1 /******************************************************************************
3 * Copyright 2014 Intel Corporation *
5 * Licensed under the Apache License, Version 2.0 (the "License"); *
6 * you may not use this file except in compliance with the License. *
7 * You may obtain a copy of the License at *
9 * http://www.apache.org/licenses/LICENSE-2.0 *
11 * Unless required by applicable law or agreed to in writing, software *
12 * distributed under the License is distributed on an "AS IS" BASIS, *
13 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. *
14 * See the License for the specific language governing permissions and *
15 * limitations under the License. *
17 ******************************************************************************
19 * Developers and authors: *
20 * Shay Gueron (1, 2), and Vlad Krasnov (1) *
21 * (1) Intel Corporation, Israel Development Center *
22 * (2) University of Haifa *
24 * S.Gueron and V.Krasnov, "Fast Prime Field Elliptic Curve Cryptography with *
27 ******************************************************************************/
32 #include "internal/bn_int.h"
36 # define TOBN(hi,lo) lo,hi
38 # define TOBN(hi,lo) ((BN_ULONG)hi<<32|lo)
42 # define ALIGN32 __attribute((aligned(32)))
43 #elif defined(_MSC_VER)
44 # define ALIGN32 __declspec(align(32))
49 #define ALIGNPTR(p,N) ((unsigned char *)p+N-(size_t)p%N)
50 #define P256_LIMBS (256/BN_BITS2)
52 typedef unsigned short u16;
55 BN_ULONG X[P256_LIMBS];
56 BN_ULONG Y[P256_LIMBS];
57 BN_ULONG Z[P256_LIMBS];
61 BN_ULONG X[P256_LIMBS];
62 BN_ULONG Y[P256_LIMBS];
65 typedef P256_POINT_AFFINE PRECOMP256_ROW[64];
67 /* structure for precomputed multiples of the generator */
68 typedef struct ec_pre_comp_st {
69 const EC_GROUP *group; /* Parent EC_GROUP object */
70 size_t w; /* Window size */
72 * Constant time access to the X and Y coordinates of the pre-computed,
73 * generator multiplies, in the Montgomery domain. Pre-calculated
74 * multiplies are stored in affine form.
76 PRECOMP256_ROW *precomp;
77 void *precomp_storage;
81 /* Functions implemented in assembly */
82 /* Modular mul by 2: res = 2*a mod P */
83 void ecp_nistz256_mul_by_2(BN_ULONG res[P256_LIMBS],
84 const BN_ULONG a[P256_LIMBS]);
85 /* Modular div by 2: res = a/2 mod P */
86 void ecp_nistz256_div_by_2(BN_ULONG res[P256_LIMBS],
87 const BN_ULONG a[P256_LIMBS]);
88 /* Modular mul by 3: res = 3*a mod P */
89 void ecp_nistz256_mul_by_3(BN_ULONG res[P256_LIMBS],
90 const BN_ULONG a[P256_LIMBS]);
91 /* Modular add: res = a+b mod P */
92 void ecp_nistz256_add(BN_ULONG res[P256_LIMBS],
93 const BN_ULONG a[P256_LIMBS],
94 const BN_ULONG b[P256_LIMBS]);
95 /* Modular sub: res = a-b mod P */
96 void ecp_nistz256_sub(BN_ULONG res[P256_LIMBS],
97 const BN_ULONG a[P256_LIMBS],
98 const BN_ULONG b[P256_LIMBS]);
99 /* Modular neg: res = -a mod P */
100 void ecp_nistz256_neg(BN_ULONG res[P256_LIMBS], const BN_ULONG a[P256_LIMBS]);
101 /* Montgomery mul: res = a*b*2^-256 mod P */
102 void ecp_nistz256_mul_mont(BN_ULONG res[P256_LIMBS],
103 const BN_ULONG a[P256_LIMBS],
104 const BN_ULONG b[P256_LIMBS]);
105 /* Montgomery sqr: res = a*a*2^-256 mod P */
106 void ecp_nistz256_sqr_mont(BN_ULONG res[P256_LIMBS],
107 const BN_ULONG a[P256_LIMBS]);
108 /* Convert a number from Montgomery domain, by multiplying with 1 */
109 void ecp_nistz256_from_mont(BN_ULONG res[P256_LIMBS],
110 const BN_ULONG in[P256_LIMBS]);
111 /* Convert a number to Montgomery domain, by multiplying with 2^512 mod P*/
112 void ecp_nistz256_to_mont(BN_ULONG res[P256_LIMBS],
113 const BN_ULONG in[P256_LIMBS]);
114 /* Functions that perform constant time access to the precomputed tables */
115 void ecp_nistz256_scatter_w5(P256_POINT *val,
116 const P256_POINT *in_t, int idx);
117 void ecp_nistz256_gather_w5(P256_POINT *val,
118 const P256_POINT *in_t, int idx);
119 void ecp_nistz256_scatter_w7(P256_POINT_AFFINE *val,
120 const P256_POINT_AFFINE *in_t, int idx);
121 void ecp_nistz256_gather_w7(P256_POINT_AFFINE *val,
122 const P256_POINT_AFFINE *in_t, int idx);
124 /* One converted into the Montgomery domain */
125 static const BN_ULONG ONE[P256_LIMBS] = {
126 TOBN(0x00000000, 0x00000001), TOBN(0xffffffff, 0x00000000),
127 TOBN(0xffffffff, 0xffffffff), TOBN(0x00000000, 0xfffffffe)
130 static void *ecp_nistz256_pre_comp_dup(void *);
131 static void ecp_nistz256_pre_comp_free(void *);
132 static void ecp_nistz256_pre_comp_clear_free(void *);
133 static EC_PRE_COMP *ecp_nistz256_pre_comp_new(const EC_GROUP *group);
135 /* Precomputed tables for the default generator */
136 extern const PRECOMP256_ROW ecp_nistz256_precomputed[37];
138 /* Recode window to a signed digit, see ecp_nistputil.c for details */
139 static unsigned int _booth_recode_w5(unsigned int in)
143 s = ~((in >> 5) - 1);
144 d = (1 << 6) - in - 1;
145 d = (d & s) | (in & ~s);
146 d = (d >> 1) + (d & 1);
148 return (d << 1) + (s & 1);
151 static unsigned int _booth_recode_w7(unsigned int in)
155 s = ~((in >> 7) - 1);
156 d = (1 << 8) - in - 1;
157 d = (d & s) | (in & ~s);
158 d = (d >> 1) + (d & 1);
160 return (d << 1) + (s & 1);
163 static void copy_conditional(BN_ULONG dst[P256_LIMBS],
