007b6e71951caac8,0x0012b42ab8a6ce91,0x0080eca677294ab7)},
+ {FIELD_LITERAL(0x00a53edc023ba69b,0x00c6afa83ddde2e8,0x00c3f638b307b14e,0x004a357a64414062,0x00e4d94d8b582dc9,0x001739caf71695b7,0x0012431b2ae28de1,0x003b6bc98682907c)},
+ {FIELD_LITERAL(0x008a9a93be1f99d6,0x0079fa627cc699c8,0x00b0cfb134ba84c8,0x001c4b778249419a,0x00df4ab3d9c44f40,0x009f596e6c1a9e3c,0x001979c0df237316,0x00501e953a919b87)}
+};
--- /dev/null
+/**
+ * @file ed448goldilocks/eddsa.c
+ * @author Mike Hamburg
+ *
+ * @copyright
+ * Copyright (c) 2015-2016 Cryptography Research, Inc. \n
+ * Released under the MIT License. See LICENSE.txt for license information.
+ *
+ * @cond internal
+ * @brief EdDSA routines.
+ *
+ * @warning This file was automatically generated in Python.
+ * Please do not edit it.
+ */
+#include "word.h"
+#include <decaf/ed448.h>
+#include <decaf/shake.h>
+#include <decaf/sha512.h>
+#include <string.h>
+
+#define API_NAME "decaf_448"
+#define API_NS(_id) decaf_448_##_id
+
+#define hash_ctx_t decaf_shake256_ctx_t
+#define hash_init decaf_shake256_init
+#define hash_update decaf_shake256_update
+#define hash_final decaf_shake256_final
+#define hash_destroy decaf_shake256_destroy
+#define hash_hash decaf_shake256_hash
+
+#define NO_CONTEXT DECAF_EDDSA_448_SUPPORTS_CONTEXTLESS_SIGS
+#define EDDSA_USE_SIGMA_ISOGENY 0
+#define COFACTOR 4
+#define EDDSA_PREHASH_BYTES 64
+
+#if NO_CONTEXT
+const uint8_t NO_CONTEXT_POINTS_HERE = 0;
+const uint8_t * const DECAF_ED448_NO_CONTEXT = &NO_CONTEXT_POINTS_HERE;
+#endif
+
+/* EDDSA_BASE_POINT_RATIO = 1 or 2
+ * Because EdDSA25519 is not on E_d but on the isogenous E_sigma_d,
+ * its base point is twice ours.
+ */
+#define EDDSA_BASE_POINT_RATIO (1+EDDSA_USE_SIGMA_ISOGENY) /* TODO: remove */
+
+static void clamp (
+ uint8_t secret_scalar_ser[DECAF_EDDSA_448_PRIVATE_BYTES]
+) {
+ /* Blarg */
+ secret_scalar_ser[0] &= -COFACTOR;
+ uint8_t hibit = (1<<0)>>1;
+ if (hibit == 0) {
+ secret_scalar_ser[DECAF_EDDSA_448_PRIVATE_BYTES - 1] = 0;
+ secret_scalar_ser[DECAF_EDDSA_448_PRIVATE_BYTES - 2] |= 0x80;
+ } else {
+ secret_scalar_ser[DECAF_EDDSA_448_PRIVATE_BYTES - 1] &= hibit-1;
+ secret_scalar_ser[DECAF_EDDSA_448_PRIVATE_BYTES - 1] |= hibit;
+ }
+}
+
+static void hash_init_with_dom(
+ hash_ctx_t hash,
+ uint8_t prehashed,
+ uint8_t for_prehash,
+ const uint8_t *context,
+ uint8_t context_len
+) {
+ hash_init(hash);
+
+#if NO_CONTEXT
+ if (context_len == 0 && context == DECAF_ED448_NO_CONTEXT) {
+ (void)prehashed;
+ (void)for_prehash;
+ (void)context;
+ (void)context_len;
+ return;
+ }
+#endif
+ const char *dom_s = "SigEd448";
+ const uint8_t dom[2] = {2+word_is_zero(prehashed)+word_is_zero(for_prehash), context_len};
+ hash_update(hash,(const unsigned char *)dom_s, strlen(dom_s));
+ hash_update(hash,dom,2);
+ hash_update(hash,context,context_len);
+}
+
+void decaf_ed448_prehash_init (
+ hash_ctx_t hash
+) {
+ hash_init(hash);
+}
+
+/* In this file because it uses the hash */
+void decaf_ed448_convert_private_key_to_x448 (
+ uint8_t x[DECAF_X448_PRIVATE_BYTES],
+ const uint8_t ed[DECAF_EDDSA_448_PRIVATE_BYTES]
+) {
+ /* pass the private key through hash_hash function */
+ /* and keep the first DECAF_X448_PRIVATE_BYTES bytes */
+ hash_hash(
+ x,
+ DECAF_X448_PRIVATE_BYTES,
+ ed,
+ DECAF_EDDSA_448_PRIVATE_BYTES
+ );
+}
+
+void decaf_ed448_derive_public_key (
+ uint8_t pubkey[DECAF_EDDSA_448_PUBLIC_BYTES],
+ const uint8_t privkey[DECAF_EDDSA_448_PRIVATE_BYTES]
+) {
+ /* only this much used for keygen */
+ uint8_t secret_scalar_ser[DECAF_EDDSA_448_PRIVATE_BYTES];
+
+ hash_hash(
+ secret_scalar_ser,
+ sizeof(secret_scalar_ser),
+ privkey,
+ DECAF_EDDSA_448_PRIVATE_BYTES
+ );
+ clamp(secret_scalar_ser);
+
+ API_NS(scalar_t) secret_scalar;
+ API_NS(scalar_decode_long)(secret_scalar, secret_scalar_ser, sizeof(secret_scalar_ser));
+
+ /* Since we are going to mul_by_cofactor during encoding, divide by it here.
+ * However, the EdDSA base point is not the same as the decaf base point if
+ * the sigma isogeny is in use: the EdDSA base point is on Etwist_d/(1-d) and
+ * the decaf base point is on Etwist_d, and when converted it effectively
+ * picks up a factor of 2 from the isogenies. So we might start at 2 instead of 1.
+ */
+ for (unsigned int c=1; c<DECAF_448_EDDSA_ENCODE_RATIO; c <<= 1) {
+ API_NS(scalar_halve)(secret_scalar,secret_scalar);
+ }
+
+ API_NS(point_t) p;
+ API_NS(precomputed_scalarmul)(p,API_NS(precomputed_base),secret_scalar);
+
+ API_NS(point_mul_by_ratio_and_encode_like_eddsa)(pubkey, p);
+
+ /* Cleanup */
+ API_NS(scalar_destroy)(secret_scalar);
+ API_NS(point_destroy)(p);
+ decaf_bzero(secret_scalar_ser, sizeof(secret_scalar_ser));
+}
+
+void decaf_ed448_sign (
+ uint8_t signature[DECAF_EDDSA_448_SIGNATURE_BYTES],
+ const uint8_t privkey[DECAF_EDDSA_448_PRIVATE_BYTES],
+ const uint8_t pubkey[DECAF_EDDSA_448_PUBLIC_BYTES],
+ const uint8_t *message,
+ size_t message_len,
+ uint8_t prehashed,
+ const uint8_t *context,
+ uint8_t context_len
+) {
+ API_NS(scalar_t) secret_scalar;
+ hash_ctx_t hash;
+ {
+ /* Schedule the secret key */
+ struct {
+ uint8_t secret_scalar_ser[DECAF_EDDSA_448_PRIVATE_BYTES];
+ uint8_t seed[DECAF_EDDSA_448_PRIVATE_BYTES];
+ } __attribute__((packed)) expanded;
+ hash_hash(
+ (uint8_t *)&expanded,
+ sizeof(expanded),
+ privkey,
+ DECAF_EDDSA_448_PRIVATE_BYTES
+ );
+ clamp(expanded.secret_scalar_ser);
+ API_NS(scalar_decode_long)(secret_scalar, expanded.secret_scalar_ser, sizeof(expanded.secret_scalar_ser));
+
+ /* Hash to create the nonce */
+ hash_init_with_dom(hash,prehashed,0,context,context_len);
+ hash_update(hash,expanded.seed,sizeof(expanded.seed));
+ hash_update(hash,message,message_len);
+ decaf_bzero(&expanded, sizeof(expanded));
+ }
+
+ /* Decode the nonce */
+ API_NS(scalar_t) nonce_scalar;
+ {
+ uint8_t nonce[2*DECAF_EDDSA_448_PRIVATE_BYTES];
+ hash_final(hash,nonce,sizeof(nonce));
+ API_NS(scalar_decode_long)(nonce_scalar, nonce, sizeof(nonce));
+ decaf_bzero(nonce, sizeof(nonce));
+ }
+
+ uint8_t nonce_point[DECAF_EDDSA_448_PUBLIC_BYTES] = {0};
+ {
+ /* Scalarmul to create the nonce-point */
+ API_NS(scalar_t) nonce_scalar_2;
+ API_NS(scalar_halve)(nonce_scalar_2,nonce_scalar);
+ for (unsigned int c = 2; c < DECAF_448_EDDSA_ENCODE_RATIO; c <<= 1) {
+ API_NS(scalar_halve)(nonce_scalar_2,nonce_scalar_2);
+ }
+
+ API_NS(point_t) p;
+ API_NS(precomputed_scalarmul)(p,API_NS(precomputed_base),nonce_scalar_2);
+ API_NS(point_mul_by_ratio_and_encode_like_eddsa)(nonce_point, p);
+ API_NS(point_destroy)(p);
+ API_NS(scalar_destroy)(nonce_scalar_2);
+ }
+
+ API_NS(scalar_t) challenge_scalar;
+ {
+ /* Compute the challenge */
+ hash_init_with_dom(hash,prehashed,0,context,context_len);
+ hash_update(hash,nonce_point,sizeof(nonce_point));
+ hash_update(hash,pubkey,DECAF_EDDSA_448_PUBLIC_BYTES);
+ hash_update(hash,message,message_len);
+ uint8_t challenge[2*DECAF_EDDSA_448_PRIVATE_BYTES];
+ hash_final(hash,challenge,sizeof(challenge));
+ hash_destroy(hash);
+ API_NS(scalar_decode_long)(challenge_scalar,challenge,sizeof(challenge));
+ decaf_bzero(challenge,sizeof(challenge));
+ }
+
+ API_NS(scalar_mul)(challenge_scalar,challenge_scalar,secret_scalar);
+ API_NS(scalar_add)(challenge_scalar,challenge_scalar,nonce_scalar);
+
+ decaf_bzero(signature,DECAF_EDDSA_448_SIGNATURE_BYTES);
+ memcpy(signature,nonce_point,sizeof(nonce_point));
+ API_NS(scalar_encode)(&signature[DECAF_EDDSA_448_PUBLIC_BYTES],challenge_scalar);
+
+ API_NS(scalar_destroy)(secret_scalar);
+ API_NS(scalar_destroy)(nonce_scalar);
+ API_NS(scalar_destroy)(challenge_scalar);
+}
+
+
+void decaf_ed448_sign_prehash (
+ uint8_t signature[DECAF_EDDSA_448_SIGNATURE_BYTES],
+ const uint8_t privkey[DECAF_EDDSA_448_PRIVATE_BYTES],
+ const uint8_t pubkey[DECAF_EDDSA_448_PUBLIC_BYTES],
+ const decaf_ed448_prehash_ctx_t hash,
+ const uint8_t *context,
+ uint8_t context_len
+) {
+ uint8_t hash_output[EDDSA_PREHASH_BYTES];
+ {
+ decaf_ed448_prehash_ctx_t hash_too;
+ memcpy(hash_too,hash,sizeof(hash_too));
+ hash_final(hash_too,hash_output,sizeof(hash_output));
+ hash_destroy(hash_too);
+ }
+
+ decaf_ed448_sign(signature,privkey,pubkey,hash_output,sizeof(hash_output),1,context,context_len);
+ decaf_bzero(hash_output,sizeof(hash_output));
+}
+
+decaf_error_t decaf_ed448_verify (
+ const uint8_t signature[DECAF_EDDSA_448_SIGNATURE_BYTES],
+ const uint8_t pubkey[DECAF_EDDSA_448_PUBLIC_BYTES],
+ const uint8_t *message,
+ size_t message_len,
+ uint8_t prehashed,
+ const uint8_t *context,
+ uint8_t context_len
+) {
+ API_NS(point_t) pk_point, r_point;
+ decaf_error_t error = API_NS(point_decode_like_eddsa_and_mul_by_ratio)(pk_point,pubkey);
+ if (DECAF_SUCCESS != error) { return error; }
+
+ error = API_NS(point_decode_like_eddsa_and_mul_by_ratio)(r_point,signature);
+ if (DECAF_SUCCESS != error) { return error; }
+
+ API_NS(scalar_t) challenge_scalar;
+ {
+ /* Compute the challenge */
+ hash_ctx_t hash;
+ hash_init_with_dom(hash,prehashed,0,context,context_len);
+ hash_update(hash,signature,DECAF_EDDSA_448_PUBLIC_BYTES);
+ hash_update(hash,pubkey,DECAF_EDDSA_448_PUBLIC_BYTES);
+ hash_update(hash,message,message_len);
+ uint8_t challenge[2*DECAF_EDDSA_448_PRIVATE_BYTES];
+ hash_final(hash,challenge,sizeof(challenge));
+ hash_destroy(hash);
+ API_NS(scalar_decode_long)(challenge_scalar,challenge,sizeof(challenge));
+ decaf_bzero(challenge,sizeof(challenge));
+ }
+ API_NS(scalar_sub)(challenge_scalar, API_NS(scalar_zero), challenge_scalar);
+
+ API_NS(scalar_t) response_scalar;
+ API_NS(scalar_decode_long)(
+ response_scalar,
+ &signature[DECAF_EDDSA_448_PUBLIC_BYTES],
+ DECAF_EDDSA_448_PRIVATE_BYTES
+ );
+
+ for (unsigned c=1; c<DECAF_448_EDDSA_DECODE_RATIO; c<<=1) {
+ API_NS(scalar_add)(response_scalar,response_scalar,response_scalar);
+ }
+
+
+ /* pk_point = -c(x(P)) + (cx + k)G = kG */
+ API_NS(base_double_scalarmul_non_secret)(
+ pk_point,
+ response_scalar,
+ pk_point,
+ challenge_scalar
+ );
+ return decaf_succeed_if(API_NS(point_eq(pk_point,r_point)));
+}
+
+
+decaf_error_t decaf_ed448_verify_prehash (
+ const uint8_t signature[DECAF_EDDSA_448_SIGNATURE_BYTES],
+ const uint8_t pubkey[DECAF_EDDSA_448_PUBLIC_BYTES],
+ const decaf_ed448_prehash_ctx_t hash,
+ const uint8_t *context,
+ uint8_t context_len
+) {
+ decaf_error_t ret;
+
+ uint8_t hash_output[EDDSA_PREHASH_BYTES];
+ {
+ decaf_ed448_prehash_ctx_t hash_too;
+ memcpy(hash_too,hash,sizeof(hash_too));
+ hash_final(hash_too,hash_output,sizeof(hash_output));
+ hash_destroy(hash_too);
+ }
+
+ ret = decaf_ed448_verify(signature,pubkey,hash_output,sizeof(hash_output),1,context,context_len);
+
+ return ret;
+}
--- /dev/null
+/**
+ * @file ed448goldilocks/scalar.c
+ * @author Mike Hamburg
+ *
+ * @copyright
+ * Copyright (c) 2015-2016 Cryptography Research, Inc. \n
+ * Released under the MIT License. See LICENSE.txt for license information.
+ *
+ * @brief Decaf high-level functions.
+ *
+ * @warning This file was automatically generated in Python.
+ * Please do not edit it.
+ */
+#include "word.h"
+#include "constant_time.h"
+#include <decaf.h>
+
+/* Template stuff */
+#define API_NS(_id) decaf_448_##_id
+#define SCALAR_BITS DECAF_448_SCALAR_BITS
+#define SCALAR_SER_BYTES DECAF_448_SCALAR_BYTES
+#define SCALAR_LIMBS DECAF_448_SCALAR_LIMBS
+#define scalar_t API_NS(scalar_t)
+
+static const decaf_word_t MONTGOMERY_FACTOR = (decaf_word_t)0x3bd440fae918bc5ull;
+static const scalar_t sc_p = {{{
+ SC_LIMB(0x2378c292ab5844f3), SC_LIMB(0x216cc2728dc58f55), SC_LIMB(0xc44edb49aed63690), SC_LIMB(0xffffffff7cca23e9), SC_LIMB(0xffffffffffffffff), SC_LIMB(0xffffffffffffffff), SC_LIMB(0x3fffffffffffffff)
+}}}, sc_r2 = {{{
+ SC_LIMB(0xe3539257049b9b60), SC_LIMB(0x7af32c4bc1b195d9), SC_LIMB(0x0d66de2388ea1859), SC_LIMB(0xae17cf725ee4d838), SC_LIMB(0x1a9cc14ba3c47c44), SC_LIMB(0x2052bcb7e4d070af), SC_LIMB(0x3402a939f823b729)
+}}};
+/* End of template stuff */
+
+#define WBITS DECAF_WORD_BITS /* NB this may be different from ARCH_WORD_BITS */
+
+const scalar_t API_NS(scalar_one) = {{{1}}}, API_NS(scalar_zero) = {{{0}}};
+
+/** {extra,accum} - sub +? p
+ * Must have extra <= 1
+ */
+static DECAF_NOINLINE void sc_subx(
+ scalar_t out,
+ const decaf_word_t accum[SCALAR_LIMBS],
+ const scalar_t sub,
+ const scalar_t p,
+ decaf_word_t extra
+) {
+ decaf_dsword_t chain = 0;
+ unsigned int i;
+ for (i=0; i<SCALAR_LIMBS; i++) {
+ chain = (chain + accum[i]) - sub->limb[i];
+ out->limb[i] = chain;
+ chain >>= WBITS;
+ }
+ decaf_word_t borrow = chain+extra; /* = 0 or -1 */
+
+ chain = 0;
+ for (i=0; i<SCALAR_LIMBS; i++) {
+ chain = (chain + out->limb[i]) + (p->limb[i] & borrow);
+ out->limb[i] = chain;
+ chain >>= WBITS;
+ }
+}
+
+static DECAF_NOINLINE void sc_montmul (
+ scalar_t out,
+ const scalar_t a,
+ const scalar_t b
+) {
+ unsigned int i,j;
+ decaf_word_t accum[SCALAR_LIMBS+1] = {0};
+ decaf_word_t hi_carry = 0;
+
+ for (i=0; i<SCALAR_LIMBS; i++) {
+ decaf_word_t mand = a->limb[i];
+ const decaf_word_t *mier = b->limb;
+
+ decaf_dword_t chain = 0;
+ for (j=0; j<SCALAR_LIMBS; j++) {
+ chain += ((decaf_dword_t)mand)*mier[j] + accum[j];
+ accum[j] = chain;
+ chain >>= WBITS;
+ }
+ accum[j] = chain;
+
+ mand = accum[0] * MONTGOMERY_FACTOR;
+ chain = 0;
+ mier = sc_p->limb;
+ for (j=0; j<SCALAR_LIMBS; j++) {
+ chain += (decaf_dword_t)mand*mier[j] + accum[j];
+ if (j) accum[j-1] = chain;
+ chain >>= WBITS;
+ }
+ chain += accum[j];
+ chain += hi_carry;
+ accum[j-1] = chain;
+ hi_carry = chain >> WBITS;
+ }
+
+ sc_subx(out, accum, sc_p, sc_p, hi_carry);
+}
+
+void API_NS(scalar_mul) (
+ scalar_t out,
+ const scalar_t a,
+ const scalar_t b
+) {
+ sc_montmul(out,a,b);
+ sc_montmul(out,out,sc_r2);
+}
+
+/* PERF: could implement this */
+static DECAF_INLINE void sc_montsqr (scalar_t out, const scalar_t a) {
+ sc_montmul(out,a,a);
+}
+
+decaf_error_t API_NS(scalar_invert) (
+ scalar_t out,
+ const scalar_t a
+) {
+ /* Fermat's little theorem, sliding window.
+ * Sliding window is fine here because the modulus isn't secret.
+ */
+ const int SCALAR_WINDOW_BITS = 3;
+ scalar_t precmp[1<<SCALAR_WINDOW_BITS];
+ const int LAST = (1<<SCALAR_WINDOW_BITS)-1;
+
+ /* Precompute precmp = [a^1,a^3,...] */
+ sc_montmul(precmp[0],a,sc_r2);
+ if (LAST > 0) sc_montmul(precmp[LAST],precmp[0],precmp[0]);
+
+ int i;
+ for (i=1; i<=LAST; i++) {
+ sc_montmul(precmp[i],precmp[i-1],precmp[LAST]);
+ }
+
+ /* Sliding window */
+ unsigned residue = 0, trailing = 0, started = 0;
+ for (i=SCALAR_BITS-1; i>=-SCALAR_WINDOW_BITS; i--) {
+
+ if (started) sc_montsqr(out,out);
+
+ decaf_word_t w = (i>=0) ? sc_p->limb[i/WBITS] : 0;
+ if (i >= 0 && i<WBITS) {
+ assert(w >= 2);
+ w-=2;
+ }
+
+ residue = (residue<<1) | ((w>>(i%WBITS))&1);
+ if (residue>>SCALAR_WINDOW_BITS != 0) {
+ assert(trailing == 0);
+ trailing = residue;
+ residue = 0;
+ }
+
+ if (trailing > 0 && (trailing & ((1<<SCALAR_WINDOW_BITS)-1)) == 0) {
+ if (started) {
+ sc_montmul(out,out,precmp[trailing>>(SCALAR_WINDOW_BITS+1)]);
+ } else {
+ API_NS(scalar_copy)(out,precmp[trailing>>(SCALAR_WINDOW_BITS+1)]);
+ started = 1;
+ }
+ trailing = 0;
+ }
+ trailing <<= 1;
+
+ }
+ assert(residue==0);
+ assert(trailing==0);
+
+ /* Demontgomerize */
+ sc_montmul(out,out,API_NS(scalar_one));
+ decaf_bzero(precmp, sizeof(precmp));
+ return decaf_succeed_if(~API_NS(scalar_eq)(out,API_NS(scalar_zero)));
+}
+
+void API_NS(scalar_sub) (
+ scalar_t out,
+ const scalar_t a,
+ const scalar_t b
+) {
+ sc_subx(out, a->limb, b, sc_p, 0);
+}
+
+void API_NS(scalar_add) (
+ scalar_t out,
+ const scalar_t a,
+ const scalar_t b
+) {
+ decaf_dword_t chain = 0;
+ unsigned int i;
+ for (i=0; i<SCALAR_LIMBS; i++) {
+ chain = (chain + a->limb[i]) + b->limb[i];
+ out->limb[i] = chain;
+ chain >>= WBITS;
+ }
+ sc_subx(out, out->limb, sc_p, sc_p, chain);
+}
+
+void
+API_NS(scalar_set_unsigned) (
+ scalar_t out,
+ uint64_t w
+) {
+ memset(out,0,sizeof(scalar_t));
+ unsigned int i = 0;
+ for (; i<sizeof(uint64_t)/sizeof(decaf_word_t); i++) {
+ out->limb[i] = w;
+#if DECAF_WORD_BITS < 64
+ w >>= 8*sizeof(decaf_word_t);
+#endif
+ }
+}
+
+decaf_bool_t
+API_NS(scalar_eq) (
+ const scalar_t a,
+ const scalar_t b
+) {
+ decaf_word_t diff = 0;
+ unsigned int i;
+ for (i=0; i<SCALAR_LIMBS; i++) {
+ diff |= a->limb[i] ^ b->limb[i];
+ }
+ return mask_to_bool(word_is_zero(diff));
+}
+
+static DECAF_INLINE void scalar_decode_short (
+ scalar_t s,
+ const unsigned char *ser,
+ unsigned int nbytes
+) {
+ unsigned int i,j,k=0;
+ for (i=0; i<SCALAR_LIMBS; i++) {
+ decaf_word_t out = 0;
+ for (j=0; j<sizeof(decaf_word_t) && k<nbytes; j++,k++) {
+ out |= ((decaf_word_t)ser[k])<<(8*j);
+ }
+ s->limb[i] = out;
+ }
+}
+
+decaf_error_t API_NS(scalar_decode)(
+ scalar_t s,
+ const unsigned char ser[SCALAR_SER_BYTES]
+) {
+ unsigned int i;
+ scalar_decode_short(s, ser, SCALAR_SER_BYTES);
+ decaf_dsword_t accum = 0;
+ for (i=0; i<SCALAR_LIMBS; i++) {
+ accum = (accum + s->limb[i] - sc_p->limb[i]) >> WBITS;
+ }
+ /* Here accum == 0 or -1 */
+
+ API_NS(scalar_mul)(s,s,API_NS(scalar_one)); /* ham-handed reduce */
+
+ return decaf_succeed_if(~word_is_zero(accum));
+}
+
+void API_NS(scalar_destroy) (
+ scalar_t scalar
+) {
+ decaf_bzero(scalar, sizeof(scalar_t));
+}
+
+void API_NS(scalar_decode_long)(
+ scalar_t s,
+ const unsigned char *ser,
+ size_t ser_len
+) {
+ if (ser_len == 0) {
+ API_NS(scalar_copy)(s, API_NS(scalar_zero));
+ return;
+ }
+
+ size_t i;
+ scalar_t t1, t2;
+
+ i = ser_len - (ser_len%SCALAR_SER_BYTES);
+ if (i==ser_len) i -= SCALAR_SER_BYTES;
+
+ scalar_decode_short(t1, &ser[i], ser_len-i);
+
+ if (ser_len == sizeof(scalar_t)) {
+ assert(i==0);
+ /* ham-handed reduce */
+ API_NS(scalar_mul)(s,t1,API_NS(scalar_one));
+ API_NS(scalar_destroy)(t1);
+ return;
+ }
+
+ while (i) {
+ i -= SCALAR_SER_BYTES;
+ sc_montmul(t1,t1,sc_r2);
+ ignore_result( API_NS(scalar_decode)(t2, ser+i) );
+ API_NS(scalar_add)(t1, t1, t2);
+ }
+
+ API_NS(scalar_copy)(s, t1);
+ API_NS(scalar_destroy)(t1);
+ API_NS(scalar_destroy)(t2);
+}
+
+void API_NS(scalar_encode)(
+ unsigned char ser[SCALAR_SER_BYTES],
+ const scalar_t s
+) {
+ unsigned int i,j,k=0;
+ for (i=0; i<SCALAR_LIMBS; i++) {
+ for (j=0; j<sizeof(decaf_word_t); j++,k++) {
+ ser[k] = s->limb[i] >> (8*j);
+ }
+ }
+}
+
+void API_NS(scalar_cond_sel) (
+ scalar_t out,
+ const scalar_t a,
+ const scalar_t b,
+ decaf_bool_t pick_b
+) {
+ constant_time_select(out,a,b,sizeof(scalar_t),bool_to_mask(pick_b),sizeof(out->limb[0]));
+}
+
+void API_NS(scalar_halve) (
+ scalar_t out,
+ const scalar_t a
+) {
+ decaf_word_t mask = -(a->limb[0] & 1);
+ decaf_dword_t chain = 0;
+ unsigned int i;
+ for (i=0; i<SCALAR_LIMBS; i++) {
+ chain = (chain + a->limb[i]) + (sc_p->limb[i] & mask);
+ out->limb[i] = chain;
+ chain >>= DECAF_WORD_BITS;
+ }
+ for (i=0; i<SCALAR_LIMBS-1; i++) {
+ out->limb[i] = out->limb[i]>>1 | out->limb[i+1]<<(WBITS-1);
+ }
+ out->limb[i] = out->limb[i]>>1 | chain<<(WBITS-1);
+}
+
--- /dev/null
+/**
+ * @file p448/f_field.h
+ * @author Mike Hamburg
+ *
+ * @copyright
+ * Copyright (c) 2015-2016 Cryptography Research, Inc. \n
+ * Released under the MIT License. See LICENSE.txt for license information.
+ *
+ * @brief Field-specific code for 2^448 - 2^224 - 1.
+ *
+ * @warning This file was automatically generated in Python.
+ * Please do not edit it.
+ */
+
+#ifndef __P448_F_FIELD_H__
+#define __P448_F_FIELD_H__ 1
+
+#include "constant_time.h"
+#include <string.h>
+#include <assert.h>
+
+#include "word.h"
+
+#define __DECAF_448_GF_DEFINED__ 1
+#define NLIMBS (64/sizeof(word_t))
+#define X_SER_BYTES 56
+#define SER_BYTES 56
+typedef struct gf_448_s {
+ word_t limb[NLIMBS];
+} __attribute__((aligned(32))) gf_448_s, gf_448_t[1];
+
+#define GF_LIT_LIMB_BITS 56
+#define GF_BITS 448
+#define ZERO gf_448_ZERO
+#define ONE gf_448_ONE
+#define MODULUS gf_448_MODULUS
+#define gf gf_448_t
+#define gf_s gf_448_s
+#define gf_eq gf_448_eq
+#define gf_hibit gf_448_hibit
+#define gf_lobit gf_448_lobit
+#define gf_copy gf_448_copy
+#define gf_add gf_448_add
+#define gf_sub gf_448_sub
+#define gf_add_RAW gf_448_add_RAW
+#define gf_sub_RAW gf_448_sub_RAW
+#define gf_bias gf_448_bias
+#define gf_weak_reduce gf_448_weak_reduce
+#define gf_strong_reduce gf_448_strong_reduce
+#define gf_mul gf_448_mul
+#define gf_sqr gf_448_sqr
+#define gf_mulw_unsigned gf_448_mulw_unsigned
+#define gf_isr gf_448_isr
+#define gf_serialize gf_448_serialize
+#define gf_deserialize gf_448_deserialize
+
+/* RFC 7748 support */
+#define X_PUBLIC_BYTES X_SER_BYTES
+#define X_PRIVATE_BYTES X_PUBLIC_BYTES
+#define X_PRIVATE_BITS 448
+
+#define SQRT_MINUS_ONE P448_SQRT_MINUS_ONE /* might not be defined */
+
+#define INLINE_UNUSED __inline__ __attribute__((unused,always_inline))
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+/* Defined below in f_impl.h */
+static INLINE_UNUSED void gf_copy (gf out, const gf a) { *out = *a; }
+static INLINE_UNUSED void gf_add_RAW (gf out, const gf a, const gf b);
+static INLINE_UNUSED void gf_sub_RAW (gf out, const gf a, const gf b);
+static INLINE_UNUSED void gf_bias (gf inout, int amount);
+static INLINE_UNUSED void gf_weak_reduce (gf inout);
+
+void gf_strong_reduce (gf inout);
+void gf_add (gf out, const gf a, const gf b);
+void gf_sub (gf out, const gf a, const gf b);
+void gf_mul (gf_s *__restrict__ out, const gf a, const gf b);
+void gf_mulw_unsigned (gf_s *__restrict__ out, const gf a, uint32_t b);
+void gf_sqr (gf_s *__restrict__ out, const gf a);
+mask_t gf_isr(gf a, const gf x); /** a^2 x = 1, QNR, or 0 if x=0. Return true if successful */
+mask_t gf_eq (const gf x, const gf y);
+mask_t gf_lobit (const gf x);
+mask_t gf_hibit (const gf x);
+
+void gf_serialize (uint8_t *serial, const gf x,int with_highbit);
+mask_t gf_deserialize (gf x, const uint8_t serial[SER_BYTES],int with_hibit,uint8_t hi_nmask);
+
+
+#ifdef __cplusplus
+} /* extern "C" */
+#endif
+
+#include "f_impl.h" /* Bring in the inline implementations */
+
+#define P_MOD_8 7
+#if P_MOD_8 == 5
+ extern const gf SQRT_MINUS_ONE;
+#endif
+
+#ifndef LIMBPERM
+ #define LIMBPERM(i) (i)
+#endif
+#define LIMB_MASK(i) (((1ull)<<LIMB_PLACE_VALUE(i))-1)
+
+static const gf ZERO = {{{0}}}, ONE = {{{ [LIMBPERM(0)] = 1 }}};
+
+#endif /* __P448_F_FIELD_H__ */
--- /dev/null
+/**
+ * @file p448/f_generic.c
+ * @author Mike Hamburg
+ *
+ * @copyright
+ * Copyright (c) 2015-2016 Cryptography Research, Inc. \n
+ * Released under the MIT License. See LICENSE.txt for license information.
+ *
+ * @brief Generic arithmetic which has to be compiled per field.
+ *
+ * @warning This file was automatically generated in Python.
+ * Please do not edit it.
+ */
+#include "field.h"
+
+static const gf MODULUS = {FIELD_LITERAL(
+ 0xffffffffffffff, 0xffffffffffffff, 0xffffffffffffff, 0xffffffffffffff, 0xfffffffffffffe, 0xffffffffffffff, 0xffffffffffffff, 0xffffffffffffff
+)};
+
+#if P_MOD_8 == 5
+ const gf SQRT_MINUS_ONE = {FIELD_LITERAL(
+ /* NOPE */
+ )};
+#endif
+
+/** Serialize to wire format. */
+void gf_serialize (uint8_t serial[SER_BYTES], const gf x, int with_hibit) {
+ gf red;
+ gf_copy(red, x);
+ gf_strong_reduce(red);
+ if (!with_hibit) { assert(gf_hibit(red) == 0); }
+
+ unsigned int j=0, fill=0;
+ dword_t buffer = 0;
+ UNROLL for (unsigned int i=0; i<(with_hibit ? X_SER_BYTES : SER_BYTES); i++) {
+ if (fill < 8 && j < NLIMBS) {
+ buffer |= ((dword_t)red->limb[LIMBPERM(j)]) << fill;
+ fill += LIMB_PLACE_VALUE(LIMBPERM(j));
+ j++;
+ }
+ serial[i] = buffer;
+ fill -= 8;
+ buffer >>= 8;
+ }
+}
+
+/** Return high bit of x = low bit of 2x mod p */
+mask_t gf_hibit(const gf x) {
+ gf y;
+ gf_add(y,x,x);
+ gf_strong_reduce(y);
+ return -(y->limb[0]&1);
+}
+
+/** Return high bit of x = low bit of 2x mod p */
+mask_t gf_lobit(const gf x) {
+ gf y;
+ gf_copy(y,x);
+ gf_strong_reduce(y);
+ return -(y->limb[0]&1);
+}
+
+/** Deserialize from wire format; return -1 on success and 0 on failure. */
+mask_t gf_deserialize (gf x, const uint8_t serial[SER_BYTES], int with_hibit, uint8_t hi_nmask) {
+ unsigned int j=0, fill=0;
+ dword_t buffer = 0;
+ dsword_t scarry = 0;
+ const unsigned nbytes = with_hibit ? X_SER_BYTES : SER_BYTES;
+ UNROLL for (unsigned int i=0; i<NLIMBS; i++) {
+ UNROLL while (fill < LIMB_PLACE_VALUE(LIMBPERM(i)) && j < nbytes) {
+ uint8_t sj = serial[j];
+ if (j==nbytes-1) sj &= ~hi_nmask;
+ buffer |= ((dword_t)sj) << fill;
+ fill += 8;
+ j++;
+ }
+ x->limb[LIMBPERM(i)] = (i<NLIMBS-1) ? buffer & LIMB_MASK(LIMBPERM(i)) : buffer;
+ fill -= LIMB_PLACE_VALUE(LIMBPERM(i));
+ buffer >>= LIMB_PLACE_VALUE(LIMBPERM(i));
+ scarry = (scarry + x->limb[LIMBPERM(i)] - MODULUS->limb[LIMBPERM(i)]) >> (8*sizeof(word_t));
+ }
+ mask_t succ = with_hibit ? -(mask_t)1 : ~gf_hibit(x);
+ return succ & word_is_zero(buffer) & ~word_is_zero(scarry);
+}
+
+/** Reduce to canonical form. */
+void gf_strong_reduce (gf a) {
+ /* first, clear high */
+ gf_weak_reduce(a); /* Determined to have negligible perf impact. */
+
+ /* now the total is less than 2p */
+
+ /* compute total_value - p. No need to reduce mod p. */
+ dsword_t scarry = 0;
+ for (unsigned int i=0; i<NLIMBS; i++) {
+ scarry = scarry + a->limb[LIMBPERM(i)] - MODULUS->limb[LIMBPERM(i)];
+ a->limb[LIMBPERM(i)] = scarry & LIMB_MASK(LIMBPERM(i));
+ scarry >>= LIMB_PLACE_VALUE(LIMBPERM(i));
+ }
+
+ /* uncommon case: it was >= p, so now scarry = 0 and this = x
+ * common case: it was < p, so now scarry = -1 and this = x - p + 2^255
+ * so let's add back in p. will carry back off the top for 2^255.
