2 * Copyright 2014-2016 The OpenSSL Project Authors. All Rights Reserved.
3 * Copyright (c) 2014, Intel Corporation. All Rights Reserved.
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 Shay Gueron (1, 2), and Vlad Krasnov (1)
11 * (1) Intel Corporation, Israel Development Center, Haifa, Israel
12 * (2) University of Haifa, Israel
15 * S.Gueron and V.Krasnov, "Fast Prime Field Elliptic Curve Cryptography with
21 #include "internal/cryptlib.h"
22 #include "internal/bn_int.h"
26 # define TOBN(hi,lo) lo,hi
28 # define TOBN(hi,lo) ((BN_ULONG)hi<<32|lo)
32 # define ALIGN32 __attribute((aligned(32)))
33 #elif defined(_MSC_VER)
34 # define ALIGN32 __declspec(align(32))
39 #define ALIGNPTR(p,N) ((unsigned char *)p+N-(size_t)p%N)
40 #define P256_LIMBS (256/BN_BITS2)
42 typedef unsigned short u16;
45 BN_ULONG X[P256_LIMBS];
46 BN_ULONG Y[P256_LIMBS];
47 BN_ULONG Z[P256_LIMBS];
51 BN_ULONG X[P256_LIMBS];
52 BN_ULONG Y[P256_LIMBS];
55 typedef P256_POINT_AFFINE PRECOMP256_ROW[64];
57 /* structure for precomputed multiples of the generator */
58 struct nistz256_pre_comp_st {
59 const EC_GROUP *group; /* Parent EC_GROUP object */
60 size_t w; /* Window size */
62 * Constant time access to the X and Y coordinates of the pre-computed,
63 * generator multiplies, in the Montgomery domain. Pre-calculated
64 * multiplies are stored in affine form.
66 PRECOMP256_ROW *precomp;
67 void *precomp_storage;
68 CRYPTO_REF_COUNT references;
72 /* Functions implemented in assembly */
74 * Most of below mentioned functions *preserve* the property of inputs
75 * being fully reduced, i.e. being in [0, modulus) range. Simply put if
76 * inputs are fully reduced, then output is too. Note that reverse is
77 * not true, in sense that given partially reduced inputs output can be
78 * either, not unlikely reduced. And "most" in first sentence refers to
79 * the fact that given the calculations flow one can tolerate that
80 * addition, 1st function below, produces partially reduced result *if*
81 * multiplications by 2 and 3, which customarily use addition, fully
82 * reduce it. This effectively gives two options: a) addition produces
83 * fully reduced result [as long as inputs are, just like remaining
84 * functions]; b) addition is allowed to produce partially reduced
85 * result, but multiplications by 2 and 3 perform additional reduction
86 * step. Choice between the two can be platform-specific, but it was a)
87 * in all cases so far...
89 /* Modular add: res = a+b mod P */
90 void ecp_nistz256_add(BN_ULONG res[P256_LIMBS],
91 const BN_ULONG a[P256_LIMBS],
92 const BN_ULONG b[P256_LIMBS]);
93 /* Modular mul by 2: res = 2*a mod P */
94 void ecp_nistz256_mul_by_2(BN_ULONG res[P256_LIMBS],
95 const BN_ULONG a[P256_LIMBS]);
96 /* Modular mul by 3: res = 3*a mod P */
97 void ecp_nistz256_mul_by_3(BN_ULONG res[P256_LIMBS],
98 const BN_ULONG a[P256_LIMBS]);
100 /* Modular div by 2: res = a/2 mod P */
101 void ecp_nistz256_div_by_2(BN_ULONG res[P256_LIMBS],
102 const BN_ULONG a[P256_LIMBS]);
103 /* Modular sub: res = a-b mod P */
104 void ecp_nistz256_sub(BN_ULONG res[P256_LIMBS],
105 const BN_ULONG a[P256_LIMBS],
106 const BN_ULONG b[P256_LIMBS]);
107 /* Modular neg: res = -a mod P */
108 void ecp_nistz256_neg(BN_ULONG res[P256_LIMBS], const BN_ULONG a[P256_LIMBS]);
109 /* Montgomery mul: res = a*b*2^-256 mod P */
110 void ecp_nistz256_mul_mont(BN_ULONG res[P256_LIMBS],
111 const BN_ULONG a[P256_LIMBS],
112 const BN_ULONG b[P256_LIMBS]);
113 /* Montgomery sqr: res = a*a*2^-256 mod P */
114 void ecp_nistz256_sqr_mont(BN_ULONG res[P256_LIMBS],
115 const BN_ULONG a[P256_LIMBS]);
116 /* Convert a number from Montgomery domain, by multiplying with 1 */
117 void ecp_nistz256_from_mont(BN_ULONG res[P256_LIMBS],
118 const BN_ULONG in[P256_LIMBS]);
119 /* Convert a number to Montgomery domain, by multiplying with 2^512 mod P*/
120 void ecp_nistz256_to_mont(BN_ULONG res[P256_LIMBS],
121 const BN_ULONG in[P256_LIMBS]);
122 /* Functions that perform constant time access to the precomputed tables */
123 void ecp_nistz256_scatter_w5(P256_POINT *val,
124 const P256_POINT *in_t, int idx);
125 void ecp_nistz256_gather_w5(P256_POINT *val,
126 const P256_POINT *in_t, int idx);
127 void ecp_nistz256_scatter_w7(P256_POINT_AFFINE *val,
128 const P256_POINT_AFFINE *in_t, int idx);
129 void ecp_nistz256_gather_w7(P256_POINT_AFFINE *val,
130 const P256_POINT_AFFINE *in_t, int idx);
132 /* One converted into the Montgomery domain */
133 static const BN_ULONG ONE[P256_LIMBS] = {
134 TOBN(0x00000000, 0x00000001), TOBN(0xffffffff, 0x00000000),
135 TOBN(0xffffffff, 0xffffffff), TOBN(0x00000000, 0xfffffffe)
138 static NISTZ256_PRE_COMP *ecp_nistz256_pre_comp_new(const EC_GROUP *group);
140 /* Precomputed tables for the default generator */
141 extern const PRECOMP256_ROW ecp_nistz256_precomputed[37];
143 /* Recode window to a signed digit, see ecp_nistputil.c for details */
144 static unsigned int _booth_recode_w5(unsigned int in)
148 s = ~((in >> 5) - 1);
149 d = (1 << 6) - in - 1;
150 d = (d & s) | (in & ~s);
151 d = (d >> 1) + (d & 1);
153 return (d << 1) + (s & 1);
156 static unsigned int _booth_recode_w7(unsigned int in)
160 s = ~((in >> 7) - 1);
161 d = (1 << 8) - in - 1;
162 d = (d & s) | (in & ~s);
163 d = (d >> 1) + (d & 1);
165 return (d << 1) + (s & 1);
168 static void copy_conditional(BN_ULONG dst[P256_LIMBS],
169 const BN_ULONG src[P256_LIMBS], BN_ULONG move)
171 BN_ULONG mask1 = 0-move;
172 BN_ULONG mask2 = ~mask1;
174 dst[0] = (src[0] & mask1) ^ (dst[0] & mask2);
175 dst[1] = (src[1] & mask1) ^ (dst[1] & mask2);
176 dst[2] = (src[2] & mask1) ^ (dst[2] & mask2);
177 dst[3] = (src[3] & mask1) ^ (dst[3] & mask2);
178 if (P256_LIMBS == 8) {
179 dst[4] = (src[4] & mask1) ^ (dst[4] & mask2);
180 dst[5] = (src[5] & mask1) ^ (dst[5] & mask2);
181 dst[6] = (src[6] & mask1) ^ (dst[6] & mask2);
182 dst[7] = (src[7] & mask1) ^ (dst[7] & mask2);
186 static BN_ULONG is_zero(BN_ULONG in)
194 static BN_ULONG is_equal(const BN_ULONG a[P256_LIMBS],
195 const BN_ULONG b[P256_LIMBS])
203 if (P256_LIMBS == 8) {
213 static BN_ULONG is_one(const BIGNUM *z)
216 BN_ULONG *a = bn_get_words(z);
218 if (bn_get_top(z) == (P256_LIMBS - P256_LIMBS / 8)) {
220 res |= a[1] ^ ONE[1];
221 res |= a[2] ^ ONE[2];
222 res |= a[3] ^ ONE[3];
223 if (P256_LIMBS == 8) {
224 res |= a[4] ^ ONE[4];
225 res |= a[5] ^ ONE[5];
226 res |= a[6] ^ ONE[6];
228 * no check for a[7] (being zero) on 32-bit platforms,
229 * because value of "one" takes only 7 limbs.
