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 ******************************************************************************/
31 #include "internal/bn_int.h"
32 #include <openssl/err.h>
33 #include <openssl/ec.h>
39 # define TOBN(hi,lo) lo,hi
41 # define TOBN(hi,lo) ((BN_ULONG)hi<<32|lo)
45 # define ALIGN32 __attribute((aligned(32)))
46 #elif defined(_MSC_VER)
47 # define ALIGN32 __declspec(align(32))
52 #define ALIGNPTR(p,N) ((unsigned char *)p+N-(size_t)p%N)
53 #define P256_LIMBS (256/BN_BITS2)
55 typedef unsigned short u16;
58 BN_ULONG X[P256_LIMBS];
59 BN_ULONG Y[P256_LIMBS];
60 BN_ULONG Z[P256_LIMBS];
64 BN_ULONG X[P256_LIMBS];
65 BN_ULONG Y[P256_LIMBS];
68 typedef P256_POINT_AFFINE PRECOMP256_ROW[64];
70 /* structure for precomputed multiples of the generator */
71 typedef struct ec_pre_comp_st {
72 const EC_GROUP *group; /* Parent EC_GROUP object */
73 size_t w; /* Window size */
74 /* Constant time access to the X and Y coordinates of the pre-computed,
75 * generator multiplies, in the Montgomery domain. Pre-calculated
76 * multiplies are stored in affine form. */
77 PRECOMP256_ROW *precomp;
78 void *precomp_storage;
82 /* Functions implemented in assembly */
83 /* Modular mul by 2: res = 2*a mod P */
84 void ecp_nistz256_mul_by_2(BN_ULONG res[P256_LIMBS],
85 const BN_ULONG a[P256_LIMBS]);
86 /* Modular div by 2: res = a/2 mod P */
87 void ecp_nistz256_div_by_2(BN_ULONG res[P256_LIMBS],
88 const BN_ULONG a[P256_LIMBS]);
89 /* Modular mul by 3: res = 3*a mod P */
90 void ecp_nistz256_mul_by_3(BN_ULONG res[P256_LIMBS],
91 const BN_ULONG a[P256_LIMBS]);
92 /* Modular add: res = a+b mod P */
93 void ecp_nistz256_add(BN_ULONG res[P256_LIMBS],
94 const BN_ULONG a[P256_LIMBS],
95 const BN_ULONG b[P256_LIMBS]);
96 /* Modular sub: res = a-b mod P */
97 void ecp_nistz256_sub(BN_ULONG res[P256_LIMBS],
98 const BN_ULONG a[P256_LIMBS],
99 const BN_ULONG b[P256_LIMBS]);
100 /* Modular neg: res = -a mod P */
101 void ecp_nistz256_neg(BN_ULONG res[P256_LIMBS], const BN_ULONG a[P256_LIMBS]);
102 /* Montgomery mul: res = a*b*2^-256 mod P */
103 void ecp_nistz256_mul_mont(BN_ULONG res[P256_LIMBS],
104 const BN_ULONG a[P256_LIMBS],
105 const BN_ULONG b[P256_LIMBS]);
106 /* Montgomery sqr: res = a*a*2^-256 mod P */
107 void ecp_nistz256_sqr_mont(BN_ULONG res[P256_LIMBS],
108 const BN_ULONG a[P256_LIMBS]);
109 /* Convert a number from Montgomery domain, by multiplying with 1 */
110 void ecp_nistz256_from_mont(BN_ULONG res[P256_LIMBS],
111 const BN_ULONG in[P256_LIMBS]);
112 /* Convert a number to Montgomery domain, by multiplying with 2^512 mod P*/
113 void ecp_nistz256_to_mont(BN_ULONG res[P256_LIMBS],
114 const BN_ULONG in[P256_LIMBS]);
115 /* Functions that perform constant time access to the precomputed tables */
116 void ecp_nistz256_scatter_w5(P256_POINT * val,
117 const P256_POINT * in_t, int index);
118 void ecp_nistz256_gather_w5(P256_POINT * val,
119 const P256_POINT * in_t, int index);
120 void ecp_nistz256_scatter_w7(P256_POINT_AFFINE * val,
121 const P256_POINT_AFFINE * in_t, int index);
122 void ecp_nistz256_gather_w7(P256_POINT_AFFINE * val,
123 const P256_POINT_AFFINE * in_t, int index);
125 /* One converted into the Montgomery domain */
126 static const BN_ULONG ONE[P256_LIMBS] = {
127 TOBN(0x00000000, 0x00000001), TOBN(0xffffffff, 0x00000000),
128 TOBN(0xffffffff, 0xffffffff), TOBN(0x00000000, 0xfffffffe)
131 static void *ecp_nistz256_pre_comp_dup(void *);
132 static void ecp_nistz256_pre_comp_free(void *);
133 static void ecp_nistz256_pre_comp_clear_free(void *);
134 static EC_PRE_COMP *ecp_nistz256_pre_comp_new(const EC_GROUP * group);
136 /* Precomputed tables for the default generator */
137 extern const PRECOMP256_ROW ecp_nistz256_precomputed[37];
139 /* Recode window to a signed digit, see ecp_nistputil.c for details */
140 static unsigned int _booth_recode_w5(unsigned int in)
144 s = ~((in >> 5) - 1);
145 d = (1 << 6) - in - 1;
146 d = (d & s) | (in & ~s);
147 d = (d >> 1) + (d & 1);
149 return (d << 1) + (s & 1);
152 static unsigned int _booth_recode_w7(unsigned int in)
156 s = ~((in >> 7) - 1);
157 d = (1 << 8) - in - 1;
158 d = (d & s) | (in & ~s);
159 d = (d >> 1) + (d & 1);
161 return (d << 1) + (s & 1);
164 static void copy_conditional(BN_ULONG dst[P256_LIMBS],
165 const BN_ULONG src[P256_LIMBS], BN_ULONG move)
167 BN_ULONG mask1 = -move;
168 BN_ULONG mask2 = ~mask1;
170 dst[0] = (src[0] & mask1) ^ (dst[0] & mask2);
171 dst[1] = (src[1] & mask1) ^ (dst[1] & mask2);
172 dst[2] = (src[2] & mask1) ^ (dst[2] & mask2);
173 dst[3] = (src[3] & mask1) ^ (dst[3] & mask2);
174 if (P256_LIMBS == 8) {
175 dst[4] = (src[4] & mask1) ^ (dst[4] & mask2);
176 dst[5] = (src[5] & mask1) ^ (dst[5] & mask2);
177 dst[6] = (src[6] & mask1) ^ (dst[6] & mask2);
178 dst[7] = (src[7] & mask1) ^ (dst[7] & mask2);
182 static BN_ULONG is_zero(BN_ULONG in)
191 static BN_ULONG is_equal(const BN_ULONG a[P256_LIMBS],
192 const BN_ULONG b[P256_LIMBS])
200 if (P256_LIMBS == 8) {
210 static BN_ULONG is_one(const BN_ULONG a[P256_LIMBS])
215 res |= a[1] ^ ONE[1];