+ */
+ assert(word_is_zero(scarry) | word_is_zero(scarry+1));
+
+ word_t scarry_0 = scarry;
+ dword_t carry = 0;
+
+ /* add it back */
+ for (unsigned int i=0; i<NLIMBS; i++) {
+ carry = carry + a->limb[LIMBPERM(i)] + (scarry_0 & MODULUS->limb[LIMBPERM(i)]);
+ a->limb[LIMBPERM(i)] = carry & LIMB_MASK(LIMBPERM(i));
+ carry >>= LIMB_PLACE_VALUE(LIMBPERM(i));
+ }
+
+ assert(word_is_zero(carry + scarry_0));
+}
+
+/** Subtract two gf elements d=a-b */
+void gf_sub (gf d, const gf a, const gf b) {
+ gf_sub_RAW ( d, a, b );
+ gf_bias( d, 2 );
+ gf_weak_reduce ( d );
+}
+
+/** Add two field elements d = a+b */
+void gf_add (gf d, const gf a, const gf b) {
+ gf_add_RAW ( d, a, b );
+ gf_weak_reduce ( d );
+}
+
+/** Compare a==b */
+mask_t gf_eq(const gf a, const gf b) {
+ gf c;
+ gf_sub(c,a,b);
+ gf_strong_reduce(c);
+ mask_t ret=0;
+ for (unsigned int i=0; i<NLIMBS; i++) {
+ ret |= c->limb[LIMBPERM(i)];
+ }
+
+ return word_is_zero(ret);
+}
--- /dev/null
+/**
+ * @file decaf.h
+ * @author Mike Hamburg
+ *
+ * @copyright
+ * Copyright (c) 2015-2016 Cryptography Research, Inc. \n
+ * Released under the MIT License. See LICENSE.txt for license information.
+ *
+ * Master header for Decaf library.
+ *
+ * The Decaf library implements cryptographic operations on a elliptic curve
+ * groups of prime order p. It accomplishes this by using a twisted Edwards
+ * curve (isogenous to Ed448-Goldilocks or Ed25519) and wiping out the cofactor.
+ *
+ * The formulas are all complete and have no special cases. However, some
+ * functions can fail. For example, decoding functions can fail because not
+ * every string is the encoding of a valid group element.
+ *
+ * The formulas contain no data-dependent branches, timing or memory accesses,
+ * except for decaf_XXX_base_double_scalarmul_non_secret.
+ *
+ * @warning This file was automatically generated in Python.
+ * Please do not edit it.
+ */
+
+#ifndef __DECAF_H__
+#define __DECAF_H__ 1
+
+#include <decaf/point_255.h>
+#include <decaf/point_448.h>
+
+#endif /* __DECAF_H__ */
--- /dev/null
+/**
+ * @file decaf/common.h
+ * @author Mike Hamburg
+ *
+ * @copyright
+ * Copyright (c) 2015 Cryptography Research, Inc. \n
+ * Released under the MIT License. See LICENSE.txt for license information.
+ *
+ * @brief Common utility headers for Decaf library.
+ */
+
+#ifndef __DECAF_COMMON_H__
+#define __DECAF_COMMON_H__ 1
+
+#include <stdint.h>
+#include <sys/types.h>
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+/* Goldilocks' build flags default to hidden and stripping executables. */
+/** @cond internal */
+#if defined(DOXYGEN) && !defined(__attribute__)
+#define __attribute__((x))
+#endif
+#define DECAF_API_VIS __attribute__((visibility("default")))
+#define DECAF_NOINLINE __attribute__((noinline))
+#define DECAF_WARN_UNUSED __attribute__((warn_unused_result))
+#define DECAF_NONNULL __attribute__((nonnull))
+#define DECAF_INLINE inline __attribute__((always_inline,unused))
+// Cribbed from libnotmuch
+#if defined (__clang_major__) && __clang_major__ >= 3 \
+ || defined (__GNUC__) && __GNUC__ >= 5 \
+ || defined (__GNUC__) && __GNUC__ == 4 && __GNUC_MINOR__ >= 5
+#define DECAF_DEPRECATED(msg) __attribute__ ((deprecated(msg)))
+#else
+#define DECAF_DEPRECATED(msg) __attribute__ ((deprecated))
+#endif
+/** @endcond */
+
+/* Internal word types.
+ *
+ * Somewhat tricky. This could be decided separately per platform. However,
+ * the structs do need to be all the same size and alignment on a given
+ * platform to support dynamic linking, since even if you header was built
+ * with eg arch_neon, you might end up linking a library built with arch_arm32.
+ */
+#ifndef DECAF_WORD_BITS
+ #if (defined(__ILP64__) || defined(__amd64__) || defined(__x86_64__) || (((__UINT_FAST32_MAX__)>>30)>>30))
+ #define DECAF_WORD_BITS 64 /**< The number of bits in a word */
+ #else
+ #define DECAF_WORD_BITS 32 /**< The number of bits in a word */
+ #endif
+#endif
+
+#if DECAF_WORD_BITS == 64
+typedef uint64_t decaf_word_t; /**< Word size for internal computations */
+typedef int64_t decaf_sword_t; /**< Signed word size for internal computations */
+typedef uint64_t decaf_bool_t; /**< "Boolean" type, will be set to all-zero or all-one (i.e. -1u) */
+typedef __uint128_t decaf_dword_t; /**< Double-word size for internal computations */
+typedef __int128_t decaf_dsword_t; /**< Signed double-word size for internal computations */
+#elif DECAF_WORD_BITS == 32 /**< The number of bits in a word */
+typedef uint32_t decaf_word_t; /**< Word size for internal computations */
+typedef int32_t decaf_sword_t; /**< Signed word size for internal computations */
+typedef uint32_t decaf_bool_t; /**< "Boolean" type, will be set to all-zero or all-one (i.e. -1u) */
+typedef uint64_t decaf_dword_t; /**< Double-word size for internal computations */
+typedef int64_t decaf_dsword_t; /**< Signed double-word size for internal computations */
+#else
+#error "Only supporting DECAF_WORD_BITS = 32 or 64 for now"
+#endif
+
+/** DECAF_TRUE = -1 so that DECAF_TRUE & x = x */
+static const decaf_bool_t DECAF_TRUE = -(decaf_bool_t)1;
+
+/** DECAF_FALSE = 0 so that DECAF_FALSE & x = 0 */
+static const decaf_bool_t DECAF_FALSE = 0;
+
+/** Another boolean type used to indicate success or failure. */
+typedef enum {
+ DECAF_SUCCESS = -1, /**< The operation succeeded. */
+ DECAF_FAILURE = 0 /**< The operation failed. */
+} decaf_error_t;
+
+
+/** Return success if x is true */
+static DECAF_INLINE decaf_error_t
+decaf_succeed_if(decaf_bool_t x) {
+ return (decaf_error_t)x;
+}
+
+/** Return DECAF_TRUE iff x == DECAF_SUCCESS */
+static DECAF_INLINE decaf_bool_t
+decaf_successful(decaf_error_t e) {
+ decaf_dword_t w = ((decaf_word_t)e) ^ ((decaf_word_t)DECAF_SUCCESS);
+ return (w-1)>>DECAF_WORD_BITS;
+}
+
+/** Overwrite data with zeros. Uses memset_s if available. */
+void decaf_bzero (
+ void *data,
+ size_t size
+) DECAF_NONNULL DECAF_API_VIS;
+
+/** Compare two buffers, returning DECAF_TRUE if they are equal. */
+decaf_bool_t decaf_memeq (
+ const void *data1,
+ const void *data2,
+ size_t size
+) DECAF_NONNULL DECAF_WARN_UNUSED DECAF_API_VIS;
+
+#ifdef __cplusplus
+} /* extern "C" */
+#endif
+
+#endif /* __DECAF_COMMON_H__ */
--- /dev/null
+/**
+ * @file decaf/ed448.h
+ * @author Mike Hamburg
+ *
+ * @copyright
+ * Copyright (c) 2015-2016 Cryptography Research, Inc. \n
+ * Released under the MIT License. See LICENSE.txt for license information.
+ *
+ * @brief A group of prime order p, based on Ed448-Goldilocks.
+ *
+ * @warning This file was automatically generated in Python.
+ * Please do not edit it.
+ */
+
+#ifndef __DECAF_ED448_H__
+#define __DECAF_ED448_H__ 1
+
+#include <decaf/point_448.h>
+#include <decaf/shake.h>
+#include <decaf/sha512.h>
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+/** Number of bytes in an EdDSA public key. */
+#define DECAF_EDDSA_448_PUBLIC_BYTES 57
+
+/** Number of bytes in an EdDSA private key. */
+#define DECAF_EDDSA_448_PRIVATE_BYTES DECAF_EDDSA_448_PUBLIC_BYTES
+
+/** Number of bytes in an EdDSA private key. */
+#define DECAF_EDDSA_448_SIGNATURE_BYTES (DECAF_EDDSA_448_PUBLIC_BYTES + DECAF_EDDSA_448_PRIVATE_BYTES)
+
+/** Does EdDSA support non-contextual signatures? */
+#define DECAF_EDDSA_448_SUPPORTS_CONTEXTLESS_SIGS 0
+
+/** Prehash context renaming macros. */
+#define decaf_ed448_prehash_ctx_s decaf_shake256_ctx_s
+#define decaf_ed448_prehash_ctx_t decaf_shake256_ctx_t
+#define decaf_ed448_prehash_update decaf_shake256_update
+#define decaf_ed448_prehash_destroy decaf_shake256_destroy
+
+/** EdDSA encoding ratio. */
+#define DECAF_448_EDDSA_ENCODE_RATIO 4
+
+/** EdDSA decoding ratio. */
+#define DECAF_448_EDDSA_DECODE_RATIO (4 / 4)
+
+/**
+ * @brief EdDSA key generation. This function uses a different (non-Decaf)
+ * encoding.
+ *
+ * @param [out] pubkey The public key.
+ * @param [in] privkey The private key.
+ */
+void decaf_ed448_derive_public_key (
+ uint8_t pubkey[DECAF_EDDSA_448_PUBLIC_BYTES],
+ const uint8_t privkey[DECAF_EDDSA_448_PRIVATE_BYTES]
+) DECAF_API_VIS DECAF_NONNULL DECAF_NOINLINE;
+
+/**
+ * @brief EdDSA signing.
+ *
+ * @param [out] signature The signature.
+ * @param [in] privkey The private key.
+ * @param [in] pubkey The public key.
+ * @param [in] message The message to sign.
+ * @param [in] message_len The length of the message.
+ * @param [in] prehashed Nonzero if the message is actually the hash of something you want to sign.
+ * @param [in] context A "context" for this signature of up to 255 bytes.
+ * @param [in] context_len Length of the context.
+ *
+ * @warning For Ed25519, it is unsafe to use the same key for both prehashed and non-prehashed
+ * messages, at least without some very careful protocol-level disambiguation. For Ed448 it is
+ * safe. The C++ wrapper is designed to make it harder to screw this up, but this C code gives
+ * you no seat belt.
+ */
+void decaf_ed448_sign (
+ uint8_t signature[DECAF_EDDSA_448_SIGNATURE_BYTES],
+ const uint8_t privkey[DECAF_EDDSA_448_PRIVATE_BYTES],
+ const uint8_t pubkey[DECAF_EDDSA_448_PUBLIC_BYTES],
+ const uint8_t *message,
+ size_t message_len,
+ uint8_t prehashed,
+ const uint8_t *context,
+ uint8_t context_len
+) DECAF_API_VIS __attribute__((nonnull(1,2,3))) DECAF_NOINLINE;
+
+/**
+ * @brief EdDSA signing with prehash.
+ *
+ * @param [out] signature The signature.
+ * @param [in] privkey The private key.
+ * @param [in] pubkey The public key.
+ * @param [in] hash The hash of the message. This object will not be modified by the call.
+ * @param [in] context A "context" for this signature of up to 255 bytes. Must be the same as what was used for the prehash.
+ * @param [in] context_len Length of the context.
+ *
+ * @warning For Ed25519, it is unsafe to use the same key for both prehashed and non-prehashed
+ * messages, at least without some very careful protocol-level disambiguation. For Ed448 it is
+ * safe. The C++ wrapper is designed to make it harder to screw this up, but this C code gives
+ * you no seat belt.
+ */
+void decaf_ed448_sign_prehash (
+ uint8_t signature[DECAF_EDDSA_448_SIGNATURE_BYTES],
+ const uint8_t privkey[DECAF_EDDSA_448_PRIVATE_BYTES],
+ const uint8_t pubkey[DECAF_EDDSA_448_PUBLIC_BYTES],
+ const decaf_ed448_prehash_ctx_t hash,
+ const uint8_t *context,
+ uint8_t context_len
+) DECAF_API_VIS __attribute__((nonnull(1,2,3,4))) DECAF_NOINLINE;
+
+/**
+ * @brief Prehash initialization, with contexts if supported.
+ *
+ * @param [out] hash The hash object to be initialized.
+ */
+void decaf_ed448_prehash_init (
+ decaf_ed448_prehash_ctx_t hash
+) DECAF_API_VIS __attribute__((nonnull(1))) DECAF_NOINLINE;
+
+/**
+ * @brief EdDSA signature verification.
+ *
+ * Uses the standard (i.e. less-strict) verification formula.
+ *
+ * @param [in] signature The signature.
+ * @param [in] pubkey The public key.
+ * @param [in] message The message to verify.
+ * @param [in] message_len The length of the message.
+ * @param [in] prehashed Nonzero if the message is actually the hash of something you want to verify.
+ * @param [in] context A "context" for this signature of up to 255 bytes.
+ * @param [in] context_len Length of the context.
+ *
+ * @warning For Ed25519, it is unsafe to use the same key for both prehashed and non-prehashed
+ * messages, at least without some very careful protocol-level disambiguation. For Ed448 it is
+ * safe. The C++ wrapper is designed to make it harder to screw this up, but this C code gives
+ * you no seat belt.
+ */
+decaf_error_t decaf_ed448_verify (
+ const uint8_t signature[DECAF_EDDSA_448_SIGNATURE_BYTES],
+ const uint8_t pubkey[DECAF_EDDSA_448_PUBLIC_BYTES],
+ const uint8_t *message,
+ size_t message_len,
+ uint8_t prehashed,
+ const uint8_t *context,
+ uint8_t context_len
+) DECAF_API_VIS __attribute__((nonnull(1,2))) DECAF_NOINLINE;
+
+/**
+ * @brief EdDSA signature verification.
+ *
+ * Uses the standard (i.e. less-strict) verification formula.
+ *
+ * @param [in] signature The signature.
+ * @param [in] pubkey The public key.
+ * @param [in] hash The hash of the message. This object will not be modified by the call.
+ * @param [in] context A "context" for this signature of up to 255 bytes. Must be the same as what was used for the prehash.
+ * @param [in] context_len Length of the context.
+ *
+ * @warning For Ed25519, it is unsafe to use the same key for both prehashed and non-prehashed
+ * messages, at least without some very careful protocol-level disambiguation. For Ed448 it is
+ * safe. The C++ wrapper is designed to make it harder to screw this up, but this C code gives
+ * you no seat belt.
+ */
+decaf_error_t decaf_ed448_verify_prehash (
+ const uint8_t signature[DECAF_EDDSA_448_SIGNATURE_BYTES],
+ const uint8_t pubkey[DECAF_EDDSA_448_PUBLIC_BYTES],
+ const decaf_ed448_prehash_ctx_t hash,
+ const uint8_t *context,
+ uint8_t context_len
+) DECAF_API_VIS __attribute__((nonnull(1,2))) DECAF_NOINLINE;
+
+/**
+ * @brief EdDSA point encoding. Used internally, exposed externally.
+ * Multiplies by DECAF_448_EDDSA_ENCODE_RATIO first.
+ *
+ * The multiplication is required because the EdDSA encoding represents
+ * the cofactor information, but the Decaf encoding ignores it (which
+ * is the whole point). So if you decode from EdDSA and re-encode to
+ * EdDSA, the cofactor info must get cleared, because the intermediate
+ * representation doesn't track it.
+ *
+ * The way libdecaf handles this is to multiply by
+ * DECAF_448_EDDSA_DECODE_RATIO when decoding, and by
+ * DECAF_448_EDDSA_ENCODE_RATIO when encoding. The product of these
+ * ratios is always exactly the cofactor 4, so the cofactor
+ * ends up cleared one way or another. But exactly how that shakes
+ * out depends on the base points specified in RFC 8032.
+ *
+ * The upshot is that if you pass the Decaf/Ristretto base point to
+ * this function, you will get DECAF_448_EDDSA_ENCODE_RATIO times the
+ * EdDSA base point.
+ *
+ * @param [out] enc The encoded point.
+ * @param [in] p The point.
+ */
+void decaf_448_point_mul_by_ratio_and_encode_like_eddsa (
+ uint8_t enc[DECAF_EDDSA_448_PUBLIC_BYTES],
+ const decaf_448_point_t p
+) DECAF_API_VIS DECAF_NONNULL DECAF_NOINLINE;
+
+/**
+ * @brief EdDSA point decoding. Multiplies by DECAF_448_EDDSA_DECODE_RATIO,
+ * and ignores cofactor information.
+ *
+ * See notes on decaf_448_point_mul_by_ratio_and_encode_like_eddsa
+ *
+ * @param [out] enc The encoded point.
+ * @param [in] p The point.
+ */
+decaf_error_t decaf_448_point_decode_like_eddsa_and_mul_by_ratio (
+ decaf_448_point_t p,
+ const uint8_t enc[DECAF_EDDSA_448_PUBLIC_BYTES]
+) DECAF_API_VIS DECAF_NONNULL DECAF_NOINLINE;
+
+/**
+ * @brief EdDSA to ECDH public key conversion
+ * Deserialize the point to get y on Edwards curve,
+ * Convert it to u coordinate on Montgomery curve.
+ *
+ * @warning This function does not check that the public key being converted
+ * is a valid EdDSA public key (FUTURE?)
+ *
+ * @param[out] x The ECDH public key as in RFC7748(point on Montgomery curve)
+ * @param[in] ed The EdDSA public key(point on Edwards curve)
+ */
+void decaf_ed448_convert_public_key_to_x448 (
+ uint8_t x[DECAF_X448_PUBLIC_BYTES],
+ const uint8_t ed[DECAF_EDDSA_448_PUBLIC_BYTES]
+) DECAF_API_VIS DECAF_NONNULL DECAF_NOINLINE;
+
+/**
+ * @brief EdDSA to ECDH private key conversion
+ * Using the appropriate hash function, hash the EdDSA private key
+ * and keep only the lower bytes to get the ECDH private key
+ *
+ * @param[out] x The ECDH private key as in RFC7748
+ * @param[in] ed The EdDSA private key
+ */
+void decaf_ed448_convert_private_key_to_x448 (
+ uint8_t x[DECAF_X448_PRIVATE_BYTES],
+ const uint8_t ed[DECAF_EDDSA_448_PRIVATE_BYTES]
+) DECAF_API_VIS DECAF_NONNULL DECAF_NOINLINE;
+
+#ifdef __cplusplus
+} /* extern "C" */
+#endif
+
+#endif /* __DECAF_ED448_H__ */
--- /dev/null
+/**
+ * @file decaf/point_255.h
+ * @author Mike Hamburg
+ *
+ * @copyright
+ * Copyright (c) 2015-2016 Cryptography Research, Inc. \n
+ * Released under the MIT License. See LICENSE.txt for license information.
+ *
+ * @brief A group of prime order p, based on Curve25519.
+ *
+ * @warning This file was automatically generated in Python.
+ * Please do not edit it.
+ */
+
+#ifndef __DECAF_POINT_255_H__
+#define __DECAF_POINT_255_H__ 1
+
+#include <decaf/common.h>
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+/** @cond internal */
+#define DECAF_255_SCALAR_LIMBS ((253-1)/DECAF_WORD_BITS+1)
+/** @endcond */
+
+/** The number of bits in a scalar */
+#define DECAF_255_SCALAR_BITS 253
+
+/** @cond internal */
+#ifndef __DECAF_25519_GF_DEFINED__
+#define __DECAF_25519_GF_DEFINED__ 1
+/** @brief Galois field element internal structure */
+typedef struct gf_25519_s {
+ decaf_word_t limb[320/DECAF_WORD_BITS];
+} __attribute__((aligned(32))) gf_25519_s, gf_25519_t[1];
+#endif /* __DECAF_25519_GF_DEFINED__ */
+/** @endcond */
+
+/** Number of bytes in a serialized point. */
+#define DECAF_255_SER_BYTES 32
+
+/** Number of bytes in an elligated point. For now set the same as SER_BYTES
+ * but could be different for other curves.
+ */
+#define DECAF_255_HASH_BYTES 32
+
+/** Number of bytes in a serialized scalar. */
+#define DECAF_255_SCALAR_BYTES 32
+
+/** Number of bits in the "which" field of an elligator inverse */
+#define DECAF_255_INVERT_ELLIGATOR_WHICH_BITS 5
+
+/** The cofactor the curve would have, if we hadn't removed it */
+#define DECAF_255_REMOVED_COFACTOR 8
+
+/** X25519 encoding ratio. */
+#define DECAF_X25519_ENCODE_RATIO 4
+
+/** Number of bytes in an x25519 public key */
+#define DECAF_X25519_PUBLIC_BYTES 32
+
+/** Number of bytes in an x25519 private key */
+#define DECAF_X25519_PRIVATE_BYTES 32
+
+/** Twisted Edwards extended homogeneous coordinates */
+typedef struct decaf_255_point_s {
+ /** @cond internal */
+ gf_25519_t x,y,z,t;
+ /** @endcond */
+} decaf_255_point_t[1];
+
+/** Precomputed table based on a point. Can be trivial implementation. */
+struct decaf_255_precomputed_s;
+
+/** Precomputed table based on a point. Can be trivial implementation. */
+typedef struct decaf_255_precomputed_s decaf_255_precomputed_s;
+
+/** Size and alignment of precomputed point tables. */
+extern const size_t decaf_255_sizeof_precomputed_s DECAF_API_VIS, decaf_255_alignof_precomputed_s DECAF_API_VIS;
+
+/** Scalar is stored packed, because we don't need the speed. */
+typedef struct decaf_255_scalar_s {
+ /** @cond internal */
+ decaf_word_t limb[DECAF_255_SCALAR_LIMBS];
+ /** @endcond */
+} decaf_255_scalar_t[1];
+
+/** A scalar equal to 1. */
+extern const decaf_255_scalar_t decaf_255_scalar_one DECAF_API_VIS;
+
+/** A scalar equal to 0. */
+extern const decaf_255_scalar_t decaf_255_scalar_zero DECAF_API_VIS;
+
+/** The identity point on the curve. */
+extern const decaf_255_point_t decaf_255_point_identity DECAF_API_VIS;
+
+/** An arbitrarily chosen base point on the curve. */
+extern const decaf_255_point_t decaf_255_point_base DECAF_API_VIS;
+
+/** Precomputed table for the base point on the curve. */
+extern const struct decaf_255_precomputed_s *decaf_255_precomputed_base DECAF_API_VIS;
+
+/**
+ * @brief Read a scalar from wire format or from bytes.
+ *
+ * @param [in] ser Serialized form of a scalar.
+ * @param [out] out Deserialized form.
+ *
+ * @retval DECAF_SUCCESS The scalar was correctly encoded.
+ * @retval DECAF_FAILURE The scalar was greater than the modulus,
+ * and has been reduced modulo that modulus.
+ */
+decaf_error_t decaf_255_scalar_decode (
+ decaf_255_scalar_t out,
+ const unsigned char ser[DECAF_255_SCALAR_BYTES]
+) DECAF_API_VIS DECAF_WARN_UNUSED DECAF_NONNULL DECAF_NOINLINE;
+
+/**
+ * @brief Read a scalar from wire format or from bytes. Reduces mod
+ * scalar prime.
+ *
+ * @param [in] ser Serialized form of a scalar.
+ * @param [in] ser_len Length of serialized form.
+ * @param [out] out Deserialized form.
+ */
+void decaf_255_scalar_decode_long (
+ decaf_255_scalar_t out,
+ const unsigned char *ser,
+ size_t ser_len
+) DECAF_API_VIS DECAF_NONNULL DECAF_NOINLINE;
+
+/**
+ * @brief Serialize a scalar to wire format.
+ *
+ * @param [out] ser Serialized form of a scalar.
+ * @param [in] s Deserialized scalar.
+ */
+void decaf_255_scalar_encode (
+ unsigned char ser[DECAF_255_SCALAR_BYTES],
+ const decaf_255_scalar_t s
+) DECAF_API_VIS DECAF_NONNULL DECAF_NOINLINE DECAF_NOINLINE;
+
+/**
+ * @brief Add two scalars. The scalars may use the same memory.
+ * @param [in] a One scalar.
+ * @param [in] b Another scalar.
+ * @param [out] out a+b.
+ */
+void decaf_255_scalar_add (
+ decaf_255_scalar_t out,
+ const decaf_255_scalar_t a,
+ const decaf_255_scalar_t b
+) DECAF_API_VIS DECAF_NONNULL DECAF_NOINLINE;
+
+/**
+ * @brief Compare two scalars.
+ * @param [in] a One scalar.
+ * @param [in] b Another scalar.
+ * @retval DECAF_TRUE The scalars are equal.
+ * @retval DECAF_FALSE The scalars are not equal.
+ */
+decaf_bool_t decaf_255_scalar_eq (
+ const decaf_255_scalar_t a,
+ const decaf_255_scalar_t b
+) DECAF_API_VIS DECAF_WARN_UNUSED DECAF_NONNULL DECAF_NOINLINE;
+
+/**
+ * @brief Subtract two scalars. The scalars may use the same memory.
+ * @param [in] a One scalar.
+ * @param [in] b Another scalar.
+ * @param [out] out a-b.
+ */
+void decaf_255_scalar_sub (
+ decaf_255_scalar_t out,
+ const decaf_255_scalar_t a,
+ const decaf_255_scalar_t b
+) DECAF_API_VIS DECAF_NONNULL DECAF_NOINLINE;
+
+/**
+ * @brief Multiply two scalars. The scalars may use the same memory.
+ * @param [in] a One scalar.
+ * @param [in] b Another scalar.
+ * @param [out] out a*b.
+ */
+void decaf_255_scalar_mul (
+ decaf_255_scalar_t out,
+ const decaf_255_scalar_t a,
+ const decaf_255_scalar_t b
+) DECAF_API_VIS DECAF_NONNULL DECAF_NOINLINE;
+
+/**
+* @brief Halve a scalar. The scalars may use the same memory.
+* @param [in] a A scalar.
+* @param [out] out a/2.
+*/
+void decaf_255_scalar_halve (
+ decaf_255_scalar_t out,
+ const decaf_255_scalar_t a
+) DECAF_API_VIS DECAF_NONNULL DECAF_NOINLINE;
+
+/**
+ * @brief Invert a scalar. When passed zero, return 0. The input and output may alias.
+ * @param [in] a A scalar.
+ * @param [out] out 1/a.
+ * @return DECAF_SUCCESS The input is nonzero.
+ */
+decaf_error_t decaf_255_scalar_invert (
+ decaf_255_scalar_t out,
+ const decaf_255_scalar_t a
+) DECAF_API_VIS DECAF_WARN_UNUSED DECAF_NONNULL DECAF_NOINLINE;
+
+/**
+ * @brief Copy a scalar. The scalars may use the same memory, in which
+ * case this function does nothing.
+ * @param [in] a A scalar.
+ * @param [out] out Will become a copy of a.
+ */
+static inline void DECAF_NONNULL decaf_255_scalar_copy (
+ decaf_255_scalar_t out,
+ const decaf_255_scalar_t a
+) {
+ *out = *a;
+}
+
+/**
+ * @brief Set a scalar to an unsigned 64-bit integer.
+ * @param [in] a An integer.
+ * @param [out] out Will become equal to a.
+ */
+void decaf_255_scalar_set_unsigned (
+ decaf_255_scalar_t out,
+ uint64_t a
+) DECAF_API_VIS DECAF_NONNULL;
+
+/**
+ * @brief Encode a point as a sequence of bytes.
+ *
+ * @param [out] ser The byte representation of the point.
+ * @param [in] pt The point to encode.
+ */
+void decaf_255_point_encode (
+ uint8_t ser[DECAF_255_SER_BYTES],
+ const decaf_255_point_t pt
+) DECAF_API_VIS DECAF_NONNULL DECAF_NOINLINE;
+
+/**
+ * @brief Decode a point from a sequence of bytes.
+ *
+ * Every point has a unique encoding, so not every
+ * sequence of bytes is a valid encoding. If an invalid
+ * encoding is given, the output is undefined.
+ *
+ * @param [out] pt The decoded point.
+ * @param [in] ser The serialized version of the point.
+ * @param [in] allow_identity DECAF_TRUE if the identity is a legal input.
+ * @retval DECAF_SUCCESS The decoding succeeded.
+ * @retval DECAF_FAILURE The decoding didn't succeed, because
+ * ser does not represent a point.
+ */
+decaf_error_t decaf_255_point_decode (
+ decaf_255_point_t pt,
+ const uint8_t ser[DECAF_255_SER_BYTES],
+ decaf_bool_t allow_identity
+) DECAF_API_VIS DECAF_WARN_UNUSED DECAF_NONNULL DECAF_NOINLINE;
+
+/**
+ * @brief Copy a point. The input and output may alias,
+ * in which case this function does nothing.
+ *
+ * @param [out] a A copy of the point.
+ * @param [in] b Any point.
+ */
+static inline void DECAF_NONNULL decaf_255_point_copy (
+ decaf_255_point_t a,
+ const decaf_255_point_t b
+) {
+ *a=*b;
+}
+
+/**
+ * @brief Test whether two points are equal. If yes, return
+ * DECAF_TRUE, else return DECAF_FALSE.
+ *
+ * @param [in] a A point.
+ * @param [in] b Another point.
+ * @retval DECAF_TRUE The points are equal.
+ * @retval DECAF_FALSE The points are not equal.
+ */
+decaf_bool_t decaf_255_point_eq (
+ const decaf_255_point_t a,
+ const decaf_255_point_t b
+) DECAF_API_VIS DECAF_WARN_UNUSED DECAF_NONNULL DECAF_NOINLINE;
+
+/**
+ * @brief Add two points to produce a third point. The
+ * input points and output point can be pointers to the same
+ * memory.
+ *
+ * @param [out] sum The sum a+b.
+ * @param [in] a An addend.
+ * @param [in] b An addend.
+ */
+void decaf_255_point_add (
+ decaf_255_point_t sum,
+ const decaf_255_point_t a,
+ const decaf_255_point_t b
+) DECAF_API_VIS DECAF_NONNULL;
+
+/**
+ * @brief Double a point. Equivalent to
+ * decaf_255_point_add(two_a,a,a), but potentially faster.
+ *
+ * @param [out] two_a The sum a+a.
+ * @param [in] a A point.
+ */
+void decaf_255_point_double (
+ decaf_255_point_t two_a,
+ const decaf_255_point_t a
+) DECAF_API_VIS DECAF_NONNULL;
+
+/**
+ * @brief Subtract two points to produce a third point. The
+ * input points and output point can be pointers to the same
+ * memory.
+ *
+ * @param [out] diff The difference a-b.
+ * @param [in] a The minuend.
+ * @param [in] b The subtrahend.
+ */
+void decaf_255_point_sub (
+ decaf_255_point_t diff,
+ const decaf_255_point_t a,
+ const decaf_255_point_t b
+) DECAF_API_VIS DECAF_NONNULL;
+
+/**
+ * @brief Negate a point to produce another point. The input
+ * and output points can use the same memory.
+ *
+ * @param [out] nega The negated input point
+ * @param [in] a The input point.
+ */
+void decaf_255_point_negate (
+ decaf_255_point_t nega,
+ const decaf_255_point_t a
+) DECAF_API_VIS DECAF_NONNULL;
+
+/**
+ * @brief Multiply a base point by a scalar: scaled = scalar*base.
+ *
+ * @param [out] scaled The scaled point base*scalar
+ * @param [in] base The point to be scaled.
+ * @param [in] scalar The scalar to multiply by.
+ */
+void decaf_255_point_scalarmul (
+ decaf_255_point_t scaled,
+ const decaf_255_point_t base,
+ const decaf_255_scalar_t scalar
+) DECAF_API_VIS DECAF_NONNULL DECAF_NOINLINE;
+
+/**
+ * @brief Multiply a base point by a scalar: scaled = scalar*base.
+ * This function operates directly on serialized forms.
+ *
+ * @warning This function is experimental. It may not be supported
+ * long-term.
+ *
+ * @param [out] scaled The scaled point base*scalar
+ * @param [in] base The point to be scaled.
+ * @param [in] scalar The scalar to multiply by.
+ * @param [in] allow_identity Allow the input to be the identity.
+ * @param [in] short_circuit Allow a fast return if the input is illegal.
+ *
+ * @retval DECAF_SUCCESS The scalarmul succeeded.
+ * @retval DECAF_FAILURE The scalarmul didn't succeed, because
+ * base does not represent a point.
+ */
+decaf_error_t decaf_255_direct_scalarmul (
+ uint8_t scaled[DECAF_255_SER_BYTES],
+ const uint8_t base[DECAF_255_SER_BYTES],
+ const decaf_255_scalar_t scalar,
+ decaf_bool_t allow_identity,
+ decaf_bool_t short_circuit
+) DECAF_API_VIS DECAF_NONNULL DECAF_WARN_UNUSED DECAF_NOINLINE;
+
+/**
+ * @brief RFC 7748 Diffie-Hellman scalarmul. This function uses a different
+ * (non-Decaf) encoding.
+ *
+ * @param [out] scaled The scaled point base*scalar
+ * @param [in] base The point to be scaled.
+ * @param [in] scalar The scalar to multiply by.
+ *
+ * @retval DECAF_SUCCESS The scalarmul succeeded.
+ * @retval DECAF_FAILURE The scalarmul didn't succeed, because the base
+ * point is in a small subgroup.
+ */
+decaf_error_t decaf_x25519 (
+ uint8_t out[DECAF_X25519_PUBLIC_BYTES],
+ const uint8_t base[DECAF_X25519_PUBLIC_BYTES],
+ const uint8_t scalar[DECAF_X25519_PRIVATE_BYTES]
+) DECAF_API_VIS DECAF_NONNULL DECAF_WARN_UNUSED DECAF_NOINLINE;
+
+/**
+ * @brief Multiply a point by DECAF_X25519_ENCODE_RATIO,
+ * then encode it like RFC 7748.
+ *
+ * This function is mainly used internally, but is exported in case
+ * it will be useful.
+ *
+ * The ratio is necessary because the internal representation doesn't
+ * track the cofactor information, so on output we must clear the cofactor.
+ * This would multiply by the cofactor, but in fact internally libdecaf's
+ * points are always even, so it multiplies by half the cofactor instead.
+ *
+ * As it happens, this aligns with the base point definitions; that is,
+ * if you pass the Decaf/Ristretto base point to this function, the result
+ * will be DECAF_X25519_ENCODE_RATIO times the X25519
+ * base point.
+ *
+ * @param [out] out The scaled and encoded point.
+ * @param [in] p The point to be scaled and encoded.
+ */
+void decaf_255_point_mul_by_ratio_and_encode_like_x25519 (
+ uint8_t out[DECAF_X25519_PUBLIC_BYTES],
+ const decaf_255_point_t p
+) DECAF_API_VIS DECAF_NONNULL;
+
+/** The base point for X25519 Diffie-Hellman */
+extern const uint8_t decaf_x25519_base_point[DECAF_X25519_PUBLIC_BYTES] DECAF_API_VIS;
+
+/**
+ * @brief RFC 7748 Diffie-Hellman base point scalarmul. This function uses
+ * a different (non-Decaf) encoding.
+ *
+ * @deprecated Renamed to decaf_x25519_derive_public_key.
+ * I have no particular timeline for removing this name.
+ *
+ * @param [out] scaled The scaled point base*scalar
+ * @param [in] scalar The scalar to multiply by.