239 * For reference, this macro is used only when new ecp_nistz256 assembly
240 * module is being developed. For example, configure with
241 * -DECP_NISTZ256_REFERENCE_IMPLEMENTATION and implement only functions
242 * performing simplest arithmetic operations on 256-bit vectors. Then
243 * work on implementation of higher-level functions performing point
244 * operations. Then remove ECP_NISTZ256_REFERENCE_IMPLEMENTATION
245 * and never define it again. (The correct macro denoting presence of
246 * ecp_nistz256 module is ECP_NISTZ256_ASM.)
248 #ifndef ECP_NISTZ256_REFERENCE_IMPLEMENTATION
249 void ecp_nistz256_point_double(P256_POINT *r, const P256_POINT *a);
250 void ecp_nistz256_point_add(P256_POINT *r,
251 const P256_POINT *a, const P256_POINT *b);
252 void ecp_nistz256_point_add_affine(P256_POINT *r,
254 const P256_POINT_AFFINE *b);
256 /* Point double: r = 2*a */
257 static void ecp_nistz256_point_double(P256_POINT *r, const P256_POINT *a)
259 BN_ULONG S[P256_LIMBS];
260 BN_ULONG M[P256_LIMBS];
261 BN_ULONG Zsqr[P256_LIMBS];
262 BN_ULONG tmp0[P256_LIMBS];
264 const BN_ULONG *in_x = a->X;
265 const BN_ULONG *in_y = a->Y;
266 const BN_ULONG *in_z = a->Z;
268 BN_ULONG *res_x = r->X;
269 BN_ULONG *res_y = r->Y;
270 BN_ULONG *res_z = r->Z;
272 ecp_nistz256_mul_by_2(S, in_y);
274 ecp_nistz256_sqr_mont(Zsqr, in_z);
276 ecp_nistz256_sqr_mont(S, S);
278 ecp_nistz256_mul_mont(res_z, in_z, in_y);
279 ecp_nistz256_mul_by_2(res_z, res_z);
281 ecp_nistz256_add(M, in_x, Zsqr);
282 ecp_nistz256_sub(Zsqr, in_x, Zsqr);
284 ecp_nistz256_sqr_mont(res_y, S);
285 ecp_nistz256_div_by_2(res_y, res_y);
287 ecp_nistz256_mul_mont(M, M, Zsqr);
288 ecp_nistz256_mul_by_3(M, M);
290 ecp_nistz256_mul_mont(S, S, in_x);
291 ecp_nistz256_mul_by_2(tmp0, S);
293 ecp_nistz256_sqr_mont(res_x, M);
295 ecp_nistz256_sub(res_x, res_x, tmp0);
296 ecp_nistz256_sub(S, S, res_x);
298 ecp_nistz256_mul_mont(S, S, M);
299 ecp_nistz256_sub(res_y, S, res_y);
302 /* Point addition: r = a+b */
303 static void ecp_nistz256_point_add(P256_POINT *r,
304 const P256_POINT *a, const P256_POINT *b)
306 BN_ULONG U2[P256_LIMBS], S2[P256_LIMBS];
307 BN_ULONG U1[P256_LIMBS], S1[P256_LIMBS];
308 BN_ULONG Z1sqr[P256_LIMBS];
309 BN_ULONG Z2sqr[P256_LIMBS];
310 BN_ULONG H[P256_LIMBS], R[P256_LIMBS];
311 BN_ULONG Hsqr[P256_LIMBS];
312 BN_ULONG Rsqr[P256_LIMBS];
313 BN_ULONG Hcub[P256_LIMBS];
315 BN_ULONG res_x[P256_LIMBS];
316 BN_ULONG res_y[P256_LIMBS];
317 BN_ULONG res_z[P256_LIMBS];
319 BN_ULONG in1infty, in2infty;
321 const BN_ULONG *in1_x = a->X;
322 const BN_ULONG *in1_y = a->Y;
323 const BN_ULONG *in1_z = a->Z;
325 const BN_ULONG *in2_x = b->X;
326 const BN_ULONG *in2_y = b->Y;
327 const BN_ULONG *in2_z = b->Z;
330 * Infinity in encoded as (,,0)
332 in1infty = (in1_z[0] | in1_z[1] | in1_z[2] | in1_z[3]);
334 in1infty |= (in1_z[4] | in1_z[5] | in1_z[6] | in1_z[7]);
336 in2infty = (in2_z[0] | in2_z[1] | in2_z[2] | in2_z[3]);
338 in2infty |= (in2_z[4] | in2_z[5] | in2_z[6] | in2_z[7]);
340 in1infty = is_zero(in1infty);
341 in2infty = is_zero(in2infty);
343 ecp_nistz256_sqr_mont(Z2sqr, in2_z); /* Z2^2 */
344 ecp_nistz256_sqr_mont(Z1sqr, in1_z); /* Z1^2 */
346 ecp_nistz256_mul_mont(S1, Z2sqr, in2_z); /* S1 = Z2^3 */
347 ecp_nistz256_mul_mont(S2, Z1sqr, in1_z); /* S2 = Z1^3 */
349 ecp_nistz256_mul_mont(S1, S1, in1_y); /* S1 = Y1*Z2^3 */
350 ecp_nistz256_mul_mont(S2, S2, in2_y); /* S2 = Y2*Z1^3 */
351 ecp_nistz256_sub(R, S2, S1); /* R = S2 - S1 */
353 ecp_nistz256_mul_mont(U1, in1_x, Z2sqr); /* U1 = X1*Z2^2 */
354 ecp_nistz256_mul_mont(U2, in2_x, Z1sqr); /* U2 = X2*Z1^2 */
355 ecp_nistz256_sub(H, U2, U1); /* H = U2 - U1 */
358 * This should not happen during sign/ecdh, so no constant time violation
360 if (is_equal(U1, U2) && !in1infty && !in2infty) {
361 if (is_equal(S1, S2)) {
362 ecp_nistz256_point_double(r, a);
365 memset(r, 0, sizeof(*r));
370 ecp_nistz256_sqr_mont(Rsqr, R); /* R^2 */
371 ecp_nistz256_mul_mont(res_z, H, in1_z); /* Z3 = H*Z1*Z2 */
372 ecp_nistz256_sqr_mont(Hsqr, H); /* H^2 */
373 ecp_nistz256_mul_mont(res_z, res_z, in2_z); /* Z3 = H*Z1*Z2 */
374 ecp_nistz256_mul_mont(Hcub, Hsqr, H); /* H^3 */
376 ecp_nistz256_mul_mont(U2, U1, Hsqr); /* U1*H^2 */
377 ecp_nistz256_mul_by_2(Hsqr, U2); /* 2*U1*H^2 */
379 ecp_nistz256_sub(res_x, Rsqr, Hsqr);
380 ecp_nistz256_sub(res_x, res_x, Hcub);
382 ecp_nistz256_sub(res_y, U2, res_x);
384 ecp_nistz256_mul_mont(S2, S1, Hcub);
385 ecp_nistz256_mul_mont(res_y, R, res_y);
386 ecp_nistz256_sub(res_y, res_y, S2);
388 copy_conditional(res_x, in2_x, in1infty);
389 copy_conditional(res_y, in2_y, in1infty);
390 copy_conditional(res_z, in2_z, in1infty);
392 copy_conditional(res_x, in1_x, in2infty);
393 copy_conditional(res_y, in1_y, in2infty);
394 copy_conditional(res_z, in1_z, in2infty);
396 memcpy(r->X, res_x, sizeof(res_x));
397 memcpy(r->Y, res_y, sizeof(res_y));