164 const BN_ULONG src[P256_LIMBS], BN_ULONG move)
166 BN_ULONG mask1 = 0-move;
167 BN_ULONG mask2 = ~mask1;
169 dst[0] = (src[0] & mask1) ^ (dst[0] & mask2);
170 dst[1] = (src[1] & mask1) ^ (dst[1] & mask2);
171 dst[2] = (src[2] & mask1) ^ (dst[2] & mask2);
172 dst[3] = (src[3] & mask1) ^ (dst[3] & mask2);
173 if (P256_LIMBS == 8) {
174 dst[4] = (src[4] & mask1) ^ (dst[4] & mask2);
175 dst[5] = (src[5] & mask1) ^ (dst[5] & mask2);
176 dst[6] = (src[6] & mask1) ^ (dst[6] & mask2);
177 dst[7] = (src[7] & mask1) ^ (dst[7] & mask2);
181 static BN_ULONG is_zero(BN_ULONG in)
190 static BN_ULONG is_equal(const BN_ULONG a[P256_LIMBS],
191 const BN_ULONG b[P256_LIMBS])
199 if (P256_LIMBS == 8) {
209 static BN_ULONG is_one(const BN_ULONG a[P256_LIMBS])
214 res |= a[1] ^ ONE[1];
215 res |= a[2] ^ ONE[2];
216 res |= a[3] ^ ONE[3];
217 if (P256_LIMBS == 8) {
218 res |= a[4] ^ ONE[4];
219 res |= a[5] ^ ONE[5];
220 res |= a[6] ^ ONE[6];
226 #ifndef ECP_NISTZ256_REFERENCE_IMPLEMENTATION
227 void ecp_nistz256_point_double(P256_POINT *r, const P256_POINT *a);
228 void ecp_nistz256_point_add(P256_POINT *r,
229 const P256_POINT *a, const P256_POINT *b);
230 void ecp_nistz256_point_add_affine(P256_POINT *r,
232 const P256_POINT_AFFINE *b);
234 /* Point double: r = 2*a */
235 static void ecp_nistz256_point_double(P256_POINT *r, const P256_POINT *a)
237 BN_ULONG S[P256_LIMBS];
238 BN_ULONG M[P256_LIMBS];
239 BN_ULONG Zsqr[P256_LIMBS];
240 BN_ULONG tmp0[P256_LIMBS];
242 const BN_ULONG *in_x = a->X;
243 const BN_ULONG *in_y = a->Y;
244 const BN_ULONG *in_z = a->Z;
246 BN_ULONG *res_x = r->X;
247 BN_ULONG *res_y = r->Y;
248 BN_ULONG *res_z = r->Z;
250 ecp_nistz256_mul_by_2(S, in_y);
252 ecp_nistz256_sqr_mont(Zsqr, in_z);
254 ecp_nistz256_sqr_mont(S, S);
256 ecp_nistz256_mul_mont(res_z, in_z, in_y);
257 ecp_nistz256_mul_by_2(res_z, res_z);
259 ecp_nistz256_add(M, in_x, Zsqr);
260 ecp_nistz256_sub(Zsqr, in_x, Zsqr);
262 ecp_nistz256_sqr_mont(res_y, S);
263 ecp_nistz256_div_by_2(res_y, res_y);
265 ecp_nistz256_mul_mont(M, M, Zsqr);
266 ecp_nistz256_mul_by_3(M, M);
268 ecp_nistz256_mul_mont(S, S, in_x);
269 ecp_nistz256_mul_by_2(tmp0, S);
271 ecp_nistz256_sqr_mont(res_x, M);
273 ecp_nistz256_sub(res_x, res_x, tmp0);
274 ecp_nistz256_sub(S, S, res_x);
276 ecp_nistz256_mul_mont(S, S, M);
277 ecp_nistz256_sub(res_y, S, res_y);
280 /* Point addition: r = a+b */
281 static void ecp_nistz256_point_add(P256_POINT *r,
282 const P256_POINT *a, const P256_POINT *b)
284 BN_ULONG U2[P256_LIMBS], S2[P256_LIMBS];
285 BN_ULONG U1[P256_LIMBS], S1[P256_LIMBS];
286 BN_ULONG Z1sqr[P256_LIMBS];
287 BN_ULONG Z2sqr[P256_LIMBS];
288 BN_ULONG H[P256_LIMBS], R[P256_LIMBS];
289 BN_ULONG Hsqr[P256_LIMBS];
290 BN_ULONG Rsqr[P256_LIMBS];
291 BN_ULONG Hcub[P256_LIMBS];
293 BN_ULONG res_x[P256_LIMBS];
294 BN_ULONG res_y[P256_LIMBS];
295 BN_ULONG res_z[P256_LIMBS];
297 BN_ULONG in1infty, in2infty;
299 const BN_ULONG *in1_x = a->X;
300 const BN_ULONG *in1_y = a->Y;
301 const BN_ULONG *in1_z = a->Z;
303 const BN_ULONG *in2_x = b->X;
304 const BN_ULONG *in2_y = b->Y;
305 const BN_ULONG *in2_z = b->Z;
307 /* We encode infinity as (0,0), which is not on the curve,
309 in1infty = (in1_x[0] | in1_x[1] | in1_x[2] | in1_x[3] |
310 in1_y[0] | in1_y[1] | in1_y[2] | in1_y[3]);
312 in1infty |= (in1_x[4] | in1_x[5] | in1_x[6] | in1_x[7] |
313 in1_y[4] | in1_y[5] | in1_y[6] | in1_y[7]);
315 in2infty = (in2_x[0] | in2_x[1] | in2_x[2] | in2_x[3] |
316 in2_y[0] | in2_y[1] | in2_y[2] | in2_y[3]);
318 in2infty |= (in2_x[4] | in2_x[5] | in2_x[6] | in2_x[7] |
319 in2_y[4] | in2_y[5] | in2_y[6] | in2_y[7]);
321 in1infty = is_zero(in1infty);
322 in2infty = is_zero(in2infty);
324 ecp_nistz256_sqr_mont(Z2sqr, in2_z); /* Z2^2 */
325 ecp_nistz256_sqr_mont(Z1sqr, in1_z); /* Z1^2 */
327 ecp_nistz256_mul_mont(S1, Z2sqr, in2_z); /* S1 = Z2^3 */
328 ecp_nistz256_mul_mont(S2, Z1sqr, in1_z); /* S2 = Z1^3 */
330 ecp_nistz256_mul_mont(S1, S1, in1_y); /* S1 = Y1*Z2^3 */
331 ecp_nistz256_mul_mont(S2, S2, in2_y); /* S2 = Y2*Z1^3 */
332 ecp_nistz256_sub(R, S2, S1); /* R = S2 - S1 */
334 ecp_nistz256_mul_mont(U1, in1_x, Z2sqr); /* U1 = X1*Z2^2 */
335 ecp_nistz256_mul_mont(U2, in2_x, Z1sqr); /* U2 = X2*Z1^2 */
336 ecp_nistz256_sub(H, U2, U1); /* H = U2 - U1 */
339 * This should not happen during sign/ecdh, so no constant time violation
341 if (is_equal(U1, U2) && !in1infty && !in2infty) {
342 if (is_equal(S1, S2)) {
343 ecp_nistz256_point_double(r, a);
346 memset(r, 0, sizeof(*r));
351 ecp_nistz256_sqr_mont(Rsqr, R); /* R^2 */
352 ecp_nistz256_mul_mont(res_z, H, in1_z); /* Z3 = H*Z1*Z2 */
353 ecp_nistz256_sqr_mont(Hsqr, H); /* H^2 */
354 ecp_nistz256_mul_mont(res_z, res_z, in2_z); /* Z3 = H*Z1*Z2 */
355 ecp_nistz256_mul_mont(Hcub, Hsqr, H); /* H^3 */
357 ecp_nistz256_mul_mont(U2, U1, Hsqr); /* U1*H^2 */
358 ecp_nistz256_mul_by_2(Hsqr, U2); /* 2*U1*H^2 */
360 ecp_nistz256_sub(res_x, Rsqr, Hsqr);
361 ecp_nistz256_sub(res_x, res_x, Hcub);
363 ecp_nistz256_sub(res_y, U2, res_x);
365 ecp_nistz256_mul_mont(S2, S1, Hcub);
366 ecp_nistz256_mul_mont(res_y, R, res_y);
367 ecp_nistz256_sub(res_y, res_y, S2);
369 copy_conditional(res_x, in2_x, in1infty);
370 copy_conditional(res_y, in2_y, in1infty);