216 res |= a[2] ^ ONE[2];
217 res |= a[3] ^ ONE[3];
218 if (P256_LIMBS == 8) {
219 res |= a[4] ^ ONE[4];
220 res |= a[5] ^ ONE[5];
221 res |= a[6] ^ ONE[6];
227 #ifndef ECP_NISTZ256_REFERENCE_IMPLEMENTATION
228 void ecp_nistz256_point_double(P256_POINT * r, const P256_POINT * a);
229 void ecp_nistz256_point_add(P256_POINT * r,
230 const P256_POINT * a, const P256_POINT * b);
231 void ecp_nistz256_point_add_affine(P256_POINT * r,
232 const P256_POINT * a,
233 const P256_POINT_AFFINE * b);
235 /* Point double: r = 2*a */
236 static void ecp_nistz256_point_double(P256_POINT * r, const P256_POINT * a)
238 BN_ULONG S[P256_LIMBS];
239 BN_ULONG M[P256_LIMBS];
240 BN_ULONG Zsqr[P256_LIMBS];
241 BN_ULONG tmp0[P256_LIMBS];
243 const BN_ULONG *in_x = a->X;
244 const BN_ULONG *in_y = a->Y;
245 const BN_ULONG *in_z = a->Z;
247 BN_ULONG *res_x = r->X;
248 BN_ULONG *res_y = r->Y;
249 BN_ULONG *res_z = r->Z;
251 ecp_nistz256_mul_by_2(S, in_y);
253 ecp_nistz256_sqr_mont(Zsqr, in_z);
255 ecp_nistz256_sqr_mont(S, S);
257 ecp_nistz256_mul_mont(res_z, in_z, in_y);
258 ecp_nistz256_mul_by_2(res_z, res_z);
260 ecp_nistz256_add(M, in_x, Zsqr);
261 ecp_nistz256_sub(Zsqr, in_x, Zsqr);
263 ecp_nistz256_sqr_mont(res_y, S);
264 ecp_nistz256_div_by_2(res_y, res_y);
266 ecp_nistz256_mul_mont(M, M, Zsqr);
267 ecp_nistz256_mul_by_3(M, M);
269 ecp_nistz256_mul_mont(S, S, in_x);
270 ecp_nistz256_mul_by_2(tmp0, S);
272 ecp_nistz256_sqr_mont(res_x, M);
274 ecp_nistz256_sub(res_x, res_x, tmp0);
275 ecp_nistz256_sub(S, S, res_x);
277 ecp_nistz256_mul_mont(S, S, M);
278 ecp_nistz256_sub(res_y, S, res_y);
281 /* Point addition: r = a+b */
282 static void ecp_nistz256_point_add(P256_POINT * r,
283 const P256_POINT * a, const P256_POINT * b)
285 BN_ULONG U2[P256_LIMBS], S2[P256_LIMBS];
286 BN_ULONG U1[P256_LIMBS], S1[P256_LIMBS];
287 BN_ULONG Z1sqr[P256_LIMBS];
288 BN_ULONG Z2sqr[P256_LIMBS];
289 BN_ULONG H[P256_LIMBS], R[P256_LIMBS];
290 BN_ULONG Hsqr[P256_LIMBS];
291 BN_ULONG Rsqr[P256_LIMBS];
292 BN_ULONG Hcub[P256_LIMBS];
294 BN_ULONG res_x[P256_LIMBS];
295 BN_ULONG res_y[P256_LIMBS];
296 BN_ULONG res_z[P256_LIMBS];
298 BN_ULONG in1infty, in2infty;
300 const BN_ULONG *in1_x = a->X;
301 const BN_ULONG *in1_y = a->Y;
302 const BN_ULONG *in1_z = a->Z;
304 const BN_ULONG *in2_x = b->X;
305 const BN_ULONG *in2_y = b->Y;
306 const BN_ULONG *in2_z = b->Z;
308 /* We encode infinity as (0,0), which is not on the curve,
310 in1infty = in1_x[0] | in1_x[1] | in1_x[2] | in1_x[3] |
311 in1_y[0] | in1_y[1] | in1_y[2] | in1_y[3];
313 in1infty |= in1_x[4] | in1_x[5] | in1_x[6] | in1_x[7] |
314 in1_y[4] | in1_y[5] | in1_y[6] | in1_y[7];
316 in2infty = in2_x[0] | in2_x[1] | in2_x[2] | in2_x[3] |
317 in2_y[0] | in2_y[1] | in2_y[2] | in2_y[3];
319 in2infty |= in2_x[4] | in2_x[5] | in2_x[6] | in2_x[7] |
320 in2_y[4] | in2_y[5] | in2_y[6] | in2_y[7];
322 in1infty = is_zero(in1infty);
323 in2infty = is_zero(in2infty);
325 ecp_nistz256_sqr_mont(Z2sqr, in2_z); /* Z2^2 */
326 ecp_nistz256_sqr_mont(Z1sqr, in1_z); /* Z1^2 */
328 ecp_nistz256_mul_mont(S1, Z2sqr, in2_z); /* S1 = Z2^3 */
329 ecp_nistz256_mul_mont(S2, Z1sqr, in1_z); /* S2 = Z1^3 */
331 ecp_nistz256_mul_mont(S1, S1, in1_y); /* S1 = Y1*Z2^3 */
332 ecp_nistz256_mul_mont(S2, S2, in2_y); /* S2 = Y2*Z1^3 */
333 ecp_nistz256_sub(R, S2, S1); /* R = S2 - S1 */
335 ecp_nistz256_mul_mont(U1, in1_x, Z2sqr); /* U1 = X1*Z2^2 */
336 ecp_nistz256_mul_mont(U2, in2_x, Z1sqr); /* U2 = X2*Z1^2 */
337 ecp_nistz256_sub(H, U2, U1); /* H = U2 - U1 */
339 /* This should not happen during sign/ecdh,
340 * 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,
384 const P256_POINT * a,
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;
407 /* In affine representation we encode infty as (0,0),
408 * which is not on the curve, so it is OK */
409 in1infty = in1_x[0] | in1_x[1] | in1_x[2] | in1_x[3] |
410 in1_y[0] | in1_y[1] | in1_y[2] | in1_y[3];
412 in1infty |= in1_x[4] | in1_x[5] | in1_x[6] | in1_x[7] |
413 in1_y[4] | in1_y[5] | in1_y[6] | in1_y[7];
415 in2infty = in2_x[0] | in2_x[1] | in2_x[2] | in2_x[3] |
416 in2_y[0] | in2_y[1] | in2_y[2] | in2_y[3];
418 in2infty |= in2_x[4] | in2_x[5] | in2_x[6] | in2_x[7] |
419 in2_y[4] | in2_y[5] | in2_y[6] | in2_y[7];
421 in1infty = is_zero(in1infty);
422 in2infty = is_zero(in2infty);
424 ecp_nistz256_sqr_mont(Z1sqr, in1_z); /* Z1^2 */
426 ecp_nistz256_mul_mont(U2, in2_x, Z1sqr); /* U2 = X2*Z1^2 */
427 ecp_nistz256_sub(H, U2, in1_x); /* H = U2 - U1 */
429 ecp_nistz256_mul_mont(S2, Z1sqr, in1_z); /* S2 = Z1^3 */
431 ecp_nistz256_mul_mont(res_z, H, in1_z); /* Z3 = H*Z1*Z2 */
433 ecp_nistz256_mul_mont(S2, S2, in2_y); /* S2 = Y2*Z1^3 */
434 ecp_nistz256_sub(R, S2, in1_y); /* R = S2 - S1 */
436 ecp_nistz256_sqr_mont(Hsqr, H); /* H^2 */
437 ecp_nistz256_sqr_mont(Rsqr, R); /* R^2 */
438 ecp_nistz256_mul_mont(Hcub, Hsqr, H); /* H^3 */
440 ecp_nistz256_mul_mont(U2, in1_x, Hsqr); /* U1*H^2 */
441 ecp_nistz256_mul_by_2(Hsqr, U2); /* 2*U1*H^2 */
443 ecp_nistz256_sub(res_x, Rsqr, Hsqr);
444 ecp_nistz256_sub(res_x, res_x, Hcub);