398 memcpy(r->Z, res_z, sizeof(res_z));
401 /* Point addition when b is known to be affine: r = a+b */
402 static void ecp_nistz256_point_add_affine(P256_POINT *r,
404 const P256_POINT_AFFINE *b)
406 BN_ULONG U2[P256_LIMBS], S2[P256_LIMBS];
407 BN_ULONG Z1sqr[P256_LIMBS];
408 BN_ULONG H[P256_LIMBS], R[P256_LIMBS];
409 BN_ULONG Hsqr[P256_LIMBS];
410 BN_ULONG Rsqr[P256_LIMBS];
411 BN_ULONG Hcub[P256_LIMBS];
413 BN_ULONG res_x[P256_LIMBS];
414 BN_ULONG res_y[P256_LIMBS];
415 BN_ULONG res_z[P256_LIMBS];
417 BN_ULONG in1infty, in2infty;
419 const BN_ULONG *in1_x = a->X;
420 const BN_ULONG *in1_y = a->Y;
421 const BN_ULONG *in1_z = a->Z;
423 const BN_ULONG *in2_x = b->X;
424 const BN_ULONG *in2_y = b->Y;
427 * Infinity in encoded as (,,0)
429 in1infty = (in1_z[0] | in1_z[1] | in1_z[2] | in1_z[3]);
431 in1infty |= (in1_z[4] | in1_z[5] | in1_z[6] | in1_z[7]);
434 * In affine representation we encode infinity as (0,0), which is
435 * not on the curve, so it is OK
437 in2infty = (in2_x[0] | in2_x[1] | in2_x[2] | in2_x[3] |
438 in2_y[0] | in2_y[1] | in2_y[2] | in2_y[3]);
440 in2infty |= (in2_x[4] | in2_x[5] | in2_x[6] | in2_x[7] |
441 in2_y[4] | in2_y[5] | in2_y[6] | in2_y[7]);
443 in1infty = is_zero(in1infty);
444 in2infty = is_zero(in2infty);
446 ecp_nistz256_sqr_mont(Z1sqr, in1_z); /* Z1^2 */
448 ecp_nistz256_mul_mont(U2, in2_x, Z1sqr); /* U2 = X2*Z1^2 */
449 ecp_nistz256_sub(H, U2, in1_x); /* H = U2 - U1 */
451 ecp_nistz256_mul_mont(S2, Z1sqr, in1_z); /* S2 = Z1^3 */
453 ecp_nistz256_mul_mont(res_z, H, in1_z); /* Z3 = H*Z1*Z2 */
455 ecp_nistz256_mul_mont(S2, S2, in2_y); /* S2 = Y2*Z1^3 */
456 ecp_nistz256_sub(R, S2, in1_y); /* R = S2 - S1 */
458 ecp_nistz256_sqr_mont(Hsqr, H); /* H^2 */
459 ecp_nistz256_sqr_mont(Rsqr, R); /* R^2 */
460 ecp_nistz256_mul_mont(Hcub, Hsqr, H); /* H^3 */
462 ecp_nistz256_mul_mont(U2, in1_x, Hsqr); /* U1*H^2 */
463 ecp_nistz256_mul_by_2(Hsqr, U2); /* 2*U1*H^2 */
465 ecp_nistz256_sub(res_x, Rsqr, Hsqr);
466 ecp_nistz256_sub(res_x, res_x, Hcub);
467 ecp_nistz256_sub(H, U2, res_x);
469 ecp_nistz256_mul_mont(S2, in1_y, Hcub);
470 ecp_nistz256_mul_mont(H, H, R);
471 ecp_nistz256_sub(res_y, H, S2);
473 copy_conditional(res_x, in2_x, in1infty);
474 copy_conditional(res_x, in1_x, in2infty);
476 copy_conditional(res_y, in2_y, in1infty);
477 copy_conditional(res_y, in1_y, in2infty);
479 copy_conditional(res_z, ONE, in1infty);
480 copy_conditional(res_z, in1_z, in2infty);
482 memcpy(r->X, res_x, sizeof(res_x));
483 memcpy(r->Y, res_y, sizeof(res_y));
484 memcpy(r->Z, res_z, sizeof(res_z));
488 /* r = in^-1 mod p */
489 static void ecp_nistz256_mod_inverse(BN_ULONG r[P256_LIMBS],
490 const BN_ULONG in[P256_LIMBS])
493 * The poly is ffffffff 00000001 00000000 00000000 00000000 ffffffff
494 * ffffffff ffffffff We use FLT and used poly-2 as exponent
496 BN_ULONG p2[P256_LIMBS];
497 BN_ULONG p4[P256_LIMBS];
498 BN_ULONG p8[P256_LIMBS];
499 BN_ULONG p16[P256_LIMBS];
500 BN_ULONG p32[P256_LIMBS];
501 BN_ULONG res[P256_LIMBS];
504 ecp_nistz256_sqr_mont(res, in);
505 ecp_nistz256_mul_mont(p2, res, in); /* 3*p */
507 ecp_nistz256_sqr_mont(res, p2);
508 ecp_nistz256_sqr_mont(res, res);
509 ecp_nistz256_mul_mont(p4, res, p2); /* f*p */
511 ecp_nistz256_sqr_mont(res, p4);
512 ecp_nistz256_sqr_mont(res, res);
513 ecp_nistz256_sqr_mont(res, res);
514 ecp_nistz256_sqr_mont(res, res);
515 ecp_nistz256_mul_mont(p8, res, p4); /* ff*p */
517 ecp_nistz256_sqr_mont(res, p8);
518 for (i = 0; i < 7; i++)
519 ecp_nistz256_sqr_mont(res, res);
520 ecp_nistz256_mul_mont(p16, res, p8); /* ffff*p */
522 ecp_nistz256_sqr_mont(res, p16);
523 for (i = 0; i < 15; i++)
524 ecp_nistz256_sqr_mont(res, res);
525 ecp_nistz256_mul_mont(p32, res, p16); /* ffffffff*p */
527 ecp_nistz256_sqr_mont(res, p32);
528 for (i = 0; i < 31; i++)
529 ecp_nistz256_sqr_mont(res, res);
530 ecp_nistz256_mul_mont(res, res, in);
532 for (i = 0; i < 32 * 4; i++)
533 ecp_nistz256_sqr_mont(res, res);
534 ecp_nistz256_mul_mont(res, res, p32);
536 for (i = 0; i < 32; i++)
537 ecp_nistz256_sqr_mont(res, res);
538 ecp_nistz256_mul_mont(res, res, p32);
540 for (i = 0; i < 16; i++)
541 ecp_nistz256_sqr_mont(res, res);
542 ecp_nistz256_mul_mont(res, res, p16);
544 for (i = 0; i < 8; i++)
545 ecp_nistz256_sqr_mont(res, res);
546 ecp_nistz256_mul_mont(res, res, p8);
548 ecp_nistz256_sqr_mont(res, res);
549 ecp_nistz256_sqr_mont(res, res);
550 ecp_nistz256_sqr_mont(res, res);
551 ecp_nistz256_sqr_mont(res, res);
552 ecp_nistz256_mul_mont(res, res, p4);
554 ecp_nistz256_sqr_mont(res, res);
555 ecp_nistz256_sqr_mont(res, res);
556 ecp_nistz256_mul_mont(res, res, p2);
558 ecp_nistz256_sqr_mont(res, res);
559 ecp_nistz256_sqr_mont(res, res);
560 ecp_nistz256_mul_mont(res, res, in);
562 memcpy(r, res, sizeof(res));
566 * ecp_nistz256_bignum_to_field_elem copies the contents of |in| to |out| and
567 * returns one if it fits. Otherwise it returns zero.