+ */
+void decaf_x25519_generate_key (
+ uint8_t out[DECAF_X25519_PUBLIC_BYTES],
+ const uint8_t scalar[DECAF_X25519_PRIVATE_BYTES]
+) DECAF_API_VIS DECAF_NONNULL DECAF_NOINLINE DECAF_DEPRECATED("Renamed to decaf_x25519_derive_public_key");
+
+/**
+ * @brief RFC 7748 Diffie-Hellman base point scalarmul. This function uses
+ * a different (non-Decaf) encoding.
+ *
+ * Does exactly the same thing as decaf_x25519_generate_key,
+ * but has a better name.
+ *
+ * @param [out] scaled The scaled point base*scalar
+ * @param [in] scalar The scalar to multiply by.
+ */
+void decaf_x25519_derive_public_key (
+ uint8_t out[DECAF_X25519_PUBLIC_BYTES],
+ const uint8_t scalar[DECAF_X25519_PRIVATE_BYTES]
+) DECAF_API_VIS DECAF_NONNULL DECAF_NOINLINE;
+
+/* FUTURE: uint8_t decaf_255_encode_like_curve25519) */
+
+/**
+ * @brief Precompute a table for fast scalar multiplication.
+ * Some implementations do not include precomputed points; for
+ * those implementations, this implementation simply copies the
+ * point.
+ *
+ * @param [out] a A precomputed table of multiples of the point.
+ * @param [in] b Any point.
+ */
+void decaf_255_precompute (
+ decaf_255_precomputed_s *a,
+ const decaf_255_point_t b
+) DECAF_API_VIS DECAF_NONNULL DECAF_NOINLINE;
+
+/**
+ * @brief Multiply a precomputed base point by a scalar:
+ * scaled = scalar*base.
+ * Some implementations do not include precomputed points; for
+ * those implementations, this function is the same as
+ * decaf_255_point_scalarmul
+ *
+ * @param [out] scaled The scaled point base*scalar
+ * @param [in] base The point to be scaled.
+ * @param [in] scalar The scalar to multiply by.
+ */
+void decaf_255_precomputed_scalarmul (
+ decaf_255_point_t scaled,
+ const decaf_255_precomputed_s *base,
+ const decaf_255_scalar_t scalar
+) DECAF_API_VIS DECAF_NONNULL DECAF_NOINLINE;
+
+/**
+ * @brief Multiply two base points by two scalars:
+ * scaled = scalar1*base1 + scalar2*base2.
+ *
+ * Equivalent to two calls to decaf_255_point_scalarmul, but may be
+ * faster.
+ *
+ * @param [out] combo The linear combination scalar1*base1 + scalar2*base2.
+ * @param [in] base1 A first point to be scaled.
+ * @param [in] scalar1 A first scalar to multiply by.
+ * @param [in] base2 A second point to be scaled.
+ * @param [in] scalar2 A second scalar to multiply by.
+ */
+void decaf_255_point_double_scalarmul (
+ decaf_255_point_t combo,
+ const decaf_255_point_t base1,
+ const decaf_255_scalar_t scalar1,
+ const decaf_255_point_t base2,
+ const decaf_255_scalar_t scalar2
+) DECAF_API_VIS DECAF_NONNULL DECAF_NOINLINE;
+
+/**
+ * Multiply one base point by two scalars:
+ *
+ * a1 = scalar1 * base
+ * a2 = scalar2 * base
+ *
+ * Equivalent to two calls to decaf_255_point_scalarmul, but may be
+ * faster.
+ *
+ * @param [out] a1 The first multiple. It may be the same as the input point.
+ * @param [out] a2 The second multiple. It may be the same as the input point.
+ * @param [in] base1 A point to be scaled.
+ * @param [in] scalar1 A first scalar to multiply by.
+ * @param [in] scalar2 A second scalar to multiply by.
+ */
+void decaf_255_point_dual_scalarmul (
+ decaf_255_point_t a1,
+ decaf_255_point_t a2,
+ const decaf_255_point_t base1,
+ const decaf_255_scalar_t scalar1,
+ const decaf_255_scalar_t scalar2
+) DECAF_API_VIS DECAF_NONNULL DECAF_NOINLINE;
+
+/**
+ * @brief Multiply two base points by two scalars:
+ * scaled = scalar1*decaf_255_point_base + scalar2*base2.
+ *
+ * Otherwise equivalent to decaf_255_point_double_scalarmul, but may be
+ * faster at the expense of being variable time.
+ *
+ * @param [out] combo The linear combination scalar1*base + scalar2*base2.
+ * @param [in] scalar1 A first scalar to multiply by.
+ * @param [in] base2 A second point to be scaled.
+ * @param [in] scalar2 A second scalar to multiply by.
+ *
+ * @warning: This function takes variable time, and may leak the scalars
+ * used. It is designed for signature verification.
+ */
+void decaf_255_base_double_scalarmul_non_secret (
+ decaf_255_point_t combo,
+ const decaf_255_scalar_t scalar1,
+ const decaf_255_point_t base2,
+ const decaf_255_scalar_t scalar2
+) DECAF_API_VIS DECAF_NONNULL DECAF_NOINLINE;
+
+/**
+ * @brief Constant-time decision between two points. If pick_b
+ * is zero, out = a; else out = b.
+ *
+ * @param [out] out The output. It may be the same as either input.
+ * @param [in] a Any point.
+ * @param [in] b Any point.
+ * @param [in] pick_b If nonzero, choose point b.
+ */
+void decaf_255_point_cond_sel (
+ decaf_255_point_t out,
+ const decaf_255_point_t a,
+ const decaf_255_point_t b,
+ decaf_word_t pick_b
+) DECAF_API_VIS DECAF_NONNULL DECAF_NOINLINE;
+
+/**
+ * @brief Constant-time decision between two scalars. If pick_b
+ * is zero, out = a; else out = b.
+ *
+ * @param [out] out The output. It may be the same as either input.
+ * @param [in] a Any scalar.
+ * @param [in] b Any scalar.
+ * @param [in] pick_b If nonzero, choose scalar b.
+ */
+void decaf_255_scalar_cond_sel (
+ decaf_255_scalar_t out,
+ const decaf_255_scalar_t a,
+ const decaf_255_scalar_t b,
+ decaf_word_t pick_b
+) DECAF_API_VIS DECAF_NONNULL DECAF_NOINLINE;
+
+/**
+ * @brief Test that a point is valid, for debugging purposes.
+ *
+ * @param [in] to_test The point to test.
+ * @retval DECAF_TRUE The point is valid.
+ * @retval DECAF_FALSE The point is invalid.
+ */
+decaf_bool_t decaf_255_point_valid (
+ const decaf_255_point_t to_test
+) DECAF_API_VIS DECAF_WARN_UNUSED DECAF_NONNULL DECAF_NOINLINE;
+
+/**
+ * @brief Torque a point, for debugging purposes. The output
+ * will be equal to the input.
+ *
+ * @param [out] q The point to torque.
+ * @param [in] p The point to torque.
+ */
+void decaf_255_point_debugging_torque (
+ decaf_255_point_t q,
+ const decaf_255_point_t p
+) DECAF_API_VIS DECAF_NONNULL DECAF_NOINLINE;
+
+/**
+ * @brief Projectively scale a point, for debugging purposes.
+ * The output will be equal to the input, and will be valid
+ * even if the factor is zero.
+ *
+ * @param [out] q The point to scale.
+ * @param [in] p The point to scale.
+ * @param [in] factor Serialized GF factor to scale.
+ */
+void decaf_255_point_debugging_pscale (
+ decaf_255_point_t q,
+ const decaf_255_point_t p,
+ const unsigned char factor[DECAF_255_SER_BYTES]
+) DECAF_API_VIS DECAF_NONNULL DECAF_NOINLINE;
+
+/**
+ * @brief Almost-Elligator-like hash to curve.
+ *
+ * Call this function with the output of a hash to make a hash to the curve.
+ *
+ * This function runs Elligator2 on the decaf_255 Jacobi quartic model. It then
+ * uses the isogeny to put the result in twisted Edwards form. As a result,
+ * it is safe (cannot produce points of order 4), and would be compatible with
+ * hypothetical other implementations of Decaf using a Montgomery or untwisted
+ * Edwards model.
+ *
+ * Unlike Elligator, this function may be up to 4:1 on [0,(p-1)/2]:
+ * A factor of 2 due to the isogeny.
+ * A factor of 2 because we quotient out the 2-torsion.
+ *
+ * This makes it about 8:1 overall, or 16:1 overall on curves with cofactor 8.
+ *
+ * Negating the input (mod q) results in the same point. Inverting the input
+ * (mod q) results in the negative point. This is the same as Elligator.
+ *
+ * This function isn't quite indifferentiable from a random oracle.
+ * However, it is suitable for many protocols, including SPEKE and SPAKE2 EE.
+ * Furthermore, calling it twice with independent seeds and adding the results
+ * is indifferentiable from a random oracle.
+ *
+ * @param [in] hashed_data Output of some hash function.
+ * @param [out] pt The data hashed to the curve.
+ */
+void
+decaf_255_point_from_hash_nonuniform (
+ decaf_255_point_t pt,
+ const unsigned char hashed_data[DECAF_255_HASH_BYTES]
+) DECAF_API_VIS DECAF_NONNULL DECAF_NOINLINE;
+
+/**
+ * @brief Indifferentiable hash function encoding to curve.
+ *
+ * Equivalent to calling decaf_255_point_from_hash_nonuniform twice and adding.
+ *
+ * @param [in] hashed_data Output of some hash function.
+ * @param [out] pt The data hashed to the curve.
+ */
+void decaf_255_point_from_hash_uniform (
+ decaf_255_point_t pt,
+ const unsigned char hashed_data[2*DECAF_255_HASH_BYTES]
+) DECAF_API_VIS DECAF_NONNULL DECAF_NOINLINE;
+
+/**
+ * @brief Inverse of elligator-like hash to curve.
+ *
+ * This function writes to the buffer, to make it so that
+ * decaf_255_point_from_hash_nonuniform(buffer) = pt if
+ * possible. Since there may be multiple preimages, the
+ * "which" parameter chooses between them. To ensure uniform
+ * inverse sampling, this function succeeds or fails
+ * independently for different "which" values.
+ *
+ * This function isn't guaranteed to find every possible
+ * preimage, but it finds all except a small finite number.
+ * In particular, when the number of bits in the modulus isn't
+ * a multiple of 8 (i.e. for curve25519), it sets the high bits
+ * independently, which enables the generated data to be uniform.
+ * But it doesn't add p, so you'll never get exactly p from this
+ * function. This might change in the future, especially if
+ * we ever support eg Brainpool curves, where this could cause
+ * real nonuniformity.
+ *
+ * @param [out] recovered_hash Encoded data.
+ * @param [in] pt The point to encode.
+ * @param [in] which A value determining which inverse point
+ * to return.
+ *
+ * @retval DECAF_SUCCESS The inverse succeeded.
+ * @retval DECAF_FAILURE The inverse failed.
+ */
+decaf_error_t
+decaf_255_invert_elligator_nonuniform (
+ unsigned char recovered_hash[DECAF_255_HASH_BYTES],
+ const decaf_255_point_t pt,
+ uint32_t which
+) DECAF_API_VIS DECAF_NONNULL DECAF_NOINLINE DECAF_WARN_UNUSED;
+
+/**
+ * @brief Inverse of elligator-like hash to curve.
+ *
+ * This function writes to the buffer, to make it so that
+ * decaf_255_point_from_hash_uniform(buffer) = pt if
+ * possible. Since there may be multiple preimages, the
+ * "which" parameter chooses between them. To ensure uniform
+ * inverse sampling, this function succeeds or fails
+ * independently for different "which" values.
+ *
+ * @param [out] recovered_hash Encoded data.
+ * @param [in] pt The point to encode.
+ * @param [in] which A value determining which inverse point
+ * to return.
+ *
+ * @retval DECAF_SUCCESS The inverse succeeded.
+ * @retval DECAF_FAILURE The inverse failed.
+ */
+decaf_error_t
+decaf_255_invert_elligator_uniform (
+ unsigned char recovered_hash[2*DECAF_255_HASH_BYTES],
+ const decaf_255_point_t pt,
+ uint32_t which
+) DECAF_API_VIS DECAF_NONNULL DECAF_NOINLINE DECAF_WARN_UNUSED;
+
+/**
+ * @brief Overwrite scalar with zeros.
+ */
+void decaf_255_scalar_destroy (
+ decaf_255_scalar_t scalar
+) DECAF_NONNULL DECAF_API_VIS;
+
+/**
+ * @brief Overwrite point with zeros.
+ */
+void decaf_255_point_destroy (
+ decaf_255_point_t point
+) DECAF_NONNULL DECAF_API_VIS;
+
+/**
+ * @brief Overwrite precomputed table with zeros.
+ */
+void decaf_255_precomputed_destroy (
+ decaf_255_precomputed_s *pre
+) DECAF_NONNULL DECAF_API_VIS;
+
+#ifdef __cplusplus
+} /* extern "C" */
+#endif
+
+#endif /* __DECAF_POINT_255_H__ */
--- /dev/null
+/**
+ * @file decaf/point_448.h
+ * @author Mike Hamburg
+ *
+ * @copyright
+ * Copyright (c) 2015-2016 Cryptography Research, Inc. \n
+ * Released under the MIT License. See LICENSE.txt for license information.
+ *
+ * @brief A group of prime order p, based on Ed448-Goldilocks.
+ *
+ * @warning This file was automatically generated in Python.
+ * Please do not edit it.
+ */
+
+#ifndef __DECAF_POINT_448_H__
+#define __DECAF_POINT_448_H__ 1
+
+#include <decaf/common.h>
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+/** @cond internal */
+#define DECAF_448_SCALAR_LIMBS ((446-1)/DECAF_WORD_BITS+1)
+/** @endcond */
+
+/** The number of bits in a scalar */
+#define DECAF_448_SCALAR_BITS 446
+
+/** @cond internal */
+#ifndef __DECAF_448_GF_DEFINED__
+#define __DECAF_448_GF_DEFINED__ 1
+/** @brief Galois field element internal structure */
+typedef struct gf_448_s {
+ decaf_word_t limb[512/DECAF_WORD_BITS];
+} __attribute__((aligned(32))) gf_448_s, gf_448_t[1];
+#endif /* __DECAF_448_GF_DEFINED__ */
+/** @endcond */
+
+/** Number of bytes in a serialized point. */
+#define DECAF_448_SER_BYTES 56
+
+/** Number of bytes in an elligated point. For now set the same as SER_BYTES
+ * but could be different for other curves.
+ */
+#define DECAF_448_HASH_BYTES 56
+
+/** Number of bytes in a serialized scalar. */
+#define DECAF_448_SCALAR_BYTES 56
+
+/** Number of bits in the "which" field of an elligator inverse */
+#define DECAF_448_INVERT_ELLIGATOR_WHICH_BITS 3
+
+/** The cofactor the curve would have, if we hadn't removed it */
+#define DECAF_448_REMOVED_COFACTOR 4
+
+/** X448 encoding ratio. */
+#define DECAF_X448_ENCODE_RATIO 2
+
+/** Number of bytes in an x448 public key */
+#define DECAF_X448_PUBLIC_BYTES 56
+
+/** Number of bytes in an x448 private key */
+#define DECAF_X448_PRIVATE_BYTES 56
+
+/** Twisted Edwards extended homogeneous coordinates */
+typedef struct decaf_448_point_s {
+ /** @cond internal */
+ gf_448_t x,y,z,t;
+ /** @endcond */
+} decaf_448_point_t[1];
+
+/** Precomputed table based on a point. Can be trivial implementation. */
+struct decaf_448_precomputed_s;
+
+/** Precomputed table based on a point. Can be trivial implementation. */
+typedef struct decaf_448_precomputed_s decaf_448_precomputed_s;
+
+/** Size and alignment of precomputed point tables. */
+extern const size_t decaf_448_sizeof_precomputed_s DECAF_API_VIS, decaf_448_alignof_precomputed_s DECAF_API_VIS;
+
+/** Scalar is stored packed, because we don't need the speed. */
+typedef struct decaf_448_scalar_s {
+ /** @cond internal */
+ decaf_word_t limb[DECAF_448_SCALAR_LIMBS];
+ /** @endcond */
+} decaf_448_scalar_t[1];
+
+/** A scalar equal to 1. */
+extern const decaf_448_scalar_t decaf_448_scalar_one DECAF_API_VIS;
+
+/** A scalar equal to 0. */
+extern const decaf_448_scalar_t decaf_448_scalar_zero DECAF_API_VIS;
+
+/** The identity point on the curve. */
+extern const decaf_448_point_t decaf_448_point_identity DECAF_API_VIS;
+
+/** An arbitrarily chosen base point on the curve. */
+extern const decaf_448_point_t decaf_448_point_base DECAF_API_VIS;
+
+/** Precomputed table for the base point on the curve. */
+extern const struct decaf_448_precomputed_s *decaf_448_precomputed_base DECAF_API_VIS;
+
+/**
+ * @brief Read a scalar from wire format or from bytes.
+ *
+ * @param [in] ser Serialized form of a scalar.
+ * @param [out] out Deserialized form.
+ *
+ * @retval DECAF_SUCCESS The scalar was correctly encoded.
+ * @retval DECAF_FAILURE The scalar was greater than the modulus,
+ * and has been reduced modulo that modulus.
+ */
+decaf_error_t decaf_448_scalar_decode (
+ decaf_448_scalar_t out,
+ const unsigned char ser[DECAF_448_SCALAR_BYTES]
+) DECAF_API_VIS DECAF_WARN_UNUSED DECAF_NONNULL DECAF_NOINLINE;
+
+/**
+ * @brief Read a scalar from wire format or from bytes. Reduces mod
+ * scalar prime.
+ *
+ * @param [in] ser Serialized form of a scalar.
+ * @param [in] ser_len Length of serialized form.
+ * @param [out] out Deserialized form.
+ */
+void decaf_448_scalar_decode_long (
+ decaf_448_scalar_t out,
+ const unsigned char *ser,
+ size_t ser_len
+) DECAF_API_VIS DECAF_NONNULL DECAF_NOINLINE;
+
+/**
+ * @brief Serialize a scalar to wire format.
+ *
+ * @param [out] ser Serialized form of a scalar.
+ * @param [in] s Deserialized scalar.
+ */
+void decaf_448_scalar_encode (
+ unsigned char ser[DECAF_448_SCALAR_BYTES],
+ const decaf_448_scalar_t s
+) DECAF_API_VIS DECAF_NONNULL DECAF_NOINLINE DECAF_NOINLINE;
+
+/**
+ * @brief Add two scalars. The scalars may use the same memory.
+ * @param [in] a One scalar.
+ * @param [in] b Another scalar.
+ * @param [out] out a+b.
+ */
+void decaf_448_scalar_add (
+ decaf_448_scalar_t out,
+ const decaf_448_scalar_t a,
+ const decaf_448_scalar_t b
+) DECAF_API_VIS DECAF_NONNULL DECAF_NOINLINE;
+
+/**
+ * @brief Compare two scalars.
+ * @param [in] a One scalar.
+ * @param [in] b Another scalar.
+ * @retval DECAF_TRUE The scalars are equal.
+ * @retval DECAF_FALSE The scalars are not equal.
+ */
+decaf_bool_t decaf_448_scalar_eq (
+ const decaf_448_scalar_t a,
+ const decaf_448_scalar_t b
+) DECAF_API_VIS DECAF_WARN_UNUSED DECAF_NONNULL DECAF_NOINLINE;
+
+/**
+ * @brief Subtract two scalars. The scalars may use the same memory.
+ * @param [in] a One scalar.
+ * @param [in] b Another scalar.
+ * @param [out] out a-b.
+ */
+void decaf_448_scalar_sub (
+ decaf_448_scalar_t out,
+ const decaf_448_scalar_t a,
+ const decaf_448_scalar_t b
+) DECAF_API_VIS DECAF_NONNULL DECAF_NOINLINE;
+
+/**
+ * @brief Multiply two scalars. The scalars may use the same memory.
+ * @param [in] a One scalar.
+ * @param [in] b Another scalar.
+ * @param [out] out a*b.
+ */
+void decaf_448_scalar_mul (
+ decaf_448_scalar_t out,
+ const decaf_448_scalar_t a,
+ const decaf_448_scalar_t b
+) DECAF_API_VIS DECAF_NONNULL DECAF_NOINLINE;
+
+/**
+* @brief Halve a scalar. The scalars may use the same memory.
+* @param [in] a A scalar.
+* @param [out] out a/2.
+*/
+void decaf_448_scalar_halve (
+ decaf_448_scalar_t out,
+ const decaf_448_scalar_t a
+) DECAF_API_VIS DECAF_NONNULL DECAF_NOINLINE;
+
+/**
+ * @brief Invert a scalar. When passed zero, return 0. The input and output may alias.
+ * @param [in] a A scalar.
+ * @param [out] out 1/a.
+ * @return DECAF_SUCCESS The input is nonzero.
+ */
+decaf_error_t decaf_448_scalar_invert (
+ decaf_448_scalar_t out,
+ const decaf_448_scalar_t a
+) DECAF_API_VIS DECAF_WARN_UNUSED DECAF_NONNULL DECAF_NOINLINE;
+
+/**
+ * @brief Copy a scalar. The scalars may use the same memory, in which
+ * case this function does nothing.
+ * @param [in] a A scalar.
+ * @param [out] out Will become a copy of a.
+ */
+static inline void DECAF_NONNULL decaf_448_scalar_copy (
+ decaf_448_scalar_t out,
+ const decaf_448_scalar_t a
+) {
+ *out = *a;
+}
+
+/**
+ * @brief Set a scalar to an unsigned 64-bit integer.
+ * @param [in] a An integer.
+ * @param [out] out Will become equal to a.
+ */
+void decaf_448_scalar_set_unsigned (
+ decaf_448_scalar_t out,
+ uint64_t a
+) DECAF_API_VIS DECAF_NONNULL;
+
+/**
+ * @brief Encode a point as a sequence of bytes.
+ *
+ * @param [out] ser The byte representation of the point.
+ * @param [in] pt The point to encode.
+ */
+void decaf_448_point_encode (
+ uint8_t ser[DECAF_448_SER_BYTES],
+ const decaf_448_point_t pt
+) DECAF_API_VIS DECAF_NONNULL DECAF_NOINLINE;
+
+/**
+ * @brief Decode a point from a sequence of bytes.
+ *
+ * Every point has a unique encoding, so not every
+ * sequence of bytes is a valid encoding. If an invalid
+ * encoding is given, the output is undefined.
+ *
+ * @param [out] pt The decoded point.
+ * @param [in] ser The serialized version of the point.
+ * @param [in] allow_identity DECAF_TRUE if the identity is a legal input.
+ * @retval DECAF_SUCCESS The decoding succeeded.
+ * @retval DECAF_FAILURE The decoding didn't succeed, because
+ * ser does not represent a point.
+ */
+decaf_error_t decaf_448_point_decode (
+ decaf_448_point_t pt,
+ const uint8_t ser[DECAF_448_SER_BYTES],
+ decaf_bool_t allow_identity
+) DECAF_API_VIS DECAF_WARN_UNUSED DECAF_NONNULL DECAF_NOINLINE;
+
+/**
+ * @brief Copy a point. The input and output may alias,
+ * in which case this function does nothing.
+ *
+ * @param [out] a A copy of the point.
+ * @param [in] b Any point.
+ */
+static inline void DECAF_NONNULL decaf_448_point_copy (
+ decaf_448_point_t a,
+ const decaf_448_point_t b
+) {
+ *a=*b;
+}
+
+/**
+ * @brief Test whether two points are equal. If yes, return
+ * DECAF_TRUE, else return DECAF_FALSE.
+ *
+ * @param [in] a A point.
+ * @param [in] b Another point.
+ * @retval DECAF_TRUE The points are equal.
+ * @retval DECAF_FALSE The points are not equal.
+ */
+decaf_bool_t decaf_448_point_eq (
+ const decaf_448_point_t a,
+ const decaf_448_point_t b
+) DECAF_API_VIS DECAF_WARN_UNUSED DECAF_NONNULL DECAF_NOINLINE;
+
+/**
+ * @brief Add two points to produce a third point. The
+ * input points and output point can be pointers to the same
+ * memory.
+ *
+ * @param [out] sum The sum a+b.
+ * @param [in] a An addend.
+ * @param [in] b An addend.
+ */
+void decaf_448_point_add (
+ decaf_448_point_t sum,
+ const decaf_448_point_t a,
+ const decaf_448_point_t b
+) DECAF_API_VIS DECAF_NONNULL;
+
+/**
+ * @brief Double a point. Equivalent to
+ * decaf_448_point_add(two_a,a,a), but potentially faster.
+ *
+ * @param [out] two_a The sum a+a.
+ * @param [in] a A point.
+ */
+void decaf_448_point_double (
+ decaf_448_point_t two_a,
+ const decaf_448_point_t a
+) DECAF_API_VIS DECAF_NONNULL;
+
+/**
+ * @brief Subtract two points to produce a third point. The
+ * input points and output point can be pointers to the same
+ * memory.
+ *
+ * @param [out] diff The difference a-b.
+ * @param [in] a The minuend.
+ * @param [in] b The subtrahend.
+ */
+void decaf_448_point_sub (
+ decaf_448_point_t diff,
+ const decaf_448_point_t a,
+ const decaf_448_point_t b
+) DECAF_API_VIS DECAF_NONNULL;
+
+/**
+ * @brief Negate a point to produce another point. The input
+ * and output points can use the same memory.
+ *
+ * @param [out] nega The negated input point
+ * @param [in] a The input point.
+ */
+void decaf_448_point_negate (
+ decaf_448_point_t nega,
+ const decaf_448_point_t a
+) DECAF_API_VIS DECAF_NONNULL;
+
+/**
+ * @brief Multiply a base point by a scalar: scaled = scalar*base.
+ *
+ * @param [out] scaled The scaled point base*scalar
+ * @param [in] base The point to be scaled.
+ * @param [in] scalar The scalar to multiply by.
+ */
+void decaf_448_point_scalarmul (
+ decaf_448_point_t scaled,
+ const decaf_448_point_t base,
+ const decaf_448_scalar_t scalar
+) DECAF_API_VIS DECAF_NONNULL DECAF_NOINLINE;
+
+/**
+ * @brief Multiply a base point by a scalar: scaled = scalar*base.
+ * This function operates directly on serialized forms.
+ *
+ * @warning This function is experimental. It may not be supported
+ * long-term.
+ *
+ * @param [out] scaled The scaled point base*scalar
+ * @param [in] base The point to be scaled.
+ * @param [in] scalar The scalar to multiply by.
+ * @param [in] allow_identity Allow the input to be the identity.
+ * @param [in] short_circuit Allow a fast return if the input is illegal.
+ *
+ * @retval DECAF_SUCCESS The scalarmul succeeded.
+ * @retval DECAF_FAILURE The scalarmul didn't succeed, because
+ * base does not represent a point.
+ */
+decaf_error_t decaf_448_direct_scalarmul (
+ uint8_t scaled[DECAF_448_SER_BYTES],
+ const uint8_t base[DECAF_448_SER_BYTES],
+ const decaf_448_scalar_t scalar,
+ decaf_bool_t allow_identity,
+ decaf_bool_t short_circuit
+) DECAF_API_VIS DECAF_NONNULL DECAF_WARN_UNUSED DECAF_NOINLINE;
+
+/**
+ * @brief RFC 7748 Diffie-Hellman scalarmul. This function uses a different
+ * (non-Decaf) encoding.
+ *
+ * @param [out] scaled The scaled point base*scalar
+ * @param [in] base The point to be scaled.
+ * @param [in] scalar The scalar to multiply by.
+ *
+ * @retval DECAF_SUCCESS The scalarmul succeeded.
+ * @retval DECAF_FAILURE The scalarmul didn't succeed, because the base
+ * point is in a small subgroup.
+ */
+decaf_error_t decaf_x448 (
+ uint8_t out[DECAF_X448_PUBLIC_BYTES],
+ const uint8_t base[DECAF_X448_PUBLIC_BYTES],
+ const uint8_t scalar[DECAF_X448_PRIVATE_BYTES]
+) DECAF_API_VIS DECAF_NONNULL DECAF_WARN_UNUSED DECAF_NOINLINE;
+
+/**
+ * @brief Multiply a point by DECAF_X448_ENCODE_RATIO,
+ * then encode it like RFC 7748.
+ *
+ * This function is mainly used internally, but is exported in case
+ * it will be useful.
+ *
+ * The ratio is necessary because the internal representation doesn't
+ * track the cofactor information, so on output we must clear the cofactor.
+ * This would multiply by the cofactor, but in fact internally libdecaf's
+ * points are always even, so it multiplies by half the cofactor instead.
+ *
+ * As it happens, this aligns with the base point definitions; that is,
+ * if you pass the Decaf/Ristretto base point to this function, the result
+ * will be DECAF_X448_ENCODE_RATIO times the X448
+ * base point.
+ *
+ * @param [out] out The scaled and encoded point.
+ * @param [in] p The point to be scaled and encoded.
+ */
+void decaf_448_point_mul_by_ratio_and_encode_like_x448 (
+ uint8_t out[DECAF_X448_PUBLIC_BYTES],
+ const decaf_448_point_t p
+) DECAF_API_VIS DECAF_NONNULL;
+
+/** The base point for X448 Diffie-Hellman */
+extern const uint8_t decaf_x448_base_point[DECAF_X448_PUBLIC_BYTES] DECAF_API_VIS;
+
+/**
+ * @brief RFC 7748 Diffie-Hellman base point scalarmul. This function uses
+ * a different (non-Decaf) encoding.
+ *
+ * @deprecated Renamed to decaf_x448_derive_public_key.
+ * I have no particular timeline for removing this name.
+ *
+ * @param [out] scaled The scaled point base*scalar
+ * @param [in] scalar The scalar to multiply by.
+ */
+void decaf_x448_generate_key (
+ uint8_t out[DECAF_X448_PUBLIC_BYTES],
+ const uint8_t scalar[DECAF_X448_PRIVATE_BYTES]
+) DECAF_API_VIS DECAF_NONNULL DECAF_NOINLINE DECAF_DEPRECATED("Renamed to decaf_x448_derive_public_key");
+
+/**
+ * @brief RFC 7748 Diffie-Hellman base point scalarmul. This function uses
+ * a different (non-Decaf) encoding.
+ *
+ * Does exactly the same thing as decaf_x448_generate_key,
+ * but has a better name.
+ *
+ * @param [out] scaled The scaled point base*scalar
+ * @param [in] scalar The scalar to multiply by.
+ */
+void decaf_x448_derive_public_key (
+ uint8_t out[DECAF_X448_PUBLIC_BYTES],
+ const uint8_t scalar[DECAF_X448_PRIVATE_BYTES]
+) DECAF_API_VIS DECAF_NONNULL DECAF_NOINLINE;
+
+/* FUTURE: uint8_t decaf_448_encode_like_curve448) */
+
+/**
+ * @brief Precompute a table for fast scalar multiplication.
+ * Some implementations do not include precomputed points; for
+ * those implementations, this implementation simply copies the
+ * point.
+ *
+ * @param [out] a A precomputed table of multiples of the point.
+ * @param [in] b Any point.
+ */
+void decaf_448_precompute (
+ decaf_448_precomputed_s *a,
+ const decaf_448_point_t b
+) DECAF_API_VIS DECAF_NONNULL DECAF_NOINLINE;
+
+/**
+ * @brief Multiply a precomputed base point by a scalar:
+ * scaled = scalar*base.
+ * Some implementations do not include precomputed points; for
+ * those implementations, this function is the same as
+ * decaf_448_point_scalarmul
+ *
+ * @param [out] scaled The scaled point base*scalar
+ * @param [in] base The point to be scaled.
+ * @param [in] scalar The scalar to multiply by.
+ */
+void decaf_448_precomputed_scalarmul (
+ decaf_448_point_t scaled,
+ const decaf_448_precomputed_s *base,
+ const decaf_448_scalar_t scalar
+) DECAF_API_VIS DECAF_NONNULL DECAF_NOINLINE;
+
+/**
+ * @brief Multiply two base points by two scalars:
+ * scaled = scalar1*base1 + scalar2*base2.
+ *
+ * Equivalent to two calls to decaf_448_point_scalarmul, but may be
+ * faster.
+ *
+ * @param [out] combo The linear combination scalar1*base1 + scalar2*base2.
+ * @param [in] base1 A first point to be scaled.
+ * @param [in] scalar1 A first scalar to multiply by.
+ * @param [in] base2 A second point to be scaled.
+ * @param [in] scalar2 A second scalar to multiply by.
+ */
+void decaf_448_point_double_scalarmul (
+ decaf_448_point_t combo,
+ const decaf_448_point_t base1,
+ const decaf_448_scalar_t scalar1,
+ const decaf_448_point_t base2,
+ const decaf_448_scalar_t scalar2
+) DECAF_API_VIS DECAF_NONNULL DECAF_NOINLINE;
+
+/**
+ * Multiply one base point by two scalars:
+ *
+ * a1 = scalar1 * base
+ * a2 = scalar2 * base
+ *
+ * Equivalent to two calls to decaf_448_point_scalarmul, but may be
+ * faster.
+ *
+ * @param [out] a1 The first multiple. It may be the same as the input point.
+ * @param [out] a2 The second multiple. It may be the same as the input point.
+ * @param [in] base1 A point to be scaled.
+ * @param [in] scalar1 A first scalar to multiply by.
+ * @param [in] scalar2 A second scalar to multiply by.
+ */
+void decaf_448_point_dual_scalarmul (
+ decaf_448_point_t a1,
+ decaf_448_point_t a2,
+ const decaf_448_point_t base1,
+ const decaf_448_scalar_t scalar1,
+ const decaf_448_scalar_t scalar2
+) DECAF_API_VIS DECAF_NONNULL DECAF_NOINLINE;
+
+/**
+ * @brief Multiply two base points by two scalars:
+ * scaled = scalar1*decaf_448_point_base + scalar2*base2.
+ *
+ * Otherwise equivalent to decaf_448_point_double_scalarmul, but may be
+ * faster at the expense of being variable time.
+ *
+ * @param [out] combo The linear combination scalar1*base + scalar2*base2.
+ * @param [in] scalar1 A first scalar to multiply by.
+ * @param [in] base2 A second point to be scaled.
+ * @param [in] scalar2 A second scalar to multiply by.
+ *
+ * @warning: This function takes variable time, and may leak the scalars
+ * used. It is designed for signature verification.
+ */
+void decaf_448_base_double_scalarmul_non_secret (
+ decaf_448_point_t combo,
+ const decaf_448_scalar_t scalar1,
+ const decaf_448_point_t base2,
+ const decaf_448_scalar_t scalar2
+) DECAF_API_VIS DECAF_NONNULL DECAF_NOINLINE;
+
+/**
+ * @brief Constant-time decision between two points. If pick_b
+ * is zero, out = a; else out = b.
+ *
+ * @param [out] out The output. It may be the same as either input.
+ * @param [in] a Any point.
+ * @param [in] b Any point.
+ * @param [in] pick_b If nonzero, choose point b.
+ */
+void decaf_448_point_cond_sel (
+ decaf_448_point_t out,
+ const decaf_448_point_t a,
+ const decaf_448_point_t b,
+ decaf_word_t pick_b
+) DECAF_API_VIS DECAF_NONNULL DECAF_NOINLINE;
+
+/**
+ * @brief Constant-time decision between two scalars. If pick_b
+ * is zero, out = a; else out = b.
+ *
+ * @param [out] out The output. It may be the same as either input.
+ * @param [in] a Any scalar.
+ * @param [in] b Any scalar.
+ * @param [in] pick_b If nonzero, choose scalar b.
+ */
+void decaf_448_scalar_cond_sel (
+ decaf_448_scalar_t out,
+ const decaf_448_scalar_t a,
+ const decaf_448_scalar_t b,
+ decaf_word_t pick_b
+) DECAF_API_VIS DECAF_NONNULL DECAF_NOINLINE;
+
+/**
+ * @brief Test that a point is valid, for debugging purposes.
+ *
+ * @param [in] to_test The point to test.
+ * @retval DECAF_TRUE The point is valid.
+ * @retval DECAF_FALSE The point is invalid.
+ */
+decaf_bool_t decaf_448_point_valid (
+ const decaf_448_point_t to_test
+) DECAF_API_VIS DECAF_WARN_UNUSED DECAF_NONNULL DECAF_NOINLINE;
+
+/**
+ * @brief Torque a point, for debugging purposes. The output
+ * will be equal to the input.