445 ecp_nistz256_sub(H, U2, res_x);
447 ecp_nistz256_mul_mont(S2, in1_y, Hcub);
448 ecp_nistz256_mul_mont(H, H, R);
449 ecp_nistz256_sub(res_y, H, S2);
451 copy_conditional(res_x, in2_x, in1infty);
452 copy_conditional(res_x, in1_x, in2infty);
454 copy_conditional(res_y, in2_y, in1infty);
455 copy_conditional(res_y, in1_y, in2infty);
457 copy_conditional(res_z, ONE, in1infty);
458 copy_conditional(res_z, in1_z, in2infty);
460 memcpy(r->X, res_x, sizeof(res_x));
461 memcpy(r->Y, res_y, sizeof(res_y));
462 memcpy(r->Z, res_z, sizeof(res_z));
466 /* r = in^-1 mod p */
467 static void ecp_nistz256_mod_inverse(BN_ULONG r[P256_LIMBS],
468 const BN_ULONG in[P256_LIMBS])
470 /* The poly is ffffffff 00000001 00000000 00000000 00000000 ffffffff ffffffff ffffffff
471 We use FLT and used poly-2 as exponent */
472 BN_ULONG p2[P256_LIMBS];
473 BN_ULONG p4[P256_LIMBS];
474 BN_ULONG p8[P256_LIMBS];
475 BN_ULONG p16[P256_LIMBS];
476 BN_ULONG p32[P256_LIMBS];
477 BN_ULONG res[P256_LIMBS];
480 ecp_nistz256_sqr_mont(res, in);
481 ecp_nistz256_mul_mont(p2, res, in); /* 3*p */
483 ecp_nistz256_sqr_mont(res, p2);
484 ecp_nistz256_sqr_mont(res, res);
485 ecp_nistz256_mul_mont(p4, res, p2); /* f*p */
487 ecp_nistz256_sqr_mont(res, p4);
488 ecp_nistz256_sqr_mont(res, res);
489 ecp_nistz256_sqr_mont(res, res);
490 ecp_nistz256_sqr_mont(res, res);
491 ecp_nistz256_mul_mont(p8, res, p4); /* ff*p */
493 ecp_nistz256_sqr_mont(res, p8);
494 for (i = 0; i < 7; i++)
495 ecp_nistz256_sqr_mont(res, res);
496 ecp_nistz256_mul_mont(p16, res, p8); /* ffff*p */
498 ecp_nistz256_sqr_mont(res, p16);
499 for (i = 0; i < 15; i++)
500 ecp_nistz256_sqr_mont(res, res);
501 ecp_nistz256_mul_mont(p32, res, p16); /* ffffffff*p */
503 ecp_nistz256_sqr_mont(res, p32);
504 for (i = 0; i < 31; i++)
505 ecp_nistz256_sqr_mont(res, res);
506 ecp_nistz256_mul_mont(res, res, in);
508 for (i = 0; i < 32 * 4; i++)
509 ecp_nistz256_sqr_mont(res, res);
510 ecp_nistz256_mul_mont(res, res, p32);
512 for (i = 0; i < 32; i++)
513 ecp_nistz256_sqr_mont(res, res);
514 ecp_nistz256_mul_mont(res, res, p32);
516 for (i = 0; i < 16; i++)
517 ecp_nistz256_sqr_mont(res, res);
518 ecp_nistz256_mul_mont(res, res, p16);
520 for (i = 0; i < 8; i++)
521 ecp_nistz256_sqr_mont(res, res);
522 ecp_nistz256_mul_mont(res, res, p8);
524 ecp_nistz256_sqr_mont(res, res);
525 ecp_nistz256_sqr_mont(res, res);
526 ecp_nistz256_sqr_mont(res, res);
527 ecp_nistz256_sqr_mont(res, res);
528 ecp_nistz256_mul_mont(res, res, p4);
530 ecp_nistz256_sqr_mont(res, res);
531 ecp_nistz256_sqr_mont(res, res);
532 ecp_nistz256_mul_mont(res, res, p2);
534 ecp_nistz256_sqr_mont(res, res);
535 ecp_nistz256_sqr_mont(res, res);
536 ecp_nistz256_mul_mont(res, res, in);
538 memcpy(r, res, sizeof(res));
541 /* ecp_nistz256_bignum_to_field_elem copies the contents of |in| to |out| and
542 * returns one if it fits. Otherwise it returns zero. */
543 static int ecp_nistz256_bignum_to_field_elem(BN_ULONG out[P256_LIMBS],
546 return bn_copy_words(out, in, P256_LIMBS);
549 /* r = sum(scalar[i]*point[i]) */
550 static void ecp_nistz256_windowed_mul(const EC_GROUP * group,
552 const BIGNUM ** scalar,
553 const EC_POINT ** point,
554 int num, BN_CTX * ctx)
558 unsigned char (*p_str)[33] = NULL;
559 const unsigned int window_size = 5;
560 const unsigned int mask = (1 << (window_size + 1)) - 1;
562 P256_POINT *temp; /* place for 5 temporary points */
563 const BIGNUM **scalars = NULL;
564 P256_POINT(*table)[16] = NULL;
565 void *table_storage = NULL;
568 OPENSSL_malloc((num * 16 + 5) * sizeof(P256_POINT) + 64)) == NULL
570 OPENSSL_malloc(num * 33 * sizeof(unsigned char))) == NULL
571 || (scalars = OPENSSL_malloc(num * sizeof(BIGNUM *))) == NULL) {
572 ECerr(EC_F_ECP_NISTZ256_WINDOWED_MUL, ERR_R_MALLOC_FAILURE);
576 table = (void *)ALIGNPTR(table_storage, 64);
577 temp = (P256_POINT *)(table + num);
579 for (i = 0; i < num; i++) {
580 P256_POINT *row = table[i];
582 if ((BN_num_bits(scalar[i]) > 256) || BN_is_negative(scalar[i])) {
585 if ((mod = BN_CTX_get(ctx)) == NULL)
587 if (!BN_nnmod(mod, scalar[i], group->order, ctx)) {
588 ECerr(EC_F_ECP_NISTZ256_WINDOWED_MUL, ERR_R_BN_LIB);
593 scalars[i] = scalar[i];
595 for (j = 0; j < bn_get_top(scalars[i]) * BN_BYTES; j += BN_BYTES) {
596 BN_ULONG d = bn_get_words(scalars[i])[j / BN_BYTES];
598 p_str[i][j + 0] = d & 0xff;
599 p_str[i][j + 1] = (d >> 8) & 0xff;
600 p_str[i][j + 2] = (d >> 16) & 0xff;
601 p_str[i][j + 3] = (d >>= 24) & 0xff;
604 p_str[i][j + 4] = d & 0xff;
605 p_str[i][j + 5] = (d >> 8) & 0xff;
606 p_str[i][j + 6] = (d >> 16) & 0xff;
607 p_str[i][j + 7] = (d >> 24) & 0xff;
613 if (!ecp_nistz256_bignum_to_field_elem(temp[0].X, point[i]->X)
614 || !ecp_nistz256_bignum_to_field_elem(temp[0].Y, point[i]->Y)
615 || !ecp_nistz256_bignum_to_field_elem(temp[0].Z, point[i]->Z)) {
616 ECerr(EC_F_ECP_NISTZ256_WINDOWED_MUL, EC_R_COORDINATES_OUT_OF_RANGE);
620 /* row[0] is implicitly (0,0,0) (the point at infinity),
621 * therefore it is not stored. All other values are actually
622 * stored with an offset of -1 in table.