569 __owur static int ecp_nistz256_bignum_to_field_elem(BN_ULONG out[P256_LIMBS],
572 return bn_copy_words(out, in, P256_LIMBS);
575 /* r = sum(scalar[i]*point[i]) */
576 __owur static int ecp_nistz256_windowed_mul(const EC_GROUP *group,
578 const BIGNUM **scalar,
579 const EC_POINT **point,
580 size_t num, BN_CTX *ctx)
585 unsigned char (*p_str)[33] = NULL;
586 const unsigned int window_size = 5;
587 const unsigned int mask = (1 << (window_size + 1)) - 1;
589 P256_POINT *temp; /* place for 5 temporary points */
590 const BIGNUM **scalars = NULL;
591 P256_POINT (*table)[16] = NULL;
592 void *table_storage = NULL;
594 if ((num * 16 + 6) > OPENSSL_MALLOC_MAX_NELEMS(P256_POINT)
596 OPENSSL_malloc((num * 16 + 5) * sizeof(P256_POINT) + 64)) == NULL
598 OPENSSL_malloc(num * 33 * sizeof(unsigned char))) == NULL
599 || (scalars = OPENSSL_malloc(num * sizeof(BIGNUM *))) == NULL) {
600 ECerr(EC_F_ECP_NISTZ256_WINDOWED_MUL, ERR_R_MALLOC_FAILURE);
604 table = (void *)ALIGNPTR(table_storage, 64);
605 temp = (P256_POINT *)(table + num);
607 for (i = 0; i < num; i++) {
608 P256_POINT *row = table[i];
610 /* This is an unusual input, we don't guarantee constant-timeness. */
611 if ((BN_num_bits(scalar[i]) > 256) || BN_is_negative(scalar[i])) {
614 if ((mod = BN_CTX_get(ctx)) == NULL)
616 if (!BN_nnmod(mod, scalar[i], group->order, ctx)) {
617 ECerr(EC_F_ECP_NISTZ256_WINDOWED_MUL, ERR_R_BN_LIB);
622 scalars[i] = scalar[i];
624 for (j = 0; j < bn_get_top(scalars[i]) * BN_BYTES; j += BN_BYTES) {
625 BN_ULONG d = bn_get_words(scalars[i])[j / BN_BYTES];
627 p_str[i][j + 0] = (unsigned char)d;
628 p_str[i][j + 1] = (unsigned char)(d >> 8);
629 p_str[i][j + 2] = (unsigned char)(d >> 16);
630 p_str[i][j + 3] = (unsigned char)(d >>= 24);
633 p_str[i][j + 4] = (unsigned char)d;
634 p_str[i][j + 5] = (unsigned char)(d >> 8);
635 p_str[i][j + 6] = (unsigned char)(d >> 16);
636 p_str[i][j + 7] = (unsigned char)(d >> 24);
642 if (!ecp_nistz256_bignum_to_field_elem(temp[0].X, point[i]->X)
643 || !ecp_nistz256_bignum_to_field_elem(temp[0].Y, point[i]->Y)
644 || !ecp_nistz256_bignum_to_field_elem(temp[0].Z, point[i]->Z)) {
645 ECerr(EC_F_ECP_NISTZ256_WINDOWED_MUL,
646 EC_R_COORDINATES_OUT_OF_RANGE);
651 * row[0] is implicitly (0,0,0) (the point at infinity), therefore it
652 * is not stored. All other values are actually stored with an offset
656 ecp_nistz256_scatter_w5 (row, &temp[0], 1);
657 ecp_nistz256_point_double(&temp[1], &temp[0]); /*1+1=2 */
658 ecp_nistz256_scatter_w5 (row, &temp[1], 2);
659 ecp_nistz256_point_add (&temp[2], &temp[1], &temp[0]); /*2+1=3 */
660 ecp_nistz256_scatter_w5 (row, &temp[2], 3);
661 ecp_nistz256_point_double(&temp[1], &temp[1]); /*2*2=4 */
662 ecp_nistz256_scatter_w5 (row, &temp[1], 4);
663 ecp_nistz256_point_double(&temp[2], &temp[2]); /*2*3=6 */
664 ecp_nistz256_scatter_w5 (row, &temp[2], 6);
665 ecp_nistz256_point_add (&temp[3], &temp[1], &temp[0]); /*4+1=5 */
666 ecp_nistz256_scatter_w5 (row, &temp[3], 5);
667 ecp_nistz256_point_add (&temp[4], &temp[2], &temp[0]); /*6+1=7 */
668 ecp_nistz256_scatter_w5 (row, &temp[4], 7);
669 ecp_nistz256_point_double(&temp[1], &temp[1]); /*2*4=8 */
670 ecp_nistz256_scatter_w5 (row, &temp[1], 8);
671 ecp_nistz256_point_double(&temp[2], &temp[2]); /*2*6=12 */
672 ecp_nistz256_scatter_w5 (row, &temp[2], 12);
673 ecp_nistz256_point_double(&temp[3], &temp[3]); /*2*5=10 */
674 ecp_nistz256_scatter_w5 (row, &temp[3], 10);
675 ecp_nistz256_point_double(&temp[4], &temp[4]); /*2*7=14 */
676 ecp_nistz256_scatter_w5 (row, &temp[4], 14);
677 ecp_nistz256_point_add (&temp[2], &temp[2], &temp[0]); /*12+1=13*/
678 ecp_nistz256_scatter_w5 (row, &temp[2], 13);
679 ecp_nistz256_point_add (&temp[3], &temp[3], &temp[0]); /*10+1=11*/
680 ecp_nistz256_scatter_w5 (row, &temp[3], 11);
681 ecp_nistz256_point_add (&temp[4], &temp[4], &temp[0]); /*14+1=15*/
682 ecp_nistz256_scatter_w5 (row, &temp[4], 15);
683 ecp_nistz256_point_add (&temp[2], &temp[1], &temp[0]); /*8+1=9 */
684 ecp_nistz256_scatter_w5 (row, &temp[2], 9);
685 ecp_nistz256_point_double(&temp[1], &temp[1]); /*2*8=16 */
686 ecp_nistz256_scatter_w5 (row, &temp[1], 16);
691 wvalue = p_str[0][(idx - 1) / 8];
692 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
695 * We gather to temp[0], because we know it's position relative
698 ecp_nistz256_gather_w5(&temp[0], table[0], _booth_recode_w5(wvalue) >> 1);
699 memcpy(r, &temp[0], sizeof(temp[0]));
702 for (i = (idx == 255 ? 1 : 0); i < num; i++) {
703 unsigned int off = (idx - 1) / 8;
705 wvalue = p_str[i][off] | p_str[i][off + 1] << 8;
706 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
708 wvalue = _booth_recode_w5(wvalue);
710 ecp_nistz256_gather_w5(&temp[0], table[i], wvalue >> 1);
