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 <openssl/bn.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 if (in->top > P256_LIMBS)
549 memset(out, 0, sizeof(BN_ULONG) * P256_LIMBS);
550 memcpy(out, in->d, sizeof(BN_ULONG) * in->top);
554 /* r = sum(scalar[i]*point[i]) */
555 static void ecp_nistz256_windowed_mul(const EC_GROUP * group,
557 const BIGNUM ** scalar,
558 const EC_POINT ** point,
559 int num, BN_CTX * ctx)
563 unsigned char (*p_str)[33] = NULL;
564 const unsigned int window_size = 5;
565 const unsigned int mask = (1 << (window_size + 1)) - 1;
567 P256_POINT *temp; /* place for 5 temporary points */
568 const BIGNUM **scalars = NULL;
569 P256_POINT(*table)[16] = NULL;
570 void *table_storage = NULL;
573 OPENSSL_malloc((num * 16 + 5) * sizeof(P256_POINT) + 64)) == NULL
575 OPENSSL_malloc(num * 33 * sizeof(unsigned char))) == NULL
576 || (scalars = OPENSSL_malloc(num * sizeof(BIGNUM *))) == NULL) {
577 ECerr(EC_F_ECP_NISTZ256_WINDOWED_MUL, ERR_R_MALLOC_FAILURE);
581 table = (void *)ALIGNPTR(table_storage, 64);
582 temp = (P256_POINT *)(table + num);
584 for (i = 0; i < num; i++) {
585 P256_POINT *row = table[i];
587 if ((BN_num_bits(scalar[i]) > 256) || BN_is_negative(scalar[i])) {
590 if ((mod = BN_CTX_get(ctx)) == NULL)
592 if (!BN_nnmod(mod, scalar[i], &group->order, ctx)) {
593 ECerr(EC_F_ECP_NISTZ256_WINDOWED_MUL, ERR_R_BN_LIB);
598 scalars[i] = scalar[i];
600 for (j = 0; j < scalars[i]->top * BN_BYTES; j += BN_BYTES) {
601 BN_ULONG d = scalars[i]->d[j / BN_BYTES];
603 p_str[i][j + 0] = d & 0xff;
604 p_str[i][j + 1] = (d >> 8) & 0xff;
605 p_str[i][j + 2] = (d >> 16) & 0xff;
606 p_str[i][j + 3] = (d >>= 24) & 0xff;
609 p_str[i][j + 4] = d & 0xff;
610 p_str[i][j + 5] = (d >> 8) & 0xff;
611 p_str[i][j + 6] = (d >> 16) & 0xff;
612 p_str[i][j + 7] = (d >> 24) & 0xff;
618 if (!ecp_nistz256_bignum_to_field_elem(temp[0].X, &point[i]->X)
619 || !ecp_nistz256_bignum_to_field_elem(temp[0].Y, &point[i]->Y)
620 || !ecp_nistz256_bignum_to_field_elem(temp[0].Z, &point[i]->Z)) {
621 ECerr(EC_F_ECP_NISTZ256_WINDOWED_MUL, EC_R_COORDINATES_OUT_OF_RANGE);
625 /* row[0] is implicitly (0,0,0) (the point at infinity),
626 * therefore it is not stored. All other values are actually
627 * stored with an offset of -1 in table.