625 ecp_nistz256_scatter_w5 (row, &temp[0], 1);
626 ecp_nistz256_point_double(&temp[1], &temp[0]); /*1+1=2 */
627 ecp_nistz256_scatter_w5 (row, &temp[1], 2);
628 ecp_nistz256_point_add (&temp[2], &temp[1], &temp[0]); /*2+1=3 */
629 ecp_nistz256_scatter_w5 (row, &temp[2], 3);
630 ecp_nistz256_point_double(&temp[1], &temp[1]); /*2*2=4 */
631 ecp_nistz256_scatter_w5 (row, &temp[1], 4);
632 ecp_nistz256_point_double(&temp[2], &temp[2]); /*2*3=6 */
633 ecp_nistz256_scatter_w5 (row, &temp[2], 6);
634 ecp_nistz256_point_add (&temp[3], &temp[1], &temp[0]); /*4+1=5 */
635 ecp_nistz256_scatter_w5 (row, &temp[3], 5);
636 ecp_nistz256_point_add (&temp[4], &temp[2], &temp[0]); /*6+1=7 */
637 ecp_nistz256_scatter_w5 (row, &temp[4], 7);
638 ecp_nistz256_point_double(&temp[1], &temp[1]); /*2*4=8 */
639 ecp_nistz256_scatter_w5 (row, &temp[1], 8);
640 ecp_nistz256_point_double(&temp[2], &temp[2]); /*2*6=12 */
641 ecp_nistz256_scatter_w5 (row, &temp[2], 12);
642 ecp_nistz256_point_double(&temp[3], &temp[3]); /*2*5=10 */
643 ecp_nistz256_scatter_w5 (row, &temp[3], 10);
644 ecp_nistz256_point_double(&temp[4], &temp[4]); /*2*7=14 */
645 ecp_nistz256_scatter_w5 (row, &temp[4], 14);
646 ecp_nistz256_point_add (&temp[2], &temp[2], &temp[0]); /*12+1=13*/
647 ecp_nistz256_scatter_w5 (row, &temp[2], 13);
648 ecp_nistz256_point_add (&temp[3], &temp[3], &temp[0]); /*10+1=11*/
649 ecp_nistz256_scatter_w5 (row, &temp[3], 11);
650 ecp_nistz256_point_add (&temp[4], &temp[4], &temp[0]); /*14+1=15*/
651 ecp_nistz256_scatter_w5 (row, &temp[4], 15);
652 ecp_nistz256_point_add (&temp[2], &temp[1], &temp[0]); /*8+1=9 */
653 ecp_nistz256_scatter_w5 (row, &temp[2], 9);
654 ecp_nistz256_point_double(&temp[1], &temp[1]); /*2*8=16 */
655 ecp_nistz256_scatter_w5 (row, &temp[1], 16);
660 wvalue = p_str[0][(index - 1) / 8];
661 wvalue = (wvalue >> ((index - 1) % 8)) & mask;
664 * We gather to temp[0], because we know it's position relative
667 ecp_nistz256_gather_w5(&temp[0], table[0], _booth_recode_w5(wvalue) >> 1);
668 memcpy(r, &temp[0], sizeof(temp[0]));
671 for (i = (index == 255 ? 1 : 0); i < num; i++) {
672 unsigned int off = (index - 1) / 8;
674 wvalue = p_str[i][off] | p_str[i][off + 1] << 8;
675 wvalue = (wvalue >> ((index - 1) % 8)) & mask;
677 wvalue = _booth_recode_w5(wvalue);
679 ecp_nistz256_gather_w5(&temp[0], table[i], wvalue >> 1);
681 ecp_nistz256_neg(temp[1].Y, temp[0].Y);
682 copy_conditional(temp[0].Y, temp[1].Y, (wvalue & 1));
684 ecp_nistz256_point_add(r, r, &temp[0]);
687 index -= window_size;
689 ecp_nistz256_point_double(r, r);
690 ecp_nistz256_point_double(r, r);
691 ecp_nistz256_point_double(r, r);
692 ecp_nistz256_point_double(r, r);
693 ecp_nistz256_point_double(r, r);
697 for (i = 0; i < num; i++) {
698 wvalue = p_str[i][0];
699 wvalue = (wvalue << 1) & mask;
701 wvalue = _booth_recode_w5(wvalue);
703 ecp_nistz256_gather_w5(&temp[0], table[i], wvalue >> 1);
705 ecp_nistz256_neg(temp[1].Y, temp[0].Y);
706 copy_conditional(temp[0].Y, temp[1].Y, wvalue & 1);
708 ecp_nistz256_point_add(r, r, &temp[0]);
713 OPENSSL_free(table_storage);
717 OPENSSL_free(scalars);
720 /* Coordinates of G, for which we have precomputed tables */
721 const static BN_ULONG def_xG[P256_LIMBS] = {
722 TOBN(0x79e730d4, 0x18a9143c), TOBN(0x75ba95fc, 0x5fedb601),
723 TOBN(0x79fb732b, 0x77622510), TOBN(0x18905f76, 0xa53755c6)
726 const static BN_ULONG def_yG[P256_LIMBS] = {
727 TOBN(0xddf25357, 0xce95560a), TOBN(0x8b4ab8e4, 0xba19e45c),
728 TOBN(0xd2e88688, 0xdd21f325), TOBN(0x8571ff18, 0x25885d85)
731 /* ecp_nistz256_is_affine_G returns one if |generator| is the standard,
732 * P-256 generator. */
733 static int ecp_nistz256_is_affine_G(const EC_POINT * generator)
735 return (bn_get_top(generator->X) == P256_LIMBS) &&
736 (bn_get_top(generator->Y) == P256_LIMBS) &&
737 (bn_get_top(generator->Z) == (P256_LIMBS - P256_LIMBS / 8)) &&
738 is_equal(bn_get_words(generator->X), def_xG) &&
739 is_equal(bn_get_words(generator->Y), def_yG) &&
740 is_one(bn_get_words(generator->Z));
743 static int ecp_nistz256_mult_precompute(EC_GROUP * group, BN_CTX * ctx)
745 /* We precompute a table for a Booth encoded exponent (wNAF) based
746 * computation. Each table holds 64 values for safe access, with an
747 * implicit value of infinity at index zero. We use window of size 7,
748 * and therefore require ceil(256/7) = 37 tables. */
750 EC_POINT *P = NULL, *T = NULL;
751 const EC_POINT *generator;
752 EC_PRE_COMP *pre_comp;
753 int i, j, k, ret = 0;
756 PRECOMP256_ROW *preComputedTable = NULL;
757 unsigned char *precomp_storage = NULL;
759 /* if there is an old EC_PRE_COMP object, throw it away */
760 EC_EX_DATA_free_data(&group->extra_data, ecp_nistz256_pre_comp_dup,
761 ecp_nistz256_pre_comp_free,
762 ecp_nistz256_pre_comp_clear_free);
764 generator = EC_GROUP_get0_generator(group);
765 if (generator == NULL) {
766 ECerr(EC_F_ECP_NISTZ256_MULT_PRECOMPUTE, EC_R_UNDEFINED_GENERATOR);