712 ecp_nistz256_neg(temp[1].Y, temp[0].Y);
713 copy_conditional(temp[0].Y, temp[1].Y, (wvalue & 1));
715 ecp_nistz256_point_add(r, r, &temp[0]);
720 ecp_nistz256_point_double(r, r);
721 ecp_nistz256_point_double(r, r);
722 ecp_nistz256_point_double(r, r);
723 ecp_nistz256_point_double(r, r);
724 ecp_nistz256_point_double(r, r);
728 for (i = 0; i < num; i++) {
729 wvalue = p_str[i][0];
730 wvalue = (wvalue << 1) & mask;
732 wvalue = _booth_recode_w5(wvalue);
734 ecp_nistz256_gather_w5(&temp[0], table[i], wvalue >> 1);
736 ecp_nistz256_neg(temp[1].Y, temp[0].Y);
737 copy_conditional(temp[0].Y, temp[1].Y, wvalue & 1);
739 ecp_nistz256_point_add(r, r, &temp[0]);
744 OPENSSL_free(table_storage);
746 OPENSSL_free(scalars);
750 /* Coordinates of G, for which we have precomputed tables */
751 static const BN_ULONG def_xG[P256_LIMBS] = {
752 TOBN(0x79e730d4, 0x18a9143c), TOBN(0x75ba95fc, 0x5fedb601),
753 TOBN(0x79fb732b, 0x77622510), TOBN(0x18905f76, 0xa53755c6)
756 static const BN_ULONG def_yG[P256_LIMBS] = {
757 TOBN(0xddf25357, 0xce95560a), TOBN(0x8b4ab8e4, 0xba19e45c),
758 TOBN(0xd2e88688, 0xdd21f325), TOBN(0x8571ff18, 0x25885d85)
762 * ecp_nistz256_is_affine_G returns one if |generator| is the standard, P-256
765 static int ecp_nistz256_is_affine_G(const EC_POINT *generator)
767 return (bn_get_top(generator->X) == P256_LIMBS) &&
768 (bn_get_top(generator->Y) == P256_LIMBS) &&
769 is_equal(bn_get_words(generator->X), def_xG) &&
770 is_equal(bn_get_words(generator->Y), def_yG) &&
771 is_one(generator->Z);
774 __owur static int ecp_nistz256_mult_precompute(EC_GROUP *group, BN_CTX *ctx)
777 * We precompute a table for a Booth encoded exponent (wNAF) based
778 * computation. Each table holds 64 values for safe access, with an
779 * implicit value of infinity at index zero. We use window of size 7, and
780 * therefore require ceil(256/7) = 37 tables.
783 EC_POINT *P = NULL, *T = NULL;
784 const EC_POINT *generator;
785 NISTZ256_PRE_COMP *pre_comp;
786 BN_CTX *new_ctx = NULL;
787 int i, j, k, ret = 0;
790 PRECOMP256_ROW *preComputedTable = NULL;
791 unsigned char *precomp_storage = NULL;
793 /* if there is an old NISTZ256_PRE_COMP object, throw it away */
794 EC_pre_comp_free(group);
795 generator = EC_GROUP_get0_generator(group);
796 if (generator == NULL) {
797 ECerr(EC_F_ECP_NISTZ256_MULT_PRECOMPUTE, EC_R_UNDEFINED_GENERATOR);
801 if (ecp_nistz256_is_affine_G(generator)) {
803 * No need to calculate tables for the standard generator because we
804 * have them statically.
809 if ((pre_comp = ecp_nistz256_pre_comp_new(group)) == NULL)
813 ctx = new_ctx = BN_CTX_new();
820 order = EC_GROUP_get0_order(group);
824 if (BN_is_zero(order)) {
825 ECerr(EC_F_ECP_NISTZ256_MULT_PRECOMPUTE, EC_R_UNKNOWN_ORDER);
831 if ((precomp_storage =
832 OPENSSL_malloc(37 * 64 * sizeof(P256_POINT_AFFINE) + 64)) == NULL) {
833 ECerr(EC_F_ECP_NISTZ256_MULT_PRECOMPUTE, ERR_R_MALLOC_FAILURE);
837 preComputedTable = (void *)ALIGNPTR(precomp_storage, 64);
839 P = EC_POINT_new(group);
840 T = EC_POINT_new(group);
841 if (P == NULL || T == NULL)
845 * The zero entry is implicitly infinity, and we skip it, storing other
846 * values with -1 offset.
848 if (!EC_POINT_copy(T, generator))
851 for (k = 0; k < 64; k++) {
852 if (!EC_POINT_copy(P, T))
854 for (j = 0; j < 37; j++) {
855 P256_POINT_AFFINE temp;
857 * It would be faster to use EC_POINTs_make_affine and
858 * make multiple points affine at the same time.
860 if (!EC_POINT_make_affine(group, P, ctx))
862 if (!ecp_nistz256_bignum_to_field_elem(temp.X, P->X) ||
863 !ecp_nistz256_bignum_to_field_elem(temp.Y, P->Y)) {
864 ECerr(EC_F_ECP_NISTZ256_MULT_PRECOMPUTE,
865 EC_R_COORDINATES_OUT_OF_RANGE);
868 ecp_nistz256_scatter_w7(preComputedTable[j], &temp, k);
869 for (i = 0; i < 7; i++) {
870 if (!EC_POINT_dbl(group, P, P, ctx))
874 if (!EC_POINT_add(group, T, T, generator, ctx))
878 pre_comp->group = group;
880 pre_comp->precomp = preComputedTable;
881 pre_comp->precomp_storage = precomp_storage;
882 precomp_storage = NULL;
883 SETPRECOMP(group, nistz256, pre_comp);
890 BN_CTX_free(new_ctx);
892 EC_nistz256_pre_comp_free(pre_comp);
893 OPENSSL_free(precomp_storage);
900 * Note that by default ECP_NISTZ256_AVX2 is undefined. While it's great
901 * code processing 4 points in parallel, corresponding serial operation
902 * is several times slower, because it uses 29x29=58-bit multiplication
903 * as opposite to 64x64=128-bit in integer-only scalar case. As result
904 * it doesn't provide *significant* performance improvement. Note that
905 * just defining ECP_NISTZ256_AVX2 is not sufficient to make it work,
906 * you'd need to compile even asm/ecp_nistz256-avx.pl module.