630 ecp_nistz256_scatter_w5 (row, &temp[0], 1);
631 ecp_nistz256_point_double(&temp[1], &temp[0]); /*1+1=2 */
632 ecp_nistz256_scatter_w5 (row, &temp[1], 2);
633 ecp_nistz256_point_add (&temp[2], &temp[1], &temp[0]); /*2+1=3 */
634 ecp_nistz256_scatter_w5 (row, &temp[2], 3);
635 ecp_nistz256_point_double(&temp[1], &temp[1]); /*2*2=4 */
636 ecp_nistz256_scatter_w5 (row, &temp[1], 4);
637 ecp_nistz256_point_double(&temp[2], &temp[2]); /*2*3=6 */
638 ecp_nistz256_scatter_w5 (row, &temp[2], 6);
639 ecp_nistz256_point_add (&temp[3], &temp[1], &temp[0]); /*4+1=5 */
640 ecp_nistz256_scatter_w5 (row, &temp[3], 5);
641 ecp_nistz256_point_add (&temp[4], &temp[2], &temp[0]); /*6+1=7 */
642 ecp_nistz256_scatter_w5 (row, &temp[4], 7);
643 ecp_nistz256_point_double(&temp[1], &temp[1]); /*2*4=8 */
644 ecp_nistz256_scatter_w5 (row, &temp[1], 8);
645 ecp_nistz256_point_double(&temp[2], &temp[2]); /*2*6=12 */
646 ecp_nistz256_scatter_w5 (row, &temp[2], 12);
647 ecp_nistz256_point_double(&temp[3], &temp[3]); /*2*5=10 */
648 ecp_nistz256_scatter_w5 (row, &temp[3], 10);
649 ecp_nistz256_point_double(&temp[4], &temp[4]); /*2*7=14 */
650 ecp_nistz256_scatter_w5 (row, &temp[4], 14);
651 ecp_nistz256_point_add (&temp[2], &temp[2], &temp[0]); /*12+1=13*/
652 ecp_nistz256_scatter_w5 (row, &temp[2], 13);
653 ecp_nistz256_point_add (&temp[3], &temp[3], &temp[0]); /*10+1=11*/
654 ecp_nistz256_scatter_w5 (row, &temp[3], 11);
655 ecp_nistz256_point_add (&temp[4], &temp[4], &temp[0]); /*14+1=15*/
656 ecp_nistz256_scatter_w5 (row, &temp[4], 15);
657 ecp_nistz256_point_add (&temp[2], &temp[1], &temp[0]); /*8+1=9 */
658 ecp_nistz256_scatter_w5 (row, &temp[2], 9);
659 ecp_nistz256_point_double(&temp[1], &temp[1]); /*2*8=16 */
660 ecp_nistz256_scatter_w5 (row, &temp[1], 16);
665 wvalue = p_str[0][(index - 1) / 8];
666 wvalue = (wvalue >> ((index - 1) % 8)) & mask;
669 * We gather to temp[0], because we know it's position relative
672 ecp_nistz256_gather_w5(&temp[0], table[0], _booth_recode_w5(wvalue) >> 1);
673 memcpy(r, &temp[0], sizeof(temp[0]));
676 for (i = (index == 255 ? 1 : 0); i < num; i++) {
677 unsigned int off = (index - 1) / 8;
679 wvalue = p_str[i][off] | p_str[i][off + 1] << 8;
680 wvalue = (wvalue >> ((index - 1) % 8)) & mask;
682 wvalue = _booth_recode_w5(wvalue);
684 ecp_nistz256_gather_w5(&temp[0], table[i], wvalue >> 1);
686 ecp_nistz256_neg(temp[1].Y, temp[0].Y);
687 copy_conditional(temp[0].Y, temp[1].Y, (wvalue & 1));
689 ecp_nistz256_point_add(r, r, &temp[0]);
692 index -= window_size;
694 ecp_nistz256_point_double(r, r);
695 ecp_nistz256_point_double(r, r);
696 ecp_nistz256_point_double(r, r);
697 ecp_nistz256_point_double(r, r);
698 ecp_nistz256_point_double(r, r);
702 for (i = 0; i < num; i++) {
703 wvalue = p_str[i][0];
704 wvalue = (wvalue << 1) & mask;
706 wvalue = _booth_recode_w5(wvalue);
708 ecp_nistz256_gather_w5(&temp[0], table[i], wvalue >> 1);
710 ecp_nistz256_neg(temp[1].Y, temp[0].Y);
711 copy_conditional(temp[0].Y, temp[1].Y, wvalue & 1);
713 ecp_nistz256_point_add(r, r, &temp[0]);
718 OPENSSL_free(table_storage);
722 OPENSSL_free(scalars);
725 /* Coordinates of G, for which we have precomputed tables */
726 const static BN_ULONG def_xG[P256_LIMBS] = {
727 TOBN(0x79e730d4, 0x18a9143c), TOBN(0x75ba95fc, 0x5fedb601),
728 TOBN(0x79fb732b, 0x77622510), TOBN(0x18905f76, 0xa53755c6)
731 const static BN_ULONG def_yG[P256_LIMBS] = {
732 TOBN(0xddf25357, 0xce95560a), TOBN(0x8b4ab8e4, 0xba19e45c),
733 TOBN(0xd2e88688, 0xdd21f325), TOBN(0x8571ff18, 0x25885d85)
736 /* ecp_nistz256_is_affine_G returns one if |generator| is the standard,