770 if (ecp_nistz256_is_affine_G(generator)) {
771 /* No need to calculate tables for the standard generator
772 * because we have them statically. */
776 if ((pre_comp = ecp_nistz256_pre_comp_new(group)) == NULL)
786 order = BN_CTX_get(ctx);
791 if (!EC_GROUP_get_order(group, order, ctx))
794 if (BN_is_zero(order)) {
795 ECerr(EC_F_ECP_NISTZ256_MULT_PRECOMPUTE, EC_R_UNKNOWN_ORDER);
801 if ((precomp_storage =
802 OPENSSL_malloc(37 * 64 * sizeof(P256_POINT_AFFINE) + 64)) == NULL) {
803 ECerr(EC_F_ECP_NISTZ256_MULT_PRECOMPUTE, ERR_R_MALLOC_FAILURE);
807 preComputedTable = (void *)ALIGNPTR(precomp_storage, 64);
809 P = EC_POINT_new(group);
810 T = EC_POINT_new(group);
812 /* The zero entry is implicitly infinity, and we skip it,
813 * storing other values with -1 offset. */
814 EC_POINT_copy(T, generator);
816 for (k = 0; k < 64; k++) {
818 for (j = 0; j < 37; j++) {
819 P256_POINT_AFFINE temp;
820 /* It would be faster to use
821 * ec_GFp_simple_points_make_affine and make multiple
822 * points affine at the same time. */
823 ec_GFp_simple_make_affine(group, P, ctx);
824 ecp_nistz256_bignum_to_field_elem(temp.X, P->X);
825 ecp_nistz256_bignum_to_field_elem(temp.Y, P->Y);
826 ecp_nistz256_scatter_w7(preComputedTable[j], &temp, k);
827 for (i = 0; i < 7; i++)
828 ec_GFp_simple_dbl(group, P, P, ctx);
830 ec_GFp_simple_add(group, T, T, generator, ctx);
833 pre_comp->group = group;
835 pre_comp->precomp = preComputedTable;
836 pre_comp->precomp_storage = precomp_storage;
838 precomp_storage = NULL;
840 if (!EC_EX_DATA_set_data(&group->extra_data, pre_comp,
841 ecp_nistz256_pre_comp_dup,
842 ecp_nistz256_pre_comp_free,
843 ecp_nistz256_pre_comp_clear_free)) {
855 ecp_nistz256_pre_comp_free(pre_comp);
857 OPENSSL_free(precomp_storage);
866 * Note that by default ECP_NISTZ256_AVX2 is undefined. While it's great
867 * code processing 4 points in parallel, corresponding serial operation
868 * is several times slower, because it uses 29x29=58-bit multiplication
869 * as opposite to 64x64=128-bit in integer-only scalar case. As result
870 * it doesn't provide *significant* performance improvement. Note that
871 * just defining ECP_NISTZ256_AVX2 is not sufficient to make it work,
872 * you'd need to compile even asm/ecp_nistz256-avx.pl module.
874 #if defined(ECP_NISTZ256_AVX2)
875 # if !(defined(__x86_64) || defined(__x86_64__) || \
876 defined(_M_AMD64) || defined(_MX64)) || \
877 !(defined(__GNUC__) || defined(_MSC_VER)) /* this is for ALIGN32 */
878 # undef ECP_NISTZ256_AVX2
880 /* Constant time access, loading four values, from four consecutive tables */
881 void ecp_nistz256_avx2_multi_gather_w7(void *result, const void *in, int index0,
882 int index1, int index2, int index3);
883 void ecp_nistz256_avx2_transpose_convert(void *RESULTx4, const void *in);
884 void ecp_nistz256_avx2_convert_transpose_back(void *result, const void *Ax4);
885 void ecp_nistz256_avx2_point_add_affine_x4(void *RESULTx4, const void *Ax4,
887 void ecp_nistz256_avx2_point_add_affines_x4(void *RESULTx4, const void *Ax4,
889 void ecp_nistz256_avx2_to_mont(void *RESULTx4, const void *Ax4);
890 void ecp_nistz256_avx2_from_mont(void *RESULTx4, const void *Ax4);
891 void ecp_nistz256_avx2_set1(void *RESULTx4);
892 int ecp_nistz_avx2_eligible(void);
894 static void booth_recode_w7(unsigned char *sign,
895 unsigned char *digit, unsigned char in)
899 s = ~((in >> 7) - 1);
900 d = (1 << 8) - in - 1;
901 d = (d & s) | (in & ~s);
902 d = (d >> 1) + (d & 1);
908 /* ecp_nistz256_avx2_mul_g performs multiplication by G, using only the
909 * precomputed table. It does 4 affine point additions in parallel,
910 * significantly speeding up point multiplication for a fixed value. */
911 static void ecp_nistz256_avx2_mul_g(P256_POINT * r,
912 unsigned char p_str[33],
914 P256_POINT_AFFINE(*preComputedTable)[64])
916 const unsigned int window_size = 7;
917 const unsigned int mask = (1 << (window_size + 1)) - 1;
919 /* Using 4 windows at a time */
920 unsigned char sign0, digit0;
921 unsigned char sign1, digit1;
922 unsigned char sign2, digit2;
923 unsigned char sign3, digit3;
924 unsigned int index = 0;
925 BN_ULONG tmp[P256_LIMBS];
928 ALIGN32 BN_ULONG aX4[4 * 9 * 3] = { 0 };
929 ALIGN32 BN_ULONG bX4[4 * 9 * 2] = { 0 };
930 ALIGN32 P256_POINT_AFFINE point_arr[4];
931 ALIGN32 P256_POINT res_point_arr[4];
933 /* Initial four windows */
934 wvalue = *((u16 *) & p_str[0]);
935 wvalue = (wvalue << 1) & mask;
936 index += window_size;
937 booth_recode_w7(&sign0, &digit0, wvalue);
938 wvalue = *((u16 *) & p_str[(index - 1) / 8]);
939 wvalue = (wvalue >> ((index - 1) % 8)) & mask;
940 index += window_size;
941 booth_recode_w7(&sign1, &digit1, wvalue);
942 wvalue = *((u16 *) & p_str[(index - 1) / 8]);
943 wvalue = (wvalue >> ((index - 1) % 8)) & mask;
944 index += window_size;
945 booth_recode_w7(&sign2, &digit2, wvalue);
946 wvalue = *((u16 *) & p_str[(index - 1) / 8]);
