2 * Copyright 2017-2018 The OpenSSL Project Authors. All Rights Reserved.
3 * Copyright 2015-2016 Cryptography Research, Inc.
5 * Licensed under the OpenSSL license (the "License"). You may not use
6 * this file except in compliance with the License. You can obtain a copy
7 * in the file LICENSE in the source distribution or at
8 * https://www.openssl.org/source/license.html
10 * Originally written by Mike Hamburg
12 #include <openssl/crypto.h>
15 #include "constant_time.h"
16 #include "point_448.h"
18 static const c448_word_t MONTGOMERY_FACTOR = (c448_word_t) 0x3bd440fae918bc5;
19 static const curve448_scalar_t sc_p = {
22 SC_LIMB(0x2378c292ab5844f3), SC_LIMB(0x216cc2728dc58f55),
23 SC_LIMB(0xc44edb49aed63690), SC_LIMB(0xffffffff7cca23e9),
24 SC_LIMB(0xffffffffffffffff), SC_LIMB(0xffffffffffffffff),
25 SC_LIMB(0x3fffffffffffffff)
32 SC_LIMB(0xe3539257049b9b60), SC_LIMB(0x7af32c4bc1b195d9),
33 SC_LIMB(0x0d66de2388ea1859), SC_LIMB(0xae17cf725ee4d838),
34 SC_LIMB(0x1a9cc14ba3c47c44), SC_LIMB(0x2052bcb7e4d070af),
35 SC_LIMB(0x3402a939f823b729)
40 #define WBITS C448_WORD_BITS /* NB this may be different from ARCH_WORD_BITS */
42 const curve448_scalar_t curve448_scalar_one = {{{1}}};
43 const curve448_scalar_t curve448_scalar_zero = {{{0}}};
46 * {extra,accum} - sub +? p
47 * Must have extra <= 1
49 static void sc_subx(curve448_scalar_t out,
50 const c448_word_t accum[C448_SCALAR_LIMBS],
51 const curve448_scalar_t sub,
52 const curve448_scalar_t p, c448_word_t extra)
54 c448_dsword_t chain = 0;
58 for (i = 0; i < C448_SCALAR_LIMBS; i++) {
59 chain = (chain + accum[i]) - sub->limb[i];
60 out->limb[i] = (c448_word_t)chain;
63 borrow = (c448_word_t)chain + extra; /* = 0 or -1 */
66 for (i = 0; i < C448_SCALAR_LIMBS; i++) {
67 chain = (chain + out->limb[i]) + (p->limb[i] & borrow);
68 out->limb[i] = (c448_word_t)chain;
73 static void sc_montmul(curve448_scalar_t out, const curve448_scalar_t a,
74 const curve448_scalar_t b)
77 c448_word_t accum[C448_SCALAR_LIMBS + 1] = { 0 };
78 c448_word_t hi_carry = 0;
80 for (i = 0; i < C448_SCALAR_LIMBS; i++) {
81 c448_word_t mand = a->limb[i];
82 const c448_word_t *mier = b->limb;
84 c448_dword_t chain = 0;
85 for (j = 0; j < C448_SCALAR_LIMBS; j++) {
86 chain += ((c448_dword_t) mand) * mier[j] + accum[j];
87 accum[j] = (c448_word_t)chain;
90 accum[j] = (c448_word_t)chain;
92 mand = accum[0] * MONTGOMERY_FACTOR;
95 for (j = 0; j < C448_SCALAR_LIMBS; j++) {
96 chain += (c448_dword_t) mand *mier[j] + accum[j];
98 accum[j - 1] = (c448_word_t)chain;
103 accum[j - 1] = (c448_word_t)chain;
104 hi_carry = chain >> WBITS;
107 sc_subx(out, accum, sc_p, sc_p, hi_carry);
110 void curve448_scalar_mul(curve448_scalar_t out, const curve448_scalar_t a,
111 const curve448_scalar_t b)
113 sc_montmul(out, a, b);
114 sc_montmul(out, out, sc_r2);