737 * P-256 generator. */
738 static int ecp_nistz256_is_affine_G(const EC_POINT * generator)
740 return (generator->X.top == P256_LIMBS) &&
741 (generator->Y.top == P256_LIMBS) &&
742 (generator->Z.top == (P256_LIMBS - P256_LIMBS / 8)) &&
743 is_equal(generator->X.d, def_xG) &&
744 is_equal(generator->Y.d, def_yG) && is_one(generator->Z.d);
747 static int ecp_nistz256_mult_precompute(EC_GROUP * group, BN_CTX * ctx)
749 /* We precompute a table for a Booth encoded exponent (wNAF) based
750 * computation. Each table holds 64 values for safe access, with an
751 * implicit value of infinity at index zero. We use window of size 7,
752 * and therefore require ceil(256/7) = 37 tables. */
754 EC_POINT *P = NULL, *T = NULL;
755 const EC_POINT *generator;
756 EC_PRE_COMP *pre_comp;
757 int i, j, k, ret = 0;
760 PRECOMP256_ROW *preComputedTable = NULL;
761 unsigned char *precomp_storage = NULL;
763 /* if there is an old EC_PRE_COMP object, throw it away */
764 EC_EX_DATA_free_data(&group->extra_data, ecp_nistz256_pre_comp_dup,
765 ecp_nistz256_pre_comp_free,
766 ecp_nistz256_pre_comp_clear_free);
768 generator = EC_GROUP_get0_generator(group);
769 if (generator == NULL) {
770 ECerr(EC_F_ECP_NISTZ256_MULT_PRECOMPUTE, EC_R_UNDEFINED_GENERATOR);
774 if (ecp_nistz256_is_affine_G(generator)) {
775 /* No need to calculate tables for the standard generator
776 * because we have them statically. */
780 if ((pre_comp = ecp_nistz256_pre_comp_new(group)) == NULL)
790 order = BN_CTX_get(ctx);
795 if (!EC_GROUP_get_order(group, order, ctx))
798 if (BN_is_zero(order)) {
799 ECerr(EC_F_ECP_NISTZ256_MULT_PRECOMPUTE, EC_R_UNKNOWN_ORDER);
805 if ((precomp_storage =
806 OPENSSL_malloc(37 * 64 * sizeof(P256_POINT_AFFINE) + 64)) == NULL) {
807 ECerr(EC_F_ECP_NISTZ256_MULT_PRECOMPUTE, ERR_R_MALLOC_FAILURE);
811 preComputedTable = (void *)ALIGNPTR(precomp_storage, 64);
813 P = EC_POINT_new(group);
814 T = EC_POINT_new(group);
816 /* The zero entry is implicitly infinity, and we skip it,
817 * storing other values with -1 offset. */
818 EC_POINT_copy(T, generator);
820 for (k = 0; k < 64; k++) {
822 for (j = 0; j < 37; j++) {
823 P256_POINT_AFFINE temp;
824 /* It would be faster to use
825 * ec_GFp_simple_points_make_affine and make multiple
826 * points affine at the same time. */
827 ec_GFp_simple_make_affine(group, P, ctx);
828 ecp_nistz256_bignum_to_field_elem(temp.X, &P->X);
829 ecp_nistz256_bignum_to_field_elem(temp.Y, &P->Y);
830 ecp_nistz256_scatter_w7(preComputedTable[j], &temp, k);
831 for (i = 0; i < 7; i++)
832 ec_GFp_simple_dbl(group, P, P, ctx);
834 ec_GFp_simple_add(group, T, T, generator, ctx);
837 pre_comp->group = group;
839 pre_comp->precomp = preComputedTable;
840 pre_comp->precomp_storage = precomp_storage;
842 precomp_storage = NULL;
844 if (!EC_EX_DATA_set_data(&group->extra_data, pre_comp,
845 ecp_nistz256_pre_comp_dup,
846 ecp_nistz256_pre_comp_free,
847 ecp_nistz256_pre_comp_clear_free)) {
859 ecp_nistz256_pre_comp_free(pre_comp);
861 OPENSSL_free(precomp_storage);
870 * Note that by default ECP_NISTZ256_AVX2 is undefined. While it's great
871 * code processing 4 points in parallel, corresponding serial operation
872 * is several times slower, because it uses 29x29=58-bit multiplication
873 * as opposite to 64x64=128-bit in integer-only scalar case. As result
874 * it doesn't provide *significant* performance improvement. Note that
875 * just defining ECP_NISTZ256_AVX2 is not sufficient to make it work,
876 * you'd need to compile even asm/ecp_nistz256-avx.pl module.