+ *
+ * @param [out] q The point to torque.
+ * @param [in] p The point to torque.
+ */
+void decaf_448_point_debugging_torque (
+ decaf_448_point_t q,
+ const decaf_448_point_t p
+) DECAF_API_VIS DECAF_NONNULL DECAF_NOINLINE;
+
+/**
+ * @brief Projectively scale a point, for debugging purposes.
+ * The output will be equal to the input, and will be valid
+ * even if the factor is zero.
+ *
+ * @param [out] q The point to scale.
+ * @param [in] p The point to scale.
+ * @param [in] factor Serialized GF factor to scale.
+ */
+void decaf_448_point_debugging_pscale (
+ decaf_448_point_t q,
+ const decaf_448_point_t p,
+ const unsigned char factor[DECAF_448_SER_BYTES]
+) DECAF_API_VIS DECAF_NONNULL DECAF_NOINLINE;
+
+/**
+ * @brief Almost-Elligator-like hash to curve.
+ *
+ * Call this function with the output of a hash to make a hash to the curve.
+ *
+ * This function runs Elligator2 on the decaf_448 Jacobi quartic model. It then
+ * uses the isogeny to put the result in twisted Edwards form. As a result,
+ * it is safe (cannot produce points of order 4), and would be compatible with
+ * hypothetical other implementations of Decaf using a Montgomery or untwisted
+ * Edwards model.
+ *
+ * Unlike Elligator, this function may be up to 4:1 on [0,(p-1)/2]:
+ * A factor of 2 due to the isogeny.
+ * A factor of 2 because we quotient out the 2-torsion.
+ *
+ * This makes it about 8:1 overall, or 16:1 overall on curves with cofactor 8.
+ *
+ * Negating the input (mod q) results in the same point. Inverting the input
+ * (mod q) results in the negative point. This is the same as Elligator.
+ *
+ * This function isn't quite indifferentiable from a random oracle.
+ * However, it is suitable for many protocols, including SPEKE and SPAKE2 EE.
+ * Furthermore, calling it twice with independent seeds and adding the results
+ * is indifferentiable from a random oracle.
+ *
+ * @param [in] hashed_data Output of some hash function.
+ * @param [out] pt The data hashed to the curve.
+ */
+void
+decaf_448_point_from_hash_nonuniform (
+ decaf_448_point_t pt,
+ const unsigned char hashed_data[DECAF_448_HASH_BYTES]
+) DECAF_API_VIS DECAF_NONNULL DECAF_NOINLINE;
+
+/**
+ * @brief Indifferentiable hash function encoding to curve.
+ *
+ * Equivalent to calling decaf_448_point_from_hash_nonuniform twice and adding.
+ *
+ * @param [in] hashed_data Output of some hash function.
+ * @param [out] pt The data hashed to the curve.
+ */
+void decaf_448_point_from_hash_uniform (
+ decaf_448_point_t pt,
+ const unsigned char hashed_data[2*DECAF_448_HASH_BYTES]
+) DECAF_API_VIS DECAF_NONNULL DECAF_NOINLINE;
+
+/**
+ * @brief Inverse of elligator-like hash to curve.
+ *
+ * This function writes to the buffer, to make it so that
+ * decaf_448_point_from_hash_nonuniform(buffer) = pt if
+ * possible. Since there may be multiple preimages, the
+ * "which" parameter chooses between them. To ensure uniform
+ * inverse sampling, this function succeeds or fails
+ * independently for different "which" values.
+ *
+ * This function isn't guaranteed to find every possible
+ * preimage, but it finds all except a small finite number.
+ * In particular, when the number of bits in the modulus isn't
+ * a multiple of 8 (i.e. for curve25519), it sets the high bits
+ * independently, which enables the generated data to be uniform.
+ * But it doesn't add p, so you'll never get exactly p from this
+ * function. This might change in the future, especially if
+ * we ever support eg Brainpool curves, where this could cause
+ * real nonuniformity.
+ *
+ * @param [out] recovered_hash Encoded data.
+ * @param [in] pt The point to encode.
+ * @param [in] which A value determining which inverse point
+ * to return.
+ *
+ * @retval DECAF_SUCCESS The inverse succeeded.
+ * @retval DECAF_FAILURE The inverse failed.
+ */
+decaf_error_t
+decaf_448_invert_elligator_nonuniform (
+ unsigned char recovered_hash[DECAF_448_HASH_BYTES],
+ const decaf_448_point_t pt,
+ uint32_t which
+) DECAF_API_VIS DECAF_NONNULL DECAF_NOINLINE DECAF_WARN_UNUSED;
+
+/**
+ * @brief Inverse of elligator-like hash to curve.
+ *
+ * This function writes to the buffer, to make it so that
+ * decaf_448_point_from_hash_uniform(buffer) = pt if
+ * possible. Since there may be multiple preimages, the
+ * "which" parameter chooses between them. To ensure uniform
+ * inverse sampling, this function succeeds or fails
+ * independently for different "which" values.
+ *
+ * @param [out] recovered_hash Encoded data.
+ * @param [in] pt The point to encode.
+ * @param [in] which A value determining which inverse point
+ * to return.
+ *
+ * @retval DECAF_SUCCESS The inverse succeeded.
+ * @retval DECAF_FAILURE The inverse failed.
+ */
+decaf_error_t
+decaf_448_invert_elligator_uniform (
+ unsigned char recovered_hash[2*DECAF_448_HASH_BYTES],
+ const decaf_448_point_t pt,
+ uint32_t which
+) DECAF_API_VIS DECAF_NONNULL DECAF_NOINLINE DECAF_WARN_UNUSED;
+
+/**
+ * @brief Overwrite scalar with zeros.
+ */
+void decaf_448_scalar_destroy (
+ decaf_448_scalar_t scalar
+) DECAF_NONNULL DECAF_API_VIS;
+
+/**
+ * @brief Overwrite point with zeros.
+ */
+void decaf_448_point_destroy (
+ decaf_448_point_t point
+) DECAF_NONNULL DECAF_API_VIS;
+
+/**
+ * @brief Overwrite precomputed table with zeros.
+ */
+void decaf_448_precomputed_destroy (
+ decaf_448_precomputed_s *pre
+) DECAF_NONNULL DECAF_API_VIS;
+
+#ifdef __cplusplus
+} /* extern "C" */
+#endif
+
+#endif /* __DECAF_POINT_448_H__ */
--- /dev/null
+/**
+ * @file decaf/shake.h
+ * @copyright Public domain.
+ * @author Mike Hamburg
+ * @brief SHA2-512
+ */
+
+#ifndef __DECAF_SHA512_H__
+#define __DECAF_SHA512_H__
+
+#include <stdint.h>
+#include <sys/types.h>
+#include <stdlib.h> /* for NULL */
+
+#include <decaf/common.h>
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+
+typedef struct decaf_sha512_ctx_s {
+ uint64_t state[8];
+ uint8_t block[128];
+ uint64_t bytes_processed;
+} decaf_sha512_ctx_s, decaf_sha512_ctx_t[1];
+
+void decaf_sha512_init(decaf_sha512_ctx_t ctx) DECAF_NONNULL DECAF_API_VIS;
+void decaf_sha512_update(decaf_sha512_ctx_t ctx, const uint8_t *message, size_t length) DECAF_NONNULL DECAF_API_VIS;
+void decaf_sha512_final(decaf_sha512_ctx_t ctx, uint8_t *out, size_t length) DECAF_NONNULL DECAF_API_VIS;
+
+static inline void decaf_sha512_destroy(decaf_sha512_ctx_t ctx) {
+ decaf_bzero(ctx,sizeof(*ctx));
+}
+
+static inline void decaf_sha512_hash(
+ uint8_t *output,
+ size_t output_len,
+ const uint8_t *message,
+ size_t message_len
+) {
+ decaf_sha512_ctx_t ctx;
+ decaf_sha512_init(ctx);
+ decaf_sha512_update(ctx,message,message_len);
+ decaf_sha512_final(ctx,output,output_len);
+ decaf_sha512_destroy(ctx);
+}
+
+#ifdef __cplusplus
+} /* extern "C" */
+#endif
+
+#endif /* __DECAF_SHA512_H__ */
--- /dev/null
+/**
+ * @file decaf/shake.h
+ * @copyright
+ * Based on CC0 code by David Leon Gil, 2015 \n
+ * Copyright (c) 2015 Cryptography Research, Inc. \n
+ * Released under the MIT License. See LICENSE.txt for license information.
+ * @author Mike Hamburg
+ * @brief SHA-3-n and DECAF_SHAKE-n instances.
+ */
+
+#ifndef __DECAF_SHAKE_H__
+#define __DECAF_SHAKE_H__
+
+#include <stdint.h>
+#include <sys/types.h>
+#include <stdlib.h> /* for NULL */
+
+#include <decaf/common.h>
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+#ifndef INTERNAL_SPONGE_STRUCT
+ /** Sponge container object for the various primitives. */
+ typedef struct decaf_keccak_sponge_s {
+ /** @cond internal */
+ uint64_t opaque[26];
+ /** @endcond */
+ } decaf_keccak_sponge_s;
+
+ /** Convenience GMP-style one-element array version */
+ typedef struct decaf_keccak_sponge_s decaf_keccak_sponge_t[1];
+
+ /** Parameters for sponge construction, distinguishing DECAF_SHA3 and
+ * DECAF_SHAKE instances.
+ */
+ struct decaf_kparams_s;
+#endif
+
+/**
+ * @brief Initialize a sponge context object.
+ * @param [out] sponge The object to initialize.
+ * @param [in] params The sponge's parameter description.
+ */
+void decaf_sha3_init (
+ decaf_keccak_sponge_t sponge,
+ const struct decaf_kparams_s *params
+) DECAF_API_VIS;
+
+/**
+ * @brief Absorb data into a DECAF_SHA3 or DECAF_SHAKE hash context.
+ * @param [inout] sponge The context.
+ * @param [in] in The input data.
+ * @param [in] len The input data's length in bytes.
+ * @return DECAF_FAILURE if the sponge has already been used for output.
+ * @return DECAF_SUCCESS otherwise.
+ */
+decaf_error_t decaf_sha3_update (
+ struct decaf_keccak_sponge_s * __restrict__ sponge,
+ const uint8_t *in,
+ size_t len
+) DECAF_API_VIS;
+
+/**
+ * @brief Squeeze output data from a DECAF_SHA3 or DECAF_SHAKE hash context.
+ * This does not destroy or re-initialize the hash context, and
+ * decaf_sha3 output can be called more times.
+ *
+ * @param [inout] sponge The context.
+ * @param [out] out The output data.
+ * @param [in] len The requested output data length in bytes.
+ * @return DECAF_FAILURE if the sponge has exhausted its output capacity.
+ * @return DECAF_SUCCESS otherwise.
+ */
+decaf_error_t decaf_sha3_output (
+ decaf_keccak_sponge_t sponge,
+ uint8_t * __restrict__ out,
+ size_t len
+) DECAF_API_VIS;
+
+/**
+ * @brief Squeeze output data from a DECAF_SHA3 or DECAF_SHAKE hash context.
+ * This re-initializes the context to its starting parameters.
+ *
+ * @param [inout] sponge The context.
+ * @param [out] out The output data.
+ * @param [in] len The requested output data length in bytes.
+ */
+decaf_error_t decaf_sha3_final (
+ decaf_keccak_sponge_t sponge,
+ uint8_t * __restrict__ out,
+ size_t len
+) DECAF_API_VIS;
+
+/**
+ * @brief Reset the sponge to the empty string.
+ *
+ * @param [inout] sponge The context.
+ */
+void decaf_sha3_reset (
+ decaf_keccak_sponge_t sponge
+) DECAF_API_VIS;
+
+/**
+ * @brief Return the default output length of the sponge construction,
+ * for the purpose of C++ default operators.
+ *
+ * Returns n/8 for DECAF_SHA3-n and 2n/8 for DECAF_SHAKE-n.
+ */
+size_t decaf_sha3_default_output_bytes (
+ const decaf_keccak_sponge_t sponge /**< [inout] The context. */
+) DECAF_API_VIS;
+
+/**
+ * @brief Return the default output length of the sponge construction,
+ * for the purpose of C++ default operators.
+ *
+ * Returns n/8 for DECAF_SHA3-n and SIZE_MAX for DECAF_SHAKE-n.
+ */
+size_t decaf_sha3_max_output_bytes (
+ const decaf_keccak_sponge_t sponge /**< [inout] The context. */
+) DECAF_API_VIS;
+
+/**
+ * @brief Destroy a DECAF_SHA3 or DECAF_SHAKE sponge context by overwriting it with 0.
+ * @param [out] sponge The context.
+ */
+void decaf_sha3_destroy (
+ decaf_keccak_sponge_t sponge
+) DECAF_API_VIS;
+
+/**
+ * @brief Hash (in) to (out)
+ * @param [in] in The input data.
+ * @param [in] inlen The length of the input data.
+ * @param [out] out A buffer for the output data.
+ * @param [in] outlen The length of the output data.
+ * @param [in] params The parameters of the sponge hash.
+ */
+decaf_error_t decaf_sha3_hash (
+ uint8_t *out,
+ size_t outlen,
+ const uint8_t *in,
+ size_t inlen,
+ const struct decaf_kparams_s *params
+) DECAF_API_VIS;
+
+/* FUTURE: expand/doxygenate individual DECAF_SHAKE/DECAF_SHA3 instances? */
+
+/** @cond internal */
+#define DECAF_DEC_SHAKE(n) \
+ extern const struct decaf_kparams_s DECAF_SHAKE##n##_params_s DECAF_API_VIS; \
+ typedef struct decaf_shake##n##_ctx_s { decaf_keccak_sponge_t s; } decaf_shake##n##_ctx_t[1]; \
+ static inline void DECAF_NONNULL decaf_shake##n##_init(decaf_shake##n##_ctx_t sponge) { \
+ decaf_sha3_init(sponge->s, &DECAF_SHAKE##n##_params_s); \
+ } \
+ static inline void DECAF_NONNULL decaf_shake##n##_gen_init(decaf_keccak_sponge_t sponge) { \
+ decaf_sha3_init(sponge, &DECAF_SHAKE##n##_params_s); \
+ } \
+ static inline decaf_error_t DECAF_NONNULL decaf_shake##n##_update(decaf_shake##n##_ctx_t sponge, const uint8_t *in, size_t inlen ) { \
+ return decaf_sha3_update(sponge->s, in, inlen); \
+ } \
+ static inline void DECAF_NONNULL decaf_shake##n##_final(decaf_shake##n##_ctx_t sponge, uint8_t *out, size_t outlen ) { \
+ decaf_sha3_output(sponge->s, out, outlen); \
+ decaf_sha3_init(sponge->s, &DECAF_SHAKE##n##_params_s); \
+ } \
+ static inline void DECAF_NONNULL decaf_shake##n##_output(decaf_shake##n##_ctx_t sponge, uint8_t *out, size_t outlen ) { \
+ decaf_sha3_output(sponge->s, out, outlen); \
+ } \
+ static inline void DECAF_NONNULL decaf_shake##n##_hash(uint8_t *out, size_t outlen, const uint8_t *in, size_t inlen) { \
+ decaf_sha3_hash(out,outlen,in,inlen,&DECAF_SHAKE##n##_params_s); \
+ } \
+ static inline void DECAF_NONNULL decaf_shake##n##_destroy( decaf_shake##n##_ctx_t sponge ) { \
+ decaf_sha3_destroy(sponge->s); \
+ }
+
+#define DECAF_DEC_SHA3(n) \
+ extern const struct decaf_kparams_s DECAF_SHA3_##n##_params_s DECAF_API_VIS; \
+ typedef struct decaf_sha3_##n##_ctx_s { decaf_keccak_sponge_t s; } decaf_sha3_##n##_ctx_t[1]; \
+ static inline void DECAF_NONNULL decaf_sha3_##n##_init(decaf_sha3_##n##_ctx_t sponge) { \
+ decaf_sha3_init(sponge->s, &DECAF_SHA3_##n##_params_s); \
+ } \
+ static inline void DECAF_NONNULL decaf_sha3_##n##_gen_init(decaf_keccak_sponge_t sponge) { \
+ decaf_sha3_init(sponge, &DECAF_SHA3_##n##_params_s); \
+ } \
+ static inline decaf_error_t DECAF_NONNULL decaf_sha3_##n##_update(decaf_sha3_##n##_ctx_t sponge, const uint8_t *in, size_t inlen ) { \
+ return decaf_sha3_update(sponge->s, in, inlen); \
+ } \
+ static inline decaf_error_t DECAF_NONNULL decaf_sha3_##n##_final(decaf_sha3_##n##_ctx_t sponge, uint8_t *out, size_t outlen ) { \
+ decaf_error_t ret = decaf_sha3_output(sponge->s, out, outlen); \
+ decaf_sha3_init(sponge->s, &DECAF_SHA3_##n##_params_s); \
+ return ret; \
+ } \
+ static inline decaf_error_t DECAF_NONNULL decaf_sha3_##n##_output(decaf_sha3_##n##_ctx_t sponge, uint8_t *out, size_t outlen ) { \
+ return decaf_sha3_output(sponge->s, out, outlen); \
+ } \
+ static inline decaf_error_t DECAF_NONNULL decaf_sha3_##n##_hash(uint8_t *out, size_t outlen, const uint8_t *in, size_t inlen) { \
+ return decaf_sha3_hash(out,outlen,in,inlen,&DECAF_SHA3_##n##_params_s); \
+ } \
+ static inline void DECAF_NONNULL decaf_sha3_##n##_destroy(decaf_sha3_##n##_ctx_t sponge) { \
+ decaf_sha3_destroy(sponge->s); \
+ }
+/** @endcond */
+
+DECAF_DEC_SHAKE(128)
+DECAF_DEC_SHAKE(256)
+DECAF_DEC_SHA3(224)
+DECAF_DEC_SHA3(256)
+DECAF_DEC_SHA3(384)
+DECAF_DEC_SHA3(512)
+#undef DECAF_DEC_SHAKE
+#undef DECAF_DEC_SHA3
+
+#ifdef __cplusplus
+} /* extern "C" */
+#endif
+
+#endif /* __DECAF_SHAKE_H__ */
--- /dev/null
+/* Copyright (c) 2016 Cryptography Research, Inc.
+ * Released under the MIT License. See LICENSE.txt for license information.
+ */
+
+#ifndef __ARCH_ARCH_32_ARCH_INTRINSICS_H__
+#define __ARCH_ARCH_32_ARCH_INTRINSICS_H__
+
+#define ARCH_WORD_BITS 32
+
+static __inline__ __attribute((always_inline,unused))
+uint32_t word_is_zero(uint32_t a) {
+ /* let's hope the compiler isn't clever enough to optimize this. */
+ return (((uint64_t)a)-1)>>32;
+}
+
+static __inline__ __attribute((always_inline,unused))
+uint64_t widemul(uint32_t a, uint32_t b) {
+ return ((uint64_t)a) * b;
+}
+
+#endif /* __ARCH_ARM_32_ARCH_INTRINSICS_H__ */
+
--- /dev/null
+/* Copyright (c) 2016 Cryptography Research, Inc.
+ * Released under the MIT License. See LICENSE.txt for license information.
+ */
+
+#ifndef __ARCH_ARM_32_ARCH_INTRINSICS_H__
+#define __ARCH_ARM_32_ARCH_INTRINSICS_H__
+
+#define ARCH_WORD_BITS 32
+
+static __inline__ __attribute((always_inline,unused))
+uint32_t word_is_zero(uint32_t a) {
+ uint32_t ret;
+ asm("subs %0, %1, #1;\n\tsbc %0, %0, %0" : "=r"(ret) : "r"(a) : "cc");
+ return ret;
+}
+
+static __inline__ __attribute((always_inline,unused))
+uint64_t widemul(uint32_t a, uint32_t b) {
+ /* Could be UMULL, but it's hard to express to CC that the registers must be different */
+ return ((uint64_t)a) * b;
+}
+
+#endif /* __ARCH_ARM_32_ARCH_INTRINSICS_H__ */
+
--- /dev/null
+/* Copyright (c) 2016 Cryptography Research, Inc.
+ * Released under the MIT License. See LICENSE.txt for license information.
+ */
+
+#ifndef __ARCH_NEON_ARCH_INTRINSICS_H__
+#define __ARCH_NEON_ARCH_INTRINSICS_H__
+
+#define ARCH_WORD_BITS 32
+
+static __inline__ __attribute((always_inline,unused))
+uint32_t word_is_zero(uint32_t a) {
+ uint32_t ret;
+ __asm__("subs %0, %1, #1;\n\tsbc %0, %0, %0" : "=r"(ret) : "r"(a) : "cc");
+ return ret;
+}
+
+static __inline__ __attribute((always_inline,unused))
+uint64_t widemul(uint32_t a, uint32_t b) {
+ /* Could be UMULL, but it's hard to express to CC that the registers must be different */
+ return ((uint64_t)a) * b;
+}
+
+#endif /* __ARCH_NEON_ARCH_INTRINSICS_H__ */
+
--- /dev/null
+/* Copyright (c) 2016 Cryptography Research, Inc.
+ * Released under the MIT License. See LICENSE.txt for license information.
+ */
+
+#ifndef __ARCH_REF64_ARCH_INTRINSICS_H__
+#define __ARCH_REF64_ARCH_INTRINSICS_H__
+
+#define ARCH_WORD_BITS 64
+
+static __inline__ __attribute((always_inline,unused))
+uint64_t word_is_zero(uint64_t a) {
+ /* let's hope the compiler isn't clever enough to optimize this. */
+ return (((__uint128_t)a)-1)>>64;
+}
+
+static __inline__ __attribute((always_inline,unused))
+__uint128_t widemul(uint64_t a, uint64_t b) {
+ return ((__uint128_t)a) * b;
+}
+
+#endif /* ARCH_REF64_ARCH_INTRINSICS_H__ */
+
--- /dev/null
+/* Copyright (c) 2014-2016 Cryptography Research, Inc.
+ * Released under the MIT License. See LICENSE.txt for license information.
+ */
+
+#ifndef __ARCH_X86_64_ARCH_INTRINSICS_H__
+#define __ARCH_X86_64_ARCH_INTRINSICS_H__
+
+#define ARCH_WORD_BITS 64
+
+#include <stdint.h>
+
+/* FUTURE: autogenerate */
+static __inline__ __uint128_t widemul(const uint64_t *a, const uint64_t *b) {
+ uint64_t c,d;
+ #ifndef __BMI2__
+ __asm__ volatile
+ ("movq %[a], %%rax;"
+ "mulq %[b];"
+ : [c]"=&a"(c), [d]"=d"(d)
+ : [b]"m"(*b), [a]"m"(*a)
+ : "cc");
+ #else
+ __asm__ volatile
+ ("movq %[a], %%rdx;"
+ "mulx %[b], %[c], %[d];"
+ : [c]"=r"(c), [d]"=r"(d)
+ : [b]"m"(*b), [a]"m"(*a)
+ : "rdx");
+ #endif
+ return (((__uint128_t)(d))<<64) | c;
+}
+
+static __inline__ __uint128_t widemul_rm(uint64_t a, const uint64_t *b) {
+ uint64_t c,d;
+ #ifndef __BMI2__
+ __asm__ volatile
+ ("movq %[a], %%rax;"
+ "mulq %[b];"
+ : [c]"=&a"(c), [d]"=d"(d)
+ : [b]"m"(*b), [a]"r"(a)
+ : "cc");
+ #else
+ __asm__ volatile
+ ("mulx %[b], %[c], %[d];"
+ : [c]"=r"(c), [d]"=r"(d)
+ : [b]"m"(*b), [a]"d"(a));
+ #endif
+ return (((__uint128_t)(d))<<64) | c;
+}
+
+static __inline__ __uint128_t widemul_rr(uint64_t a, uint64_t b) {
+ uint64_t c,d;
+ #ifndef __BMI2__
+ __asm__ volatile
+ ("mulq %[b];"
+ : [c]"=a"(c), [d]"=d"(d)
+ : [b]"r"(b), "a"(a)
+ : "cc");
+ #else
+ __asm__ volatile
+ ("mulx %[b], %[c], %[d];"
+ : [c]"=r"(c), [d]"=r"(d)
+ : [b]"r"(b), [a]"d"(a));
+ #endif
+ return (((__uint128_t)(d))<<64) | c;
+}
+
+static __inline__ __uint128_t widemul2(const uint64_t *a, const uint64_t *b) {
+ uint64_t c,d;
+ #ifndef __BMI2__
+ __asm__ volatile
+ ("movq %[a], %%rax; "
+ "addq %%rax, %%rax; "
+ "mulq %[b];"
+ : [c]"=&a"(c), [d]"=d"(d)
+ : [b]"m"(*b), [a]"m"(*a)
+ : "cc");
+ #else
+ __asm__ volatile
+ ("movq %[a], %%rdx;"
+ "leaq (,%%rdx,2), %%rdx;"
+ "mulx %[b], %[c], %[d];"
+ : [c]"=r"(c), [d]"=r"(d)
+ : [b]"m"(*b), [a]"m"(*a)
+ : "rdx");
+ #endif
+ return (((__uint128_t)(d))<<64) | c;
+}
+
+static __inline__ void mac(__uint128_t *acc, const uint64_t *a, const uint64_t *b) {
+ uint64_t lo = *acc, hi = *acc>>64;
+
+ #ifdef __BMI2__
+ uint64_t c,d;
+ __asm__ volatile
+ ("movq %[a], %%rdx; "
+ "mulx %[b], %[c], %[d]; "
+ "addq %[c], %[lo]; "
+ "adcq %[d], %[hi]; "
+ : [c]"=&r"(c), [d]"=&r"(d), [lo]"+r"(lo), [hi]"+r"(hi)
+ : [b]"m"(*b), [a]"m"(*a)
+ : "rdx", "cc");
+ #else
+ __asm__ volatile
+ ("movq %[a], %%rax; "
+ "mulq %[b]; "
+ "addq %%rax, %[lo]; "
+ "adcq %%rdx, %[hi]; "
+ : [lo]"+r"(lo), [hi]"+r"(hi)
+ : [b]"m"(*b), [a]"m"(*a)
+ : "rax", "rdx", "cc");
+ #endif
+
+ *acc = (((__uint128_t)(hi))<<64) | lo;
+}
+
+static __inline__ void macac(__uint128_t *acc, __uint128_t *acc2, const uint64_t *a, const uint64_t *b) {
+ uint64_t lo = *acc, hi = *acc>>64;
+ uint64_t lo2 = *acc2, hi2 = *acc2>>64;
+
+ #ifdef __BMI2__
+ uint64_t c,d;
+ __asm__ volatile
+ ("movq %[a], %%rdx; "
+ "mulx %[b], %[c], %[d]; "
+ "addq %[c], %[lo]; "
+ "adcq %[d], %[hi]; "
+ "addq %[c], %[lo2]; "
+ "adcq %[d], %[hi2]; "
+ : [c]"=r"(c), [d]"=r"(d), [lo]"+r"(lo), [hi]"+r"(hi), [lo2]"+r"(lo2), [hi2]"+r"(hi2)
+ : [b]"m"(*b), [a]"m"(*a)
+ : "rdx", "cc");
+ #else
+ __asm__ volatile
+ ("movq %[a], %%rax; "
+ "mulq %[b]; "
+ "addq %%rax, %[lo]; "
+ "adcq %%rdx, %[hi]; "
+ "addq %%rax, %[lo2]; "
+ "adcq %%rdx, %[hi2]; "
+ : [lo]"+r"(lo), [hi]"+r"(hi), [lo2]"+r"(lo2), [hi2]"+r"(hi2)
+ : [b]"m"(*b), [a]"m"(*a)
+ : "rax", "rdx", "cc");
+ #endif
+
+ *acc = (((__uint128_t)(hi))<<64) | lo;
+ *acc2 = (((__uint128_t)(hi2))<<64) | lo2;
+}
+
+static __inline__ void mac_rm(__uint128_t *acc, uint64_t a, const uint64_t *b) {
+ uint64_t lo = *acc, hi = *acc>>64;
+
+ #ifdef __BMI2__
+ uint64_t c,d;
+ __asm__ volatile
+ ("mulx %[b], %[c], %[d]; "
+ "addq %[c], %[lo]; "
+ "adcq %[d], %[hi]; "
+ : [c]"=r"(c), [d]"=r"(d), [lo]"+r"(lo), [hi]"+r"(hi)
+ : [b]"m"(*b), [a]"d"(a)
+ : "cc");
+ #else
+ __asm__ volatile
+ ("movq %[a], %%rax; "
+ "mulq %[b]; "
+ "addq %%rax, %[lo]; "
+ "adcq %%rdx, %[hi]; "
+ : [lo]"+r"(lo), [hi]"+r"(hi)
+ : [b]"m"(*b), [a]"r"(a)
+ : "rax", "rdx", "cc");
+ #endif
+
+ *acc = (((__uint128_t)(hi))<<64) | lo;
+}
+
+static __inline__ void mac_rr(__uint128_t *acc, uint64_t a, const uint64_t b) {
+ uint64_t lo = *acc, hi = *acc>>64;
+
+ #ifdef __BMI2__
+ uint64_t c,d;
+ __asm__ volatile
+ ("mulx %[b], %[c], %[d]; "
+ "addq %[c], %[lo]; "
+ "adcq %[d], %[hi]; "
+ : [c]"=r"(c), [d]"=r"(d), [lo]"+r"(lo), [hi]"+r"(hi)
+ : [b]"r"(b), [a]"d"(a)
+ : "cc");
+ #else
+ __asm__ volatile
+ ("mulq %[b]; "
+ "addq %%rax, %[lo]; "
+ "adcq %%rdx, %[hi]; "
+ : [lo]"+r"(lo), [hi]"+r"(hi), "+a"(a)
+ : [b]"r"(b)
+ : "rdx", "cc");
+ #endif
+
+ *acc = (((__uint128_t)(hi))<<64) | lo;
+}
+
+static __inline__ void mac2(__uint128_t *acc, const uint64_t *a, const uint64_t *b) {
+ uint64_t lo = *acc, hi = *acc>>64;
+
+ #ifdef __BMI2__
+ uint64_t c,d;
+ __asm__ volatile
+ ("movq %[a], %%rdx; "
+ "addq %%rdx, %%rdx; "
+ "mulx %[b], %[c], %[d]; "
+ "addq %[c], %[lo]; "
+ "adcq %[d], %[hi]; "
+ : [c]"=r"(c), [d]"=r"(d), [lo]"+r"(lo), [hi]"+r"(hi)
+ : [b]"m"(*b), [a]"m"(*a)
+ : "rdx", "cc");
+ #else
+ __asm__ volatile
+ ("movq %[a], %%rax; "
+ "addq %%rax, %%rax; "
+ "mulq %[b]; "
+ "addq %%rax, %[lo]; "
+ "adcq %%rdx, %[hi]; "
+ : [lo]"+r"(lo), [hi]"+r"(hi)
+ : [b]"m"(*b), [a]"m"(*a)
+ : "rax", "rdx", "cc");
+ #endif
+
+ *acc = (((__uint128_t)(hi))<<64) | lo;
+}
+
+static __inline__ void msb(__uint128_t *acc, const uint64_t *a, const uint64_t *b) {
+ uint64_t lo = *acc, hi = *acc>>64;
+ #ifdef __BMI2__
+ uint64_t c,d;
+ __asm__ volatile
+ ("movq %[a], %%rdx; "
+ "mulx %[b], %[c], %[d]; "
+ "subq %[c], %[lo]; "
+ "sbbq %[d], %[hi]; "
+ : [c]"=r"(c), [d]"=r"(d), [lo]"+r"(lo), [hi]"+r"(hi)
+ : [b]"m"(*b), [a]"m"(*a)
+ : "rdx", "cc");
+ #else
+ __asm__ volatile
+ ("movq %[a], %%rax; "
+ "mulq %[b]; "
+ "subq %%rax, %[lo]; "
+ "sbbq %%rdx, %[hi]; "
+ : [lo]"+r"(lo), [hi]"+r"(hi)
+ : [b]"m"(*b), [a]"m"(*a)
+ : "rax", "rdx", "cc");
+ #endif
+ *acc = (((__uint128_t)(hi))<<64) | lo;
+}
+
+static __inline__ void msb2(__uint128_t *acc, const uint64_t *a, const uint64_t *b) {
+ uint64_t lo = *acc, hi = *acc>>64;
+ #ifdef __BMI2__
+ uint64_t c,d;
+ __asm__ volatile
+ ("movq %[a], %%rdx; "
+ "addq %%rdx, %%rdx; "
+ "mulx %[b], %[c], %[d]; "
+ "subq %[c], %[lo]; "
+ "sbbq %[d], %[hi]; "
+ : [c]"=r"(c), [d]"=r"(d), [lo]"+r"(lo), [hi]"+r"(hi)
+ : [b]"m"(*b), [a]"m"(*a)
+ : "rdx", "cc");
+ #else
+ __asm__ volatile
+ ("movq %[a], %%rax; "
+ "addq %%rax, %%rax; "
+ "mulq %[b]; "
+ "subq %%rax, %[lo]; "
+ "sbbq %%rdx, %[hi]; "
+ : [lo]"+r"(lo), [hi]"+r"(hi)
+ : [b]"m"(*b), [a]"m"(*a)
+ : "rax", "rdx", "cc");
+ #endif
+ *acc = (((__uint128_t)(hi))<<64) | lo;
+
+}
+
+static __inline__ void mrs(__uint128_t *acc, const uint64_t *a, const uint64_t *b) {
+ uint64_t c,d, lo = *acc, hi = *acc>>64;
+ __asm__ volatile
+ ("movq %[a], %%rdx; "
+ "mulx %[b], %[c], %[d]; "
+ "subq %[lo], %[c]; "
+ "sbbq %[hi], %[d]; "
+ : [c]"=r"(c), [d]"=r"(d), [lo]"+r"(lo), [hi]"+r"(hi)
+ : [b]"m"(*b), [a]"m"(*a)
+ : "rdx", "cc");
+ *acc = (((__uint128_t)(d))<<64) | c;
+}
+
+static __inline__ uint64_t word_is_zero(uint64_t x) {
+ __asm__ volatile("neg %0; sbb %0, %0;" : "+r"(x));
+ return ~x;
+}
+
+static inline uint64_t shrld(__uint128_t x, int n) {
+ return x>>n;
+}
+
+#endif /* __ARCH_X86_64_ARCH_INTRINSICS_H__ */
--- /dev/null
+/**
+ * @file constant_time.h
+ * @copyright
+ * Copyright (c) 2014 Cryptography Research, Inc. \n
+ * Released under the MIT License. See LICENSE.txt for license information.
+ * @author Mike Hamburg
+ *
+ * @brief Constant-time routines.
+ */
+
+#ifndef __CONSTANT_TIME_H__
+#define __CONSTANT_TIME_H__ 1
+
+#include "word.h"
+#include <string.h>
+
+/*
+ * Constant-time operations on hopefully-compile-time-sized memory
+ * regions. Needed for flexibility / demagication: not all fields
+ * have sizes which are multiples of the vector width, necessitating
+ * a change from the Ed448 versions.
+ *
+ * These routines would be much simpler to define at the byte level,
+ * but if not vectorized they would be a significant fraction of the
+ * runtime. Eg on NEON-less ARM, constant_time_lookup is like 15% of
+ * signing time, vs 6% on Haswell with its fancy AVX2 vectors.
+ *
+ * If the compiler could do a good job of autovectorizing the code,
+ * we could just leave it with the byte definition. But that's unlikely
+ * on most deployed compilers, especially if you consider that pcmpeq[size]
+ * is much faster than moving a scalar to the vector unit (which is what
+ * a naive autovectorizer will do with constant_time_lookup on Intel).
+ *
+ * Instead, we're putting our trust in the loop unroller and unswitcher.
+ */
+
+
+/**
+ * Unaligned big (vector?) register.
+ */
+typedef struct {
+ big_register_t unaligned;
+} __attribute__((packed)) unaligned_br_t;
+
+/**
+ * Unaligned word register, for architectures where that matters.
+ */
+typedef struct {
+ word_t unaligned;
+} __attribute__((packed)) unaligned_word_t;
+
+/**
+ * @brief Constant-time conditional swap.
+ *
+ * If doswap, then swap elem_bytes between *a and *b.
+ *
+ * *a and *b must not alias. Also, they must be at least as aligned
+ * as their sizes, if the CPU cares about that sort of thing.