908 #if defined(ECP_NISTZ256_AVX2)
909 # if !(defined(__x86_64) || defined(__x86_64__) || \
910 defined(_M_AMD64) || defined(_MX64)) || \
911 !(defined(__GNUC__) || defined(_MSC_VER)) /* this is for ALIGN32 */
912 # undef ECP_NISTZ256_AVX2
914 /* Constant time access, loading four values, from four consecutive tables */
915 void ecp_nistz256_avx2_multi_gather_w7(void *result, const void *in,
916 int index0, int index1, int index2,
918 void ecp_nistz256_avx2_transpose_convert(void *RESULTx4, const void *in);
919 void ecp_nistz256_avx2_convert_transpose_back(void *result, const void *Ax4);
920 void ecp_nistz256_avx2_point_add_affine_x4(void *RESULTx4, const void *Ax4,
922 void ecp_nistz256_avx2_point_add_affines_x4(void *RESULTx4, const void *Ax4,
924 void ecp_nistz256_avx2_to_mont(void *RESULTx4, const void *Ax4);
925 void ecp_nistz256_avx2_from_mont(void *RESULTx4, const void *Ax4);
926 void ecp_nistz256_avx2_set1(void *RESULTx4);
927 int ecp_nistz_avx2_eligible(void);
929 static void booth_recode_w7(unsigned char *sign,
930 unsigned char *digit, unsigned char in)
934 s = ~((in >> 7) - 1);
935 d = (1 << 8) - in - 1;
936 d = (d & s) | (in & ~s);
937 d = (d >> 1) + (d & 1);
944 * ecp_nistz256_avx2_mul_g performs multiplication by G, using only the
945 * precomputed table. It does 4 affine point additions in parallel,
946 * significantly speeding up point multiplication for a fixed value.
948 static void ecp_nistz256_avx2_mul_g(P256_POINT *r,
949 unsigned char p_str[33],
950 const P256_POINT_AFFINE(*preComputedTable)[64])
952 const unsigned int window_size = 7;
953 const unsigned int mask = (1 << (window_size + 1)) - 1;
955 /* Using 4 windows at a time */
956 unsigned char sign0, digit0;
957 unsigned char sign1, digit1;
958 unsigned char sign2, digit2;
959 unsigned char sign3, digit3;
960 unsigned int idx = 0;
961 BN_ULONG tmp[P256_LIMBS];
964 ALIGN32 BN_ULONG aX4[4 * 9 * 3] = { 0 };
965 ALIGN32 BN_ULONG bX4[4 * 9 * 2] = { 0 };
966 ALIGN32 P256_POINT_AFFINE point_arr[4];
967 ALIGN32 P256_POINT res_point_arr[4];
969 /* Initial four windows */
970 wvalue = *((u16 *) & p_str[0]);
971 wvalue = (wvalue << 1) & mask;
973 booth_recode_w7(&sign0, &digit0, wvalue);
974 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
975 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
977 booth_recode_w7(&sign1, &digit1, wvalue);
978 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
979 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
981 booth_recode_w7(&sign2, &digit2, wvalue);
982 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
983 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
985 booth_recode_w7(&sign3, &digit3, wvalue);
987 ecp_nistz256_avx2_multi_gather_w7(point_arr, preComputedTable[0],
988 digit0, digit1, digit2, digit3);
990 ecp_nistz256_neg(tmp, point_arr[0].Y);
991 copy_conditional(point_arr[0].Y, tmp, sign0);
992 ecp_nistz256_neg(tmp, point_arr[1].Y);
993 copy_conditional(point_arr[1].Y, tmp, sign1);
994 ecp_nistz256_neg(tmp, point_arr[2].Y);
995 copy_conditional(point_arr[2].Y, tmp, sign2);
996 ecp_nistz256_neg(tmp, point_arr[3].Y);
997 copy_conditional(point_arr[3].Y, tmp, sign3);
999 ecp_nistz256_avx2_transpose_convert(aX4, point_arr);
1000 ecp_nistz256_avx2_to_mont(aX4, aX4);
1001 ecp_nistz256_avx2_to_mont(&aX4[4 * 9], &aX4[4 * 9]);
1002 ecp_nistz256_avx2_set1(&aX4[4 * 9 * 2]);
1004 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
1005 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
1007 booth_recode_w7(&sign0, &digit0, wvalue);
1008 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
1009 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
1011 booth_recode_w7(&sign1, &digit1, wvalue);
1012 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
1013 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
1015 booth_recode_w7(&sign2, &digit2, wvalue);
1016 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
1017 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
1019 booth_recode_w7(&sign3, &digit3, wvalue);
1021 ecp_nistz256_avx2_multi_gather_w7(point_arr, preComputedTable[4 * 1],
1022 digit0, digit1, digit2, digit3);
1024 ecp_nistz256_neg(tmp, point_arr[0].Y);
1025 copy_conditional(point_arr[0].Y, tmp, sign0);
1026 ecp_nistz256_neg(tmp, point_arr[1].Y);
1027 copy_conditional(point_arr[1].Y, tmp, sign1);
1028 ecp_nistz256_neg(tmp, point_arr[2].Y);
1029 copy_conditional(point_arr[2].Y, tmp, sign2);
1030 ecp_nistz256_neg(tmp, point_arr[3].Y);
1031 copy_conditional(point_arr[3].Y, tmp, sign3);
1033 ecp_nistz256_avx2_transpose_convert(bX4, point_arr);
1034 ecp_nistz256_avx2_to_mont(bX4, bX4);
1035 ecp_nistz256_avx2_to_mont(&bX4[4 * 9], &bX4[4 * 9]);
1036 /* Optimized when both inputs are affine */
1037 ecp_nistz256_avx2_point_add_affines_x4(aX4, aX4, bX4);
1039 for (i = 2; i < 9; i++) {
1040 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
1041 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
1043 booth_recode_w7(&sign0, &digit0, wvalue);
1044 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
1045 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
1047 booth_recode_w7(&sign1, &digit1, wvalue);
1048 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
1049 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
1051 booth_recode_w7(&sign2, &digit2, wvalue);
1052 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
1053 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
1055 booth_recode_w7(&sign3, &digit3, wvalue);
1057 ecp_nistz256_avx2_multi_gather_w7(point_arr,
1058 preComputedTable[4 * i],
1059 digit0, digit1, digit2, digit3);
1061 ecp_nistz256_neg(tmp, point_arr[0].Y);
1062 copy_conditional(point_arr[0].Y, tmp, sign0);
1063 ecp_nistz256_neg(tmp, point_arr[1].Y);
1064 copy_conditional(point_arr[1].Y, tmp, sign1);
1065 ecp_nistz256_neg(tmp, point_arr[2].Y);
1066 copy_conditional(point_arr[2].Y, tmp, sign2);
1067 ecp_nistz256_neg(tmp, point_arr[3].Y);
1068 copy_conditional(point_arr[3].Y, tmp, sign3);
1070 ecp_nistz256_avx2_transpose_convert(bX4, point_arr);
1071 ecp_nistz256_avx2_to_mont(bX4, bX4);
1072 ecp_nistz256_avx2_to_mont(&bX4[4 * 9], &bX4[4 * 9]);
1074 ecp_nistz256_avx2_point_add_affine_x4(aX4, aX4, bX4);
1077 ecp_nistz256_avx2_from_mont(&aX4[4 * 9 * 0], &aX4[4 * 9 * 0]);