878 #if defined(ECP_NISTZ256_AVX2)
879 # if !(defined(__x86_64) || defined(__x86_64__) || \
880 defined(_M_AMD64) || defined(_MX64)) || \
881 !(defined(__GNUC__) || defined(_MSC_VER)) /* this is for ALIGN32 */
882 # undef ECP_NISTZ256_AVX2
884 /* Constant time access, loading four values, from four consecutive tables */
885 void ecp_nistz256_avx2_multi_gather_w7(void *result, const void *in, int index0,
886 int index1, int index2, int index3);
887 void ecp_nistz256_avx2_transpose_convert(void *RESULTx4, const void *in);
888 void ecp_nistz256_avx2_convert_transpose_back(void *result, const void *Ax4);
889 void ecp_nistz256_avx2_point_add_affine_x4(void *RESULTx4, const void *Ax4,
891 void ecp_nistz256_avx2_point_add_affines_x4(void *RESULTx4, const void *Ax4,
893 void ecp_nistz256_avx2_to_mont(void *RESULTx4, const void *Ax4);
894 void ecp_nistz256_avx2_from_mont(void *RESULTx4, const void *Ax4);
895 void ecp_nistz256_avx2_set1(void *RESULTx4);
896 int ecp_nistz_avx2_eligible(void);
898 static void booth_recode_w7(unsigned char *sign,
899 unsigned char *digit, unsigned char in)
903 s = ~((in >> 7) - 1);
904 d = (1 << 8) - in - 1;
905 d = (d & s) | (in & ~s);
906 d = (d >> 1) + (d & 1);
912 /* ecp_nistz256_avx2_mul_g performs multiplication by G, using only the
913 * precomputed table. It does 4 affine point additions in parallel,
914 * significantly speeding up point multiplication for a fixed value. */
915 static void ecp_nistz256_avx2_mul_g(P256_POINT * r,
916 unsigned char p_str[33],
918 P256_POINT_AFFINE(*preComputedTable)[64])
920 const unsigned int window_size = 7;
921 const unsigned int mask = (1 << (window_size + 1)) - 1;
923 /* Using 4 windows at a time */
924 unsigned char sign0, digit0;
925 unsigned char sign1, digit1;
926 unsigned char sign2, digit2;
927 unsigned char sign3, digit3;
928 unsigned int index = 0;
929 BN_ULONG tmp[P256_LIMBS];
932 ALIGN32 BN_ULONG aX4[4 * 9 * 3] = { 0 };
933 ALIGN32 BN_ULONG bX4[4 * 9 * 2] = { 0 };
934 ALIGN32 P256_POINT_AFFINE point_arr[4];
935 ALIGN32 P256_POINT res_point_arr[4];
937 /* Initial four windows */
938 wvalue = *((u16 *) & p_str[0]);
939 wvalue = (wvalue << 1) & mask;
940 index += window_size;
941 booth_recode_w7(&sign0, &digit0, wvalue);
942 wvalue = *((u16 *) & p_str[(index - 1) / 8]);
943 wvalue = (wvalue >> ((index - 1) % 8)) & mask;
944 index += window_size;
945 booth_recode_w7(&sign1, &digit1, wvalue);
946 wvalue = *((u16 *) & p_str[(index - 1) / 8]);
947 wvalue = (wvalue >> ((index - 1) % 8)) & mask;
948 index += window_size;