+ */
+static __inline__ void
+__attribute__((unused,always_inline))
+constant_time_cond_swap (
+ void *__restrict__ a_,
+ void *__restrict__ b_,
+ word_t elem_bytes,
+ mask_t doswap
+) {
+ word_t k;
+ unsigned char *a = (unsigned char *)a_;
+ unsigned char *b = (unsigned char *)b_;
+
+ big_register_t br_mask = br_set_to_mask(doswap);
+ for (k=0; k<=elem_bytes-sizeof(big_register_t); k+=sizeof(big_register_t)) {
+ if (elem_bytes % sizeof(big_register_t)) {
+ /* unaligned */
+ big_register_t xor =
+ ((unaligned_br_t*)(&a[k]))->unaligned
+ ^ ((unaligned_br_t*)(&b[k]))->unaligned;
+ xor &= br_mask;
+ ((unaligned_br_t*)(&a[k]))->unaligned ^= xor;
+ ((unaligned_br_t*)(&b[k]))->unaligned ^= xor;
+ } else {
+ /* aligned */
+ big_register_t xor =
+ *((big_register_t*)(&a[k]))
+ ^ *((big_register_t*)(&b[k]));
+ xor &= br_mask;
+ *((big_register_t*)(&a[k])) ^= xor;
+ *((big_register_t*)(&b[k])) ^= xor;
+ }
+ }
+
+ if (elem_bytes % sizeof(big_register_t) >= sizeof(word_t)) {
+ for (; k<=elem_bytes-sizeof(word_t); k+=sizeof(word_t)) {
+ if (elem_bytes % sizeof(word_t)) {
+ /* unaligned */
+ word_t xor =
+ ((unaligned_word_t*)(&a[k]))->unaligned
+ ^ ((unaligned_word_t*)(&b[k]))->unaligned;
+ xor &= doswap;
+ ((unaligned_word_t*)(&a[k]))->unaligned ^= xor;
+ ((unaligned_word_t*)(&b[k]))->unaligned ^= xor;
+ } else {
+ /* aligned */
+ word_t xor =
+ *((word_t*)(&a[k]))
+ ^ *((word_t*)(&b[k]));
+ xor &= doswap;
+ *((word_t*)(&a[k])) ^= xor;
+ *((word_t*)(&b[k])) ^= xor;
+ }
+ }
+ }
+
+ if (elem_bytes % sizeof(word_t)) {
+ for (; k<elem_bytes; k+=1) {
+ unsigned char xor = a[k] ^ b[k];
+ xor &= doswap;
+ a[k] ^= xor;
+ b[k] ^= xor;
+ }
+ }
+}
+
+/**
+ * @brief Constant-time equivalent of memcpy(out, table + elem_bytes*idx, elem_bytes);
+ *
+ * The table must be at least as aligned as elem_bytes. The output must be word aligned,
+ * and if the input size is vector aligned it must also be vector aligned.
+ *
+ * The table and output must not alias.
+ */
+static __inline__ void
+__attribute__((unused,always_inline))
+constant_time_lookup (
+ void *__restrict__ out_,
+ const void *table_,
+ word_t elem_bytes,
+ word_t n_table,
+ word_t idx
+) {
+ big_register_t big_one = br_set_to_mask(1), big_i = br_set_to_mask(idx);
+
+ /* Can't do pointer arithmetic on void* */
+ unsigned char *out = (unsigned char *)out_;
+ const unsigned char *table = (const unsigned char *)table_;
+ word_t j,k;
+
+ memset(out, 0, elem_bytes);
+ for (j=0; j<n_table; j++, big_i-=big_one) {
+ big_register_t br_mask = br_is_zero(big_i);
+ for (k=0; k<=elem_bytes-sizeof(big_register_t); k+=sizeof(big_register_t)) {
+ if (elem_bytes % sizeof(big_register_t)) {
+ /* unaligned */
+ ((unaligned_br_t *)(out+k))->unaligned
+ |= br_mask & ((const unaligned_br_t*)(&table[k+j*elem_bytes]))->unaligned;
+ } else {
+ /* aligned */
+ *(big_register_t *)(out+k) |= br_mask & *(const big_register_t*)(&table[k+j*elem_bytes]);
+ }
+ }
+
+ word_t mask = word_is_zero(idx^j);
+ if (elem_bytes % sizeof(big_register_t) >= sizeof(word_t)) {
+ for (; k<=elem_bytes-sizeof(word_t); k+=sizeof(word_t)) {
+ if (elem_bytes % sizeof(word_t)) {
+ /* input unaligned, output aligned */
+ *(word_t *)(out+k) |= mask & ((const unaligned_word_t*)(&table[k+j*elem_bytes]))->unaligned;
+ } else {
+ /* aligned */
+ *(word_t *)(out+k) |= mask & *(const word_t*)(&table[k+j*elem_bytes]);
+ }
+ }
+ }
+
+ if (elem_bytes % sizeof(word_t)) {
+ for (; k<elem_bytes; k+=1) {
+ out[k] |= mask & table[k+j*elem_bytes];
+ }
+ }
+ }
+}
+
+/**
+ * @brief Constant-time equivalent of memcpy(table + elem_bytes*idx, in, elem_bytes);
+ *
+ * The table must be at least as aligned as elem_bytes. The input must be word aligned,
+ * and if the output size is vector aligned it must also be vector aligned.
+ *
+ * The table and input must not alias.
+ */
+static __inline__ void
+__attribute__((unused,always_inline))
+constant_time_insert (
+ void *__restrict__ table_,
+ const void *in_,
+ word_t elem_bytes,
+ word_t n_table,
+ word_t idx
+) {
+ big_register_t big_one = br_set_to_mask(1), big_i = br_set_to_mask(idx);
+
+ /* Can't do pointer arithmetic on void* */
+ const unsigned char *in = (const unsigned char *)in_;
+ unsigned char *table = (unsigned char *)table_;
+ word_t j,k;
+
+ for (j=0; j<n_table; j++, big_i-=big_one) {
+ big_register_t br_mask = br_is_zero(big_i);
+ for (k=0; k<=elem_bytes-sizeof(big_register_t); k+=sizeof(big_register_t)) {
+ if (elem_bytes % sizeof(big_register_t)) {
+ /* unaligned */
+ ((unaligned_br_t*)(&table[k+j*elem_bytes]))->unaligned
+ = ( ((unaligned_br_t*)(&table[k+j*elem_bytes]))->unaligned & ~br_mask )
+ | ( ((const unaligned_br_t *)(in+k))->unaligned & br_mask );
+ } else {
+ /* aligned */
+ *(big_register_t*)(&table[k+j*elem_bytes])
+ = ( *(big_register_t*)(&table[k+j*elem_bytes]) & ~br_mask )
+ | ( *(const big_register_t *)(in+k) & br_mask );
+ }
+ }
+
+ word_t mask = word_is_zero(idx^j);
+ if (elem_bytes % sizeof(big_register_t) >= sizeof(word_t)) {
+ for (; k<=elem_bytes-sizeof(word_t); k+=sizeof(word_t)) {
+ if (elem_bytes % sizeof(word_t)) {
+ /* output unaligned, input aligned */
+ ((unaligned_word_t*)(&table[k+j*elem_bytes]))->unaligned
+ = ( ((unaligned_word_t*)(&table[k+j*elem_bytes]))->unaligned & ~mask )
+ | ( *(const word_t *)(in+k) & mask );
+ } else {
+ /* aligned */
+ *(word_t*)(&table[k+j*elem_bytes])
+ = ( *(word_t*)(&table[k+j*elem_bytes]) & ~mask )
+ | ( *(const word_t *)(in+k) & mask );
+ }
+ }
+ }
+
+ if (elem_bytes % sizeof(word_t)) {
+ for (; k<elem_bytes; k+=1) {
+ table[k+j*elem_bytes]
+ = ( table[k+j*elem_bytes] & ~mask )
+ | ( in[k] & mask );
+ }
+ }
+ }
+}
+
+/**
+ * @brief Constant-time a = b&mask.
+ *
+ * The input and output must be at least as aligned as elem_bytes.
+ */
+static __inline__ void
+__attribute__((unused,always_inline))
+constant_time_mask (
+ void * a_,
+ const void *b_,
+ word_t elem_bytes,
+ mask_t mask
+) {
+ unsigned char *a = (unsigned char *)a_;
+ const unsigned char *b = (const unsigned char *)b_;
+
+ word_t k;
+ big_register_t br_mask = br_set_to_mask(mask);
+ for (k=0; k<=elem_bytes-sizeof(big_register_t); k+=sizeof(big_register_t)) {
+ if (elem_bytes % sizeof(big_register_t)) {
+ /* unaligned */
+ ((unaligned_br_t*)(&a[k]))->unaligned = br_mask & ((const unaligned_br_t*)(&b[k]))->unaligned;
+ } else {
+ /* aligned */
+ *(big_register_t *)(a+k) = br_mask & *(const big_register_t*)(&b[k]);
+ }
+ }
+
+ if (elem_bytes % sizeof(big_register_t) >= sizeof(word_t)) {
+ for (; k<=elem_bytes-sizeof(word_t); k+=sizeof(word_t)) {
+ if (elem_bytes % sizeof(word_t)) {
+ /* unaligned */
+ ((unaligned_word_t*)(&a[k]))->unaligned = mask & ((const unaligned_word_t*)(&b[k]))->unaligned;
+ } else {
+ /* aligned */
+ *(word_t *)(a+k) = mask & *(const word_t*)(&b[k]);
+ }
+ }
+ }
+
+ if (elem_bytes % sizeof(word_t)) {
+ for (; k<elem_bytes; k+=1) {
+ a[k] = mask & b[k];
+ }
+ }
+}
+
+/**
+ * @brief Constant-time a = mask ? bTrue : bFalse.
+ *
+ * The input and output must be at least as aligned as alignment_bytes
+ * or their size, whichever is smaller.
+ *
+ * Note that the output is not __restrict__, but if it overlaps either
+ * input, it must be equal and not partially overlap.
+ */
+static __inline__ void
+__attribute__((unused,always_inline))
+constant_time_select (
+ void *a_,
+ const void *bFalse_,
+ const void *bTrue_,
+ word_t elem_bytes,
+ mask_t mask,
+ size_t alignment_bytes
+) {
+ unsigned char *a = (unsigned char *)a_;
+ const unsigned char *bTrue = (const unsigned char *)bTrue_;
+ const unsigned char *bFalse = (const unsigned char *)bFalse_;
+
+ alignment_bytes |= elem_bytes;
+
+ word_t k;
+ big_register_t br_mask = br_set_to_mask(mask);
+ for (k=0; k<=elem_bytes-sizeof(big_register_t); k+=sizeof(big_register_t)) {
+ if (alignment_bytes % sizeof(big_register_t)) {
+ /* unaligned */
+ ((unaligned_br_t*)(&a[k]))->unaligned =
+ ( br_mask & ((const unaligned_br_t*)(&bTrue [k]))->unaligned)
+ | (~br_mask & ((const unaligned_br_t*)(&bFalse[k]))->unaligned);
+ } else {
+ /* aligned */
+ *(big_register_t *)(a+k) =
+ ( br_mask & *(const big_register_t*)(&bTrue [k]))
+ | (~br_mask & *(const big_register_t*)(&bFalse[k]));
+ }
+ }
+
+ if (elem_bytes % sizeof(big_register_t) >= sizeof(word_t)) {
+ for (; k<=elem_bytes-sizeof(word_t); k+=sizeof(word_t)) {
+ if (alignment_bytes % sizeof(word_t)) {
+ /* unaligned */
+ ((unaligned_word_t*)(&a[k]))->unaligned =
+ ( mask & ((const unaligned_word_t*)(&bTrue [k]))->unaligned)
+ | (~mask & ((const unaligned_word_t*)(&bFalse[k]))->unaligned);
+ } else {
+ /* aligned */
+ *(word_t *)(a+k) =
+ ( mask & *(const word_t*)(&bTrue [k]))
+ | (~mask & *(const word_t*)(&bFalse[k]));
+ }
+ }
+ }
+
+ if (elem_bytes % sizeof(word_t)) {
+ for (; k<elem_bytes; k+=1) {
+ a[k] = ( mask & bTrue[k]) | (~mask & bFalse[k]);
+ }
+ }
+}
+
+#endif /* __CONSTANT_TIME_H__ */
--- /dev/null
+/**
+ * @file field.h
+ * @brief Generic gf header.
+ * @copyright
+ * Copyright (c) 2014 Cryptography Research, Inc. \n
+ * Released under the MIT License. See LICENSE.txt for license information.
+ * @author Mike Hamburg
+ */
+
+#ifndef __GF_H__
+#define __GF_H__
+
+#include "constant_time.h"
+#include "f_field.h"
+#include <string.h>
+
+/** Square x, n times. */
+static DECAF_INLINE void gf_sqrn (
+ gf_s *__restrict__ y,
+ const gf x,
+ int n
+) {
+ gf tmp;
+ assert(n>0);
+ if (n&1) {
+ gf_sqr(y,x);
+ n--;
+ } else {
+ gf_sqr(tmp,x);
+ gf_sqr(y,tmp);
+ n-=2;
+ }
+ for (; n; n-=2) {
+ gf_sqr(tmp,y);
+ gf_sqr(y,tmp);
+ }
+}
+
+#define gf_add_nr gf_add_RAW
+
+/** Subtract mod p. Bias by 2 and don't reduce */
+static inline void gf_sub_nr ( gf c, const gf a, const gf b ) {
+ gf_sub_RAW(c,a,b);
+ gf_bias(c, 2);
+ if (GF_HEADROOM < 3) gf_weak_reduce(c);
+}
+
+/** Subtract mod p. Bias by amt but don't reduce. */
+static inline void gf_subx_nr ( gf c, const gf a, const gf b, int amt ) {
+ gf_sub_RAW(c,a,b);
+ gf_bias(c, amt);
+ if (GF_HEADROOM < amt+1) gf_weak_reduce(c);
+}
+
+/** Mul by signed int. Not constant-time WRT the sign of that int. */
+static inline void gf_mulw(gf c, const gf a, int32_t w) {
+ if (w>0) {
+ gf_mulw_unsigned(c, a, w);
+ } else {
+ gf_mulw_unsigned(c, a, -w);
+ gf_sub(c,ZERO,c);
+ }
+}
+
+/** Constant time, x = is_z ? z : y */
+static inline void gf_cond_sel(gf x, const gf y, const gf z, mask_t is_z) {
+ constant_time_select(x,y,z,sizeof(gf),is_z,0);
+}
+
+/** Constant time, if (neg) x=-x; */
+static inline void gf_cond_neg(gf x, mask_t neg) {
+ gf y;
+ gf_sub(y,ZERO,x);
+ gf_cond_sel(x,x,y,neg);
+}
+
+/** Constant time, if (swap) (x,y) = (y,x); */
+static inline void
+gf_cond_swap(gf x, gf_s *__restrict__ y, mask_t swap) {
+ constant_time_cond_swap(x,y,sizeof(gf_s),swap);
+}
+
+static DECAF_INLINE void gf_mul_qnr(gf_s *__restrict__ out, const gf x) {
+#if P_MOD_8 == 5
+ /* r = QNR * r0^2 */
+ gf_mul(out,x,SQRT_MINUS_ONE);
+#elif P_MOD_8 == 3 || P_MOD_8 == 7
+ gf_sub(out,ZERO,x);
+#else
+ #error "Only supporting p=3,5,7 mod 8"
+#endif
+}
+
+static DECAF_INLINE void gf_div_qnr(gf_s *__restrict__ out, const gf x) {
+#if P_MOD_8 == 5
+ /* r = QNR * r0^2 */
+ gf_mul(out,x,SQRT_MINUS_ONE);
+ gf_sub(out,ZERO,out);
+#elif P_MOD_8 == 3 || P_MOD_8 == 7
+ gf_sub(out,ZERO,x);
+#else
+ #error "Only supporting p=3,5,7 mod 8"
+#endif
+}
+
+#if P_MOD_8 == 5
+#define gf_mul_i gf_mul_qnr
+#define gf_div_i gf_div_qnr
+#endif
+
+
+#endif // __GF_H__
--- /dev/null
+/**
+ * @cond internal
+ * @file keccak_internal.h
+ * @copyright
+ * Copyright (c) 2016 Cryptography Research, Inc. \n
+ * Released under the MIT License. See LICENSE.txt for license information.
+ * @author Mike Hamburg
+ * @brief Keccak internal interfaces. Will be used by STROBE once reintegrated.
+ */
+#ifndef __DECAF_KECCAK_INTERNAL_H__
+#define __DECAF_KECCAK_INTERNAL_H__ 1
+
+#include <stdint.h>
+
+/* The internal, non-opaque definition of the decaf_sponge struct. */
+typedef union {
+ uint64_t w[25]; uint8_t b[25*8];
+} kdomain_t[1];
+
+typedef struct decaf_kparams_s {
+ uint8_t position, flags, rate, start_round, pad, rate_pad, max_out, remaining;
+} decaf_kparams_s, decaf_kparams_t[1];
+
+typedef struct decaf_keccak_sponge_s {
+ kdomain_t state;
+ decaf_kparams_t params;
+} decaf_keccak_sponge_s, decaf_keccak_sponge_t[1];
+
+#define INTERNAL_SPONGE_STRUCT 1
+
+void __attribute__((noinline)) keccakf(kdomain_t state, uint8_t start_round);
+
+static inline void dokeccak (decaf_keccak_sponge_t decaf_sponge) {
+ keccakf(decaf_sponge->state, decaf_sponge->params->start_round);
+ decaf_sponge->params->position = 0;
+}
+
+#endif /* __DECAF_KECCAK_INTERNAL_H__ */
--- /dev/null
+/* Subset of Mathias Panzenböck's portable endian code, public domain */
+
+#ifndef __PORTABLE_ENDIAN_H__
+#define __PORTABLE_ENDIAN_H__
+
+#if defined(__linux__) || defined(__CYGWIN__)
+# include <endian.h>
+#elif defined(__OpenBSD__)
+# include <sys/endian.h>
+#elif defined(__APPLE__)
+# include <libkern/OSByteOrder.h>
+# define htole64(x) OSSwapHostToLittleInt64(x)
+# define le64toh(x) OSSwapLittleToHostInt64(x)
+#elif defined(__NetBSD__) || defined(__FreeBSD__) || defined(__DragonFly__)
+# include <sys/endian.h>
+# ifndef le64toh
+# define le64toh(x) letoh64(x)
+# endif
+#elif defined(__sun) && defined(__SVR4)
+# include <sys/byteorder.h>
+# define htole64(x) LE_64(x)
+# define le64toh(x) LE_64(x)
+#elif defined(_WIN16) || defined(_WIN32) || defined(_WIN64) || defined(__WINDOWS__)
+# include <winsock2.h>
+# include <sys/param.h>
+# if BYTE_ORDER == LITTLE_ENDIAN
+# define htole64(x) (x)
+# define le64toh(x) (x)
+# elif BYTE_ORDER == BIG_ENDIAN
+# define htole64(x) __builtin_bswap64(x)
+# define le64toh(x) __builtin_bswap64(x)
+# else
+# error byte order not supported
+# endif
+#else
+# error platform not supported
+#endif
+
+#endif // __PORTABLE_ENDIAN_H__
--- /dev/null
+/* Copyright (c) 2014 Cryptography Research, Inc.
+ * Released under the MIT License. See LICENSE.txt for license information.
+ */
+
+#ifndef __WORD_H__
+#define __WORD_H__
+
+/* for posix_memalign */
+#define _XOPEN_SOURCE 600
+#define __STDC_WANT_LIB_EXT1__ 1 /* for memset_s */
+#include <string.h>
+#if defined(__sun) && defined(__SVR4)
+extern int posix_memalign(void **, size_t, size_t);
+#endif
+
+#include <assert.h>
+#include <stdint.h>
+#include "arch_intrinsics.h"
+
+#include <decaf/common.h>
+
+#ifndef _BSD_SOURCE
+#define _BSD_SOURCE 1
+#endif
+
+#ifndef _DEFAULT_SOURCE
+#define _DEFAULT_SOURCE 1
+#endif
+
+#include "portable_endian.h"
+
+#include <stdlib.h>
+#include <sys/types.h>
+#include <inttypes.h>
+
+#if defined(__ARM_NEON__)
+#include <arm_neon.h>
+#elif defined(__SSE2__)
+ #if !defined(__GNUC__) || __clang__ || __GNUC__ >= 5 || (__GNUC__==4 && __GNUC_MINOR__ >= 4)
+ #include <immintrin.h>
+ #else
+ #include <emmintrin.h>
+ #endif
+#endif
+
+#if (ARCH_WORD_BITS == 64)
+ typedef uint64_t word_t, mask_t;
+ typedef __uint128_t dword_t;
+ typedef int32_t hsword_t;
+ typedef int64_t sword_t;
+ typedef __int128_t dsword_t;
+#elif (ARCH_WORD_BITS == 32)
+ typedef uint32_t word_t, mask_t;
+ typedef uint64_t dword_t;
+ typedef int16_t hsword_t;
+ typedef int32_t sword_t;
+ typedef int64_t dsword_t;
+#else
+ #error "For now, libdecaf only supports 32- and 64-bit architectures."
+#endif
+
+/* Scalar limbs are keyed off of the API word size instead of the arch word size. */
+#if DECAF_WORD_BITS == 64
+ #define SC_LIMB(x) (x##ull)
+#elif DECAF_WORD_BITS == 32
+ #define SC_LIMB(x) ((uint32_t)x##ull),(x##ull>>32)
+#else
+ #error "For now, libdecaf only supports 32- and 64-bit architectures."
+#endif
+
+#ifdef __ARM_NEON__
+ typedef uint32x4_t vecmask_t;
+#elif __clang__
+ typedef uint64_t uint64x2_t __attribute__((ext_vector_type(2)));
+ typedef int64_t int64x2_t __attribute__((ext_vector_type(2)));
+ typedef uint64_t uint64x4_t __attribute__((ext_vector_type(4)));
+ typedef int64_t int64x4_t __attribute__((ext_vector_type(4)));
+ typedef uint32_t uint32x4_t __attribute__((ext_vector_type(4)));
+ typedef int32_t int32x4_t __attribute__((ext_vector_type(4)));
+ typedef uint32_t uint32x2_t __attribute__((ext_vector_type(2)));
+ typedef int32_t int32x2_t __attribute__((ext_vector_type(2)));
+ typedef uint32_t uint32x8_t __attribute__((ext_vector_type(8)));
+ typedef int32_t int32x8_t __attribute__((ext_vector_type(8)));
+ typedef word_t vecmask_t __attribute__((ext_vector_type(4)));
+#else /* GCC, hopefully? */
+ typedef uint64_t uint64x2_t __attribute__((vector_size(16)));
+ typedef int64_t int64x2_t __attribute__((vector_size(16)));
+ typedef uint64_t uint64x4_t __attribute__((vector_size(32)));
+ typedef int64_t int64x4_t __attribute__((vector_size(32)));
+ typedef uint32_t uint32x4_t __attribute__((vector_size(16)));
+ typedef int32_t int32x4_t __attribute__((vector_size(16)));
+ typedef uint32_t uint32x2_t __attribute__((vector_size(8)));
+ typedef int32_t int32x2_t __attribute__((vector_size(8)));
+ typedef uint32_t uint32x8_t __attribute__((vector_size(32)));
+ typedef int32_t int32x8_t __attribute__((vector_size(32)));
+ typedef word_t vecmask_t __attribute__((vector_size(32)));
+#endif
+
+#if __AVX2__
+ #define VECTOR_ALIGNED __attribute__((aligned(32)))
+ typedef uint32x8_t big_register_t;
+ typedef uint64x4_t uint64xn_t;
+ typedef uint32x8_t uint32xn_t;
+
+ static DECAF_INLINE big_register_t
+ br_set_to_mask(mask_t x) {
+ uint32_t y = (uint32_t)x;
+ big_register_t ret = {y,y,y,y,y,y,y,y};
+ return ret;
+ }
+#elif __SSE2__
+ #define VECTOR_ALIGNED __attribute__((aligned(16)))
+ typedef uint32x4_t big_register_t;
+ typedef uint64x2_t uint64xn_t;
+ typedef uint32x4_t uint32xn_t;
+
+ static DECAF_INLINE big_register_t
+ br_set_to_mask(mask_t x) {
+ uint32_t y = x;
+ big_register_t ret = {y,y,y,y};
+ return ret;
+ }
+#elif __ARM_NEON__
+ #define VECTOR_ALIGNED __attribute__((aligned(16)))
+ typedef uint32x4_t big_register_t;
+ typedef uint64x2_t uint64xn_t;
+ typedef uint32x4_t uint32xn_t;
+
+ static DECAF_INLINE big_register_t
+ br_set_to_mask(mask_t x) {
+ return vdupq_n_u32(x);
+ }
+#elif _WIN64 || __amd64__ || __X86_64__ || __aarch64__
+ #define VECTOR_ALIGNED __attribute__((aligned(8)))
+ typedef uint64_t big_register_t, uint64xn_t;
+
+ typedef uint32_t uint32xn_t;
+ static DECAF_INLINE big_register_t
+ br_set_to_mask(mask_t x) {
+ return (big_register_t)x;
+ }
+#else
+ #define VECTOR_ALIGNED __attribute__((aligned(4)))
+ typedef uint64_t uint64xn_t;
+ typedef uint32_t uint32xn_t;
+ typedef uint32_t big_register_t;
+
+ static DECAF_INLINE big_register_t
+ br_set_to_mask(mask_t x) {
+ return (big_register_t)x;
+ }
+#endif
+
+typedef struct {
+ uint64xn_t unaligned;
+} __attribute__((packed)) unaligned_uint64xn_t;
+
+typedef struct {
+ uint32xn_t unaligned;
+} __attribute__((packed)) unaligned_uint32xn_t;
+
+#if __AVX2__
+ static DECAF_INLINE big_register_t
+ br_is_zero(big_register_t x) {
+ return (big_register_t)(x == br_set_to_mask(0));
+ }
+#elif __SSE2__
+ static DECAF_INLINE big_register_t
+ br_is_zero(big_register_t x) {
+ return (big_register_t)_mm_cmpeq_epi32((__m128i)x, _mm_setzero_si128());
+ //return (big_register_t)(x == br_set_to_mask(0));
+ }
+#elif __ARM_NEON__
+ static DECAF_INLINE big_register_t
+ br_is_zero(big_register_t x) {
+ return vceqq_u32(x,x^x);
+ }
+#else
+ #define br_is_zero word_is_zero
+#endif
+
+/**
+ * Really call memset, in a way that prevents the compiler from optimizing it out.
+ * @param p The object to zeroize.
+ * @param c The char to set it to (probably zero).
+ * @param s The size of the object.
+ */
+#if defined(__DARWIN_C_LEVEL) || defined(__STDC_LIB_EXT1__)
+#define HAS_MEMSET_S
+#endif
+
+#if !defined(__STDC_WANT_LIB_EXT1__) || __STDC_WANT_LIB_EXT1__ != 1
+#define NEED_MEMSET_S_EXTERN
+#endif
+
+#ifdef HAS_MEMSET_S
+ #ifdef NEED_MEMSET_S_EXTERN
+ extern int memset_s(void *, size_t, int, size_t);
+ #endif
+ static DECAF_INLINE void
+ really_memset(void *p, char c, size_t s) {
+ memset_s(p, s, c, s);
+ }
+#else
+ /* PERF: use words? */
+ static DECAF_INLINE void
+ really_memset(void *p, char c, size_t s) {
+ volatile char *pv = (volatile char *)p;
+ size_t i;
+ for (i=0; i<s; i++) pv[i] = c;
+ }
+#endif
+
+/**
+ * Allocate memory which is sufficiently aligned to be used for the
+ * largest vector on the system (for now that's a big_register_t).
+ *
+ * Man malloc says that it does this, but at least for AVX2 on MacOS X,
+ * it's lying.
+ *
+ * @param size The size of the region to allocate.
+ * @return A suitable pointer, which can be free'd with free(),
+ * or NULL if no memory can be allocated.
+ */
+static DECAF_INLINE void *
+malloc_vector(size_t size) {
+ void *out = NULL;
+
+ int ret = posix_memalign(&out, sizeof(big_register_t), size);
+
+ if (ret) {
+ return NULL;
+ } else {
+ return out;
+ }
+}
+
+/* PERF: vectorize vs unroll */
+#ifdef __clang__
+#if 100*__clang_major__ + __clang_minor__ > 305
+#define UNROLL _Pragma("clang loop unroll(full)")
+#endif
+#endif
+
+#ifndef UNROLL
+#define UNROLL
+#endif
+
+/* The plan on booleans:
+ *
+ * The external interface uses decaf_bool_t, but this might be a different
+ * size than our particular arch's word_t (and thus mask_t). Also, the caller
+ * isn't guaranteed to pass it as nonzero. So bool_to_mask converts word sizes
+ * and checks nonzero.
+ *
+ * On the flip side, mask_t is always -1 or 0, but it might be a different size
+ * than decaf_bool_t.
+ *
+ * On the third hand, we have success vs boolean types, but that's handled in
+ * common.h: it converts between decaf_bool_t and decaf_error_t.
+ */
+static DECAF_INLINE decaf_bool_t mask_to_bool (mask_t m) {
+ return (decaf_sword_t)(sword_t)m;
+}
+
+static DECAF_INLINE mask_t bool_to_mask (decaf_bool_t m) {
+ /* On most arches this will be optimized to a simple cast. */
+ mask_t ret = 0;
+ unsigned int limit = sizeof(decaf_bool_t)/sizeof(mask_t);
+ if (limit < 1) limit = 1;
+ for (unsigned int i=0; i<limit; i++) {
+ ret |= ~ word_is_zero(m >> (i*8*sizeof(word_t)));
+ }
+ return ret;
+}
+
+static DECAF_INLINE void ignore_result ( decaf_bool_t boo ) {
+ (void)boo;
+}
+
+#endif /* __WORD_H__ */
--- /dev/null
+/* Copyright (c) 2014 Cryptography Research, Inc.
+ * Released under the MIT License. See LICENSE.txt for license information.
+ */
+
+#include "f_field.h"
+
+#if (defined(__OPTIMIZE__) && !defined(__OPTIMIZE_SIZE__) && !I_HATE_UNROLLED_LOOPS) \
+ || defined(DECAF_FORCE_UNROLL)
+#define REPEAT8(_x) _x _x _x _x _x _x _x _x
+#define FOR_LIMB(_i,_start,_end,_x) do { _i=_start; REPEAT8( if (_i<_end) { _x; } _i++;) } while (0)
+#else
+#define FOR_LIMB(_i,_start,_end,_x) do { for (_i=_start; _i<_end; _i++) _x; } while (0)
+#endif
+
+void gf_mul (gf_s *__restrict__ cs, const gf as, const gf bs) {
+ const uint32_t *a = as->limb, *b = bs->limb;
+ uint32_t *c = cs->limb;
+
+ uint64_t accum0 = 0, accum1 = 0, accum2 = 0;
+ uint32_t mask = (1<<28) - 1;
+
+ uint32_t aa[8], bb[8];
+
+ int i,j;
+ for (i=0; i<8; i++) {
+ aa[i] = a[i] + a[i+8];
+ bb[i] = b[i] + b[i+8];
+ }
+
+ FOR_LIMB(j,0,8,{
+ accum2 = 0;
+
+ FOR_LIMB (i,0,j+1,{
+ accum2 += widemul(a[j-i],b[i]);
+ accum1 += widemul(aa[j-i],bb[i]);
+ accum0 += widemul(a[8+j-i], b[8+i]);
+ });
+
+ accum1 -= accum2;
+ accum0 += accum2;
+ accum2 = 0;
+
+ FOR_LIMB (i,j+1,8,{
+ accum0 -= widemul(a[8+j-i], b[i]);
+ accum2 += widemul(aa[8+j-i], bb[i]);
+ accum1 += widemul(a[16+j-i], b[8+i]);
+ });
+
+ accum1 += accum2;
+ accum0 += accum2;
+
+ c[j] = ((uint32_t)(accum0)) & mask;
+ c[j+8] = ((uint32_t)(accum1)) & mask;
+
+ accum0 >>= 28;
+ accum1 >>= 28;
+ });
+
+ accum0 += accum1;
+ accum0 += c[8];
+ accum1 += c[0];
+ c[8] = ((uint32_t)(accum0)) & mask;
+ c[0] = ((uint32_t)(accum1)) & mask;
+
+ accum0 >>= 28;
+ accum1 >>= 28;
+ c[9] += ((uint32_t)(accum0));
+ c[1] += ((uint32_t)(accum1));
+}
+
+void gf_mulw_unsigned (gf_s *__restrict__ cs, const gf as, uint32_t b) {
+ assert(b<1<<28);
+
+ const uint32_t *a = as->limb;
+ uint32_t *c = cs->limb;
+
+ uint64_t accum0 = 0, accum8 = 0;
+ uint32_t mask = (1ull<<28)-1;
+
+ int i;
+ FOR_LIMB(i,0,8,{
+ accum0 += widemul(b, a[i]);
+ accum8 += widemul(b, a[i+8]);
+
+ c[i] = accum0 & mask; accum0 >>= 28;
+ c[i+8] = accum8 & mask; accum8 >>= 28;
+ });
+
+ accum0 += accum8 + c[8];
+ c[8] = accum0 & mask;
+ c[9] += accum0 >> 28;
+
+ accum8 += c[0];
+ c[0] = accum8 & mask;
+ c[1] += accum8 >> 28;
+}
+
+void gf_sqr (gf_s *__restrict__ cs, const gf as) {
+ gf_mul(cs,as,as); /* Performs better with a dedicated square */
+}
+
--- /dev/null
+/* Copyright (c) 2014-2016 Cryptography Research, Inc.
+ * Released under the MIT License. See LICENSE.txt for license information.
+ */
+
+#define GF_HEADROOM 2
+#define LIMB(x) (x##ull)&((1ull<<28)-1), (x##ull)>>28
+#define FIELD_LITERAL(a,b,c,d,e,f,g,h) \
+ {{LIMB(a),LIMB(b),LIMB(c),LIMB(d),LIMB(e),LIMB(f),LIMB(g),LIMB(h)}}
+
+#define LIMB_PLACE_VALUE(i) 28
+
+void gf_add_RAW (gf out, const gf a, const gf b) {
+ for (unsigned int i=0; i<sizeof(*out)/sizeof(out->limb[0]); i++) {
+ out->limb[i] = a->limb[i] + b->limb[i];
+ }
+}
+
+void gf_sub_RAW (gf out, const gf a, const gf b) {
+ for (unsigned int i=0; i<sizeof(*out)/sizeof(out->limb[0]); i++) {
+ out->limb[i] = a->limb[i] - b->limb[i];
+ }
+}
+
+void gf_bias (gf a, int amt) {
+ uint32_t co1 = ((1ull<<28)-1)*amt, co2 = co1-amt;
+ for (unsigned int i=0; i<sizeof(*a)/sizeof(a->limb[0]); i++) {
+ a->limb[i] += (i==sizeof(*a)/sizeof(a->limb[0])/2) ? co2 : co1;
+ }
+}
+
+void gf_weak_reduce (gf a) {
+ uint32_t mask = (1ull<<28) - 1;
+ uint32_t tmp = a->limb[15] >> 28;
+ a->limb[8] += tmp;
+ for (unsigned int i=15; i>0; i--) {
+ a->limb[i] = (a->limb[i] & mask) + (a->limb[i-1]>>28);
+ }
+ a->limb[0] = (a->limb[0] & mask) + tmp;
+}
+
--- /dev/null
+/* Copyright (c) 2014 Cryptography Research, Inc.
+ * Released under the MIT License. See LICENSE.txt for license information.