371 copy_conditional(res_z, in2_z, in1infty);
373 copy_conditional(res_x, in1_x, in2infty);
374 copy_conditional(res_y, in1_y, in2infty);
375 copy_conditional(res_z, in1_z, in2infty);
377 memcpy(r->X, res_x, sizeof(res_x));
378 memcpy(r->Y, res_y, sizeof(res_y));
379 memcpy(r->Z, res_z, sizeof(res_z));
382 /* Point addition when b is known to be affine: r = a+b */
383 static void ecp_nistz256_point_add_affine(P256_POINT *r,
385 const P256_POINT_AFFINE *b)
387 BN_ULONG U2[P256_LIMBS], S2[P256_LIMBS];
388 BN_ULONG Z1sqr[P256_LIMBS];
389 BN_ULONG H[P256_LIMBS], R[P256_LIMBS];
390 BN_ULONG Hsqr[P256_LIMBS];
391 BN_ULONG Rsqr[P256_LIMBS];
392 BN_ULONG Hcub[P256_LIMBS];
394 BN_ULONG res_x[P256_LIMBS];
395 BN_ULONG res_y[P256_LIMBS];
396 BN_ULONG res_z[P256_LIMBS];
398 BN_ULONG in1infty, in2infty;
400 const BN_ULONG *in1_x = a->X;
401 const BN_ULONG *in1_y = a->Y;
402 const BN_ULONG *in1_z = a->Z;
404 const BN_ULONG *in2_x = b->X;
405 const BN_ULONG *in2_y = b->Y;
408 * In affine representation we encode infty as (0,0), which is not on the
411 in1infty = (in1_x[0] | in1_x[1] | in1_x[2] | in1_x[3] |
412 in1_y[0] | in1_y[1] | in1_y[2] | in1_y[3]);
414 in1infty |= (in1_x[4] | in1_x[5] | in1_x[6] | in1_x[7] |
415 in1_y[4] | in1_y[5] | in1_y[6] | in1_y[7]);
417 in2infty = (in2_x[0] | in2_x[1] | in2_x[2] | in2_x[3] |
418 in2_y[0] | in2_y[1] | in2_y[2] | in2_y[3]);
420 in2infty |= (in2_x[4] | in2_x[5] | in2_x[6] | in2_x[7] |
421 in2_y[4] | in2_y[5] | in2_y[6] | in2_y[7]);
423 in1infty = is_zero(in1infty);
424 in2infty = is_zero(in2infty);
426 ecp_nistz256_sqr_mont(Z1sqr, in1_z); /* Z1^2 */
428 ecp_nistz256_mul_mont(U2, in2_x, Z1sqr); /* U2 = X2*Z1^2 */
429 ecp_nistz256_sub(H, U2, in1_x); /* H = U2 - U1 */
431 ecp_nistz256_mul_mont(S2, Z1sqr, in1_z); /* S2 = Z1^3 */
433 ecp_nistz256_mul_mont(res_z, H, in1_z); /* Z3 = H*Z1*Z2 */
435 ecp_nistz256_mul_mont(S2, S2, in2_y); /* S2 = Y2*Z1^3 */
436 ecp_nistz256_sub(R, S2, in1_y); /* R = S2 - S1 */
438 ecp_nistz256_sqr_mont(Hsqr, H); /* H^2 */
439 ecp_nistz256_sqr_mont(Rsqr, R); /* R^2 */
440 ecp_nistz256_mul_mont(Hcub, Hsqr, H); /* H^3 */
442 ecp_nistz256_mul_mont(U2, in1_x, Hsqr); /* U1*H^2 */
443 ecp_nistz256_mul_by_2(Hsqr, U2); /* 2*U1*H^2 */
445 ecp_nistz256_sub(res_x, Rsqr, Hsqr);
446 ecp_nistz256_sub(res_x, res_x, Hcub);
447 ecp_nistz256_sub(H, U2, res_x);
449 ecp_nistz256_mul_mont(S2, in1_y, Hcub);
450 ecp_nistz256_mul_mont(H, H, R);
451 ecp_nistz256_sub(res_y, H, S2);
453 copy_conditional(res_x, in2_x, in1infty);
454 copy_conditional(res_x, in1_x, in2infty);
456 copy_conditional(res_y, in2_y, in1infty);
457 copy_conditional(res_y, in1_y, in2infty);
459 copy_conditional(res_z, ONE, in1infty);
460 copy_conditional(res_z, in1_z, in2infty);
462 memcpy(r->X, res_x, sizeof(res_x));
463 memcpy(r->Y, res_y, sizeof(res_y));
464 memcpy(r->Z, res_z, sizeof(res_z));
468 /* r = in^-1 mod p */
469 static void ecp_nistz256_mod_inverse(BN_ULONG r[P256_LIMBS],
470 const BN_ULONG in[P256_LIMBS])
473 * The poly is ffffffff 00000001 00000000 00000000 00000000 ffffffff
474 * ffffffff ffffffff We use FLT and used poly-2 as exponent
476 BN_ULONG p2[P256_LIMBS];
477 BN_ULONG p4[P256_LIMBS];
478 BN_ULONG p8[P256_LIMBS];
479 BN_ULONG p16[P256_LIMBS];
480 BN_ULONG p32[P256_LIMBS];
481 BN_ULONG res[P256_LIMBS];
484 ecp_nistz256_sqr_mont(res, in);
485 ecp_nistz256_mul_mont(p2, res, in); /* 3*p */
487 ecp_nistz256_sqr_mont(res, p2);
488 ecp_nistz256_sqr_mont(res, res);
489 ecp_nistz256_mul_mont(p4, res, p2); /* f*p */
491 ecp_nistz256_sqr_mont(res, p4);
492 ecp_nistz256_sqr_mont(res, res);
493 ecp_nistz256_sqr_mont(res, res);
494 ecp_nistz256_sqr_mont(res, res);
495 ecp_nistz256_mul_mont(p8, res, p4); /* ff*p */
497 ecp_nistz256_sqr_mont(res, p8);
498 for (i = 0; i < 7; i++)
499 ecp_nistz256_sqr_mont(res, res);
500 ecp_nistz256_mul_mont(p16, res, p8); /* ffff*p */
502 ecp_nistz256_sqr_mont(res, p16);
503 for (i = 0; i < 15; i++)
504 ecp_nistz256_sqr_mont(res, res);
505 ecp_nistz256_mul_mont(p32, res, p16); /* ffffffff*p */
507 ecp_nistz256_sqr_mont(res, p32);
508 for (i = 0; i < 31; i++)
509 ecp_nistz256_sqr_mont(res, res);
510 ecp_nistz256_mul_mont(res, res, in);
512 for (i = 0; i < 32 * 4; i++)
513 ecp_nistz256_sqr_mont(res, res);
514 ecp_nistz256_mul_mont(res, res, p32);
516 for (i = 0; i < 32; i++)
517 ecp_nistz256_sqr_mont(res, res);
518 ecp_nistz256_mul_mont(res, res, p32);
520 for (i = 0; i < 16; i++)
521 ecp_nistz256_sqr_mont(res, res);
522 ecp_nistz256_mul_mont(res, res, p16);
524 for (i = 0; i < 8; i++)
525 ecp_nistz256_sqr_mont(res, res);
526 ecp_nistz256_mul_mont(res, res, p8);
528 ecp_nistz256_sqr_mont(res, res);
529 ecp_nistz256_sqr_mont(res, res);
530 ecp_nistz256_sqr_mont(res, res);
531 ecp_nistz256_sqr_mont(res, res);
532 ecp_nistz256_mul_mont(res, res, p4);
534 ecp_nistz256_sqr_mont(res, res);
535 ecp_nistz256_sqr_mont(res, res);
536 ecp_nistz256_mul_mont(res, res, p2);
538 ecp_nistz256_sqr_mont(res, res);
539 ecp_nistz256_sqr_mont(res, res);
540 ecp_nistz256_mul_mont(res, res, in);
542 memcpy(r, res, sizeof(res));
546 * ecp_nistz256_bignum_to_field_elem copies the contents of |in| to |out| and
547 * returns one if it fits. Otherwise it returns zero.