949 booth_recode_w7(&sign2, &digit2, wvalue);
950 wvalue = *((u16 *) & p_str[(index - 1) / 8]);
951 wvalue = (wvalue >> ((index - 1) % 8)) & mask;
952 index += window_size;
953 booth_recode_w7(&sign3, &digit3, wvalue);
955 ecp_nistz256_avx2_multi_gather_w7(point_arr, preComputedTable[0],
956 digit0, digit1, digit2, digit3);
958 ecp_nistz256_neg(tmp, point_arr[0].Y);
959 copy_conditional(point_arr[0].Y, tmp, sign0);
960 ecp_nistz256_neg(tmp, point_arr[1].Y);
961 copy_conditional(point_arr[1].Y, tmp, sign1);
962 ecp_nistz256_neg(tmp, point_arr[2].Y);
963 copy_conditional(point_arr[2].Y, tmp, sign2);
964 ecp_nistz256_neg(tmp, point_arr[3].Y);
965 copy_conditional(point_arr[3].Y, tmp, sign3);
967 ecp_nistz256_avx2_transpose_convert(aX4, point_arr);
968 ecp_nistz256_avx2_to_mont(aX4, aX4);
969 ecp_nistz256_avx2_to_mont(&aX4[4 * 9], &aX4[4 * 9]);
970 ecp_nistz256_avx2_set1(&aX4[4 * 9 * 2]);
972 wvalue = *((u16 *) & p_str[(index - 1) / 8]);
973 wvalue = (wvalue >> ((index - 1) % 8)) & mask;
974 index += window_size;
975 booth_recode_w7(&sign0, &digit0, wvalue);
976 wvalue = *((u16 *) & p_str[(index - 1) / 8]);
977 wvalue = (wvalue >> ((index - 1) % 8)) & mask;
978 index += window_size;
979 booth_recode_w7(&sign1, &digit1, wvalue);
980 wvalue = *((u16 *) & p_str[(index - 1) / 8]);
981 wvalue = (wvalue >> ((index - 1) % 8)) & mask;
982 index += window_size;
983 booth_recode_w7(&sign2, &digit2, wvalue);
984 wvalue = *((u16 *) & p_str[(index - 1) / 8]);
985 wvalue = (wvalue >> ((index - 1) % 8)) & mask;
986 index += window_size;
987 booth_recode_w7(&sign3, &digit3, wvalue);
989 ecp_nistz256_avx2_multi_gather_w7(point_arr, preComputedTable[4 * 1],
990 digit0, digit1, digit2, digit3);
992 ecp_nistz256_neg(tmp, point_arr[0].Y);
993 copy_conditional(point_arr[0].Y, tmp, sign0);
994 ecp_nistz256_neg(tmp, point_arr[1].Y);
995 copy_conditional(point_arr[1].Y, tmp, sign1);
996 ecp_nistz256_neg(tmp, point_arr[2].Y);
997 copy_conditional(point_arr[2].Y, tmp, sign2);
998 ecp_nistz256_neg(tmp, point_arr[3].Y);
999 copy_conditional(point_arr[3].Y, tmp, sign3);
1001 ecp_nistz256_avx2_transpose_convert(bX4, point_arr);
1002 ecp_nistz256_avx2_to_mont(bX4, bX4);
1003 ecp_nistz256_avx2_to_mont(&bX4[4 * 9], &bX4[4 * 9]);
1004 /* Optimized when both inputs are affine */
1005 ecp_nistz256_avx2_point_add_affines_x4(aX4, aX4, bX4);
1007 for (i = 2; i < 9; i++) {
1008 wvalue = *((u16 *) & p_str[(index - 1) / 8]);
1009 wvalue = (wvalue >> ((index - 1) % 8)) & mask;
1010 index += window_size;