+ */
+
+#include "f_field.h"
+
+static inline void __attribute__((gnu_inline,always_inline))
+smlal (
+ uint64_t *acc,
+ const uint32_t a,
+ const uint32_t b
+) {
+
+#ifdef __ARMEL__
+ uint32_t lo = *acc, hi = (*acc)>>32;
+
+ __asm__ __volatile__ ("smlal %[lo], %[hi], %[a], %[b]"
+ : [lo]"+&r"(lo), [hi]"+&r"(hi)
+ : [a]"r"(a), [b]"r"(b));
+
+ *acc = lo + (((uint64_t)hi)<<32);
+#else
+ *acc += (int64_t)(int32_t)a * (int64_t)(int32_t)b;
+#endif
+}
+
+static inline void __attribute__((gnu_inline,always_inline))
+smlal2 (
+ uint64_t *acc,
+ const uint32_t a,
+ const uint32_t b
+) {
+#ifdef __ARMEL__
+ uint32_t lo = *acc, hi = (*acc)>>32;
+
+ __asm__ __volatile__ ("smlal %[lo], %[hi], %[a], %[b]"
+ : [lo]"+&r"(lo), [hi]"+&r"(hi)
+ : [a]"r"(a), [b]"r"(2*b));
+
+ *acc = lo + (((uint64_t)hi)<<32);
+#else
+ *acc += (int64_t)(int32_t)a * (int64_t)(int32_t)(b * 2);
+#endif
+}
+
+static inline void __attribute__((gnu_inline,always_inline))
+smull (
+ uint64_t *acc,
+ const uint32_t a,
+ const uint32_t b
+) {
+#ifdef __ARMEL__
+ uint32_t lo, hi;
+
+ __asm__ __volatile__ ("smull %[lo], %[hi], %[a], %[b]"
+ : [lo]"=&r"(lo), [hi]"=&r"(hi)
+ : [a]"r"(a), [b]"r"(b));
+
+ *acc = lo + (((uint64_t)hi)<<32);
+#else
+ *acc = (int64_t)(int32_t)a * (int64_t)(int32_t)b;
+#endif
+}
+
+static inline void __attribute__((gnu_inline,always_inline))
+smull2 (
+ uint64_t *acc,
+ const uint32_t a,
+ const uint32_t b
+) {
+#ifdef __ARMEL__
+ uint32_t lo, hi;
+
+ __asm__ /*__volatile__*/ ("smull %[lo], %[hi], %[a], %[b]"
+ : [lo]"=&r"(lo), [hi]"=&r"(hi)
+ : [a]"r"(a), [b]"r"(2*b));
+
+ *acc = lo + (((uint64_t)hi)<<32);
+#else
+ *acc = (int64_t)(int32_t)a * (int64_t)(int32_t)(b * 2);
+#endif
+}
+
+void gf_mul (gf_s *__restrict__ cs, const gf as, const gf bs) {
+
+ const uint32_t *a = as->limb, *b = bs->limb;
+ uint32_t *c = cs->limb;
+
+ uint64_t accum0 = 0, accum1 = 0, accum2, accum3, accumC0, accumC1;
+ uint32_t mask = (1<<28) - 1;
+
+ uint32_t aa[8], bm[8];
+
+ int i;
+ for (i=0; i<8; i++) {
+ aa[i] = a[i] + a[i+8];
+ bm[i] = b[i] - b[i+8];
+ }
+
+ uint32_t ax,bx;
+ {
+ /* t^3 terms */
+ smull(&accum1, ax = aa[1], bx = b[15]);
+ smull(&accum3, ax = aa[2], bx);
+ smlal(&accum1, ax, bx = b[14]);
+ smlal(&accum3, ax = aa[3], bx);
+ smlal(&accum1, ax, bx = b[13]);
+ smlal(&accum3, ax = aa[4], bx);
+ smlal(&accum1, ax, bx = b[12]);
+ smlal(&accum3, ax = aa[5], bx);
+ smlal(&accum1, ax, bx = b[11]);
+ smlal(&accum3, ax = aa[6], bx);
+ smlal(&accum1, ax, bx = b[10]);
+ smlal(&accum3, ax = aa[7], bx);
+ smlal(&accum1, ax, bx = b[9]);
+
+ accum0 = accum1;
+ accum2 = accum3;
+
+ /* t^2 terms */
+ smlal(&accum2, ax = aa[0], bx);
+ smlal(&accum0, ax, bx = b[8]);
+ smlal(&accum2, ax = aa[1], bx);
+
+ smlal(&accum0, ax = a[9], bx = b[7]);
+ smlal(&accum2, ax = a[10], bx);
+ smlal(&accum0, ax, bx = b[6]);
+ smlal(&accum2, ax = a[11], bx);
+ smlal(&accum0, ax, bx = b[5]);
+ smlal(&accum2, ax = a[12], bx);
+ smlal(&accum0, ax, bx = b[4]);
+ smlal(&accum2, ax = a[13], bx);
+ smlal(&accum0, ax, bx = b[3]);
+ smlal(&accum2, ax = a[14], bx);
+ smlal(&accum0, ax, bx = b[2]);
+ smlal(&accum2, ax = a[15], bx);
+ smlal(&accum0, ax, bx = b[1]);
+
+ /* t terms */
+ accum1 += accum0;
+ accum3 += accum2;
+ smlal(&accum3, ax = a[8], bx);
+ smlal(&accum1, ax, bx = b[0]);
+ smlal(&accum3, ax = a[9], bx);
+
+ smlal(&accum1, ax = a[1], bx = bm[7]);
+ smlal(&accum3, ax = a[2], bx);
+ smlal(&accum1, ax, bx = bm[6]);
+ smlal(&accum3, ax = a[3], bx);
+ smlal(&accum1, ax, bx = bm[5]);
+ smlal(&accum3, ax = a[4], bx);
+ smlal(&accum1, ax, bx = bm[4]);
+ smlal(&accum3, ax = a[5], bx);
+ smlal(&accum1, ax, bx = bm[3]);
+ smlal(&accum3, ax = a[6], bx);
+ smlal(&accum1, ax, bx = bm[2]);
+ smlal(&accum3, ax = a[7], bx);
+ smlal(&accum1, ax, bx = bm[1]);
+
+ /* 1 terms */
+ smlal(&accum2, ax = a[0], bx);
+ smlal(&accum0, ax, bx = bm[0]);
+ smlal(&accum2, ax = a[1], bx);
+
+ accum2 += accum0 >> 28;
+ accum3 += accum1 >> 28;
+
+ c[0] = ((uint32_t)(accum0)) & mask;
+ c[1] = ((uint32_t)(accum2)) & mask;
+ c[8] = ((uint32_t)(accum1)) & mask;
+ c[9] = ((uint32_t)(accum3)) & mask;
+
+ accumC0 = accum2 >> 28;
+ accumC1 = accum3 >> 28;
+ }
+ {
+ /* t^3 terms */
+ smull(&accum1, ax = aa[3], bx = b[15]);
+ smull(&accum3, ax = aa[4], bx);
+ smlal(&accum1, ax, bx = b[14]);
+ smlal(&accum3, ax = aa[5], bx);
+ smlal(&accum1, ax, bx = b[13]);
+ smlal(&accum3, ax = aa[6], bx);
+ smlal(&accum1, ax, bx = b[12]);
+ smlal(&accum3, ax = aa[7], bx);
+ smlal(&accum1, ax, bx = b[11]);
+
+ accum0 = accum1;
+ accum2 = accum3;
+
+ /* t^2 terms */
+ smlal(&accum2, ax = aa[0], bx);
+ smlal(&accum0, ax, bx = b[10]);
+ smlal(&accum2, ax = aa[1], bx);
+ smlal(&accum0, ax, bx = b[9]);
+ smlal(&accum2, ax = aa[2], bx);
+ smlal(&accum0, ax, bx = b[8]);
+ smlal(&accum2, ax = aa[3], bx);
+
+ smlal(&accum0, ax = a[11], bx = b[7]);
+ smlal(&accum2, ax = a[12], bx);
+ smlal(&accum0, ax, bx = b[6]);
+ smlal(&accum2, ax = a[13], bx);
+ smlal(&accum0, ax, bx = b[5]);
+ smlal(&accum2, ax = a[14], bx);
+ smlal(&accum0, ax, bx = b[4]);
+ smlal(&accum2, ax = a[15], bx);
+ smlal(&accum0, ax, bx = b[3]);
+
+ /* t terms */
+ accum1 += accum0;
+ accum3 += accum2;
+ smlal(&accum3, ax = a[8], bx);
+ smlal(&accum1, ax, bx = b[2]);
+ smlal(&accum3, ax = a[9], bx);
+ smlal(&accum1, ax, bx = b[1]);
+ smlal(&accum3, ax = a[10], bx);
+ smlal(&accum1, ax, bx = b[0]);
+ smlal(&accum3, ax = a[11], bx);
+
+ smlal(&accum1, ax = a[3], bx = bm[7]);
+ smlal(&accum3, ax = a[4], bx);
+ smlal(&accum1, ax, bx = bm[6]);
+ smlal(&accum3, ax = a[5], bx);
+ smlal(&accum1, ax, bx = bm[5]);
+ smlal(&accum3, ax = a[6], bx);
+ smlal(&accum1, ax, bx = bm[4]);
+ smlal(&accum3, ax = a[7], bx);
+ smlal(&accum1, ax, bx = bm[3]);
+
+ /* 1 terms */
+ smlal(&accum2, ax = a[0], bx);
+ smlal(&accum0, ax, bx = bm[2]);
+ smlal(&accum2, ax = a[1], bx);
+ smlal(&accum0, ax, bx = bm[1]);
+ smlal(&accum2, ax = a[2], bx);
+ smlal(&accum0, ax, bx = bm[0]);
+ smlal(&accum2, ax = a[3], bx);
+
+ accum0 += accumC0;
+ accum1 += accumC1;
+ accum2 += accum0 >> 28;
+ accum3 += accum1 >> 28;
+
+ c[2] = ((uint32_t)(accum0)) & mask;
+ c[3] = ((uint32_t)(accum2)) & mask;
+ c[10] = ((uint32_t)(accum1)) & mask;
+ c[11] = ((uint32_t)(accum3)) & mask;
+
+ accumC0 = accum2 >> 28;
+ accumC1 = accum3 >> 28;
+ }
+ {
+
+ /* t^3 terms */
+ smull(&accum1, ax = aa[5], bx = b[15]);
+ smull(&accum3, ax = aa[6], bx);
+ smlal(&accum1, ax, bx = b[14]);
+ smlal(&accum3, ax = aa[7], bx);
+ smlal(&accum1, ax, bx = b[13]);
+
+ accum0 = accum1;
+ accum2 = accum3;
+
+ /* t^2 terms */
+
+ smlal(&accum2, ax = aa[0], bx);
+ smlal(&accum0, ax, bx = b[12]);
+ smlal(&accum2, ax = aa[1], bx);
+ smlal(&accum0, ax, bx = b[11]);
+ smlal(&accum2, ax = aa[2], bx);
+ smlal(&accum0, ax, bx = b[10]);
+ smlal(&accum2, ax = aa[3], bx);
+ smlal(&accum0, ax, bx = b[9]);
+ smlal(&accum2, ax = aa[4], bx);
+ smlal(&accum0, ax, bx = b[8]);
+ smlal(&accum2, ax = aa[5], bx);
+
+
+ smlal(&accum0, ax = a[13], bx = b[7]);
+ smlal(&accum2, ax = a[14], bx);
+ smlal(&accum0, ax, bx = b[6]);
+ smlal(&accum2, ax = a[15], bx);
+ smlal(&accum0, ax, bx = b[5]);
+
+ /* t terms */
+ accum1 += accum0;
+ accum3 += accum2;
+
+ smlal(&accum3, ax = a[8], bx);
+ smlal(&accum1, ax, bx = b[4]);
+ smlal(&accum3, ax = a[9], bx);
+ smlal(&accum1, ax, bx = b[3]);
+ smlal(&accum3, ax = a[10], bx);
+ smlal(&accum1, ax, bx = b[2]);
+ smlal(&accum3, ax = a[11], bx);
+ smlal(&accum1, ax, bx = b[1]);
+ smlal(&accum3, ax = a[12], bx);
+ smlal(&accum1, ax, bx = b[0]);
+ smlal(&accum3, ax = a[13], bx);
+
+
+ smlal(&accum1, ax = a[5], bx = bm[7]);
+ smlal(&accum3, ax = a[6], bx);
+ smlal(&accum1, ax, bx = bm[6]);
+ smlal(&accum3, ax = a[7], bx);
+ smlal(&accum1, ax, bx = bm[5]);
+
+ /* 1 terms */
+
+ smlal(&accum2, ax = a[0], bx);
+ smlal(&accum0, ax, bx = bm[4]);
+ smlal(&accum2, ax = a[1], bx);
+ smlal(&accum0, ax, bx = bm[3]);
+ smlal(&accum2, ax = a[2], bx);
+ smlal(&accum0, ax, bx = bm[2]);
+ smlal(&accum2, ax = a[3], bx);
+ smlal(&accum0, ax, bx = bm[1]);
+ smlal(&accum2, ax = a[4], bx);
+ smlal(&accum0, ax, bx = bm[0]);
+ smlal(&accum2, ax = a[5], bx);
+
+ accum0 += accumC0;
+ accum1 += accumC1;
+ accum2 += accum0 >> 28;
+ accum3 += accum1 >> 28;
+
+ c[4] = ((uint32_t)(accum0)) & mask;
+ c[5] = ((uint32_t)(accum2)) & mask;
+ c[12] = ((uint32_t)(accum1)) & mask;
+ c[13] = ((uint32_t)(accum3)) & mask;
+
+ accumC0 = accum2 >> 28;
+ accumC1 = accum3 >> 28;
+ }
+ {
+
+ /* t^3 terms */
+ smull(&accum1, ax = aa[7], bx = b[15]);
+ accum0 = accum1;
+
+ /* t^2 terms */
+
+ smull(&accum2, ax = aa[0], bx);
+ smlal(&accum0, ax, bx = b[14]);
+ smlal(&accum2, ax = aa[1], bx);
+ smlal(&accum0, ax, bx = b[13]);
+ smlal(&accum2, ax = aa[2], bx);
+ smlal(&accum0, ax, bx = b[12]);
+ smlal(&accum2, ax = aa[3], bx);
+ smlal(&accum0, ax, bx = b[11]);
+ smlal(&accum2, ax = aa[4], bx);
+ smlal(&accum0, ax, bx = b[10]);
+ smlal(&accum2, ax = aa[5], bx);
+ smlal(&accum0, ax, bx = b[9]);
+ smlal(&accum2, ax = aa[6], bx);
+ smlal(&accum0, ax, bx = b[8]);
+ smlal(&accum2, ax = aa[7], bx);
+
+
+ smlal(&accum0, ax = a[15], bx = b[7]);
+
+ /* t terms */
+ accum1 += accum0;
+ accum3 = accum2;
+
+ smlal(&accum3, ax = a[8], bx);
+ smlal(&accum1, ax, bx = b[6]);
+ smlal(&accum3, ax = a[9], bx);
+ smlal(&accum1, ax, bx = b[5]);
+ smlal(&accum3, ax = a[10], bx);
+ smlal(&accum1, ax, bx = b[4]);
+ smlal(&accum3, ax = a[11], bx);
+ smlal(&accum1, ax, bx = b[3]);
+ smlal(&accum3, ax = a[12], bx);
+ smlal(&accum1, ax, bx = b[2]);
+ smlal(&accum3, ax = a[13], bx);
+ smlal(&accum1, ax, bx = b[1]);
+ smlal(&accum3, ax = a[14], bx);
+ smlal(&accum1, ax, bx = b[0]);
+ smlal(&accum3, ax = a[15], bx);
+
+
+ smlal(&accum1, ax = a[7], bx = bm[7]);
+
+ /* 1 terms */
+
+ smlal(&accum2, ax = a[0], bx);
+ smlal(&accum0, ax, bx = bm[6]);
+ smlal(&accum2, ax = a[1], bx);
+ smlal(&accum0, ax, bx = bm[5]);
+ smlal(&accum2, ax = a[2], bx);
+ smlal(&accum0, ax, bx = bm[4]);
+ smlal(&accum2, ax = a[3], bx);
+ smlal(&accum0, ax, bx = bm[3]);
+ smlal(&accum2, ax = a[4], bx);
+ smlal(&accum0, ax, bx = bm[2]);
+ smlal(&accum2, ax = a[5], bx);
+ smlal(&accum0, ax, bx = bm[1]);
+ smlal(&accum2, ax = a[6], bx);
+ smlal(&accum0, ax, bx = bm[0]);
+ smlal(&accum2, ax = a[7], bx);
+
+ accum0 += accumC0;
+ accum1 += accumC1;
+ accum2 += accum0 >> 28;
+ accum3 += accum1 >> 28;
+
+ c[6] = ((uint32_t)(accum0)) & mask;
+ c[7] = ((uint32_t)(accum2)) & mask;
+ c[14] = ((uint32_t)(accum1)) & mask;
+ c[15] = ((uint32_t)(accum3)) & mask;
+
+ accum0 = accum2 >> 28;
+ accum1 = accum3 >> 28;
+ }
+
+ accum0 += accum1;
+ accum0 += c[8];
+ accum1 += c[0];
+ c[8] = ((uint32_t)(accum0)) & mask;
+ c[0] = ((uint32_t)(accum1)) & mask;
+
+ accum0 >>= 28;
+ accum1 >>= 28;
+ c[9] += ((uint32_t)(accum0));
+ c[1] += ((uint32_t)(accum1));
+}
+
+void gf_sqr (gf_s *__restrict__ cs, const gf as) {
+ const uint32_t *a = as->limb;
+ uint32_t *c = cs->limb;
+
+ uint64_t accum0 = 0, accum1 = 0, accum2, accum3, accumC0, accumC1, tmp;
+ uint32_t mask = (1<<28) - 1;
+
+ uint32_t bm[8];
+
+ int i;
+ for (i=0; i<8; i++) {
+ bm[i] = a[i] - a[i+8];
+ }
+
+ uint32_t ax,bx;
+ {
+ /* t^3 terms */
+ smull2(&accum1, ax = a[9], bx = a[15]);
+ smull2(&accum3, ax = a[10], bx);
+ smlal2(&accum1, ax, bx = a[14]);
+ smlal2(&accum3, ax = a[11], bx);
+ smlal2(&accum1, ax, bx = a[13]);
+ smlal2(&accum3, ax = a[12], bx);
+ smlal(&accum1, ax, ax);
+
+ accum0 = accum1;
+ accum2 = accum3;
+
+ /* t^2 terms */
+ smlal2(&accum2, ax = a[8], a[9]);
+ smlal(&accum0, ax, ax);
+
+ smlal2(&accum0, ax = a[1], bx = a[7]);
+ smlal2(&accum2, ax = a[2], bx);
+ smlal2(&accum0, ax, bx = a[6]);
+ smlal2(&accum2, ax = a[3], bx);
+ smlal2(&accum0, ax, bx = a[5]);
+ smlal2(&accum2, ax = a[4], bx);
+ smlal(&accum0, ax, ax);
+
+ /* t terms */
+ accum1 += accum0;
+ accum3 += accum2;
+ smlal2(&accum3, ax = a[0], bx = a[1]);
+ smlal(&accum1, ax, ax);
+
+ accum1 = -accum1;
+ accum3 = -accum3;
+ accum2 = -accum2;
+ accum0 = -accum0;
+
+ smlal2(&accum1, ax = bm[1], bx = bm[7]);
+ smlal2(&accum3, ax = bm[2], bx);
+ smlal2(&accum1, ax, bx = bm[6]);
+ smlal2(&accum3, ax = bm[3], bx);
+ smlal2(&accum1, ax, bx = bm[5]);
+ smlal2(&accum3, ax = bm[4], bx);
+ smlal(&accum1, ax, ax);
+
+ /* 1 terms */
+ smlal2(&accum2, ax = bm[0], bx = bm[1]);
+ smlal(&accum0, ax, ax);
+
+ tmp = -accum3; accum3 = tmp-accum2; accum2 = tmp;
+ tmp = -accum1; accum1 = tmp-accum0; accum0 = tmp;
+
+ accum2 += accum0 >> 28;
+ accum3 += accum1 >> 28;
+
+ c[0] = ((uint32_t)(accum0)) & mask;
+ c[1] = ((uint32_t)(accum2)) & mask;
+ c[8] = ((uint32_t)(accum1)) & mask;
+ c[9] = ((uint32_t)(accum3)) & mask;
+
+ accumC0 = accum2 >> 28;
+ accumC1 = accum3 >> 28;
+ }
+ {
+ /* t^3 terms */
+ smull2(&accum1, ax = a[11], bx = a[15]);
+ smull2(&accum3, ax = a[12], bx);
+ smlal2(&accum1, ax, bx = a[14]);
+ smlal2(&accum3, ax = a[13], bx);
+ smlal(&accum1, ax, ax);
+
+ accum0 = accum1;
+ accum2 = accum3;
+
+ /* t^2 terms */
+ smlal2(&accum2, ax = a[8], bx = a[11]);
+ smlal2(&accum0, ax, bx = a[10]);
+ smlal2(&accum2, ax = a[9], bx);
+ smlal(&accum0, ax, ax);
+
+ smlal2(&accum0, ax = a[3], bx = a[7]);
+ smlal2(&accum2, ax = a[4], bx);
+ smlal2(&accum0, ax, bx = a[6]);
+ smlal2(&accum2, ax = a[5], bx);
+ smlal(&accum0, ax, ax);
+
+ /* t terms */
+ accum1 += accum0;
+ accum3 += accum2;
+ smlal2(&accum3, ax = a[0], bx = a[3]);
+ smlal2(&accum1, ax, bx = a[2]);
+ smlal2(&accum3, ax = a[1], bx);
+ smlal(&accum1, ax, ax);
+
+ accum1 = -accum1;
+ accum3 = -accum3;
+ accum2 = -accum2;
+ accum0 = -accum0;
+
+ smlal2(&accum1, ax = bm[3], bx = bm[7]);
+ smlal2(&accum3, ax = bm[4], bx);
+ smlal2(&accum1, ax, bx = bm[6]);
+ smlal2(&accum3, ax = bm[5], bx);
+ smlal(&accum1, ax, ax);
+
+ /* 1 terms */
+ smlal2(&accum2, ax = bm[0], bx = bm[3]);
+ smlal2(&accum0, ax, bx = bm[2]);
+ smlal2(&accum2, ax = bm[1], bx);
+ smlal(&accum0, ax, ax);
+
+
+ tmp = -accum3; accum3 = tmp-accum2; accum2 = tmp;
+ tmp = -accum1; accum1 = tmp-accum0; accum0 = tmp;
+
+ accum0 += accumC0;
+ accum1 += accumC1;
+ accum2 += accum0 >> 28;
+ accum3 += accum1 >> 28;
+
+ c[2] = ((uint32_t)(accum0)) & mask;
+ c[3] = ((uint32_t)(accum2)) & mask;
+ c[10] = ((uint32_t)(accum1)) & mask;
+ c[11] = ((uint32_t)(accum3)) & mask;
+
+ accumC0 = accum2 >> 28;
+ accumC1 = accum3 >> 28;
+ }
+ {
+
+ /* t^3 terms */
+ smull2(&accum1, ax = a[13], bx = a[15]);
+ smull2(&accum3, ax = a[14], bx);
+ smlal(&accum1, ax, ax);
+
+ accum0 = accum1;
+ accum2 = accum3;
+
+ /* t^2 terms */
+
+ smlal2(&accum2, ax = a[8], bx = a[13]);
+ smlal2(&accum0, ax, bx = a[12]);
+ smlal2(&accum2, ax = a[9], bx);
+ smlal2(&accum0, ax, bx = a[11]);
+ smlal2(&accum2, ax = a[10], bx);
+ smlal(&accum0, ax, ax);
+
+
+ smlal2(&accum0, ax = a[5], bx = a[7]);
+ smlal2(&accum2, ax = a[6], bx);
+ smlal(&accum0, ax, ax);
+
+ /* t terms */
+ accum1 += accum0;
+ accum3 += accum2;
+
+ smlal2(&accum3, ax = a[0], bx = a[5]);
+ smlal2(&accum1, ax, bx = a[4]);
+ smlal2(&accum3, ax = a[1], bx);
+ smlal2(&accum1, ax, bx = a[3]);
+ smlal2(&accum3, ax = a[2], bx);
+ smlal(&accum1, ax, ax);
+
+ accum1 = -accum1;
+ accum3 = -accum3;
+ accum2 = -accum2;
+ accum0 = -accum0;
+
+ smlal2(&accum1, ax = bm[5], bx = bm[7]);
+ smlal2(&accum3, ax = bm[6], bx);
+ smlal(&accum1, ax, ax);
+
+ /* 1 terms */
+
+ smlal2(&accum2, ax = bm[0], bx = bm[5]);
+ smlal2(&accum0, ax, bx = bm[4]);
+ smlal2(&accum2, ax = bm[1], bx);
+ smlal2(&accum0, ax, bx = bm[3]);
+ smlal2(&accum2, ax = bm[2], bx);
+ smlal(&accum0, ax, ax);
+
+
+ tmp = -accum3; accum3 = tmp-accum2; accum2 = tmp;
+ tmp = -accum1; accum1 = tmp-accum0; accum0 = tmp;
+
+ accum0 += accumC0;
+ accum1 += accumC1;
+ accum2 += accum0 >> 28;
+ accum3 += accum1 >> 28;
+
+ c[4] = ((uint32_t)(accum0)) & mask;
+ c[5] = ((uint32_t)(accum2)) & mask;
+ c[12] = ((uint32_t)(accum1)) & mask;
+ c[13] = ((uint32_t)(accum3)) & mask;
+
+ accumC0 = accum2 >> 28;
+ accumC1 = accum3 >> 28;
+ }
+ {
+
+ /* t^3 terms */
+ smull(&accum1, ax = a[15], bx = a[15]);
+ accum0 = accum1;
+
+ /* t^2 terms */
+
+ smull2(&accum2, ax = a[8], bx);
+ smlal2(&accum0, ax, bx = a[14]);
+ smlal2(&accum2, ax = a[9], bx);
+ smlal2(&accum0, ax, bx = a[13]);
+ smlal2(&accum2, ax = a[10], bx);
+ smlal2(&accum0, ax, bx = a[12]);
+ smlal2(&accum2, ax = a[11], bx);
+ smlal(&accum0, ax, ax);
+
+
+ smlal(&accum0, ax = a[7], bx = a[7]);
+
+ /* t terms */
+ accum1 += accum0;
+ accum3 = accum2;
+
+ smlal2(&accum3, ax = a[0], bx);
+ smlal2(&accum1, ax, bx = a[6]);
+ smlal2(&accum3, ax = a[1], bx);
+ smlal2(&accum1, ax, bx = a[5]);
+ smlal2(&accum3, ax = a[2], bx);
+ smlal2(&accum1, ax, bx = a[4]);
+ smlal2(&accum3, ax = a[3], bx);
+ smlal(&accum1, ax, ax);
+
+ accum1 = -accum1;
+ accum3 = -accum3;
+ accum2 = -accum2;
+ accum0 = -accum0;
+
+ bx = bm[7];
+ smlal(&accum1, bx, bx);
+
+ /* 1 terms */
+
+ smlal2(&accum2, ax = bm[0], bx);
+ smlal2(&accum0, ax, bx = bm[6]);
+ smlal2(&accum2, ax = bm[1], bx);
+ smlal2(&accum0, ax, bx = bm[5]);
+ smlal2(&accum2, ax = bm[2], bx);
+ smlal2(&accum0, ax, bx = bm[4]);
+ smlal2(&accum2, ax = bm[3], bx);
+ smlal(&accum0, ax, ax);
+
+ tmp = -accum3; accum3 = tmp-accum2; accum2 = tmp;
+ tmp = -accum1; accum1 = tmp-accum0; accum0 = tmp;
+
+
+ accum0 += accumC0;
+ accum1 += accumC1;
+ accum2 += accum0 >> 28;
+ accum3 += accum1 >> 28;
+
+ c[6] = ((uint32_t)(accum0)) & mask;
+ c[7] = ((uint32_t)(accum2)) & mask;
+ c[14] = ((uint32_t)(accum1)) & mask;
+ c[15] = ((uint32_t)(accum3)) & mask;
+
+ accum0 = accum2 >> 28;
+ accum1 = accum3 >> 28;
+ }
+
+ accum0 += accum1;
+ accum0 += c[8];
+ accum1 += c[0];
+ c[8] = ((uint32_t)(accum0)) & mask;
+ c[0] = ((uint32_t)(accum1)) & mask;
+
+ accum0 >>= 28;
+ accum1 >>= 28;
+ c[9] += ((uint32_t)(accum0));
+ c[1] += ((uint32_t)(accum1));
+}
+
+void gf_mulw_unsigned (
+ gf_s *__restrict__ cs,
+ const gf as,
+ uint32_t b
+) {
+ uint32_t mask = (1ull<<28)-1;
+ assert(b <= mask);
+
+ const uint32_t *a = as->limb;
+ uint32_t *c = cs->limb;
+
+ uint64_t accum0, accum8;
+
+ int i;
+
+ uint32_t c0, c8, n0, n8;
+ c0 = a[0]; c8 = a[8];
+ accum0 = widemul(b, c0);
+ accum8 = widemul(b, c8);
+
+ c[0] = accum0 & mask; accum0 >>= 28;
+ c[8] = accum8 & mask; accum8 >>= 28;
+
+ i=1;
+ {
+ n0 = a[i]; n8 = a[i+8];
+ smlal(&accum0, b, n0);
+ smlal(&accum8, b, n8);
+
+ c[i] = accum0 & mask; accum0 >>= 28;
+ c[i+8] = accum8 & mask; accum8 >>= 28;
+ i++;
+ }
+ {
+ c0 = a[i]; c8 = a[i+8];
+ smlal(&accum0, b, c0);
+ smlal(&accum8, b, c8);
+
+ c[i] = accum0 & mask; accum0 >>= 28;
+ c[i+8] = accum8 & mask; accum8 >>= 28;
+ i++;
+ }
+ {
+ n0 = a[i]; n8 = a[i+8];
+ smlal(&accum0, b, n0);
+ smlal(&accum8, b, n8);
+
+ c[i] = accum0 & mask; accum0 >>= 28;
+ c[i+8] = accum8 & mask; accum8 >>= 28;
+ i++;
+ }
+ {
+ c0 = a[i]; c8 = a[i+8];
+ smlal(&accum0, b, c0);
+ smlal(&accum8, b, c8);
+
+ c[i] = accum0 & mask; accum0 >>= 28;
+ c[i+8] = accum8 & mask; accum8 >>= 28;
+ i++;
+ }
+ {
+ n0 = a[i]; n8 = a[i+8];
+ smlal(&accum0, b, n0);
+ smlal(&accum8, b, n8);
+
+ c[i] = accum0 & mask; accum0 >>= 28;
+ c[i+8] = accum8 & mask; accum8 >>= 28;
+ i++;
+ }
+ {
+ c0 = a[i]; c8 = a[i+8];
+ smlal(&accum0, b, c0);
+ smlal(&accum8, b, c8);
+
+ c[i] = accum0 & mask; accum0 >>= 28;
+ c[i+8] = accum8 & mask; accum8 >>= 28;
+ i++;
+ }
+ {
+ n0 = a[i]; n8 = a[i+8];
+ smlal(&accum0, b, n0);
+ smlal(&accum8, b, n8);
+
+ c[i] = accum0 & mask; accum0 >>= 28;
+ c[i+8] = accum8 & mask; accum8 >>= 28;
+ i++;
+ }
+
+ accum0 += accum8 + c[8];
+ c[8] = accum0 & mask;
+ c[9] += accum0 >> 28;
+
+ accum8 += c[0];
+ c[0] = accum8 & mask;
+ c[1] += accum8 >> 28;
+}
--- /dev/null
+/* Copyright (c) 2014-2016 Cryptography Research, Inc.
+ * Released under the MIT License. See LICENSE.txt for license information.
+ */
+
+#define GF_HEADROOM 2
+#define LIMB(x) (x##ull)&((1ull<<28)-1), (x##ull)>>28
+#define FIELD_LITERAL(a,b,c,d,e,f,g,h) \
+ {{LIMB(a),LIMB(b),LIMB(c),LIMB(d),LIMB(e),LIMB(f),LIMB(g),LIMB(h)}}
+
+#define LIMB_PLACE_VALUE(i) 28
+
+void gf_add_RAW (gf out, const gf a, const gf b) {
+ for (unsigned int i=0; i<sizeof(*out)/sizeof(uint32xn_t); i++) {
+ ((uint32xn_t*)out)[i] = ((const uint32xn_t*)a)[i] + ((const uint32xn_t*)b)[i];
+ }
+ /*
+ for (unsigned int i=0; i<sizeof(*out)/sizeof(out->limb[0]); i++) {
+ out->limb[i] = a->limb[i] + b->limb[i];
+ }
+ */
+}
+
+void gf_sub_RAW (gf out, const gf a, const gf b) {
+ for (unsigned int i=0; i<sizeof(*out)/sizeof(uint32xn_t); i++) {
+ ((uint32xn_t*)out)[i] = ((const uint32xn_t*)a)[i] - ((const uint32xn_t*)b)[i];
+ }
+ /*
+ for (unsigned int i=0; i<sizeof(*out)/sizeof(out->limb[0]); i++) {
+ out->limb[i] = a->limb[i] - b->limb[i];
+ }
+ */
+}
+
+void gf_bias (gf a, int amt) {
+ uint32_t co1 = ((1ull<<28)-1)*amt, co2 = co1-amt;
+ uint32x4_t lo = {co1,co1,co1,co1}, hi = {co2,co1,co1,co1};
+ uint32x4_t *aa = (uint32x4_t*) a;
+ aa[0] += lo;
+ aa[1] += lo;
+ aa[2] += hi;
+ aa[3] += lo;
+}
+
+void gf_weak_reduce (gf a) {
+ uint64_t mask = (1ull<<28) - 1;
+ uint64_t tmp = a->limb[15] >> 28;
+ a->limb[8] += tmp;
+ for (unsigned int i=15; i>0; i--) {
+ a->limb[i] = (a->limb[i] & mask) + (a->limb[i-1]>>28);
+ }
+ a->limb[0] = (a->limb[0] & mask) + tmp;
+}
+
--- /dev/null
+/* Copyright (c) 2014 Cryptography Research, Inc.
+ * Released under the MIT License. See LICENSE.txt for license information.