549 static int ecp_nistz256_bignum_to_field_elem(BN_ULONG out[P256_LIMBS],
552 return bn_copy_words(out, in, P256_LIMBS);
555 /* r = sum(scalar[i]*point[i]) */
556 static void ecp_nistz256_windowed_mul(const EC_GROUP *group,
558 const BIGNUM **scalar,
559 const EC_POINT **point,
560 size_t num, BN_CTX *ctx)
565 unsigned char (*p_str)[33] = NULL;
566 const unsigned int window_size = 5;
567 const unsigned int mask = (1 << (window_size + 1)) - 1;
569 P256_POINT *temp; /* place for 5 temporary points */
570 const BIGNUM **scalars = NULL;
571 P256_POINT (*table)[16] = NULL;
572 void *table_storage = NULL;
574 if ((num * 16 + 6) > OPENSSL_MALLOC_MAX_NELEMS(P256_POINT)
576 OPENSSL_malloc((num * 16 + 5) * sizeof(P256_POINT) + 64)) == NULL
578 OPENSSL_malloc(num * 33 * sizeof(unsigned char))) == NULL
579 || (scalars = OPENSSL_malloc(num * sizeof(BIGNUM *))) == NULL) {
580 ECerr(EC_F_ECP_NISTZ256_WINDOWED_MUL, ERR_R_MALLOC_FAILURE);
584 table = (void *)ALIGNPTR(table_storage, 64);
585 temp = (P256_POINT *)(table + num);
587 for (i = 0; i < num; i++) {
588 P256_POINT *row = table[i];
590 if ((BN_num_bits(scalar[i]) > 256) || BN_is_negative(scalar[i])) {
593 if ((mod = BN_CTX_get(ctx)) == NULL)
595 if (!BN_nnmod(mod, scalar[i], group->order, ctx)) {
596 ECerr(EC_F_ECP_NISTZ256_WINDOWED_MUL, ERR_R_BN_LIB);
601 scalars[i] = scalar[i];
603 for (j = 0; j < bn_get_top(scalars[i]) * BN_BYTES; j += BN_BYTES) {
604 BN_ULONG d = bn_get_words(scalars[i])[j / BN_BYTES];
606 p_str[i][j + 0] = (unsigned char)d;
607 p_str[i][j + 1] = (unsigned char)(d >> 8);
608 p_str[i][j + 2] = (unsigned char)(d >> 16);
609 p_str[i][j + 3] = (unsigned char)(d >>= 24);
612 p_str[i][j + 4] = (unsigned char)d;
613 p_str[i][j + 5] = (unsigned char)(d >> 8);
614 p_str[i][j + 6] = (unsigned char)(d >> 16);
615 p_str[i][j + 7] = (unsigned char)(d >> 24);
621 if (!ecp_nistz256_bignum_to_field_elem(temp[0].X, point[i]->X)
622 || !ecp_nistz256_bignum_to_field_elem(temp[0].Y, point[i]->Y)
623 || !ecp_nistz256_bignum_to_field_elem(temp[0].Z, point[i]->Z)) {
624 ECerr(EC_F_ECP_NISTZ256_WINDOWED_MUL,
625 EC_R_COORDINATES_OUT_OF_RANGE);
630 * row[0] is implicitly (0,0,0) (the point at infinity), therefore it
631 * is not stored. All other values are actually stored with an offset
635 ecp_nistz256_scatter_w5 (row, &temp[0], 1);
636 ecp_nistz256_point_double(&temp[1], &temp[0]); /*1+1=2 */
637 ecp_nistz256_scatter_w5 (row, &temp[1], 2);
638 ecp_nistz256_point_add (&temp[2], &temp[1], &temp[0]); /*2+1=3 */
639 ecp_nistz256_scatter_w5 (row, &temp[2], 3);
640 ecp_nistz256_point_double(&temp[1], &temp[1]); /*2*2=4 */
641 ecp_nistz256_scatter_w5 (row, &temp[1], 4);
642 ecp_nistz256_point_double(&temp[2], &temp[2]); /*2*3=6 */
643 ecp_nistz256_scatter_w5 (row, &temp[2], 6);
644 ecp_nistz256_point_add (&temp[3], &temp[1], &temp[0]); /*4+1=5 */
645 ecp_nistz256_scatter_w5 (row, &temp[3], 5);
646 ecp_nistz256_point_add (&temp[4], &temp[2], &temp[0]); /*6+1=7 */
647 ecp_nistz256_scatter_w5 (row, &temp[4], 7);
648 ecp_nistz256_point_double(&temp[1], &temp[1]); /*2*4=8 */
649 ecp_nistz256_scatter_w5 (row, &temp[1], 8);
650 ecp_nistz256_point_double(&temp[2], &temp[2]); /*2*6=12 */
651 ecp_nistz256_scatter_w5 (row, &temp[2], 12);
652 ecp_nistz256_point_double(&temp[3], &temp[3]); /*2*5=10 */
653 ecp_nistz256_scatter_w5 (row, &temp[3], 10);
654 ecp_nistz256_point_double(&temp[4], &temp[4]); /*2*7=14 */
655 ecp_nistz256_scatter_w5 (row, &temp[4], 14);
656 ecp_nistz256_point_add (&temp[2], &temp[2], &temp[0]); /*12+1=13*/
657 ecp_nistz256_scatter_w5 (row, &temp[2], 13);
658 ecp_nistz256_point_add (&temp[3], &temp[3], &temp[0]); /*10+1=11*/
659 ecp_nistz256_scatter_w5 (row, &temp[3], 11);
660 ecp_nistz256_point_add (&temp[4], &temp[4], &temp[0]); /*14+1=15*/
661 ecp_nistz256_scatter_w5 (row, &temp[4], 15);
662 ecp_nistz256_point_add (&temp[2], &temp[1], &temp[0]); /*8+1=9 */
663 ecp_nistz256_scatter_w5 (row, &temp[2], 9);
664 ecp_nistz256_point_double(&temp[1], &temp[1]); /*2*8=16 */
665 ecp_nistz256_scatter_w5 (row, &temp[1], 16);
670 wvalue = p_str[0][(idx - 1) / 8];
671 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
674 * We gather to temp[0], because we know it's position relative
677 ecp_nistz256_gather_w5(&temp[0], table[0], _booth_recode_w5(wvalue) >> 1);
678 memcpy(r, &temp[0], sizeof(temp[0]));
681 for (i = (idx == 255 ? 1 : 0); i < num; i++) {
682 unsigned int off = (idx - 1) / 8;
684 wvalue = p_str[i][off] | p_str[i][off + 1] << 8;
685 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
687 wvalue = _booth_recode_w5(wvalue);
689 ecp_nistz256_gather_w5(&temp[0], table[i], wvalue >> 1);
691 ecp_nistz256_neg(temp[1].Y, temp[0].Y);