117 void curve448_scalar_sub(curve448_scalar_t out, const curve448_scalar_t a,
118 const curve448_scalar_t b)
120 sc_subx(out, a->limb, b, sc_p, 0);
123 void curve448_scalar_add(curve448_scalar_t out, const curve448_scalar_t a,
124 const curve448_scalar_t b)
126 c448_dword_t chain = 0;
129 for (i = 0; i < C448_SCALAR_LIMBS; i++) {
130 chain = (chain + a->limb[i]) + b->limb[i];
131 out->limb[i] = (c448_word_t)chain;
134 sc_subx(out, out->limb, sc_p, sc_p, (c448_word_t)chain);
137 static ossl_inline void scalar_decode_short(curve448_scalar_t s,
138 const unsigned char *ser,
141 unsigned int i, j, k = 0;
143 for (i = 0; i < C448_SCALAR_LIMBS; i++) {
146 for (j = 0; j < sizeof(c448_word_t) && k < nbytes; j++, k++)
147 out |= ((c448_word_t) ser[k]) << (8 * j);
152 c448_error_t curve448_scalar_decode(
154 const unsigned char ser[C448_SCALAR_BYTES])
157 c448_dsword_t accum = 0;
159 scalar_decode_short(s, ser, C448_SCALAR_BYTES);
160 for (i = 0; i < C448_SCALAR_LIMBS; i++)
161 accum = (accum + s->limb[i] - sc_p->limb[i]) >> WBITS;
162 /* Here accum == 0 or -1 */
164 curve448_scalar_mul(s, s, curve448_scalar_one); /* ham-handed reduce */
166 return c448_succeed_if(~word_is_zero((uint32_t)accum));
169 void curve448_scalar_destroy(curve448_scalar_t scalar)
171 OPENSSL_cleanse(scalar, sizeof(curve448_scalar_t));
174 void curve448_scalar_decode_long(curve448_scalar_t s,
175 const unsigned char *ser, size_t ser_len)
178 curve448_scalar_t t1, t2;
181 curve448_scalar_copy(s, curve448_scalar_zero);
185 i = ser_len - (ser_len % C448_SCALAR_BYTES);
187 i -= C448_SCALAR_BYTES;
189 scalar_decode_short(t1, &ser[i], ser_len - i);
191 if (ser_len == sizeof(curve448_scalar_t)) {
193 /* ham-handed reduce */
194 curve448_scalar_mul(s, t1, curve448_scalar_one);
195 curve448_scalar_destroy(t1);
200 i -= C448_SCALAR_BYTES;
201 sc_montmul(t1, t1, sc_r2);
202 ignore_result(curve448_scalar_decode(t2, ser + i));
203 curve448_scalar_add(t1, t1, t2);
206 curve448_scalar_copy(s, t1);
207 curve448_scalar_destroy(t1);
208 curve448_scalar_destroy(t2);
211 void curve448_scalar_encode(unsigned char ser[C448_SCALAR_BYTES],
212 const curve448_scalar_t s)
214 unsigned int i, j, k = 0;
216 for (i = 0; i < C448_SCALAR_LIMBS; i++) {
217 for (j = 0; j < sizeof(c448_word_t); j++, k++)
218 ser[k] = s->limb[i] >> (8 * j);
222 void curve448_scalar_halve(curve448_scalar_t out, const curve448_scalar_t a)
224 c448_word_t mask = 0 - (a->limb[0] & 1);
225 c448_dword_t chain = 0;
227 for (i = 0; i < C448_SCALAR_LIMBS; i++) {
228 chain = (chain + a->limb[i]) + (sc_p->limb[i] & mask);
229 out->limb[i] = (c448_word_t)chain;
230 chain >>= C448_WORD_BITS;
232 for (i = 0; i < C448_SCALAR_LIMBS - 1; i++)
233 out->limb[i] = out->limb[i] >> 1 | out->limb[i + 1] << (WBITS - 1);
234 out->limb[i] = out->limb[i] >> 1 | (c448_word_t)(chain << (WBITS - 1));