947 wvalue = (wvalue >> ((index - 1) % 8)) & mask;
948 index += window_size;
949 booth_recode_w7(&sign3, &digit3, wvalue);
951 ecp_nistz256_avx2_multi_gather_w7(point_arr, preComputedTable[0],
952 digit0, digit1, digit2, digit3);
954 ecp_nistz256_neg(tmp, point_arr[0].Y);
955 copy_conditional(point_arr[0].Y, tmp, sign0);
956 ecp_nistz256_neg(tmp, point_arr[1].Y);
957 copy_conditional(point_arr[1].Y, tmp, sign1);
958 ecp_nistz256_neg(tmp, point_arr[2].Y);
959 copy_conditional(point_arr[2].Y, tmp, sign2);
960 ecp_nistz256_neg(tmp, point_arr[3].Y);
961 copy_conditional(point_arr[3].Y, tmp, sign3);
963 ecp_nistz256_avx2_transpose_convert(aX4, point_arr);
964 ecp_nistz256_avx2_to_mont(aX4, aX4);
965 ecp_nistz256_avx2_to_mont(&aX4[4 * 9], &aX4[4 * 9]);
966 ecp_nistz256_avx2_set1(&aX4[4 * 9 * 2]);
968 wvalue = *((u16 *) & p_str[(index - 1) / 8]);
969 wvalue = (wvalue >> ((index - 1) % 8)) & mask;
970 index += window_size;
971 booth_recode_w7(&sign0, &digit0, wvalue);
972 wvalue = *((u16 *) & p_str[(index - 1) / 8]);
973 wvalue = (wvalue >> ((index - 1) % 8)) & mask;
974 index += window_size;
975 booth_recode_w7(&sign1, &digit1, wvalue);
976 wvalue = *((u16 *) & p_str[(index - 1) / 8]);
977 wvalue = (wvalue >> ((index - 1) % 8)) & mask;
978 index += window_size;
979 booth_recode_w7(&sign2, &digit2, wvalue);
980 wvalue = *((u16 *) & p_str[(index - 1) / 8]);
981 wvalue = (wvalue >> ((index - 1) % 8)) & mask;
982 index += window_size;
983 booth_recode_w7(&sign3, &digit3, wvalue);
985 ecp_nistz256_avx2_multi_gather_w7(point_arr, preComputedTable[4 * 1],
986 digit0, digit1, digit2, digit3);
988 ecp_nistz256_neg(tmp, point_arr[0].Y);
989 copy_conditional(point_arr[0].Y, tmp, sign0);
990 ecp_nistz256_neg(tmp, point_arr[1].Y);
991 copy_conditional(point_arr[1].Y, tmp, sign1);
992 ecp_nistz256_neg(tmp, point_arr[2].Y);
993 copy_conditional(point_arr[2].Y, tmp, sign2);
994 ecp_nistz256_neg(tmp, point_arr[3].Y);
995 copy_conditional(point_arr[3].Y, tmp, sign3);
997 ecp_nistz256_avx2_transpose_convert(bX4, point_arr);
998 ecp_nistz256_avx2_to_mont(bX4, bX4);
999 ecp_nistz256_avx2_to_mont(&bX4[4 * 9], &bX4[4 * 9]);
1000 /* Optimized when both inputs are affine */
1001 ecp_nistz256_avx2_point_add_affines_x4(aX4, aX4, bX4);
1003 for (i = 2; i < 9; i++) {
1004 wvalue = *((u16 *) & p_str[(index - 1) / 8]);
1005 wvalue = (wvalue >> ((index - 1) % 8)) & mask;
1006 index += window_size;
1007 booth_recode_w7(&sign0, &digit0, wvalue);
1008 wvalue = *((u16 *) & p_str[(index - 1) / 8]);
1009 wvalue = (wvalue >> ((index - 1) % 8)) & mask;
1010 index += window_size;
1011 booth_recode_w7(&sign1, &digit1, wvalue);
1012 wvalue = *((u16 *) & p_str[(index - 1) / 8]);
1013 wvalue = (wvalue >> ((index - 1) % 8)) & mask;
1014 index += window_size;
1015 booth_recode_w7(&sign2, &digit2, wvalue);
1016 wvalue = *((u16 *) & p_str[(index - 1) / 8]);
1017 wvalue = (wvalue >> ((index - 1) % 8)) & mask;
1018 index += window_size;
1019 booth_recode_w7(&sign3, &digit3, wvalue);
1021 ecp_nistz256_avx2_multi_gather_w7(point_arr,
1022 preComputedTable[4 * i],
1023 digit0, digit1, digit2, digit3);
1025 ecp_nistz256_neg(tmp, point_arr[0].Y);
1026 copy_conditional(point_arr[0].Y, tmp, sign0);
1027 ecp_nistz256_neg(tmp, point_arr[1].Y);
1028 copy_conditional(point_arr[1].Y, tmp, sign1);
1029 ecp_nistz256_neg(tmp, point_arr[2].Y);
1030 copy_conditional(point_arr[2].Y, tmp, sign2);
1031 ecp_nistz256_neg(tmp, point_arr[3].Y);
1032 copy_conditional(point_arr[3].Y, tmp, sign3);
1034 ecp_nistz256_avx2_transpose_convert(bX4, point_arr);
1035 ecp_nistz256_avx2_to_mont(bX4, bX4);
1036 ecp_nistz256_avx2_to_mont(&bX4[4 * 9], &bX4[4 * 9]);
1038 ecp_nistz256_avx2_point_add_affine_x4(aX4, aX4, bX4);
1041 ecp_nistz256_avx2_from_mont(&aX4[4 * 9 * 0], &aX4[4 * 9 * 0]);
1042 ecp_nistz256_avx2_from_mont(&aX4[4 * 9 * 1], &aX4[4 * 9 * 1]);
1043 ecp_nistz256_avx2_from_mont(&aX4[4 * 9 * 2], &aX4[4 * 9 * 2]);
1045 ecp_nistz256_avx2_convert_transpose_back(res_point_arr, aX4);
1046 /* Last window is performed serially */
1047 wvalue = *((u16 *) & p_str[(index - 1) / 8]);
1048 wvalue = (wvalue >> ((index - 1) % 8)) & mask;
1049 booth_recode_w7(&sign0, &digit0, wvalue);
1050 ecp_nistz256_gather_w7((P256_POINT_AFFINE *) r,
1051 preComputedTable[36], digit0);
1052 ecp_nistz256_neg(tmp, r->Y);
1053 copy_conditional(r->Y, tmp, sign0);
1054 memcpy(r->Z, ONE, sizeof(ONE));
1055 /* Sum the four windows */
1056 ecp_nistz256_point_add(r, r, &res_point_arr[0]);
1057 ecp_nistz256_point_add(r, r, &res_point_arr[1]);
1058 ecp_nistz256_point_add(r, r, &res_point_arr[2]);
1059 ecp_nistz256_point_add(r, r, &res_point_arr[3]);
1064 static int ecp_nistz256_set_from_affine(EC_POINT * out, const EC_GROUP * group,
1065 const P256_POINT_AFFINE * in,
1069 BN_ULONG d_x[P256_LIMBS], d_y[P256_LIMBS];
1080 memcpy(d_x, in->X, sizeof(d_x));
1081 bn_set_static_words(x, d_x, P256_LIMBS);
1083 memcpy(d_y, in->Y, sizeof(d_y));