692 copy_conditional(temp[0].Y, temp[1].Y, (wvalue & 1));
694 ecp_nistz256_point_add(r, r, &temp[0]);
699 ecp_nistz256_point_double(r, r);
700 ecp_nistz256_point_double(r, r);
701 ecp_nistz256_point_double(r, r);
702 ecp_nistz256_point_double(r, r);
703 ecp_nistz256_point_double(r, r);
707 for (i = 0; i < num; i++) {
708 wvalue = p_str[i][0];
709 wvalue = (wvalue << 1) & mask;
711 wvalue = _booth_recode_w5(wvalue);
713 ecp_nistz256_gather_w5(&temp[0], table[i], wvalue >> 1);
715 ecp_nistz256_neg(temp[1].Y, temp[0].Y);
716 copy_conditional(temp[0].Y, temp[1].Y, wvalue & 1);
718 ecp_nistz256_point_add(r, r, &temp[0]);
723 OPENSSL_free(table_storage);
727 OPENSSL_free(scalars);
730 /* Coordinates of G, for which we have precomputed tables */
731 const static BN_ULONG def_xG[P256_LIMBS] = {
732 TOBN(0x79e730d4, 0x18a9143c), TOBN(0x75ba95fc, 0x5fedb601),
733 TOBN(0x79fb732b, 0x77622510), TOBN(0x18905f76, 0xa53755c6)
736 const static BN_ULONG def_yG[P256_LIMBS] = {
737 TOBN(0xddf25357, 0xce95560a), TOBN(0x8b4ab8e4, 0xba19e45c),
738 TOBN(0xd2e88688, 0xdd21f325), TOBN(0x8571ff18, 0x25885d85)
742 * ecp_nistz256_is_affine_G returns one if |generator| is the standard, P-256
745 static int ecp_nistz256_is_affine_G(const EC_POINT *generator)
747 return (bn_get_top(generator->X) == P256_LIMBS) &&
748 (bn_get_top(generator->Y) == P256_LIMBS) &&
749 (bn_get_top(generator->Z) == (P256_LIMBS - P256_LIMBS / 8)) &&
750 is_equal(bn_get_words(generator->X), def_xG) &&
751 is_equal(bn_get_words(generator->Y), def_yG) &&
752 is_one(bn_get_words(generator->Z));
755 static int ecp_nistz256_mult_precompute(EC_GROUP *group, BN_CTX *ctx)
758 * We precompute a table for a Booth encoded exponent (wNAF) based
759 * computation. Each table holds 64 values for safe access, with an
760 * implicit value of infinity at index zero. We use window of size 7, and
761 * therefore require ceil(256/7) = 37 tables.
764 EC_POINT *P = NULL, *T = NULL;
765 const EC_POINT *generator;
766 EC_PRE_COMP *pre_comp;
767 int i, j, k, ret = 0;
770 PRECOMP256_ROW *preComputedTable = NULL;
771 unsigned char *precomp_storage = NULL;
773 /* if there is an old EC_PRE_COMP object, throw it away */
774 EC_EX_DATA_free_data(&group->extra_data, ecp_nistz256_pre_comp_dup,
775 ecp_nistz256_pre_comp_free,
776 ecp_nistz256_pre_comp_clear_free);
778 generator = EC_GROUP_get0_generator(group);
779 if (generator == NULL) {
780 ECerr(EC_F_ECP_NISTZ256_MULT_PRECOMPUTE, EC_R_UNDEFINED_GENERATOR);
784 if (ecp_nistz256_is_affine_G(generator)) {
786 * No need to calculate tables for the standard generator because we
787 * have them statically.
792 if ((pre_comp = ecp_nistz256_pre_comp_new(group)) == NULL)
802 order = BN_CTX_get(ctx);
807 if (!EC_GROUP_get_order(group, order, ctx))
810 if (BN_is_zero(order)) {
811 ECerr(EC_F_ECP_NISTZ256_MULT_PRECOMPUTE, EC_R_UNKNOWN_ORDER);
817 if ((precomp_storage =
818 OPENSSL_malloc(37 * 64 * sizeof(P256_POINT_AFFINE) + 64)) == NULL) {
819 ECerr(EC_F_ECP_NISTZ256_MULT_PRECOMPUTE, ERR_R_MALLOC_FAILURE);
823 preComputedTable = (void *)ALIGNPTR(precomp_storage, 64);
825 P = EC_POINT_new(group);
826 T = EC_POINT_new(group);
829 * The zero entry is implicitly infinity, and we skip it, storing other
830 * values with -1 offset.
832 EC_POINT_copy(T, generator);
834 for (k = 0; k < 64; k++) {
836 for (j = 0; j < 37; j++) {
837 P256_POINT_AFFINE temp;
839 * It would be faster to use ec_GFp_simple_points_make_affine and
840 * make multiple points affine at the same time.
842 ec_GFp_simple_make_affine(group, P, ctx);
843 ecp_nistz256_bignum_to_field_elem(temp.X, P->X);
844 ecp_nistz256_bignum_to_field_elem(temp.Y, P->Y);
845 ecp_nistz256_scatter_w7(preComputedTable[j], &temp, k);
846 for (i = 0; i < 7; i++)
847 ec_GFp_simple_dbl(group, P, P, ctx);
849 ec_GFp_simple_add(group, T, T, generator, ctx);
852 pre_comp->group = group;
854 pre_comp->precomp = preComputedTable;
855 pre_comp->precomp_storage = precomp_storage;
857 precomp_storage = NULL;
859 if (!EC_EX_DATA_set_data(&group->extra_data, pre_comp,
860 ecp_nistz256_pre_comp_dup,
861 ecp_nistz256_pre_comp_free,
862 ecp_nistz256_pre_comp_clear_free)) {
874 ecp_nistz256_pre_comp_free(pre_comp);
876 OPENSSL_free(precomp_storage);
885 * Note that by default ECP_NISTZ256_AVX2 is undefined. While it's great
886 * code processing 4 points in parallel, corresponding serial operation
887 * is several times slower, because it uses 29x29=58-bit multiplication
888 * as opposite to 64x64=128-bit in integer-only scalar case. As result
889 * it doesn't provide *significant* performance improvement. Note that
890 * just defining ECP_NISTZ256_AVX2 is not sufficient to make it work,
891 * you'd need to compile even asm/ecp_nistz256-avx.pl module.