+ */
+
+#include "f_field.h"
+
+static __inline__ uint64x2_t __attribute__((gnu_inline,always_inline,unused))
+xx_vaddup_u64(uint64x2_t x) {
+ __asm__ ("vadd.s64 %f0, %e0" : "+w"(x));
+ return x;
+}
+
+static __inline__ int64x2_t __attribute__((gnu_inline,always_inline,unused))
+vrev128_s64(int64x2_t x) {
+ __asm__ ("vswp.s64 %e0, %f0" : "+w"(x));
+ return x;
+}
+
+static __inline__ uint64x2_t __attribute__((gnu_inline,always_inline))
+vrev128_u64(uint64x2_t x) {
+ __asm__ ("vswp.s64 %e0, %f0" : "+w"(x));
+ return x;
+}
+
+static inline void __attribute__((gnu_inline,always_inline,unused))
+smlal (
+ uint64_t *acc,
+ const uint32_t a,
+ const uint32_t b
+) {
+ *acc += (int64_t)(int32_t)a * (int64_t)(int32_t)b;
+}
+
+static inline void __attribute__((gnu_inline,always_inline,unused))
+smlal2 (
+ uint64_t *acc,
+ const uint32_t a,
+ const uint32_t b
+) {
+ *acc += (int64_t)(int32_t)a * (int64_t)(int32_t)b * 2;
+}
+
+static inline void __attribute__((gnu_inline,always_inline,unused))
+smull (
+ uint64_t *acc,
+ const uint32_t a,
+ const uint32_t b
+) {
+ *acc = (int64_t)(int32_t)a * (int64_t)(int32_t)b;
+}
+
+static inline void __attribute__((gnu_inline,always_inline,unused))
+smull2 (
+ uint64_t *acc,
+ const uint32_t a,
+ const uint32_t b
+) {
+ *acc = (int64_t)(int32_t)a * (int64_t)(int32_t)b * 2;
+}
+
+void gf_mul (gf_s *__restrict__ cs, const gf as, const gf bs) {
+ #define _bl0 "q0"
+ #define _bl0_0 "d0"
+ #define _bl0_1 "d1"
+ #define _bh0 "q1"
+ #define _bh0_0 "d2"
+ #define _bh0_1 "d3"
+ #define _bs0 "q2"
+ #define _bs0_0 "d4"
+ #define _bs0_1 "d5"
+ #define _bl2 "q3"
+ #define _bl2_0 "d6"
+ #define _bl2_1 "d7"
+ #define _bh2 "q4"
+ #define _bh2_0 "d8"
+ #define _bh2_1 "d9"
+ #define _bs2 "q5"
+ #define _bs2_0 "d10"
+ #define _bs2_1 "d11"
+
+ #define _as0 "q6"
+ #define _as0_0 "d12"
+ #define _as0_1 "d13"
+ #define _as2 "q7"
+ #define _as2_0 "d14"
+ #define _as2_1 "d15"
+ #define _al0 "q8"
+ #define _al0_0 "d16"
+ #define _al0_1 "d17"
+ #define _ah0 "q9"
+ #define _ah0_0 "d18"
+ #define _ah0_1 "d19"
+ #define _al2 "q10"
+ #define _al2_0 "d20"
+ #define _al2_1 "d21"
+ #define _ah2 "q11"
+ #define _ah2_0 "d22"
+ #define _ah2_1 "d23"
+
+ #define _a0a "q12"
+ #define _a0a_0 "d24"
+ #define _a0a_1 "d25"
+ #define _a0b "q13"
+ #define _a0b_0 "d26"
+ #define _a0b_1 "d27"
+ #define _a1a "q14"
+ #define _a1a_0 "d28"
+ #define _a1a_1 "d29"
+ #define _a1b "q15"
+ #define _a1b_0 "d30"
+ #define _a1b_1 "d31"
+ #define VMAC(op,result,a,b,n) #op" "result", "a", "b"[" #n "]\n\t"
+ #define VOP3(op,result,a,b) #op" "result", "a", "b"\n\t"
+ #define VOP2(op,result,a) #op" "result", "a"\n\t"
+
+ int32x2_t *vc = (int32x2_t*) cs->limb;
+
+ __asm__ __volatile__(
+
+ "vld2.32 {"_al0_0","_al0_1","_ah0_0","_ah0_1"}, [%[a],:128]!" "\n\t"
+ VOP3(vadd.i32,_as0,_al0,_ah0)
+
+ "vld2.32 {"_bl0_0","_bl0_1","_bh0_0","_bh0_1"}, [%[b],:128]!" "\n\t"
+ VOP3(vadd.i32,_bs0_1,_bl0_1,_bh0_1)
+ VOP3(vsub.i32,_bs0_0,_bl0_0,_bh0_0)
+
+ "vld2.32 {"_bl2_0","_bl2_1","_bh2_0","_bh2_1"}, [%[b],:128]!" "\n\t"
+ VOP3(vadd.i32,_bs2,_bl2,_bh2)
+
+ "vld2.32 {"_al2_0","_al2_1","_ah2_0","_ah2_1"}, [%[a],:128]!" "\n\t"
+ VOP3(vadd.i32,_as2,_al2,_ah2)
+
+ VMAC(vmull.s32,_a0b,_as0_1,_bs2_1,0)
+ VMAC(vmlal.s32,_a0b,_as2_0,_bs2_0,0)
+ VMAC(vmlal.s32,_a0b,_as2_1,_bs0_1,0)
+ VMAC(vmlal.s32,_a0b,_as0_0,_bh0_0,0)
+
+ VMAC(vmull.s32,_a1b,_as0_1,_bs2_1,1)
+ VMAC(vmlal.s32,_a1b,_as2_0,_bs2_0,1)
+ VMAC(vmlal.s32,_a1b,_as2_1,_bs0_1,1)
+ VMAC(vmlal.s32,_a1b,_as0_0,_bh0_0,1)
+
+ VOP2(vmov,_a0a,_a0b)
+ VMAC(vmlal.s32,_a0a,_ah0_1,_bh2_1,0)
+ VMAC(vmlal.s32,_a0a,_ah2_0,_bh2_0,0)
+ VMAC(vmlal.s32,_a0a,_ah2_1,_bh0_1,0)
+ VMAC(vmlal.s32,_a0a,_ah0_0,_bl0_0,0)
+
+ VMAC(vmlsl.s32,_a0b,_al0_1,_bl2_1,0)
+ VMAC(vmlsl.s32,_a0b,_al2_0,_bl2_0,0)
+ VMAC(vmlsl.s32,_a0b,_al2_1,_bl0_1,0)
+ VMAC(vmlal.s32,_a0b,_al0_0,_bs0_0,0)
+
+ VOP2(vmov,_a1a,_a1b)
+ VMAC(vmlal.s32,_a1a,_ah0_1,_bh2_1,1)
+ VMAC(vmlal.s32,_a1a,_ah2_0,_bh2_0,1)
+ VMAC(vmlal.s32,_a1a,_ah2_1,_bh0_1,1)
+ VMAC(vmlal.s32,_a1a,_ah0_0,_bl0_0,1)
+
+ VOP2(vswp,_a0b_1,_a0a_0)
+
+ VMAC(vmlsl.s32,_a1b,_al0_1,_bl2_1,1)
+ VMAC(vmlsl.s32,_a1b,_al2_0,_bl2_0,1)
+ VMAC(vmlsl.s32,_a1b,_al2_1,_bl0_1,1)
+ VMAC(vmlal.s32,_a1b,_al0_0,_bs0_0,1)
+
+ VOP3(vsra.u64,_a0a,_a0b,"#28")
+ VOP3(vsub.i32,_bs0_1,_bl0_1,_bh0_1)
+ VOP2(vmovn.i64,_a0b_0,_a0b)
+
+ VOP2(vswp,_a1b_1,_a1a_0)
+ VOP3(vadd.i64,_a1b,_a0a,_a1b)
+
+
+ VMAC(vmull.s32,_a0a,_as2_0,_bs2_1,0)
+ VOP2(vmovn.i64,_a0b_1,_a1b)
+ VMAC(vmlal.s32,_a0a,_as2_1,_bs2_0,0)
+ VOP3(vsra.u64,_a1a,_a1b,"#28")
+ VMAC(vmlal.s32,_a0a,_as0_0,_bh0_1,0)
+ VOP2(vbic.i32,_a0b,"#0xf0000000")
+ VMAC(vmlal.s32,_a0a,_as0_1,_bh0_0,0)
+ "vstmia %[c]!, {"_a0b_0", "_a0b_1"}" "\n\t"
+
+ VMAC(vmull.s32,_a1b,_as2_0,_bs2_1,1)
+ VMAC(vmlal.s32,_a1b,_as2_1,_bs2_0,1)
+ VMAC(vmlal.s32,_a1b,_as0_0,_bh0_1,1)
+ VMAC(vmlal.s32,_a1b,_as0_1,_bh0_0,1)
+
+ VOP2(vmov,_a0b_1,_a0a_1)
+ VOP3(vadd.i64,_a0b_0,_a0a_0,_a1a_0)
+ VOP3(vadd.i64,_a0a_0,_a0a_0,_a1a_1)
+ VMAC(vmlal.s32,_a0a,_ah2_0,_bh2_1,0)
+ VMAC(vmlal.s32,_a0a,_ah2_1,_bh2_0,0)
+ VMAC(vmlal.s32,_a0a,_ah0_0,_bl0_1,0)
+ VMAC(vmlal.s32,_a0a,_ah0_1,_bl0_0,0)
+
+ VMAC(vmlsl.s32,_a0b,_al2_0,_bl2_1,0)
+ VMAC(vmlsl.s32,_a0b,_al2_1,_bl2_0,0)
+ VMAC(vmlal.s32,_a0b,_al0_0,_bs0_1,0)
+ VMAC(vmlal.s32,_a0b,_al0_1,_bs0_0,0)
+
+ VOP2(vmov,_a1a,_a1b)
+ VMAC(vmlal.s32,_a1a,_ah2_0,_bh2_1,1)
+ VMAC(vmlal.s32,_a1a,_ah2_1,_bh2_0,1)
+ VMAC(vmlal.s32,_a1a,_ah0_0,_bl0_1,1)
+ VMAC(vmlal.s32,_a1a,_ah0_1,_bl0_0,1)
+
+ VOP2(vswp,_a0b_1,_a0a_0)
+
+ VMAC(vmlsl.s32,_a1b,_al2_0,_bl2_1,1)
+ VMAC(vmlsl.s32,_a1b,_al2_1,_bl2_0,1)
+ VMAC(vmlal.s32,_a1b,_al0_0,_bs0_1,1)
+ VMAC(vmlal.s32,_a1b,_al0_1,_bs0_0,1)
+
+ VOP3(vsra.u64,_a0a,_a0b,"#28")
+ VOP3(vsub.i32,_bs2_0,_bl2_0,_bh2_0)
+ VOP2(vmovn.i64,_a0b_0,_a0b)
+
+ VOP2(vswp,_a1b_1,_a1a_0)
+ VOP3(vadd.i64,_a1b,_a0a,_a1b)
+
+ VMAC(vmull.s32,_a0a,_as2_1,_bs2_1,0)
+ VOP2(vmovn.i64,_a0b_1,_a1b)
+ VMAC(vmlal.s32,_a0a,_as0_0,_bh2_0,0)
+ VOP3(vsra.u64,_a1a,_a1b,"#28")
+ VMAC(vmlal.s32,_a0a,_as0_1,_bh0_1,0)
+ VOP2(vbic.i32,_a0b,"#0xf0000000")
+ VMAC(vmlal.s32,_a0a,_as2_0,_bh0_0,0)
+ "vstmia %[c]!, {"_a0b_0", "_a0b_1"}" "\n\t"
+
+ VMAC(vmull.s32,_a1b,_as2_1,_bs2_1,1)
+ VMAC(vmlal.s32,_a1b,_as0_0,_bh2_0,1)
+ VMAC(vmlal.s32,_a1b,_as0_1,_bh0_1,1)
+ VMAC(vmlal.s32,_a1b,_as2_0,_bh0_0,1)
+
+ VOP2(vmov,_a0b_1,_a0a_1)
+ VOP3(vadd.i64,_a0b_0,_a0a_0,_a1a_0)
+ VOP3(vadd.i64,_a0a_0,_a0a_0,_a1a_1)
+ VMAC(vmlal.s32,_a0a,_ah2_1,_bh2_1,0)
+ VMAC(vmlal.s32,_a0a,_ah0_0,_bl2_0,0)
+ VMAC(vmlal.s32,_a0a,_ah0_1,_bl0_1,0)
+ VMAC(vmlal.s32,_a0a,_ah2_0,_bl0_0,0)
+
+ VMAC(vmlsl.s32,_a0b,_al2_1,_bl2_1,0)
+ VMAC(vmlal.s32,_a0b,_al0_0,_bs2_0,0)
+ VMAC(vmlal.s32,_a0b,_al0_1,_bs0_1,0)
+ VMAC(vmlal.s32,_a0b,_al2_0,_bs0_0,0)
+
+ VOP2(vmov,_a1a,_a1b)
+ VMAC(vmlal.s32,_a1a,_ah2_1,_bh2_1,1)
+ VMAC(vmlal.s32,_a1a,_ah0_0,_bl2_0,1)
+ VMAC(vmlal.s32,_a1a,_ah0_1,_bl0_1,1)
+ VMAC(vmlal.s32,_a1a,_ah2_0,_bl0_0,1)
+
+ VOP2(vswp,_a0b_1,_a0a_0)
+
+ VMAC(vmlsl.s32,_a1b,_al2_1,_bl2_1,1)
+ VMAC(vmlal.s32,_a1b,_al0_0,_bs2_0,1)
+ VMAC(vmlal.s32,_a1b,_al0_1,_bs0_1,1)
+ VMAC(vmlal.s32,_a1b,_al2_0,_bs0_0,1)
+
+ VOP3(vsub.i32,_bs2_1,_bl2_1,_bh2_1)
+ VOP3(vsra.u64,_a0a,_a0b,"#28")
+ VOP2(vmovn.i64,_a0b_0,_a0b)
+
+ VOP2(vswp,_a1b_1,_a1a_0)
+ VOP3(vadd.i64,_a1b,_a0a,_a1b)
+
+ VMAC(vmull.s32,_a0a,_as0_0,_bh2_1,0)
+ VOP2(vmovn.i64,_a0b_1,_a1b)
+ VMAC(vmlal.s32,_a0a,_as0_1,_bh2_0,0)
+ VOP3(vsra.u64,_a1a,_a1b,"#28")
+ VMAC(vmlal.s32,_a0a,_as2_0,_bh0_1,0)
+ VOP2(vbic.i32,_a0b,"#0xf0000000")
+ VMAC(vmlal.s32,_a0a,_as2_1,_bh0_0,0)
+ "vstmia %[c]!, {"_a0b_0", "_a0b_1"}" "\n\t"
+
+ VMAC(vmull.s32,_a1b,_as0_0,_bh2_1,1)
+ VMAC(vmlal.s32,_a1b,_as0_1,_bh2_0,1)
+ VMAC(vmlal.s32,_a1b,_as2_0,_bh0_1,1)
+ VMAC(vmlal.s32,_a1b,_as2_1,_bh0_0,1)
+
+ VOP2(vmov,_a0b_1,_a0a_1)
+ VOP3(vadd.i64,_a0b_0,_a0a_0,_a1a_0)
+ VOP3(vadd.i64,_a0a_0,_a0a_0,_a1a_1)
+ VMAC(vmlal.s32,_a0a,_ah0_0,_bl2_1,0)
+ VMAC(vmlal.s32,_a0a,_ah0_1,_bl2_0,0)
+ VMAC(vmlal.s32,_a0a,_ah2_0,_bl0_1,0)
+ VMAC(vmlal.s32,_a0a,_ah2_1,_bl0_0,0)
+
+ VMAC(vmlal.s32,_a0b,_al0_0,_bs2_1,0)
+ VMAC(vmlal.s32,_a0b,_al0_1,_bs2_0,0)
+ VMAC(vmlal.s32,_a0b,_al2_0,_bs0_1,0)
+ VMAC(vmlal.s32,_a0b,_al2_1,_bs0_0,0)
+
+ VOP2(vmov,_a1a,_a1b)
+ VMAC(vmlal.s32,_a1a,_ah0_0,_bl2_1,1)
+ VMAC(vmlal.s32,_a1a,_ah0_1,_bl2_0,1)
+ VMAC(vmlal.s32,_a1a,_ah2_0,_bl0_1,1)
+ VMAC(vmlal.s32,_a1a,_ah2_1,_bl0_0,1)
+
+ VOP2(vswp,_a0b_1,_a0a_0)
+
+ VMAC(vmlal.s32,_a1b,_al0_0,_bs2_1,1)
+ VMAC(vmlal.s32,_a1b,_al0_1,_bs2_0,1)
+ VMAC(vmlal.s32,_a1b,_al2_0,_bs0_1,1)
+ VMAC(vmlal.s32,_a1b,_al2_1,_bs0_0,1)
+
+ VOP3(vsra.u64,_a0a,_a0b,"#28")
+ VOP2(vmovn.i64,_a0b_0,_a0b)
+
+ VOP2(vswp,_a1b_1,_a1a_0)
+ VOP3(vadd.i64,_a0a,_a0a,_a1b)
+
+ VOP2(vmovn.i64,_a0b_1,_a0a)
+ VOP3(vsra.u64,_a1a,_a0a,"#28")
+
+ VOP2(vbic.i32,_a0b,"#0xf0000000")
+
+ VOP2(vswp,_a1a_0,_a1a_1)
+
+ "vstmia %[c]!, {"_a0b_0", "_a0b_1"}" "\n\t"
+ "sub %[c], #64" "\n\t"
+
+ VOP3(vadd.i64,_a1a_1,_a1a_1,_a1a_0)
+
+ "vldmia %[c], {"_a0a_0", "_a0a_1", "_a0b_0"}" "\n\t"
+ VOP2(vaddw.s32,_a1a,_a0a_0)
+ VOP2(vmovn.i64,_a0a_0,_a1a)
+ VOP2(vshr.s64,_a1a,"#28")
+
+ VOP2(vaddw.s32,_a1a,_a0a_1)
+ VOP2(vmovn.i64,_a0a_1,_a1a)
+ VOP2(vshr.s64,_a1a,"#28")
+
+ VOP2(vbic.i32,_a0a,"#0xf0000000")
+
+ VOP2(vaddw.s32,_a1a,_a0b_0)
+ VOP2(vmovn.i64,_a0b_0,_a1a)
+
+ "vstmia %[c], {"_a0a_0", "_a0a_1", "_a0b_0"}" "\n\t"
+
+ : [a]"+r"(as)
+ , [b]"+r"(bs)
+ , [c]"+r"(vc)
+
+ :: "q0","q1","q2","q3",
+ "q4","q5","q6","q7",
+ "q8","q9","q10","q11",
+ "q12","q13","q14","q15",
+ "memory"
+ );
+}
+
+void gf_sqr (gf_s *__restrict__ cs, const gf bs) {
+ int32x2_t *vc = (int32x2_t*) cs->limb;
+
+ __asm__ __volatile__ (
+ "vld2.32 {"_bl0_0","_bl0_1","_bh0_0","_bh0_1"}, [%[b],:128]!" "\n\t"
+ VOP3(vadd.i32,_bs0_1,_bl0_1,_bh0_1) /* 0 .. 2^30 */
+ VOP3(vsub.i32,_bs0_0,_bl0_0,_bh0_0) /* +- 2^29 */
+ VOP3(vadd.i32,_as0,_bl0,_bh0) /* 0 .. 2^30 */
+
+ "vld2.32 {"_bl2_0","_bl2_1","_bh2_0","_bh2_1"}, [%[b],:128]!" "\n\t"
+ VOP3(vadd.i32,_bs2,_bl2,_bh2) /* 0 .. 2^30 */
+ VOP2(vmov,_as2,_bs2)
+
+ VMAC(vqdmull.s32,_a0b,_as0_1,_bs2_1,0) /* 0 .. 8 * 2^58. danger for vqdmlal is 32 */
+ VMAC(vmlal.s32,_a0b,_as2_0,_bs2_0,0) /* 0 .. 12 */
+ VMAC(vmlal.s32,_a0b,_as0_0,_bh0_0,0) /* 0 .. 14 */
+
+ VMAC(vqdmull.s32,_a1b,_as0_1,_bs2_1,1) /* 0 .. 8 */
+ VMAC(vmlal.s32,_a1b,_as2_0,_bs2_0,1) /* 0 .. 14 */
+ VMAC(vmlal.s32,_a1b,_as0_0,_bh0_0,1) /* 0 .. 16 */
+
+ VOP2(vmov,_a0a,_a0b) /* 0 .. 14 */
+ VMAC(vqdmlal.s32,_a0a,_bh0_1,_bh2_1,0) /* 0 .. 16 */
+ VMAC(vmlal.s32,_a0a,_bh2_0,_bh2_0,0) /* 0 .. 17 */
+ VMAC(vmlal.s32,_a0a,_bh0_0,_bl0_0,0) /* 0 .. 18 */
+
+ VMAC(vqdmlsl.s32,_a0b,_bl0_1,_bl2_1,0) /*-2 .. 14 */
+ VMAC(vmlsl.s32,_a0b,_bl2_0,_bl2_0,0) /*-3 .. 14 */
+ VMAC(vmlal.s32,_a0b,_bl0_0,_bs0_0,0) /*-4 .. 15 */
+
+ VOP2(vmov,_a1a,_a1b)
+ VMAC(vqdmlal.s32,_a1a,_bh0_1,_bh2_1,1) /* 0 .. 18 */
+ VMAC(vmlal.s32,_a1a,_bh2_0,_bh2_0,1) /* 0 .. 19 */
+ VMAC(vmlal.s32,_a1a,_bh0_0,_bl0_0,1) /* 0 .. 20 */
+
+ VOP2(vswp,_a0b_1,_a0a_0)
+
+ VMAC(vqdmlsl.s32,_a1b,_bl0_1,_bl2_1,1) /*-2 .. 16 */
+ VMAC(vmlsl.s32,_a1b,_bl2_0,_bl2_0,1) /*-3 .. 16 */
+ VMAC(vmlal.s32,_a1b,_bl0_0,_bs0_0,1) /*-4 .. 17 */
+
+ VOP3(vsra.u64,_a0a,_a0b,"#28")
+ VOP3(vsub.i32,_bs0_1,_bl0_1,_bh0_1)
+ VOP2(vmovn.i64,_a0b_0,_a0b)
+
+ VOP2(vswp,_a1b_1,_a1a_0)
+ VOP3(vadd.i64,_a1b,_a0a,_a1b)
+
+
+ VMAC(vqdmull.s32,_a0a,_as2_0,_bs2_1,0) /* 0 .. 8 */
+ VOP2(vmovn.i64,_a0b_1,_a1b)
+ VOP3(vsra.u64,_a1a,_a1b,"#28")
+ VMAC(vqdmlal.s32,_a0a,_as0_0,_bh0_1,0) /* 0 .. 12 */
+ VOP2(vbic.i32,_a0b,"#0xf0000000")
+ "vstmia %[c]!, {"_a0b_0", "_a0b_1"}" "\n\t"
+
+ VMAC(vqdmull.s32,_a1b,_as2_0,_bs2_1,1) /* 0 .. 8 */
+ VMAC(vqdmlal.s32,_a1b,_as0_0,_bh0_1,1) /* 0 .. 12 */
+
+ VOP2(vmov,_a0b,_a0a) /* 0 .. 12 */
+ VMAC(vqdmlal.s32,_a0a,_bh2_0,_bh2_1,0) /* 0 .. 14 */
+ VMAC(vqdmlal.s32,_a0a,_bh0_0,_bl0_1,0) /* 0 .. 16 */
+
+ VMAC(vqdmlsl.s32,_a0b,_bl2_0,_bl2_1,0) /*-2 .. 12 */
+ VMAC(vqdmlal.s32,_a0b,_bl0_0,_bs0_1,0) /*-4 .. 14 */
+ VOP3(vadd.i64,_a0a_0,_a0a_0,_a1a_1)
+ VOP3(vadd.i64,_a0b_0,_a0b_0,_a1a_0)
+
+ VOP2(vmov,_a1a,_a1b) /* 0 .. 12 */
+ VMAC(vqdmlal.s32,_a1a,_bh2_0,_bh2_1,1) /* 0 .. 14 */
+ VMAC(vqdmlal.s32,_a1a,_bh0_0,_bl0_1,1) /* 0 .. 16 */
+
+ VOP2(vswp,_a0b_1,_a0a_0)
+
+ VMAC(vqdmlsl.s32,_a1b,_bl2_0,_bl2_1,1) /*-2 .. 12 */
+ VMAC(vqdmlal.s32,_a1b,_bl0_0,_bs0_1,1) /*-4 .. 14 */
+
+ VOP3(vsra.u64,_a0a,_a0b,"#28")
+ VOP3(vsub.i32,_bs2_0,_bl2_0,_bh2_0)
+ VOP2(vmovn.i64,_a0b_0,_a0b)
+
+ VOP2(vswp,_a1b_1,_a1a_0)
+ VOP3(vadd.i64,_a1b,_a0a,_a1b)
+
+ VMAC(vmull.s32,_a0a,_as2_1,_bs2_1,0)
+ VOP2(vmovn.i64,_a0b_1,_a1b)
+ VMAC(vqdmlal.s32,_a0a,_as0_0,_bh2_0,0)
+ VOP3(vsra.u64,_a1a,_a1b,"#28")
+ VMAC(vmlal.s32,_a0a,_as0_1,_bh0_1,0)
+ VOP2(vbic.i32,_a0b,"#0xf0000000")
+ "vstmia %[c]!, {"_a0b_0", "_a0b_1"}" "\n\t"
+
+ VMAC(vmull.s32,_a1b,_as2_1,_bs2_1,1)
+ VMAC(vqdmlal.s32,_a1b,_as0_0,_bh2_0,1)
+ VMAC(vmlal.s32,_a1b,_as0_1,_bh0_1,1)
+
+ VOP2(vmov,_a0b_1,_a0a_1)
+ VOP3(vadd.i64,_a0b_0,_a0a_0,_a1a_0)
+ VOP3(vadd.i64,_a0a_0,_a0a_0,_a1a_1)
+ VMAC(vmlal.s32,_a0a,_bh2_1,_bh2_1,0)
+ VMAC(vqdmlal.s32,_a0a,_bh0_0,_bl2_0,0)
+ VMAC(vmlal.s32,_a0a,_bh0_1,_bl0_1,0)
+
+ VMAC(vmlsl.s32,_a0b,_bl2_1,_bl2_1,0)
+ VMAC(vqdmlal.s32,_a0b,_bl0_0,_bs2_0,0)
+ VMAC(vmlal.s32,_a0b,_bl0_1,_bs0_1,0)
+
+ VOP2(vmov,_a1a,_a1b)
+ VMAC(vmlal.s32,_a1a,_bh2_1,_bh2_1,1)
+ VMAC(vqdmlal.s32,_a1a,_bh0_0,_bl2_0,1)
+ VMAC(vmlal.s32,_a1a,_bh0_1,_bl0_1,1)
+
+ VOP2(vswp,_a0b_1,_a0a_0)
+
+ VMAC(vmlsl.s32,_a1b,_bl2_1,_bl2_1,1)
+ VMAC(vqdmlal.s32,_a1b,_bl0_0,_bs2_0,1)
+ VMAC(vmlal.s32,_a1b,_bl0_1,_bs0_1,1)
+
+ VOP3(vsub.i32,_bs2_1,_bl2_1,_bh2_1)
+ VOP3(vsra.u64,_a0a,_a0b,"#28")
+ VOP2(vmovn.i64,_a0b_0,_a0b)
+
+ VOP2(vswp,_a1b_1,_a1a_0)
+ VOP3(vadd.i64,_a1b,_a0a,_a1b)
+
+ VMAC(vqdmull.s32,_a0a,_as0_0,_bh2_1,0)
+ VOP2(vmovn.i64,_a0b_1,_a1b)
+ VOP3(vsra.u64,_a1a,_a1b,"#28")
+ VMAC(vqdmlal.s32,_a0a,_as2_0,_bh0_1,0)
+ VOP2(vbic.i32,_a0b,"#0xf0000000")
+ "vstmia %[c]!, {"_a0b_0", "_a0b_1"}" "\n\t"
+
+ VMAC(vqdmull.s32,_a1b,_as0_0,_bh2_1,1)
+ VMAC(vqdmlal.s32,_a1b,_as2_0,_bh0_1,1)
+
+ VOP2(vmov,_a0b_1,_a0a_1)
+ VOP3(vadd.i64,_a0b_0,_a0a_0,_a1a_0)
+ VOP3(vadd.i64,_a0a_0,_a0a_0,_a1a_1)
+ VMAC(vqdmlal.s32,_a0a,_bh0_0,_bl2_1,0)
+ VMAC(vqdmlal.s32,_a0a,_bh2_0,_bl0_1,0)
+
+ VMAC(vqdmlal.s32,_a0b,_bl0_0,_bs2_1,0)
+ VMAC(vqdmlal.s32,_a0b,_bl2_0,_bs0_1,0)
+
+ VOP2(vmov,_a1a,_a1b)
+ VMAC(vqdmlal.s32,_a1a,_bh0_0,_bl2_1,1)
+ VMAC(vqdmlal.s32,_a1a,_bh2_0,_bl0_1,1)
+
+ VOP2(vswp,_a0b_1,_a0a_0)
+
+ VMAC(vqdmlal.s32,_a1b,_bl0_0,_bs2_1,1)
+ VMAC(vqdmlal.s32,_a1b,_bl2_0,_bs0_1,1)
+
+ VOP3(vsra.u64,_a0a,_a0b,"#28")
+ VOP2(vmovn.i64,_a0b_0,_a0b)
+
+ VOP2(vswp,_a1b_1,_a1a_0)
+ VOP3(vadd.i64,_a0a,_a0a,_a1b)
+
+ VOP2(vmovn.i64,_a0b_1,_a0a)
+ VOP3(vsra.u64,_a1a,_a0a,"#28")
+
+ VOP2(vbic.i32,_a0b,"#0xf0000000")
+
+ VOP2(vswp,_a1a_0,_a1a_1)
+
+ "vstmia %[c]!, {"_a0b_0", "_a0b_1"}" "\n\t"
+ "sub %[c], #64" "\n\t"
+
+ VOP3(vadd.i64,_a1a_1,_a1a_1,_a1a_0)
+
+ "vldmia %[c], {"_a0a_0", "_a0a_1", "_a0b_0"}" "\n\t"
+ VOP2(vaddw.s32,_a1a,_a0a_0)
+ VOP2(vmovn.i64,_a0a_0,_a1a)
+ VOP2(vshr.s64,_a1a,"#28")
+
+ VOP2(vaddw.s32,_a1a,_a0a_1)
+ VOP2(vmovn.i64,_a0a_1,_a1a)
+ VOP2(vshr.s64,_a1a,"#28")
+
+ VOP2(vbic.i32,_a0a,"#0xf0000000")
+
+ VOP2(vaddw.s32,_a1a,_a0b_0)
+ VOP2(vmovn.i64,_a0b_0,_a1a)
+
+ "vstmia %[c], {"_a0a_0", "_a0a_1", "_a0b_0"}" "\n\t"
+
+ : [b]"+r"(bs)
+ , [c]"+r"(vc)
+
+ :: "q0","q1","q2","q3",
+ "q4","q5","q6","q7",
+ "q12","q13","q14","q15",
+ "memory"
+ );
+}
+
+void gf_mulw_unsigned (gf_s *__restrict__ cs, const gf as, uint32_t b) {
+ uint32x2_t vmask = {(1<<28) - 1, (1<<28)-1};
+ assert(b<(1<<28));
+
+ uint64x2_t accum;
+ const uint32x2_t *va = (const uint32x2_t *) as->limb;
+ uint32x2_t *vo = (uint32x2_t *) cs->limb;
+ uint32x2_t vc, vn;
+ uint32x2_t vb = {b, 0};
+
+ vc = va[0];
+ accum = vmull_lane_u32(vc, vb, 0);
+ vo[0] = vmovn_u64(accum) & vmask;
+ accum = vshrq_n_u64(accum,28);
+
+ /* PERF: the right way to do this is to reduce behind, i.e.
+ * vmull + vmlal round 0
+ * vmull + vmlal round 1
+ * vmull + vmlal round 2
+ * vsraq round 0, 1
+ * vmull + vmlal round 3
+ * vsraq round 1, 2
+ * ...
+ */
+
+ int i;
+ for (i=1; i<8; i++) {
+ vn = va[i];
+ accum = vmlal_lane_u32(accum, vn, vb, 0);
+ vo[i] = vmovn_u64(accum) & vmask;
+ accum = vshrq_n_u64(accum,28);
+ vc = vn;
+ }
+
+ accum = xx_vaddup_u64(vrev128_u64(accum));
+ accum = vaddw_u32(accum, vo[0]);
+ vo[0] = vmovn_u64(accum) & vmask;
+
+ accum = vshrq_n_u64(accum,28);
+ vo[1] += vmovn_u64(accum);
+}
--- /dev/null
+/* Copyright (c) 2014-2016 Cryptography Research, Inc.
+ * Released under the MIT License. See LICENSE.txt for license information.
+ */
+
+#define GF_HEADROOM 2
+#define LIMBPERM(x) (((x)<<1 | (x)>>3) & 15)
+#define USE_NEON_PERM 1
+#define LIMBHI(x) ((x##ull)>>28)
+#define LIMBLO(x) ((x##ull)&((1ull<<28)-1))
+# define FIELD_LITERAL(a,b,c,d,e,f,g,h) \
+ {{LIMBLO(a),LIMBLO(e), LIMBHI(a),LIMBHI(e), \
+ LIMBLO(b),LIMBLO(f), LIMBHI(b),LIMBHI(f), \
+ LIMBLO(c),LIMBLO(g), LIMBHI(c),LIMBHI(g), \
+ LIMBLO(d),LIMBLO(h), LIMBHI(d),LIMBHI(h)}}
+
+#define LIMB_PLACE_VALUE(i) 28
+
+void gf_add_RAW (gf out, const gf a, const gf b) {
+ for (unsigned int i=0; i<sizeof(*out)/sizeof(uint32xn_t); i++) {
+ ((uint32xn_t*)out)[i] = ((const uint32xn_t*)a)[i] + ((const uint32xn_t*)b)[i];
+ }
+}
+
+void gf_sub_RAW (gf out, const gf a, const gf b) {
+ for (unsigned int i=0; i<sizeof(*out)/sizeof(uint32xn_t); i++) {
+ ((uint32xn_t*)out)[i] = ((const uint32xn_t*)a)[i] - ((const uint32xn_t*)b)[i];
+ }
+ /*
+ unsigned int i;
+ for (i=0; i<sizeof(*out)/sizeof(out->limb[0]); i++) {
+ out->limb[i] = a->limb[i] - b->limb[i];
+ }
+ */
+}
+
+void gf_bias (gf a, int amt) {
+ uint32_t co1 = ((1ull<<28)-1)*amt, co2 = co1-amt;
+ uint32x4_t lo = {co1,co2,co1,co1}, hi = {co1,co1,co1,co1};
+ uint32x4_t *aa = (uint32x4_t*) a;
+ aa[0] += lo;
+ aa[1] += hi;
+ aa[2] += hi;
+ aa[3] += hi;
+}
+
+void gf_weak_reduce (gf a) {
+
+ uint32x2_t *aa = (uint32x2_t*) a, vmask = {(1ull<<28)-1, (1ull<<28)-1}, vm2 = {0,-1},
+ tmp = vshr_n_u32(aa[7],28);
+
+ for (unsigned int i=7; i>=1; i--) {
+ aa[i] = vsra_n_u32(aa[i] & vmask, aa[i-1], 28);
+ }
+ aa[0] = (aa[0] & vmask) + vrev64_u32(tmp) + (tmp&vm2);
+}
+
--- /dev/null
+/* Copyright (c) 2014 Cryptography Research, Inc.
+ * Released under the MIT License. See LICENSE.txt for license information.
+ */
+
+#include "f_field.h"
+
+void gf_mul (gf_s *__restrict__ cs, const gf as, const gf bs) {
+ const uint64_t *a = as->limb, *b = bs->limb;
+ uint64_t *c = cs->limb;
+
+ __uint128_t accum0 = 0, accum1 = 0, accum2;
+ uint64_t mask = (1ull<<56) - 1;
+
+ uint64_t aa[4], bb[4], bbb[4];
+
+ unsigned int i;
+ for (i=0; i<4; i++) {
+ aa[i] = a[i] + a[i+4];
+ bb[i] = b[i] + b[i+4];
+ bbb[i] = bb[i] + b[i+4];
+ }
+
+ int I_HATE_UNROLLED_LOOPS = 0;
+
+ if (I_HATE_UNROLLED_LOOPS) {
+ /* The compiler probably won't unroll this,
+ * so it's like 80% slower.