1084 bn_set_static_words(y, d_y, P256_LIMBS);
1086 ret = EC_POINT_set_affine_coordinates_GFp(group, out, x, y, ctx);
1094 /* r = scalar*G + sum(scalars[i]*points[i]) */
1095 static int ecp_nistz256_points_mul(const EC_GROUP * group,
1097 const BIGNUM * scalar,
1099 const EC_POINT * points[],
1100 const BIGNUM * scalars[], BN_CTX * ctx)
1102 int i = 0, ret = 0, no_precomp_for_generator = 0, p_is_infinity = 0;
1104 unsigned char p_str[33] = { 0 };
1105 const PRECOMP256_ROW *preComputedTable = NULL;
1106 const EC_PRE_COMP *pre_comp = NULL;
1107 const EC_POINT *generator = NULL;
1108 unsigned int index = 0;
1109 const unsigned int window_size = 7;
1110 const unsigned int mask = (1 << (window_size + 1)) - 1;
1111 unsigned int wvalue;
1114 P256_POINT_AFFINE a;
1118 if ((num+1) == 0 || (num+1) > OPENSSL_MALLOC_MAX_NELEMS(void *)) {
1119 ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, ERR_R_MALLOC_FAILURE);
1123 if (group->meth != r->meth) {
1124 ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, EC_R_INCOMPATIBLE_OBJECTS);
1127 if ((scalar == NULL) && (num == 0))
1128 return EC_POINT_set_to_infinity(group, r);
1130 for (j = 0; j < num; j++) {
1131 if (group->meth != points[j]->meth) {
1132 ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, EC_R_INCOMPATIBLE_OBJECTS);
1137 /* Need 256 bits for space for all coordinates. */
1138 bn_wexpand(r->X, P256_LIMBS);
1139 bn_wexpand(r->Y, P256_LIMBS);
1140 bn_wexpand(r->Z, P256_LIMBS);
1141 bn_set_top(r->X, P256_LIMBS);
1142 bn_set_top(r->Y, P256_LIMBS);
1143 bn_set_top(r->Z, P256_LIMBS);
1146 generator = EC_GROUP_get0_generator(group);
1147 if (generator == NULL) {
1148 ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, EC_R_UNDEFINED_GENERATOR);
1152 /* look if we can use precomputed multiples of generator */
1154 EC_EX_DATA_get_data(group->extra_data, ecp_nistz256_pre_comp_dup,
1155 ecp_nistz256_pre_comp_free,
1156 ecp_nistz256_pre_comp_clear_free);
1159 /* If there is a precomputed table for the generator,
1160 * check that it was generated with the same
1162 EC_POINT *pre_comp_generator = EC_POINT_new(group);
1163 if (pre_comp_generator == NULL)
1166 if (!ecp_nistz256_set_from_affine(pre_comp_generator,
1167 group, pre_comp->precomp[0],
1171 if (0 == EC_POINT_cmp(group, generator, pre_comp_generator, ctx))
1172 preComputedTable = (const PRECOMP256_ROW *)pre_comp->precomp;
1174 EC_POINT_free(pre_comp_generator);
1177 if (preComputedTable == NULL && ecp_nistz256_is_affine_G(generator)) {
1178 /* If there is no precomputed data, but the generator
1179 * is the default, a hardcoded table of precomputed
1180 * data is used. This is because applications, such as
1181 * Apache, do not use EC_KEY_precompute_mult. */
1182 preComputedTable = ecp_nistz256_precomputed;
1185 if (preComputedTable) {
1186 if ((BN_num_bits(scalar) > 256)
1187 || BN_is_negative(scalar)) {
1188 if ((tmp_scalar = BN_CTX_get(ctx)) == NULL)
1191 if (!BN_nnmod(tmp_scalar, scalar, group->order, ctx)) {
1192 ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, ERR_R_BN_LIB);
1195 scalar = tmp_scalar;
1198 for (i = 0; i < bn_get_top(scalar) * BN_BYTES; i += BN_BYTES) {
1199 BN_ULONG d = bn_get_words(scalar)[i / BN_BYTES];
1201 p_str[i + 0] = d & 0xff;
1202 p_str[i + 1] = (d >> 8) & 0xff;
1203 p_str[i + 2] = (d >> 16) & 0xff;
1204 p_str[i + 3] = (d >>= 24) & 0xff;
1205 if (BN_BYTES == 8) {
1207 p_str[i + 4] = d & 0xff;
1208 p_str[i + 5] = (d >> 8) & 0xff;
1209 p_str[i + 6] = (d >> 16) & 0xff;
1210 p_str[i + 7] = (d >> 24) & 0xff;
1217 #if defined(ECP_NISTZ256_AVX2)
1218 if (ecp_nistz_avx2_eligible()) {
1219 ecp_nistz256_avx2_mul_g(&p.p, p_str, preComputedTable);
1224 wvalue = (p_str[0] << 1) & mask;
1225 index += window_size;
1227 wvalue = _booth_recode_w7(wvalue);
1229 ecp_nistz256_gather_w7(&p.a, preComputedTable[0], wvalue >> 1);
1231 ecp_nistz256_neg(p.p.Z, p.p.Y);
1232 copy_conditional(p.p.Y, p.p.Z, wvalue & 1);
1234 memcpy(p.p.Z, ONE, sizeof(ONE));
1236 for (i = 1; i < 37; i++) {
1237 unsigned int off = (index - 1) / 8;
1238 wvalue = p_str[off] | p_str[off + 1] << 8;
1239 wvalue = (wvalue >> ((index - 1) % 8)) & mask;
1240 index += window_size;
1242 wvalue = _booth_recode_w7(wvalue);
1244 ecp_nistz256_gather_w7(&t.a,
1245 preComputedTable[i], wvalue >> 1);
1247 ecp_nistz256_neg(t.p.Z, t.a.Y);
1248 copy_conditional(t.a.Y, t.p.Z, wvalue & 1);
1250 ecp_nistz256_point_add_affine(&p.p, &p.p, &t.a);
1255 no_precomp_for_generator = 1;
1260 if (no_precomp_for_generator) {
1261 /* Without a precomputed table for the generator, it has to be
1262 * handled like a normal point. */
1263 const BIGNUM **new_scalars;
1264 const EC_POINT **new_points;
1266 new_scalars = OPENSSL_malloc((num + 1) * sizeof(BIGNUM *));
1268 ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, ERR_R_MALLOC_FAILURE);
1272 new_points = OPENSSL_malloc((num + 1) * sizeof(EC_POINT *));
1274 OPENSSL_free(new_scalars);