893 #if defined(ECP_NISTZ256_AVX2)
894 # if !(defined(__x86_64) || defined(__x86_64__) || \
895 defined(_M_AMD64) || defined(_MX64)) || \
896 !(defined(__GNUC__) || defined(_MSC_VER)) /* this is for ALIGN32 */
897 # undef ECP_NISTZ256_AVX2
899 /* Constant time access, loading four values, from four consecutive tables */
900 void ecp_nistz256_avx2_multi_gather_w7(void *result, const void *in,
901 int index0, int index1, int index2,
903 void ecp_nistz256_avx2_transpose_convert(void *RESULTx4, const void *in);
904 void ecp_nistz256_avx2_convert_transpose_back(void *result, const void *Ax4);
905 void ecp_nistz256_avx2_point_add_affine_x4(void *RESULTx4, const void *Ax4,
907 void ecp_nistz256_avx2_point_add_affines_x4(void *RESULTx4, const void *Ax4,
909 void ecp_nistz256_avx2_to_mont(void *RESULTx4, const void *Ax4);
910 void ecp_nistz256_avx2_from_mont(void *RESULTx4, const void *Ax4);
911 void ecp_nistz256_avx2_set1(void *RESULTx4);
912 int ecp_nistz_avx2_eligible(void);
914 static void booth_recode_w7(unsigned char *sign,
915 unsigned char *digit, unsigned char in)
919 s = ~((in >> 7) - 1);
920 d = (1 << 8) - in - 1;
921 d = (d & s) | (in & ~s);
922 d = (d >> 1) + (d & 1);
929 * ecp_nistz256_avx2_mul_g performs multiplication by G, using only the
930 * precomputed table. It does 4 affine point additions in parallel,
931 * significantly speeding up point multiplication for a fixed value.
933 static void ecp_nistz256_avx2_mul_g(P256_POINT *r,
934 unsigned char p_str[33],
935 const P256_POINT_AFFINE(*preComputedTable)[64])
937 const unsigned int window_size = 7;
938 const unsigned int mask = (1 << (window_size + 1)) - 1;
940 /* Using 4 windows at a time */
941 unsigned char sign0, digit0;
942 unsigned char sign1, digit1;
943 unsigned char sign2, digit2;
944 unsigned char sign3, digit3;
945 unsigned int idx = 0;
946 BN_ULONG tmp[P256_LIMBS];
949 ALIGN32 BN_ULONG aX4[4 * 9 * 3] = { 0 };
950 ALIGN32 BN_ULONG bX4[4 * 9 * 2] = { 0 };
951 ALIGN32 P256_POINT_AFFINE point_arr[4];
952 ALIGN32 P256_POINT res_point_arr[4];
954 /* Initial four windows */
955 wvalue = *((u16 *) & p_str[0]);
956 wvalue = (wvalue << 1) & mask;
958 booth_recode_w7(&sign0, &digit0, wvalue);
959 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
960 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
962 booth_recode_w7(&sign1, &digit1, wvalue);
963 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
964 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
966 booth_recode_w7(&sign2, &digit2, wvalue);
967 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
968 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
970 booth_recode_w7(&sign3, &digit3, wvalue);
972 ecp_nistz256_avx2_multi_gather_w7(point_arr, preComputedTable[0],
973 digit0, digit1, digit2, digit3);
975 ecp_nistz256_neg(tmp, point_arr[0].Y);
976 copy_conditional(point_arr[0].Y, tmp, sign0);
977 ecp_nistz256_neg(tmp, point_arr[1].Y);
978 copy_conditional(point_arr[1].Y, tmp, sign1);
979 ecp_nistz256_neg(tmp, point_arr[2].Y);
980 copy_conditional(point_arr[2].Y, tmp, sign2);
981 ecp_nistz256_neg(tmp, point_arr[3].Y);
982 copy_conditional(point_arr[3].Y, tmp, sign3);
984 ecp_nistz256_avx2_transpose_convert(aX4, point_arr);
985 ecp_nistz256_avx2_to_mont(aX4, aX4);
986 ecp_nistz256_avx2_to_mont(&aX4[4 * 9], &aX4[4 * 9]);
987 ecp_nistz256_avx2_set1(&aX4[4 * 9 * 2]);
989 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
990 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
992 booth_recode_w7(&sign0, &digit0, wvalue);
993 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
994 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
996 booth_recode_w7(&sign1, &digit1, wvalue);
997 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
998 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
1000 booth_recode_w7(&sign2, &digit2, wvalue);
1001 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
1002 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
1004 booth_recode_w7(&sign3, &digit3, wvalue);
1006 ecp_nistz256_avx2_multi_gather_w7(point_arr, preComputedTable[4 * 1],
1007 digit0, digit1, digit2, digit3);
1009 ecp_nistz256_neg(tmp, point_arr[0].Y);
1010 copy_conditional(point_arr[0].Y, tmp, sign0);
1011 ecp_nistz256_neg(tmp, point_arr[1].Y);
1012 copy_conditional(point_arr[1].Y, tmp, sign1);
1013 ecp_nistz256_neg(tmp, point_arr[2].Y);
1014 copy_conditional(point_arr[2].Y, tmp, sign2);
1015 ecp_nistz256_neg(tmp, point_arr[3].Y);
1016 copy_conditional(point_arr[3].Y, tmp, sign3);
1018 ecp_nistz256_avx2_transpose_convert(bX4, point_arr);
1019 ecp_nistz256_avx2_to_mont(bX4, bX4);
1020 ecp_nistz256_avx2_to_mont(&bX4[4 * 9], &bX4[4 * 9]);
1021 /* Optimized when both inputs are affine */
1022 ecp_nistz256_avx2_point_add_affines_x4(aX4, aX4, bX4);
1024 for (i = 2; i < 9; i++) {
1025 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
1026 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
1028 booth_recode_w7(&sign0, &digit0, wvalue);
1029 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
1030 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
1032 booth_recode_w7(&sign1, &digit1, wvalue);
1033 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
1034 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
1036 booth_recode_w7(&sign2, &digit2, wvalue);
1037 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
1038 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
1040 booth_recode_w7(&sign3, &digit3, wvalue);
1042 ecp_nistz256_avx2_multi_gather_w7(point_arr,
1043 preComputedTable[4 * i],
1044 digit0, digit1, digit2, digit3);
1046 ecp_nistz256_neg(tmp, point_arr[0].Y);
1047 copy_conditional(point_arr[0].Y, tmp, sign0);
1048 ecp_nistz256_neg(tmp, point_arr[1].Y);
1049 copy_conditional(point_arr[1].Y, tmp, sign1);
1050 ecp_nistz256_neg(tmp, point_arr[2].Y);
1051 copy_conditional(point_arr[2].Y, tmp, sign2);
1052 ecp_nistz256_neg(tmp, point_arr[3].Y);
1053 copy_conditional(point_arr[3].Y, tmp, sign3);