1078 ecp_nistz256_avx2_from_mont(&aX4[4 * 9 * 1], &aX4[4 * 9 * 1]);
1079 ecp_nistz256_avx2_from_mont(&aX4[4 * 9 * 2], &aX4[4 * 9 * 2]);
1081 ecp_nistz256_avx2_convert_transpose_back(res_point_arr, aX4);
1082 /* Last window is performed serially */
1083 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
1084 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
1085 booth_recode_w7(&sign0, &digit0, wvalue);
1086 ecp_nistz256_gather_w7((P256_POINT_AFFINE *)r,
1087 preComputedTable[36], digit0);
1088 ecp_nistz256_neg(tmp, r->Y);
1089 copy_conditional(r->Y, tmp, sign0);
1090 memcpy(r->Z, ONE, sizeof(ONE));
1091 /* Sum the four windows */
1092 ecp_nistz256_point_add(r, r, &res_point_arr[0]);
1093 ecp_nistz256_point_add(r, r, &res_point_arr[1]);
1094 ecp_nistz256_point_add(r, r, &res_point_arr[2]);
1095 ecp_nistz256_point_add(r, r, &res_point_arr[3]);
1100 __owur static int ecp_nistz256_set_from_affine(EC_POINT *out, const EC_GROUP *group,
1101 const P256_POINT_AFFINE *in,
1105 BN_ULONG d_x[P256_LIMBS], d_y[P256_LIMBS];
1116 memcpy(d_x, in->X, sizeof(d_x));
1117 bn_set_static_words(x, d_x, P256_LIMBS);
1119 memcpy(d_y, in->Y, sizeof(d_y));
1120 bn_set_static_words(y, d_y, P256_LIMBS);
1122 ret = EC_POINT_set_affine_coordinates_GFp(group, out, x, y, ctx);
1130 /* r = scalar*G + sum(scalars[i]*points[i]) */
1131 __owur static int ecp_nistz256_points_mul(const EC_GROUP *group,
1133 const BIGNUM *scalar,
1135 const EC_POINT *points[],
1136 const BIGNUM *scalars[], BN_CTX *ctx)
1138 int i = 0, ret = 0, no_precomp_for_generator = 0, p_is_infinity = 0;
1140 unsigned char p_str[33] = { 0 };
1141 const PRECOMP256_ROW *preComputedTable = NULL;
1142 const NISTZ256_PRE_COMP *pre_comp = NULL;
1143 const EC_POINT *generator = NULL;
1144 BN_CTX *new_ctx = NULL;
1145 const BIGNUM **new_scalars = NULL;
1146 const EC_POINT **new_points = NULL;
1147 unsigned int idx = 0;
1148 const unsigned int window_size = 7;
1149 const unsigned int mask = (1 << (window_size + 1)) - 1;
1150 unsigned int wvalue;
1153 P256_POINT_AFFINE a;
1157 if ((num + 1) == 0 || (num + 1) > OPENSSL_MALLOC_MAX_NELEMS(void *)) {
1158 ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, ERR_R_MALLOC_FAILURE);
1162 if (group->meth != r->meth) {
1163 ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, EC_R_INCOMPATIBLE_OBJECTS);
1167 if ((scalar == NULL) && (num == 0))
1168 return EC_POINT_set_to_infinity(group, r);
1170 for (j = 0; j < num; j++) {
1171 if (group->meth != points[j]->meth) {
1172 ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, EC_R_INCOMPATIBLE_OBJECTS);
1178 ctx = new_ctx = BN_CTX_new();
1186 generator = EC_GROUP_get0_generator(group);
1187 if (generator == NULL) {
1188 ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, EC_R_UNDEFINED_GENERATOR);
1192 /* look if we can use precomputed multiples of generator */
1193 pre_comp = group->pre_comp.nistz256;
1197 * If there is a precomputed table for the generator, check that
1198 * it was generated with the same generator.
1200 EC_POINT *pre_comp_generator = EC_POINT_new(group);
1201 if (pre_comp_generator == NULL)
1204 if (!ecp_nistz256_set_from_affine(pre_comp_generator,
1205 group, pre_comp->precomp[0],
1207 EC_POINT_free(pre_comp_generator);
1211 if (0 == EC_POINT_cmp(group, generator, pre_comp_generator, ctx))
1212 preComputedTable = (const PRECOMP256_ROW *)pre_comp->precomp;
1214 EC_POINT_free(pre_comp_generator);
1217 if (preComputedTable == NULL && ecp_nistz256_is_affine_G(generator)) {
1219 * If there is no precomputed data, but the generator is the
1220 * default, a hardcoded table of precomputed data is used. This
1221 * is because applications, such as Apache, do not use
1222 * EC_KEY_precompute_mult.
1224 preComputedTable = ecp_nistz256_precomputed;
1227 if (preComputedTable) {
1228 if ((BN_num_bits(scalar) > 256)
1229 || BN_is_negative(scalar)) {
1230 if ((tmp_scalar = BN_CTX_get(ctx)) == NULL)
1233 if (!BN_nnmod(tmp_scalar, scalar, group->order, ctx)) {
1234 ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, ERR_R_BN_LIB);
1237 scalar = tmp_scalar;
1240 for (i = 0; i < bn_get_top(scalar) * BN_BYTES; i += BN_BYTES) {
1241 BN_ULONG d = bn_get_words(scalar)[i / BN_BYTES];
1243 p_str[i + 0] = (unsigned char)d;
1244 p_str[i + 1] = (unsigned char)(d >> 8);
1245 p_str[i + 2] = (unsigned char)(d >> 16);
1246 p_str[i + 3] = (unsigned char)(d >>= 24);
1247 if (BN_BYTES == 8) {
1249 p_str[i + 4] = (unsigned char)d;
1250 p_str[i + 5] = (unsigned char)(d >> 8);
1251 p_str[i + 6] = (unsigned char)(d >> 16);
1252 p_str[i + 7] = (unsigned char)(d >> 24);
1259 #if defined(ECP_NISTZ256_AVX2)
1260 if (ecp_nistz_avx2_eligible()) {
1261 ecp_nistz256_avx2_mul_g(&p.p, p_str, preComputedTable);
1268 wvalue = (p_str[0] << 1) & mask;
1271 wvalue = _booth_recode_w7(wvalue);
1273 ecp_nistz256_gather_w7(&p.a, preComputedTable[0],
1276 ecp_nistz256_neg(p.p.Z, p.p.Y);
1277 copy_conditional(p.p.Y, p.p.Z, wvalue & 1);
1280 * Since affine infinity is encoded as (0,0) and
1281 * Jacobian ias (,,0), we need to harmonize them
1282 * by assigning "one" or zero to Z.
1284 infty = (p.p.X[0] | p.p.X[1] | p.p.X[2] | p.p.X[3] |
1285 p.p.Y[0] | p.p.Y[1] | p.p.Y[2] | p.p.Y[3]);
1286 if (P256_LIMBS == 8)
1287 infty |= (p.p.X[4] | p.p.X[5] | p.p.X[6] | p.p.X[7] |
1288 p.p.Y[4] | p.p.Y[5] | p.p.Y[6] | p.p.Y[7]);
1290 infty = 0 - is_zero(infty);
1293 p.p.Z[0] = ONE[0] & infty;
1294 p.p.Z[1] = ONE[1] & infty;
1295 p.p.Z[2] = ONE[2] & infty;
1296 p.p.Z[3] = ONE[3] & infty;
1297 if (P256_LIMBS == 8) {
1298 p.p.Z[4] = ONE[4] & infty;
1299 p.p.Z[5] = ONE[5] & infty;
1300 p.p.Z[6] = ONE[6] & infty;
1301 p.p.Z[7] = ONE[7] & infty;
1304 for (i = 1; i < 37; i++) {
1305 unsigned int off = (idx - 1) / 8;
1306 wvalue = p_str[off] | p_str[off + 1] << 8;
1307 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
1310 wvalue = _booth_recode_w7(wvalue);
1312 ecp_nistz256_gather_w7(&t.a,
1313 preComputedTable[i], wvalue >> 1);
1315 ecp_nistz256_neg(t.p.Z, t.a.Y);
1316 copy_conditional(t.a.Y, t.p.Z, wvalue & 1);
1318 ecp_nistz256_point_add_affine(&p.p, &p.p, &t.a);
1323 no_precomp_for_generator = 1;
1328 if (no_precomp_for_generator) {
1330 * Without a precomputed table for the generator, it has to be
1331 * handled like a normal point.