+ */
+ for (i=0; i<4; i++) {
+ accum2 = 0;
+
+ unsigned int j;
+ for (j=0; j<=i; j++) {
+ accum2 += widemul(a[j], b[i-j]);
+ accum1 += widemul(aa[j], bb[i-j]);
+ accum0 += widemul(a[j+4], b[i-j+4]);
+ }
+ for (; j<4; j++) {
+ accum2 += widemul(a[j], b[i-j+8]);
+ accum1 += widemul(aa[j], bbb[i-j+4]);
+ accum0 += widemul(a[j+4], bb[i-j+4]);
+ }
+
+ accum1 -= accum2;
+ accum0 += accum2;
+
+ c[i] = ((uint64_t)(accum0)) & mask;
+ c[i+4] = ((uint64_t)(accum1)) & mask;
+
+ accum0 >>= 56;
+ accum1 >>= 56;
+ }
+ } else {
+ accum2 = widemul(a[0], b[0]);
+ accum1 += widemul(aa[0], bb[0]);
+ accum0 += widemul(a[4], b[4]);
+
+ accum2 += widemul(a[1], b[7]);
+ accum1 += widemul(aa[1], bbb[3]);
+ accum0 += widemul(a[5], bb[3]);
+
+ accum2 += widemul(a[2], b[6]);
+ accum1 += widemul(aa[2], bbb[2]);
+ accum0 += widemul(a[6], bb[2]);
+
+ accum2 += widemul(a[3], b[5]);
+ accum1 += widemul(aa[3], bbb[1]);
+ accum0 += widemul(a[7], bb[1]);
+
+ accum1 -= accum2;
+ accum0 += accum2;
+
+ c[0] = ((uint64_t)(accum0)) & mask;
+ c[4] = ((uint64_t)(accum1)) & mask;
+
+ accum0 >>= 56;
+ accum1 >>= 56;
+
+ accum2 = widemul(a[0], b[1]);
+ accum1 += widemul(aa[0], bb[1]);
+ accum0 += widemul(a[4], b[5]);
+
+ accum2 += widemul(a[1], b[0]);
+ accum1 += widemul(aa[1], bb[0]);
+ accum0 += widemul(a[5], b[4]);
+
+ accum2 += widemul(a[2], b[7]);
+ accum1 += widemul(aa[2], bbb[3]);
+ accum0 += widemul(a[6], bb[3]);
+
+ accum2 += widemul(a[3], b[6]);
+ accum1 += widemul(aa[3], bbb[2]);
+ accum0 += widemul(a[7], bb[2]);
+
+ accum1 -= accum2;
+ accum0 += accum2;
+
+ c[1] = ((uint64_t)(accum0)) & mask;
+ c[5] = ((uint64_t)(accum1)) & mask;
+
+ accum0 >>= 56;
+ accum1 >>= 56;
+
+ accum2 = widemul(a[0], b[2]);
+ accum1 += widemul(aa[0], bb[2]);
+ accum0 += widemul(a[4], b[6]);
+
+ accum2 += widemul(a[1], b[1]);
+ accum1 += widemul(aa[1], bb[1]);
+ accum0 += widemul(a[5], b[5]);
+
+ accum2 += widemul(a[2], b[0]);
+ accum1 += widemul(aa[2], bb[0]);
+ accum0 += widemul(a[6], b[4]);
+
+ accum2 += widemul(a[3], b[7]);
+ accum1 += widemul(aa[3], bbb[3]);
+ accum0 += widemul(a[7], bb[3]);
+
+ accum1 -= accum2;
+ accum0 += accum2;
+
+ c[2] = ((uint64_t)(accum0)) & mask;
+ c[6] = ((uint64_t)(accum1)) & mask;
+
+ accum0 >>= 56;
+ accum1 >>= 56;
+
+ accum2 = widemul(a[0], b[3]);
+ accum1 += widemul(aa[0], bb[3]);
+ accum0 += widemul(a[4], b[7]);
+
+ accum2 += widemul(a[1], b[2]);
+ accum1 += widemul(aa[1], bb[2]);
+ accum0 += widemul(a[5], b[6]);
+
+ accum2 += widemul(a[2], b[1]);
+ accum1 += widemul(aa[2], bb[1]);
+ accum0 += widemul(a[6], b[5]);
+
+ accum2 += widemul(a[3], b[0]);
+ accum1 += widemul(aa[3], bb[0]);
+ accum0 += widemul(a[7], b[4]);
+
+ accum1 -= accum2;
+ accum0 += accum2;
+
+ c[3] = ((uint64_t)(accum0)) & mask;
+ c[7] = ((uint64_t)(accum1)) & mask;
+
+ accum0 >>= 56;
+ accum1 >>= 56;
+ } /* !I_HATE_UNROLLED_LOOPS */
+
+ accum0 += accum1;
+ accum0 += c[4];
+ accum1 += c[0];
+ c[4] = ((uint64_t)(accum0)) & mask;
+ c[0] = ((uint64_t)(accum1)) & mask;
+
+ accum0 >>= 56;
+ accum1 >>= 56;
+
+ c[5] += ((uint64_t)(accum0));
+ c[1] += ((uint64_t)(accum1));
+}
+
+void gf_mulw_unsigned (gf_s *__restrict__ cs, const gf as, uint32_t b) {
+ const uint64_t *a = as->limb;
+ uint64_t *c = cs->limb;
+
+ __uint128_t accum0 = 0, accum4 = 0;
+ uint64_t mask = (1ull<<56) - 1;
+
+ int i;
+ for (i=0; i<4; i++) {
+ accum0 += widemul(b, a[i]);
+ accum4 += widemul(b, a[i+4]);
+ c[i] = accum0 & mask; accum0 >>= 56;
+ c[i+4] = accum4 & mask; accum4 >>= 56;
+ }
+
+ accum0 += accum4 + c[4];
+ c[4] = accum0 & mask;
+ c[5] += accum0 >> 56;
+
+ accum4 += c[0];
+ c[0] = accum4 & mask;
+ c[1] += accum4 >> 56;
+}
+
+void gf_sqr (gf_s *__restrict__ cs, const gf as) {
+ const uint64_t *a = as->limb;
+ uint64_t *c = cs->limb;
+
+ __uint128_t accum0 = 0, accum1 = 0, accum2;
+ uint64_t mask = (1ull<<56) - 1;
+
+ uint64_t aa[4];
+
+ /* For some reason clang doesn't vectorize this without prompting? */
+ unsigned int i;
+ for (i=0; i<4; i++) {
+ aa[i] = a[i] + a[i+4];
+ }
+
+ accum2 = widemul(a[0],a[3]);
+ accum0 = widemul(aa[0],aa[3]);
+ accum1 = widemul(a[4],a[7]);
+
+ accum2 += widemul(a[1], a[2]);
+ accum0 += widemul(aa[1], aa[2]);
+ accum1 += widemul(a[5], a[6]);
+
+ accum0 -= accum2;
+ accum1 += accum2;
+
+ c[3] = ((uint64_t)(accum1))<<1 & mask;
+ c[7] = ((uint64_t)(accum0))<<1 & mask;
+
+ accum0 >>= 55;
+ accum1 >>= 55;
+
+ accum0 += widemul(2*aa[1],aa[3]);
+ accum1 += widemul(2*a[5], a[7]);
+ accum0 += widemul(aa[2], aa[2]);
+ accum1 += accum0;
+
+ accum0 -= widemul(2*a[1], a[3]);
+ accum1 += widemul(a[6], a[6]);
+
+ accum2 = widemul(a[0],a[0]);
+ accum1 -= accum2;
+ accum0 += accum2;
+
+ accum0 -= widemul(a[2], a[2]);
+ accum1 += widemul(aa[0], aa[0]);
+ accum0 += widemul(a[4], a[4]);
+
+ c[0] = ((uint64_t)(accum0)) & mask;
+ c[4] = ((uint64_t)(accum1)) & mask;
+
+ accum0 >>= 56;
+ accum1 >>= 56;
+
+ accum2 = widemul(2*aa[2],aa[3]);
+ accum0 -= widemul(2*a[2], a[3]);
+ accum1 += widemul(2*a[6], a[7]);
+
+ accum1 += accum2;
+ accum0 += accum2;
+
+ accum2 = widemul(2*a[0],a[1]);
+ accum1 += widemul(2*aa[0], aa[1]);
+ accum0 += widemul(2*a[4], a[5]);
+
+ accum1 -= accum2;
+ accum0 += accum2;
+
+ c[1] = ((uint64_t)(accum0)) & mask;
+ c[5] = ((uint64_t)(accum1)) & mask;
+
+ accum0 >>= 56;
+ accum1 >>= 56;
+
+ accum2 = widemul(aa[3],aa[3]);
+ accum0 -= widemul(a[3], a[3]);
+ accum1 += widemul(a[7], a[7]);
+
+ accum1 += accum2;
+ accum0 += accum2;
+
+ accum2 = widemul(2*a[0],a[2]);
+ accum1 += widemul(2*aa[0], aa[2]);
+ accum0 += widemul(2*a[4], a[6]);
+
+ accum2 += widemul(a[1], a[1]);
+ accum1 += widemul(aa[1], aa[1]);
+ accum0 += widemul(a[5], a[5]);
+
+ accum1 -= accum2;
+ accum0 += accum2;
+
+ c[2] = ((uint64_t)(accum0)) & mask;
+ c[6] = ((uint64_t)(accum1)) & mask;
+
+ accum0 >>= 56;
+ accum1 >>= 56;
+
+ accum0 += c[3];
+ accum1 += c[7];
+ c[3] = ((uint64_t)(accum0)) & mask;
+ c[7] = ((uint64_t)(accum1)) & mask;
+
+ /* we could almost stop here, but it wouldn't be stable, so... */
+
+ accum0 >>= 56;
+ accum1 >>= 56;
+ c[4] += ((uint64_t)(accum0)) + ((uint64_t)(accum1));
+ c[0] += ((uint64_t)(accum1));
+}
+
--- /dev/null
+/* Copyright (c) 2014-2016 Cryptography Research, Inc.
+ * Released under the MIT License. See LICENSE.txt for license information.
+ */
+
+#define GF_HEADROOM 9999 /* Everything is reduced anyway */
+#define FIELD_LITERAL(a,b,c,d,e,f,g,h) {{a,b,c,d,e,f,g,h}}
+
+#define LIMB_PLACE_VALUE(i) 56
+
+void gf_add_RAW (gf out, const gf a, const gf b) {
+ for (unsigned int i=0; i<8; i++) {
+ out->limb[i] = a->limb[i] + b->limb[i];
+ }
+ gf_weak_reduce(out);
+}
+
+void gf_sub_RAW (gf out, const gf a, const gf b) {
+ uint64_t co1 = ((1ull<<56)-1)*2, co2 = co1-2;
+ for (unsigned int i=0; i<8; i++) {
+ out->limb[i] = a->limb[i] - b->limb[i] + ((i==4) ? co2 : co1);
+ }
+ gf_weak_reduce(out);
+}
+
+void gf_bias (gf a, int amt) {
+ (void) a;
+ (void) amt;
+}
+
+void gf_weak_reduce (gf a) {
+ uint64_t mask = (1ull<<56) - 1;
+ uint64_t tmp = a->limb[7] >> 56;
+ a->limb[4] += tmp;
+ for (unsigned int i=7; i>0; i--) {
+ a->limb[i] = (a->limb[i] & mask) + (a->limb[i-1]>>56);
+ }
+ a->limb[0] = (a->limb[0] & mask) + tmp;
+}
--- /dev/null
+/* Copyright (c) 2014 Cryptography Research, Inc.
+ * Released under the MIT License. See LICENSE.txt for license information.
+ */
+
+#include "f_field.h"
+
+void gf_mul (gf_s *__restrict__ cs, const gf as, const gf bs) {
+ const uint64_t *a = as->limb, *b = bs->limb;
+ uint64_t *c = cs->limb;
+
+ __uint128_t accum0 = 0, accum1 = 0, accum2;
+ uint64_t mask = (1ull<<56) - 1;
+
+ uint64_t aa[4] VECTOR_ALIGNED, bb[4] VECTOR_ALIGNED, bbb[4] VECTOR_ALIGNED;
+
+ /* For some reason clang doesn't vectorize this without prompting? */
+ unsigned int i;
+ for (i=0; i<sizeof(aa)/sizeof(uint64xn_t); i++) {
+ ((uint64xn_t*)aa)[i] = ((const uint64xn_t*)a)[i] + ((const uint64xn_t*)(&a[4]))[i];
+ ((uint64xn_t*)bb)[i] = ((const uint64xn_t*)b)[i] + ((const uint64xn_t*)(&b[4]))[i];
+ ((uint64xn_t*)bbb)[i] = ((const uint64xn_t*)bb)[i] + ((const uint64xn_t*)(&b[4]))[i];
+ }
+ /*
+ for (int i=0; i<4; i++) {
+ aa[i] = a[i] + a[i+4];
+ bb[i] = b[i] + b[i+4];
+ }
+ */
+
+ accum2 = widemul(&a[0],&b[3]);
+ accum0 = widemul(&aa[0],&bb[3]);
+ accum1 = widemul(&a[4],&b[7]);
+
+ mac(&accum2, &a[1], &b[2]);
+ mac(&accum0, &aa[1], &bb[2]);
+ mac(&accum1, &a[5], &b[6]);
+
+ mac(&accum2, &a[2], &b[1]);
+ mac(&accum0, &aa[2], &bb[1]);
+ mac(&accum1, &a[6], &b[5]);
+
+ mac(&accum2, &a[3], &b[0]);
+ mac(&accum0, &aa[3], &bb[0]);
+ mac(&accum1, &a[7], &b[4]);
+
+ accum0 -= accum2;
+ accum1 += accum2;
+
+ c[3] = ((uint64_t)(accum1)) & mask;
+ c[7] = ((uint64_t)(accum0)) & mask;
+
+ accum0 >>= 56;
+ accum1 >>= 56;
+
+ mac(&accum0, &aa[1],&bb[3]);
+ mac(&accum1, &a[5], &b[7]);
+ mac(&accum0, &aa[2], &bb[2]);
+ mac(&accum1, &a[6], &b[6]);
+ mac(&accum0, &aa[3], &bb[1]);
+ accum1 += accum0;
+
+ accum2 = widemul(&a[0],&b[0]);
+ accum1 -= accum2;
+ accum0 += accum2;
+
+ msb(&accum0, &a[1], &b[3]);
+ msb(&accum0, &a[2], &b[2]);
+ mac(&accum1, &a[7], &b[5]);
+ msb(&accum0, &a[3], &b[1]);
+ mac(&accum1, &aa[0], &bb[0]);
+ mac(&accum0, &a[4], &b[4]);
+
+ c[0] = ((uint64_t)(accum0)) & mask;
+ c[4] = ((uint64_t)(accum1)) & mask;
+
+ accum0 >>= 56;
+ accum1 >>= 56;
+
+ accum2 = widemul(&a[2],&b[7]);
+ mac(&accum0, &a[6], &bb[3]);
+ mac(&accum1, &aa[2], &bbb[3]);
+
+ mac(&accum2, &a[3], &b[6]);
+ mac(&accum0, &a[7], &bb[2]);
+ mac(&accum1, &aa[3], &bbb[2]);
+
+ mac(&accum2, &a[0],&b[1]);
+ mac(&accum1, &aa[0], &bb[1]);
+ mac(&accum0, &a[4], &b[5]);
+
+ mac(&accum2, &a[1], &b[0]);
+ mac(&accum1, &aa[1], &bb[0]);
+ mac(&accum0, &a[5], &b[4]);
+
+ accum1 -= accum2;
+ accum0 += accum2;
+
+ c[1] = ((uint64_t)(accum0)) & mask;
+ c[5] = ((uint64_t)(accum1)) & mask;
+
+ accum0 >>= 56;
+ accum1 >>= 56;
+
+ accum2 = widemul(&a[3],&b[7]);
+ mac(&accum0, &a[7], &bb[3]);
+ mac(&accum1, &aa[3], &bbb[3]);
+
+ mac(&accum2, &a[0],&b[2]);
+ mac(&accum1, &aa[0], &bb[2]);
+ mac(&accum0, &a[4], &b[6]);
+
+ mac(&accum2, &a[1], &b[1]);
+ mac(&accum1, &aa[1], &bb[1]);
+ mac(&accum0, &a[5], &b[5]);
+
+ mac(&accum2, &a[2], &b[0]);
+ mac(&accum1, &aa[2], &bb[0]);
+ mac(&accum0, &a[6], &b[4]);
+
+ accum1 -= accum2;
+ accum0 += accum2;
+
+ c[2] = ((uint64_t)(accum0)) & mask;
+ c[6] = ((uint64_t)(accum1)) & mask;
+
+ accum0 >>= 56;
+ accum1 >>= 56;
+
+ accum0 += c[3];
+ accum1 += c[7];
+ c[3] = ((uint64_t)(accum0)) & mask;
+ c[7] = ((uint64_t)(accum1)) & mask;
+
+ /* we could almost stop here, but it wouldn't be stable, so... */
+
+ accum0 >>= 56;
+ accum1 >>= 56;
+ c[4] += ((uint64_t)(accum0)) + ((uint64_t)(accum1));
+ c[0] += ((uint64_t)(accum1));
+}
+
+void gf_mulw_unsigned (gf_s *__restrict__ cs, const gf as, uint32_t b) {
+ const uint64_t *a = as->limb;
+ uint64_t *c = cs->limb;
+
+ __uint128_t accum0, accum4;
+ uint64_t mask = (1ull<<56) - 1;
+
+ accum0 = widemul_rm(b, &a[0]);
+ accum4 = widemul_rm(b, &a[4]);
+
+ c[0] = accum0 & mask; accum0 >>= 56;
+ c[4] = accum4 & mask; accum4 >>= 56;
+
+ mac_rm(&accum0, b, &a[1]);
+ mac_rm(&accum4, b, &a[5]);
+
+ c[1] = accum0 & mask; accum0 >>= 56;
+ c[5] = accum4 & mask; accum4 >>= 56;
+
+ mac_rm(&accum0, b, &a[2]);
+ mac_rm(&accum4, b, &a[6]);
+
+ c[2] = accum0 & mask; accum0 >>= 56;
+ c[6] = accum4 & mask; accum4 >>= 56;
+
+ mac_rm(&accum0, b, &a[3]);
+ mac_rm(&accum4, b, &a[7]);
+
+ c[3] = accum0 & mask; accum0 >>= 56;
+ c[7] = accum4 & mask; accum4 >>= 56;
+
+ accum0 += accum4 + c[4];
+ c[4] = accum0 & mask;
+ c[5] += accum0 >> 56;
+
+ accum4 += c[0];
+ c[0] = accum4 & mask;
+ c[1] += accum4 >> 56;
+}
+
+void gf_sqr (gf_s *__restrict__ cs, const gf as) {
+ const uint64_t *a = as->limb;
+ uint64_t *c = cs->limb;
+
+ __uint128_t accum0 = 0, accum1 = 0, accum2;
+ uint64_t mask = (1ull<<56) - 1;
+
+ uint64_t aa[4] VECTOR_ALIGNED;
+
+ /* For some reason clang doesn't vectorize this without prompting? */
+ unsigned int i;
+ for (i=0; i<sizeof(aa)/sizeof(uint64xn_t); i++) {
+ ((uint64xn_t*)aa)[i] = ((const uint64xn_t*)a)[i] + ((const uint64xn_t*)(&a[4]))[i];
+ }
+
+ accum2 = widemul(&a[0],&a[3]);
+ accum0 = widemul(&aa[0],&aa[3]);
+ accum1 = widemul(&a[4],&a[7]);
+
+ mac(&accum2, &a[1], &a[2]);
+ mac(&accum0, &aa[1], &aa[2]);
+ mac(&accum1, &a[5], &a[6]);
+
+ accum0 -= accum2;
+ accum1 += accum2;
+
+ c[3] = ((uint64_t)(accum1))<<1 & mask;
+ c[7] = ((uint64_t)(accum0))<<1 & mask;
+
+ accum0 >>= 55;
+ accum1 >>= 55;
+
+ mac2(&accum0, &aa[1],&aa[3]);
+ mac2(&accum1, &a[5], &a[7]);
+ mac(&accum0, &aa[2], &aa[2]);
+ accum1 += accum0;
+
+ msb2(&accum0, &a[1], &a[3]);
+ mac(&accum1, &a[6], &a[6]);
+
+ accum2 = widemul(&a[0],&a[0]);
+ accum1 -= accum2;
+ accum0 += accum2;
+
+ msb(&accum0, &a[2], &a[2]);
+ mac(&accum1, &aa[0], &aa[0]);
+ mac(&accum0, &a[4], &a[4]);
+
+ c[0] = ((uint64_t)(accum0)) & mask;
+ c[4] = ((uint64_t)(accum1)) & mask;
+
+ accum0 >>= 56;
+ accum1 >>= 56;
+
+ accum2 = widemul2(&aa[2],&aa[3]);
+ msb2(&accum0, &a[2], &a[3]);
+ mac2(&accum1, &a[6], &a[7]);
+
+ accum1 += accum2;
+ accum0 += accum2;
+
+ accum2 = widemul2(&a[0],&a[1]);
+ mac2(&accum1, &aa[0], &aa[1]);
+ mac2(&accum0, &a[4], &a[5]);
+
+ accum1 -= accum2;
+ accum0 += accum2;
+
+ c[1] = ((uint64_t)(accum0)) & mask;
+ c[5] = ((uint64_t)(accum1)) & mask;
+
+ accum0 >>= 56;
+ accum1 >>= 56;
+
+ accum2 = widemul(&aa[3],&aa[3]);
+ msb(&accum0, &a[3], &a[3]);
+ mac(&accum1, &a[7], &a[7]);
+
+ accum1 += accum2;
+ accum0 += accum2;
+
+ accum2 = widemul2(&a[0],&a[2]);
+ mac2(&accum1, &aa[0], &aa[2]);
+ mac2(&accum0, &a[4], &a[6]);
+
+ mac(&accum2, &a[1], &a[1]);
+ mac(&accum1, &aa[1], &aa[1]);
+ mac(&accum0, &a[5], &a[5]);
+
+ accum1 -= accum2;
+ accum0 += accum2;
+
+ c[2] = ((uint64_t)(accum0)) & mask;
+ c[6] = ((uint64_t)(accum1)) & mask;
+
+ accum0 >>= 56;
+ accum1 >>= 56;
+
+ accum0 += c[3];
+ accum1 += c[7];
+ c[3] = ((uint64_t)(accum0)) & mask;
+ c[7] = ((uint64_t)(accum1)) & mask;
+
+ /* we could almost stop here, but it wouldn't be stable, so... */
+
+ accum0 >>= 56;
+ accum1 >>= 56;
+ c[4] += ((uint64_t)(accum0)) + ((uint64_t)(accum1));
+ c[0] += ((uint64_t)(accum1));
+}
--- /dev/null
+/* Copyright (c) 2014-2016 Cryptography Research, Inc.
+ * Released under the MIT License. See LICENSE.txt for license information.
+ */
+
+#define GF_HEADROOM 60
+#define FIELD_LITERAL(a,b,c,d,e,f,g,h) {{a,b,c,d,e,f,g,h}}
+#define LIMB_PLACE_VALUE(i) 56
+
+void gf_add_RAW (gf out, const gf a, const gf b) {
+ for (unsigned int i=0; i<sizeof(*out)/sizeof(uint64xn_t); i++) {
+ ((uint64xn_t*)out)[i] = ((const uint64xn_t*)a)[i] + ((const uint64xn_t*)b)[i];
+ }
+ /*
+ unsigned int i;
+ for (i=0; i<sizeof(*out)/sizeof(out->limb[0]); i++) {
+ out->limb[i] = a->limb[i] + b->limb[i];
+ }
+ */
+}
+
+void gf_sub_RAW (gf out, const gf a, const gf b) {
+ for (unsigned int i=0; i<sizeof(*out)/sizeof(uint64xn_t); i++) {
+ ((uint64xn_t*)out)[i] = ((const uint64xn_t*)a)[i] - ((const uint64xn_t*)b)[i];
+ }
+ /*
+ unsigned int i;
+ for (i=0; i<sizeof(*out)/sizeof(out->limb[0]); i++) {
+ out->limb[i] = a->limb[i] - b->limb[i];
+ }
+ */
+}
+
+void gf_bias (gf a, int amt) {
+ uint64_t co1 = ((1ull<<56)-1)*amt, co2 = co1-amt;
+
+#if __AVX2__
+ uint64x4_t lo = {co1,co1,co1,co1}, hi = {co2,co1,co1,co1};
+ uint64x4_t *aa = (uint64x4_t*) a;
+ aa[0] += lo;
+ aa[1] += hi;
+#elif __SSE2__
+ uint64x2_t lo = {co1,co1}, hi = {co2,co1};
+ uint64x2_t *aa = (uint64x2_t*) a;
+ aa[0] += lo;
+ aa[1] += lo;
+ aa[2] += hi;
+ aa[3] += lo;
+#else
+ for (unsigned int i=0; i<sizeof(*a)/sizeof(uint64_t); i++) {
+ a->limb[i] += (i==4) ? co2 : co1;
+ }
+#endif
+}
+
+void gf_weak_reduce (gf a) {
+ /* PERF: use pshufb/palignr if anyone cares about speed of this */
+ uint64_t mask = (1ull<<56) - 1;
+ uint64_t tmp = a->limb[7] >> 56;
+ a->limb[4] += tmp;
+ for (unsigned int i=7; i>0; i--) {
+ a->limb[i] = (a->limb[i] & mask) + (a->limb[i-1]>>56);
+ }
+ a->limb[0] = (a->limb[0] & mask) + tmp;
+}
+
--- /dev/null
+/**
+ * @cond internal
+ * @file f_arithmetic.c
+ * @copyright
+ * Copyright (c) 2014 Cryptography Research, Inc. \n
+ * Released under the MIT License. See LICENSE.txt for license information.
+ * @author Mike Hamburg
+ * @brief Field-specific arithmetic.
+ */
+
+#include "field.h"
+
+mask_t gf_isr (
+ gf a,
+ const gf x
+) {
+ gf L0, L1, L2;
+ gf_sqr (L1, x );
+ gf_mul (L2, x, L1 );
+ gf_sqr (L1, L2 );
+ gf_mul (L2, x, L1 );
+ gf_sqrn (L1, L2, 3 );
+ gf_mul (L0, L2, L1 );
+ gf_sqrn (L1, L0, 3 );
+ gf_mul (L0, L2, L1 );
+ gf_sqrn (L2, L0, 9 );
+ gf_mul (L1, L0, L2 );
+ gf_sqr (L0, L1 );
+ gf_mul (L2, x, L0 );
+ gf_sqrn (L0, L2, 18 );
+ gf_mul (L2, L1, L0 );
+ gf_sqrn (L0, L2, 37 );
+ gf_mul (L1, L2, L0 );
+ gf_sqrn (L0, L1, 37 );
+ gf_mul (L1, L2, L0 );
+ gf_sqrn (L0, L1, 111 );
+ gf_mul (L2, L1, L0 );
+ gf_sqr (L0, L2 );
+ gf_mul (L1, x, L0 );
+ gf_sqrn (L0, L1, 223 );
+ gf_mul (L1, L2, L0 );
+ gf_sqr (L2, L1);
+ gf_mul (L0, L2, x);
+ gf_copy(a,L1);
+ return gf_eq(L0,ONE);
+}
--- /dev/null
+/**
+ * @cond internal
+ * @file shake.c
+ * @copyright
+ * Uses public domain code by Mathias Panzenböck \n
+ * Uses CC0 code by David Leon Gil, 2015 \n
+ * Copyright (c) 2015 Cryptography Research, Inc. \n
+ * Released under the MIT License. See LICENSE.txt for license information.
+ * @author Mike Hamburg
+ * @brief SHA-3-n and SHAKE-n instances.
+ * @warning EXPERIMENTAL! The names, parameter orders etc are likely to change.
+ */
+
+#define __STDC_WANT_LIB_EXT1__ 1 /* for memset_s */
+#define _BSD_SOURCE 1 /* for endian */
+#define _DEFAULT_SOURCE 1 /* for endian with glibc 2.20 */
+#include <assert.h>
+#include <stdint.h>
+#include <string.h>
+
+#include "portable_endian.h"
+#include "keccak_internal.h"
+#include <decaf/shake.h>
+
+#define FLAG_ABSORBING 'A'
+#define FLAG_SQUEEZING 'Z'
+
+/** Constants. **/
+static const uint8_t pi[24] = {
+ 10, 7, 11, 17, 18, 3, 5, 16, 8, 21, 24, 4,
+ 15, 23, 19, 13, 12, 2, 20, 14, 22, 9, 6, 1
+};
+
+#define RC_B(x,n) ((((x##ull)>>n)&1)<<((1<<n)-1))
+#define RC_X(x) (RC_B(x,0)|RC_B(x,1)|RC_B(x,2)|RC_B(x,3)|RC_B(x,4)|RC_B(x,5)|RC_B(x,6))
+static const uint64_t RC[24] = {
+ RC_X(0x01), RC_X(0x1a), RC_X(0x5e), RC_X(0x70), RC_X(0x1f), RC_X(0x21),
+ RC_X(0x79), RC_X(0x55), RC_X(0x0e), RC_X(0x0c), RC_X(0x35), RC_X(0x26),
+ RC_X(0x3f), RC_X(0x4f), RC_X(0x5d), RC_X(0x53), RC_X(0x52), RC_X(0x48),
+ RC_X(0x16), RC_X(0x66), RC_X(0x79), RC_X(0x58), RC_X(0x21), RC_X(0x74)
+};
+
+static inline uint64_t rol(uint64_t x, int s) {
+ return (x << s) | (x >> (64 - s));
+}
+
+/* Helper macros to unroll the permutation. */
+#define REPEAT5(e) e e e e e
+#define FOR51(v, e) v = 0; REPEAT5(e; v += 1;)
+#ifndef SHAKE_NO_UNROLL_LOOPS
+# define FOR55(v, e) v = 0; REPEAT5(e; v += 5;)
+# define REPEAT24(e) e e e e e e e e e e e e e e e e e e e e e e e e
+#else
+# define FOR55(v, e) for (v=0; v<25; v+= 5) { e; }
+# define REPEAT24(e) {int _j=0; for (_j=0; _j<24; _j++) { e }}
+#endif
+
+/*** The Keccak-f[1600] permutation ***/
+void keccakf(kdomain_t state, uint8_t start_round) {
+ uint64_t* a = state->w;
+ uint64_t b[5] = {0}, t, u;
+ uint8_t x, y, i;
+
+ for (i=0; i<25; i++) a[i] = le64toh(a[i]);
+
+ for (i = start_round; i < 24; i++) {
+ FOR51(x, b[x] = 0; )
+ FOR55(y, FOR51(x, b[x] ^= a[x + y]; ))
+ FOR55(y, FOR51(x,
+ a[y + x] ^= b[(x + 4) % 5] ^ rol(b[(x + 1) % 5], 1);
+ ))
+ // Rho and pi
+ t = a[1];
+ x = y = 0;
+ REPEAT24(u = a[pi[x]]; y += x+1; a[pi[x]] = rol(t, y % 64); t = u; x++; )
+ // Chi
+ FOR55(y,
+ FOR51(x, b[x] = a[y + x];)
+ FOR51(x, a[y + x] = b[x] ^ ((~b[(x + 1) % 5]) & b[(x + 2) % 5]);)
+ )
+ // Iota
+ a[0] ^= RC[i];
+ }
+
+ for (i=0; i<25; i++) a[i] = htole64(a[i]);
+}
+
+decaf_error_t decaf_sha3_update (
+ struct decaf_keccak_sponge_s * __restrict__ decaf_sponge,
+ const uint8_t *in,
+ size_t len
+) {
+ assert(decaf_sponge->params->position < decaf_sponge->params->rate);
+ assert(decaf_sponge->params->rate < sizeof(decaf_sponge->state));
+ assert(decaf_sponge->params->flags == FLAG_ABSORBING);
+ while (len) {
+ size_t cando = decaf_sponge->params->rate - decaf_sponge->params->position, i;
+ uint8_t* state = &decaf_sponge->state->b[decaf_sponge->params->position];
+ if (cando > len) {
+ for (i = 0; i < len; i += 1) state[i] ^= in[i];
+ decaf_sponge->params->position += len;
+ break;
+ } else {
+ for (i = 0; i < cando; i += 1) state[i] ^= in[i];
+ dokeccak(decaf_sponge);
+ len -= cando;
+ in += cando;
+ }
+ }
+ return (decaf_sponge->params->flags == FLAG_ABSORBING) ? DECAF_SUCCESS : DECAF_FAILURE;
+}
+
+decaf_error_t decaf_sha3_output (
+ decaf_keccak_sponge_t decaf_sponge,
+ uint8_t * __restrict__ out,
+ size_t len
+) {
+ decaf_error_t ret = DECAF_SUCCESS;
+ assert(decaf_sponge->params->position < decaf_sponge->params->rate);
+ assert(decaf_sponge->params->rate < sizeof(decaf_sponge->state));
+
+ if (decaf_sponge->params->max_out != 0xFF) {
+ if (decaf_sponge->params->remaining >= len) {
+ decaf_sponge->params->remaining -= len;
+ } else {
+ decaf_sponge->params->remaining = 0;
+ ret = DECAF_FAILURE;
+ }
+ }
+
+ switch (decaf_sponge->params->flags) {
+ case FLAG_SQUEEZING: break;
+ case FLAG_ABSORBING:
+ {
+ uint8_t* state = decaf_sponge->state->b;
+ state[decaf_sponge->params->position] ^= decaf_sponge->params->pad;
+ state[decaf_sponge->params->rate - 1] ^= decaf_sponge->params->rate_pad;
+ dokeccak(decaf_sponge);
+ decaf_sponge->params->flags = FLAG_SQUEEZING;
+ break;
+ }
+ default:
+ assert(0);
+ }
+
+ while (len) {
+ size_t cando = decaf_sponge->params->rate - decaf_sponge->params->position;
+ uint8_t* state = &decaf_sponge->state->b[decaf_sponge->params->position];
+ if (cando > len) {
+ memcpy(out, state, len);
+ decaf_sponge->params->position += len;
+ return ret;
+ } else {
+ memcpy(out, state, cando);
+ dokeccak(decaf_sponge);
+ len -= cando;
+ out += cando;
+ }
+ }
+ return ret;
+}
+
+decaf_error_t decaf_sha3_final (
+ decaf_keccak_sponge_t decaf_sponge,
+ uint8_t * __restrict__ out,
+ size_t len
+) {
+ decaf_error_t ret = decaf_sha3_output(decaf_sponge,out,len);
+ decaf_sha3_reset(decaf_sponge);
+ return ret;
+}
+
+void decaf_sha3_reset (
+ decaf_keccak_sponge_t decaf_sponge
+) {
+ decaf_sha3_init(decaf_sponge, decaf_sponge->params);
+ decaf_sponge->params->flags = FLAG_ABSORBING;
+ decaf_sponge->params->remaining = decaf_sponge->params->max_out;
+}
+
+void decaf_sha3_destroy (decaf_keccak_sponge_t decaf_sponge) {
+ decaf_bzero(decaf_sponge, sizeof(decaf_keccak_sponge_t));
+}
+
+void decaf_sha3_init (
+ decaf_keccak_sponge_t decaf_sponge,
+ const struct decaf_kparams_s *params
+) {
+ memset(decaf_sponge->state, 0, sizeof(decaf_sponge->state));
+ decaf_sponge->params[0] = params[0];
+ decaf_sponge->params->position = 0;
+}
+
+decaf_error_t decaf_sha3_hash (
+ uint8_t *out,
+ size_t outlen,
+ const uint8_t *in,
+ size_t inlen,
+ const struct decaf_kparams_s *params
+) {
+ decaf_keccak_sponge_t decaf_sponge;
+ decaf_sha3_init(decaf_sponge, params);
+ decaf_sha3_update(decaf_sponge, in, inlen);
+ decaf_error_t ret = decaf_sha3_output(decaf_sponge, out, outlen);
+ decaf_sha3_destroy(decaf_sponge);
+ return ret;
+}
+
+#define DEFSHAKE(n) \
+ const struct decaf_kparams_s DECAF_SHAKE##n##_params_s = \
+ { 0, FLAG_ABSORBING, 200-n/4, 0, 0x1f, 0x80, 0xFF, 0xFF };
+
+#define DEFSHA3(n) \
+ const struct decaf_kparams_s DECAF_SHA3_##n##_params_s = \
+ { 0, FLAG_ABSORBING, 200-n/4, 0, 0x06, 0x80, n/8, n/8 };
+
+size_t decaf_sha3_default_output_bytes (
+ const decaf_keccak_sponge_t s
+) {
+ return (s->params->max_out == 0xFF)
+ ? (200-s->params->rate)
+ : ((200-s->params->rate)/2);
+}
+
+size_t decaf_sha3_max_output_bytes (
+ const decaf_keccak_sponge_t s
+) {
+ return (s->params->max_out == 0xFF)
+ ? SIZE_MAX
+ : (size_t)((200-s->params->rate)/2);
+}
+
+DEFSHAKE(128)
+DEFSHAKE(256)
+DEFSHA3(224)
+DEFSHA3(256)
+DEFSHA3(384)
+DEFSHA3(512)
+
+/* FUTURE: Keyak instances, etc */
--- /dev/null
+/* Copyright (c) 2015 Cryptography Research, Inc.
+ * Released under the MIT License. See LICENSE.txt for license information.
+ */
+
+/**
+ * @file utils.c
+ * @author Mike Hamburg
+ * @brief Decaf utility functions.
+ */
+
+#include <decaf/common.h>
+
+void decaf_bzero (
+ void *s,
+ size_t size
+) {
+#ifdef __STDC_LIB_EXT1__
+ memset_s(s, size, 0, size);
+#else
+ const size_t sw = sizeof(decaf_word_t);
+ volatile uint8_t *destroy = (volatile uint8_t *)s;
+ for (; size && ((uintptr_t)destroy)%sw; size--, destroy++)
+ *destroy = 0;
+ for (; size >= sw; size -= sw, destroy += sw)
+ *(volatile decaf_word_t *)destroy = 0;
+ for (; size; size--, destroy++)
+ *destroy = 0;
+#endif
+}
+
+decaf_bool_t decaf_memeq (
+ const void *data1_,
+ const void *data2_,
+ size_t size
+) {
+ const unsigned char *data1 = (const unsigned char *)data1_;
+ const unsigned char *data2 = (const unsigned char *)data2_;
+ unsigned char ret = 0;
+ for (; size; size--, data1++, data2++) {
+ ret |= *data1 ^ *data2;
+ }
+ return (((decaf_dword_t)ret) - 1) >> 8;
+}
projects / oweals / openssl.git / commitdiff