1055 ecp_nistz256_avx2_transpose_convert(bX4, point_arr);
1056 ecp_nistz256_avx2_to_mont(bX4, bX4);
1057 ecp_nistz256_avx2_to_mont(&bX4[4 * 9], &bX4[4 * 9]);
1059 ecp_nistz256_avx2_point_add_affine_x4(aX4, aX4, bX4);
1062 ecp_nistz256_avx2_from_mont(&aX4[4 * 9 * 0], &aX4[4 * 9 * 0]);
1063 ecp_nistz256_avx2_from_mont(&aX4[4 * 9 * 1], &aX4[4 * 9 * 1]);
1064 ecp_nistz256_avx2_from_mont(&aX4[4 * 9 * 2], &aX4[4 * 9 * 2]);
1066 ecp_nistz256_avx2_convert_transpose_back(res_point_arr, aX4);
1067 /* Last window is performed serially */
1068 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
1069 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
1070 booth_recode_w7(&sign0, &digit0, wvalue);
1071 ecp_nistz256_gather_w7((P256_POINT_AFFINE *)r,
1072 preComputedTable[36], digit0);
1073 ecp_nistz256_neg(tmp, r->Y);
1074 copy_conditional(r->Y, tmp, sign0);
1075 memcpy(r->Z, ONE, sizeof(ONE));
1076 /* Sum the four windows */
1077 ecp_nistz256_point_add(r, r, &res_point_arr[0]);
1078 ecp_nistz256_point_add(r, r, &res_point_arr[1]);
1079 ecp_nistz256_point_add(r, r, &res_point_arr[2]);
1080 ecp_nistz256_point_add(r, r, &res_point_arr[3]);
1085 static int ecp_nistz256_set_from_affine(EC_POINT *out, const EC_GROUP *group,
1086 const P256_POINT_AFFINE *in,
1090 BN_ULONG d_x[P256_LIMBS], d_y[P256_LIMBS];
1101 memcpy(d_x, in->X, sizeof(d_x));
1102 bn_set_static_words(x, d_x, P256_LIMBS);
1104 memcpy(d_y, in->Y, sizeof(d_y));
1105 bn_set_static_words(y, d_y, P256_LIMBS);
1107 ret = EC_POINT_set_affine_coordinates_GFp(group, out, x, y, ctx);
1117 /* r = scalar*G + sum(scalars[i]*points[i]) */
1118 static int ecp_nistz256_points_mul(const EC_GROUP *group,
1120 const BIGNUM *scalar,
1122 const EC_POINT *points[],
1123 const BIGNUM *scalars[], BN_CTX *ctx)
1125 int i = 0, ret = 0, no_precomp_for_generator = 0, p_is_infinity = 0;
1127 unsigned char p_str[33] = { 0 };
1128 const PRECOMP256_ROW *preComputedTable = NULL;
1129 const EC_PRE_COMP *pre_comp = NULL;
1130 const EC_POINT *generator = NULL;
1131 unsigned int idx = 0;
1132 const unsigned int window_size = 7;
1133 const unsigned int mask = (1 << (window_size + 1)) - 1;
1134 unsigned int wvalue;
1137 P256_POINT_AFFINE a;
1141 if ((num + 1) == 0 || (num + 1) > OPENSSL_MALLOC_MAX_NELEMS(void *)) {
1142 ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, ERR_R_MALLOC_FAILURE);
1146 if (group->meth != r->meth) {
1147 ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, EC_R_INCOMPATIBLE_OBJECTS);
1150 if ((scalar == NULL) && (num == 0))
1151 return EC_POINT_set_to_infinity(group, r);
1153 for (j = 0; j < num; j++) {
1154 if (group->meth != points[j]->meth) {
1155 ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, EC_R_INCOMPATIBLE_OBJECTS);
1160 /* Need 256 bits for space for all coordinates. */
1161 bn_wexpand(r->X, P256_LIMBS);
1162 bn_wexpand(r->Y, P256_LIMBS);
1163 bn_wexpand(r->Z, P256_LIMBS);
1164 bn_set_top(r->X, P256_LIMBS);
1165 bn_set_top(r->Y, P256_LIMBS);
1166 bn_set_top(r->Z, P256_LIMBS);
1169 generator = EC_GROUP_get0_generator(group);
1170 if (generator == NULL) {
1171 ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, EC_R_UNDEFINED_GENERATOR);
1175 /* look if we can use precomputed multiples of generator */
1177 EC_EX_DATA_get_data(group->extra_data, ecp_nistz256_pre_comp_dup,
1178 ecp_nistz256_pre_comp_free,
1179 ecp_nistz256_pre_comp_clear_free);
1183 * If there is a precomputed table for the generator, check that
1184 * it was generated with the same generator.
1186 EC_POINT *pre_comp_generator = EC_POINT_new(group);
1187 if (pre_comp_generator == NULL)
1190 if (!ecp_nistz256_set_from_affine(pre_comp_generator,
1191 group, pre_comp->precomp[0],
1195 if (0 == EC_POINT_cmp(group, generator, pre_comp_generator, ctx))
1196 preComputedTable = (const PRECOMP256_ROW *)pre_comp->precomp;
1198 EC_POINT_free(pre_comp_generator);
1201 if (preComputedTable == NULL && ecp_nistz256_is_affine_G(generator)) {
1203 * If there is no precomputed data, but the generator is the
1204 * default, a hardcoded table of precomputed data is used. This
1205 * is because applications, such as Apache, do not use
1206 * EC_KEY_precompute_mult.
1208 preComputedTable = ecp_nistz256_precomputed;
1211 if (preComputedTable) {
1212 if ((BN_num_bits(scalar) > 256)
1213 || BN_is_negative(scalar)) {
1214 if ((tmp_scalar = BN_CTX_get(ctx)) == NULL)
1217 if (!BN_nnmod(tmp_scalar, scalar, group->order, ctx)) {
1218 ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, ERR_R_BN_LIB);
1221 scalar = tmp_scalar;
1224 for (i = 0; i < bn_get_top(scalar) * BN_BYTES; i += BN_BYTES) {
1225 BN_ULONG d = bn_get_words(scalar)[i / BN_BYTES];
1227 p_str[i + 0] = (unsigned char)d;
1228 p_str[i + 1] = (unsigned char)(d >> 8);
1229 p_str[i + 2] = (unsigned char)(d >> 16);
1230 p_str[i + 3] = (unsigned char)(d >>= 24);
1231 if (BN_BYTES == 8) {
1233 p_str[i + 4] = (unsigned char)d;
1234 p_str[i + 5] = (unsigned char)(d >> 8);
1235 p_str[i + 6] = (unsigned char)(d >> 16);
1236 p_str[i + 7] = (unsigned char)(d >> 24);
1243 #if defined(ECP_NISTZ256_AVX2)
1244 if (ecp_nistz_avx2_eligible()) {
1245 ecp_nistz256_avx2_mul_g(&p.p, p_str, preComputedTable);
1250 wvalue = (p_str[0] << 1) & mask;
1253 wvalue = _booth_recode_w7(wvalue);
1255 ecp_nistz256_gather_w7(&p.a, preComputedTable[0],
1258 ecp_nistz256_neg(p.p.Z, p.p.Y);
1259 copy_conditional(p.p.Y, p.p.Z, wvalue & 1);
1261 memcpy(p.p.Z, ONE, sizeof(ONE));
1263 for (i = 1; i < 37; i++) {
1264 unsigned int off = (idx - 1) / 8;
1265 wvalue = p_str[off] | p_str[off + 1] << 8;
1266 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
1269 wvalue = _booth_recode_w7(wvalue);
1271 ecp_nistz256_gather_w7(&t.a,
1272 preComputedTable[i], wvalue >> 1);
1274 ecp_nistz256_neg(t.p.Z, t.a.Y);
1275 copy_conditional(t.a.Y, t.p.Z, wvalue & 1);
1277 ecp_nistz256_point_add_affine(&p.p, &p.p, &t.a);
1282 no_precomp_for_generator = 1;
1287 if (no_precomp_for_generator) {
1289 * Without a precomputed table for the generator, it has to be
1290 * handled like a normal point.