1333 new_scalars = OPENSSL_malloc((num + 1) * sizeof(BIGNUM *));
1334 if (new_scalars == NULL) {
1335 ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, ERR_R_MALLOC_FAILURE);
1339 new_points = OPENSSL_malloc((num + 1) * sizeof(EC_POINT *));
1340 if (new_points == NULL) {
1341 ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, ERR_R_MALLOC_FAILURE);
1345 memcpy(new_scalars, scalars, num * sizeof(BIGNUM *));
1346 new_scalars[num] = scalar;
1347 memcpy(new_points, points, num * sizeof(EC_POINT *));
1348 new_points[num] = generator;
1350 scalars = new_scalars;
1351 points = new_points;
1356 P256_POINT *out = &t.p;
1360 if (!ecp_nistz256_windowed_mul(group, out, scalars, points, num, ctx))
1364 ecp_nistz256_point_add(&p.p, &p.p, out);
1367 /* Not constant-time, but we're only operating on the public output. */
1368 if (!bn_set_words(r->X, p.p.X, P256_LIMBS) ||
1369 !bn_set_words(r->Y, p.p.Y, P256_LIMBS) ||
1370 !bn_set_words(r->Z, p.p.Z, P256_LIMBS)) {
1373 r->Z_is_one = is_one(r->Z) & 1;
1380 BN_CTX_free(new_ctx);
1381 OPENSSL_free(new_points);
1382 OPENSSL_free(new_scalars);
1386 __owur static int ecp_nistz256_get_affine(const EC_GROUP *group,
1387 const EC_POINT *point,
1388 BIGNUM *x, BIGNUM *y, BN_CTX *ctx)
1390 BN_ULONG z_inv2[P256_LIMBS];
1391 BN_ULONG z_inv3[P256_LIMBS];
1392 BN_ULONG x_aff[P256_LIMBS];
1393 BN_ULONG y_aff[P256_LIMBS];
1394 BN_ULONG point_x[P256_LIMBS], point_y[P256_LIMBS], point_z[P256_LIMBS];
1395 BN_ULONG x_ret[P256_LIMBS], y_ret[P256_LIMBS];
1397 if (EC_POINT_is_at_infinity(group, point)) {
1398 ECerr(EC_F_ECP_NISTZ256_GET_AFFINE, EC_R_POINT_AT_INFINITY);
1402 if (!ecp_nistz256_bignum_to_field_elem(point_x, point->X) ||
1403 !ecp_nistz256_bignum_to_field_elem(point_y, point->Y) ||
1404 !ecp_nistz256_bignum_to_field_elem(point_z, point->Z)) {
1405 ECerr(EC_F_ECP_NISTZ256_GET_AFFINE, EC_R_COORDINATES_OUT_OF_RANGE);
1409 ecp_nistz256_mod_inverse(z_inv3, point_z);
1410 ecp_nistz256_sqr_mont(z_inv2, z_inv3);
1411 ecp_nistz256_mul_mont(x_aff, z_inv2, point_x);
1414 ecp_nistz256_from_mont(x_ret, x_aff);
1415 if (!bn_set_words(x, x_ret, P256_LIMBS))
1420 ecp_nistz256_mul_mont(z_inv3, z_inv3, z_inv2);
1421 ecp_nistz256_mul_mont(y_aff, z_inv3, point_y);
1422 ecp_nistz256_from_mont(y_ret, y_aff);
1423 if (!bn_set_words(y, y_ret, P256_LIMBS))
1430 static NISTZ256_PRE_COMP *ecp_nistz256_pre_comp_new(const EC_GROUP *group)
1432 NISTZ256_PRE_COMP *ret = NULL;
1437 ret = OPENSSL_zalloc(sizeof(*ret));
1440 ECerr(EC_F_ECP_NISTZ256_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE);
1445 ret->w = 6; /* default */
1446 ret->references = 1;
1448 ret->lock = CRYPTO_THREAD_lock_new();
1449 if (ret->lock == NULL) {
1450 ECerr(EC_F_ECP_NISTZ256_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE);
1457 NISTZ256_PRE_COMP *EC_nistz256_pre_comp_dup(NISTZ256_PRE_COMP *p)
1461 CRYPTO_UP_REF(&p->references, &i, p->lock);
1465 void EC_nistz256_pre_comp_free(NISTZ256_PRE_COMP *pre)
1472 CRYPTO_DOWN_REF(&pre->references, &i, pre->lock);
1473 REF_PRINT_COUNT("EC_nistz256", x);
1476 REF_ASSERT_ISNT(i < 0);
1478 OPENSSL_free(pre->precomp_storage);
1479 CRYPTO_THREAD_lock_free(pre->lock);
1484 static int ecp_nistz256_window_have_precompute_mult(const EC_GROUP *group)
1486 /* There is a hard-coded table for the default generator. */
1487 const EC_POINT *generator = EC_GROUP_get0_generator(group);
1489 if (generator != NULL && ecp_nistz256_is_affine_G(generator)) {
1490 /* There is a hard-coded table for the default generator. */
1494 return HAVEPRECOMP(group, nistz256);
1497 const EC_METHOD *EC_GFp_nistz256_method(void)
1499 static const EC_METHOD ret = {
1500 EC_FLAGS_DEFAULT_OCT,
1501 NID_X9_62_prime_field,
1502 ec_GFp_mont_group_init,
1503 ec_GFp_mont_group_finish,
1504 ec_GFp_mont_group_clear_finish,
1505 ec_GFp_mont_group_copy,
1506 ec_GFp_mont_group_set_curve,
1507 ec_GFp_simple_group_get_curve,
1508 ec_GFp_simple_group_get_degree,
1509 ec_group_simple_order_bits,
1510 ec_GFp_simple_group_check_discriminant,
1511 ec_GFp_simple_point_init,
1512 ec_GFp_simple_point_finish,
1513 ec_GFp_simple_point_clear_finish,
1514 ec_GFp_simple_point_copy,
1515 ec_GFp_simple_point_set_to_infinity,
1516 ec_GFp_simple_set_Jprojective_coordinates_GFp,
1517 ec_GFp_simple_get_Jprojective_coordinates_GFp,
1518 ec_GFp_simple_point_set_affine_coordinates,
1519 ecp_nistz256_get_affine,
1523 ec_GFp_simple_invert,
1524 ec_GFp_simple_is_at_infinity,
1525 ec_GFp_simple_is_on_curve,
1527 ec_GFp_simple_make_affine,
1528 ec_GFp_simple_points_make_affine,
1529 ecp_nistz256_points_mul, /* mul */
1530 ecp_nistz256_mult_precompute, /* precompute_mult */
1531 ecp_nistz256_window_have_precompute_mult, /* have_precompute_mult */
1532 ec_GFp_mont_field_mul,
1533 ec_GFp_mont_field_sqr,
1535 ec_GFp_mont_field_encode,
1536 ec_GFp_mont_field_decode,
1537 ec_GFp_mont_field_set_to_one,
1538 ec_key_simple_priv2oct,
1539 ec_key_simple_oct2priv,
1540 0, /* set private */
1541 ec_key_simple_generate_key,
1542 ec_key_simple_check_key,
1543 ec_key_simple_generate_public_key,
1546 ecdh_simple_compute_key