1275 ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, ERR_R_MALLOC_FAILURE);
1279 memcpy(new_scalars, scalars, num * sizeof(BIGNUM *));
1280 new_scalars[num] = scalar;
1281 memcpy(new_points, points, num * sizeof(EC_POINT *));
1282 new_points[num] = generator;
1284 scalars = new_scalars;
1285 points = new_points;
1290 P256_POINT *out = &t.p;
1294 ecp_nistz256_windowed_mul(group, out, scalars, points, num, ctx);
1297 ecp_nistz256_point_add(&p.p, &p.p, out);
1300 if (no_precomp_for_generator) {
1301 OPENSSL_free(points);
1302 OPENSSL_free(scalars);
1305 bn_set_data(r->X, p.p.X, sizeof(p.p.X));
1306 bn_set_data(r->Y, p.p.Y, sizeof(p.p.Y));
1307 bn_set_data(r->Z, p.p.Z, sizeof(p.p.Z));
1308 bn_correct_top(r->X);
1309 bn_correct_top(r->Y);
1310 bn_correct_top(r->Z);
1318 static int ecp_nistz256_get_affine(const EC_GROUP * group,
1319 const EC_POINT * point,
1320 BIGNUM * x, BIGNUM * y, BN_CTX * ctx)
1322 BN_ULONG z_inv2[P256_LIMBS];
1323 BN_ULONG z_inv3[P256_LIMBS];
1324 BN_ULONG x_aff[P256_LIMBS];
1325 BN_ULONG y_aff[P256_LIMBS];
1326 BN_ULONG point_x[P256_LIMBS], point_y[P256_LIMBS], point_z[P256_LIMBS];
1328 if (EC_POINT_is_at_infinity(group, point)) {
1329 ECerr(EC_F_ECP_NISTZ256_GET_AFFINE, EC_R_POINT_AT_INFINITY);
1333 if (!ecp_nistz256_bignum_to_field_elem(point_x, point->X) ||
1334 !ecp_nistz256_bignum_to_field_elem(point_y, point->Y) ||
1335 !ecp_nistz256_bignum_to_field_elem(point_z, point->Z)) {
1336 ECerr(EC_F_ECP_NISTZ256_GET_AFFINE, EC_R_COORDINATES_OUT_OF_RANGE);
1340 ecp_nistz256_mod_inverse(z_inv3, point_z);
1341 ecp_nistz256_sqr_mont(z_inv2, z_inv3);
1342 ecp_nistz256_mul_mont(x_aff, z_inv2, point_x);
1345 bn_wexpand(x, P256_LIMBS);
1346 bn_set_top(x, P256_LIMBS);
1347 ecp_nistz256_from_mont(bn_get_words(x), x_aff);
1352 ecp_nistz256_mul_mont(z_inv3, z_inv3, z_inv2);
1353 ecp_nistz256_mul_mont(y_aff, z_inv3, point_y);
1354 bn_wexpand(y, P256_LIMBS);
1355 bn_set_top(y, P256_LIMBS);
1356 ecp_nistz256_from_mont(bn_get_words(y), y_aff);
1363 static EC_PRE_COMP *ecp_nistz256_pre_comp_new(const EC_GROUP * group)
1365 EC_PRE_COMP *ret = NULL;
1370 ret = (EC_PRE_COMP *) OPENSSL_malloc(sizeof(EC_PRE_COMP));
1373 ECerr(EC_F_ECP_NISTZ256_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE);
1378 ret->w = 6; /* default */
1379 ret->precomp = NULL;
1380 ret->precomp_storage = NULL;
1381 ret->references = 1;
1385 static void *ecp_nistz256_pre_comp_dup(void *src_)
1387 EC_PRE_COMP *src = src_;
1389 /* no need to actually copy, these objects never change! */
1390 CRYPTO_add(&src->references, 1, CRYPTO_LOCK_EC_PRE_COMP);
1395 static void ecp_nistz256_pre_comp_free(void *pre_)
1398 EC_PRE_COMP *pre = pre_;
1403 i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP);
1407 if (pre->precomp_storage)
1408 OPENSSL_free(pre->precomp_storage);
1413 static void ecp_nistz256_pre_comp_clear_free(void *pre_)
1416 EC_PRE_COMP *pre = pre_;
1421 i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP);
1425 if (pre->precomp_storage) {
1426 OPENSSL_cleanse(pre->precomp,
1427 32 * sizeof(unsigned char) * (1 << pre->w) * 2 * 37);
1428 OPENSSL_free(pre->precomp_storage);
1430 OPENSSL_cleanse(pre, sizeof *pre);
1434 static int ecp_nistz256_window_have_precompute_mult(const EC_GROUP * group)
1436 /* There is a hard-coded table for the default generator. */
1437 const EC_POINT *generator = EC_GROUP_get0_generator(group);
1438 if (generator != NULL && ecp_nistz256_is_affine_G(generator)) {
1439 /* There is a hard-coded table for the default generator. */
1443 return EC_EX_DATA_get_data(group->extra_data, ecp_nistz256_pre_comp_dup,
1444 ecp_nistz256_pre_comp_free,
1445 ecp_nistz256_pre_comp_clear_free) != NULL;
1448 const EC_METHOD *EC_GFp_nistz256_method(void)
1450 static const EC_METHOD ret = {
1451 EC_FLAGS_DEFAULT_OCT,
1452 NID_X9_62_prime_field,
1453 ec_GFp_mont_group_init,
1454 ec_GFp_mont_group_finish,
1455 ec_GFp_mont_group_clear_finish,
1456 ec_GFp_mont_group_copy,
1457 ec_GFp_mont_group_set_curve,
1458 ec_GFp_simple_group_get_curve,
1459 ec_GFp_simple_group_get_degree,
1460 ec_GFp_simple_group_check_discriminant,
1461 ec_GFp_simple_point_init,
1462 ec_GFp_simple_point_finish,
1463 ec_GFp_simple_point_clear_finish,
1464 ec_GFp_simple_point_copy,
1465 ec_GFp_simple_point_set_to_infinity,
1466 ec_GFp_simple_set_Jprojective_coordinates_GFp,
1467 ec_GFp_simple_get_Jprojective_coordinates_GFp,
1468 ec_GFp_simple_point_set_affine_coordinates,
1469 ecp_nistz256_get_affine,
1473 ec_GFp_simple_invert,
1474 ec_GFp_simple_is_at_infinity,
1475 ec_GFp_simple_is_on_curve,
1477 ec_GFp_simple_make_affine,
1478 ec_GFp_simple_points_make_affine,
1479 ecp_nistz256_points_mul, /* mul */
1480 ecp_nistz256_mult_precompute, /* precompute_mult */
1481 ecp_nistz256_window_have_precompute_mult, /* have_precompute_mult */
1482 ec_GFp_mont_field_mul,
1483 ec_GFp_mont_field_sqr,
1485 ec_GFp_mont_field_encode,
1486 ec_GFp_mont_field_decode,
1487 ec_GFp_mont_field_set_to_one