1292 const BIGNUM **new_scalars;
1293 const EC_POINT **new_points;
1295 new_scalars = OPENSSL_malloc((num + 1) * sizeof(BIGNUM *));
1297 ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, ERR_R_MALLOC_FAILURE);
1301 new_points = OPENSSL_malloc((num + 1) * sizeof(EC_POINT *));
1303 OPENSSL_free(new_scalars);
1304 ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, ERR_R_MALLOC_FAILURE);
1308 memcpy(new_scalars, scalars, num * sizeof(BIGNUM *));
1309 new_scalars[num] = scalar;
1310 memcpy(new_points, points, num * sizeof(EC_POINT *));
1311 new_points[num] = generator;
1313 scalars = new_scalars;
1314 points = new_points;
1319 P256_POINT *out = &t.p;
1323 ecp_nistz256_windowed_mul(group, out, scalars, points, num, ctx);
1326 ecp_nistz256_point_add(&p.p, &p.p, out);
1329 if (no_precomp_for_generator) {
1330 OPENSSL_free(points);
1331 OPENSSL_free(scalars);
1334 bn_set_data(r->X, p.p.X, sizeof(p.p.X));
1335 bn_set_data(r->Y, p.p.Y, sizeof(p.p.Y));
1336 bn_set_data(r->Z, p.p.Z, sizeof(p.p.Z));
1337 bn_correct_top(r->X);
1338 bn_correct_top(r->Y);
1339 bn_correct_top(r->Z);
1347 static int ecp_nistz256_get_affine(const EC_GROUP *group,
1348 const EC_POINT *point,
1349 BIGNUM *x, BIGNUM *y, BN_CTX *ctx)
1351 BN_ULONG z_inv2[P256_LIMBS];
1352 BN_ULONG z_inv3[P256_LIMBS];
1353 BN_ULONG x_aff[P256_LIMBS];
1354 BN_ULONG y_aff[P256_LIMBS];
1355 BN_ULONG point_x[P256_LIMBS], point_y[P256_LIMBS], point_z[P256_LIMBS];
1357 if (EC_POINT_is_at_infinity(group, point)) {
1358 ECerr(EC_F_ECP_NISTZ256_GET_AFFINE, EC_R_POINT_AT_INFINITY);
1362 if (!ecp_nistz256_bignum_to_field_elem(point_x, point->X) ||
1363 !ecp_nistz256_bignum_to_field_elem(point_y, point->Y) ||
1364 !ecp_nistz256_bignum_to_field_elem(point_z, point->Z)) {
1365 ECerr(EC_F_ECP_NISTZ256_GET_AFFINE, EC_R_COORDINATES_OUT_OF_RANGE);
1369 ecp_nistz256_mod_inverse(z_inv3, point_z);
1370 ecp_nistz256_sqr_mont(z_inv2, z_inv3);
1371 ecp_nistz256_mul_mont(x_aff, z_inv2, point_x);
1374 bn_wexpand(x, P256_LIMBS);
1375 bn_set_top(x, P256_LIMBS);
1376 ecp_nistz256_from_mont(bn_get_words(x), x_aff);
1381 ecp_nistz256_mul_mont(z_inv3, z_inv3, z_inv2);
1382 ecp_nistz256_mul_mont(y_aff, z_inv3, point_y);
1383 bn_wexpand(y, P256_LIMBS);
1384 bn_set_top(y, P256_LIMBS);
1385 ecp_nistz256_from_mont(bn_get_words(y), y_aff);
1392 static EC_PRE_COMP *ecp_nistz256_pre_comp_new(const EC_GROUP *group)
1394 EC_PRE_COMP *ret = NULL;
1399 ret = (EC_PRE_COMP *)OPENSSL_malloc(sizeof(EC_PRE_COMP));
1402 ECerr(EC_F_ECP_NISTZ256_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE);
1407 ret->w = 6; /* default */
1408 ret->precomp = NULL;
1409 ret->precomp_storage = NULL;
1410 ret->references = 1;
1414 static void *ecp_nistz256_pre_comp_dup(void *src_)
1416 EC_PRE_COMP *src = src_;
1418 /* no need to actually copy, these objects never change! */
1419 CRYPTO_add(&src->references, 1, CRYPTO_LOCK_EC_PRE_COMP);
1424 static void ecp_nistz256_pre_comp_free(void *pre_)
1427 EC_PRE_COMP *pre = pre_;
1432 i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP);
1436 if (pre->precomp_storage)
1437 OPENSSL_free(pre->precomp_storage);
1442 static void ecp_nistz256_pre_comp_clear_free(void *pre_)
1445 EC_PRE_COMP *pre = pre_;
1450 i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP);
1454 if (pre->precomp_storage) {
1455 OPENSSL_cleanse(pre->precomp,
1456 32 * sizeof(unsigned char) * (1 << pre->w) * 2 * 37);
1457 OPENSSL_free(pre->precomp_storage);
1459 OPENSSL_cleanse(pre, sizeof *pre);
1463 static int ecp_nistz256_window_have_precompute_mult(const EC_GROUP *group)
1465 /* There is a hard-coded table for the default generator. */
1466 const EC_POINT *generator = EC_GROUP_get0_generator(group);
1467 if (generator != NULL && ecp_nistz256_is_affine_G(generator)) {
1468 /* There is a hard-coded table for the default generator. */
1472 return EC_EX_DATA_get_data(group->extra_data, ecp_nistz256_pre_comp_dup,
1473 ecp_nistz256_pre_comp_free,
1474 ecp_nistz256_pre_comp_clear_free) != NULL;
1477 const EC_METHOD *EC_GFp_nistz256_method(void)
1479 static const EC_METHOD ret = {
1480 EC_FLAGS_DEFAULT_OCT,
1481 NID_X9_62_prime_field,
1482 ec_GFp_mont_group_init,
1483 ec_GFp_mont_group_finish,
1484 ec_GFp_mont_group_clear_finish,
1485 ec_GFp_mont_group_copy,
1486 ec_GFp_mont_group_set_curve,
1487 ec_GFp_simple_group_get_curve,
1488 ec_GFp_simple_group_get_degree,
1489 ec_GFp_simple_group_check_discriminant,
1490 ec_GFp_simple_point_init,
1491 ec_GFp_simple_point_finish,
1492 ec_GFp_simple_point_clear_finish,
1493 ec_GFp_simple_point_copy,
1494 ec_GFp_simple_point_set_to_infinity,
1495 ec_GFp_simple_set_Jprojective_coordinates_GFp,
1496 ec_GFp_simple_get_Jprojective_coordinates_GFp,
1497 ec_GFp_simple_point_set_affine_coordinates,
1498 ecp_nistz256_get_affine,
1502 ec_GFp_simple_invert,
1503 ec_GFp_simple_is_at_infinity,
1504 ec_GFp_simple_is_on_curve,
1506 ec_GFp_simple_make_affine,
1507 ec_GFp_simple_points_make_affine,
1508 ecp_nistz256_points_mul, /* mul */
1509 ecp_nistz256_mult_precompute, /* precompute_mult */
1510 ecp_nistz256_window_have_precompute_mult, /* have_precompute_mult */
1511 ec_GFp_mont_field_mul,
1512 ec_GFp_mont_field_sqr,
1514 ec_GFp_mont_field_encode,
1515 ec_GFp_mont_field_decode,
1516 ec_GFp_mont_field_set_to_one