1011 booth_recode_w7(&sign0, &digit0, wvalue);
1012 wvalue = *((u16 *) & p_str[(index - 1) / 8]);
1013 wvalue = (wvalue >> ((index - 1) % 8)) & mask;
1014 index += window_size;
1015 booth_recode_w7(&sign1, &digit1, wvalue);
1016 wvalue = *((u16 *) & p_str[(index - 1) / 8]);
1017 wvalue = (wvalue >> ((index - 1) % 8)) & mask;
1018 index += window_size;
1019 booth_recode_w7(&sign2, &digit2, wvalue);
1020 wvalue = *((u16 *) & p_str[(index - 1) / 8]);
1021 wvalue = (wvalue >> ((index - 1) % 8)) & mask;
1022 index += window_size;
1023 booth_recode_w7(&sign3, &digit3, wvalue);
1025 ecp_nistz256_avx2_multi_gather_w7(point_arr,
1026 preComputedTable[4 * i],
1027 digit0, digit1, digit2, digit3);
1029 ecp_nistz256_neg(tmp, point_arr[0].Y);
1030 copy_conditional(point_arr[0].Y, tmp, sign0);
1031 ecp_nistz256_neg(tmp, point_arr[1].Y);
1032 copy_conditional(point_arr[1].Y, tmp, sign1);
1033 ecp_nistz256_neg(tmp, point_arr[2].Y);
1034 copy_conditional(point_arr[2].Y, tmp, sign2);
1035 ecp_nistz256_neg(tmp, point_arr[3].Y);
1036 copy_conditional(point_arr[3].Y, tmp, sign3);
1038 ecp_nistz256_avx2_transpose_convert(bX4, point_arr);
1039 ecp_nistz256_avx2_to_mont(bX4, bX4);
1040 ecp_nistz256_avx2_to_mont(&bX4[4 * 9], &bX4[4 * 9]);
1042 ecp_nistz256_avx2_point_add_affine_x4(aX4, aX4, bX4);
1045 ecp_nistz256_avx2_from_mont(&aX4[4 * 9 * 0], &aX4[4 * 9 * 0]);
1046 ecp_nistz256_avx2_from_mont(&aX4[4 * 9 * 1], &aX4[4 * 9 * 1]);
1047 ecp_nistz256_avx2_from_mont(&aX4[4 * 9 * 2], &aX4[4 * 9 * 2]);
1049 ecp_nistz256_avx2_convert_transpose_back(res_point_arr, aX4);
1050 /* Last window is performed serially */
1051 wvalue = *((u16 *) & p_str[(index - 1) / 8]);
1052 wvalue = (wvalue >> ((index - 1) % 8)) & mask;
1053 booth_recode_w7(&sign0, &digit0, wvalue);
1054 ecp_nistz256_gather_w7((P256_POINT_AFFINE *) r,
1055 preComputedTable[36], digit0);
1056 ecp_nistz256_neg(tmp, r->Y);
1057 copy_conditional(r->Y, tmp, sign0);
1058 memcpy(r->Z, ONE, sizeof(ONE));
1059 /* Sum the four windows */
1060 ecp_nistz256_point_add(r, r, &res_point_arr[0]);
1061 ecp_nistz256_point_add(r, r, &res_point_arr[1]);
1062 ecp_nistz256_point_add(r, r, &res_point_arr[2]);
1063 ecp_nistz256_point_add(r, r, &res_point_arr[3]);
1068 static int ecp_nistz256_set_from_affine(EC_POINT * out, const EC_GROUP * group,
1069 const P256_POINT_AFFINE * in,
1073 BN_ULONG d_x[P256_LIMBS], d_y[P256_LIMBS];
1076 memcpy(d_x, in->X, sizeof(d_x));
1078 x.dmax = x.top = P256_LIMBS;
1080 x.flags = BN_FLG_STATIC_DATA;
1082 memcpy(d_y, in->Y, sizeof(d_y));
1084 y.dmax = y.top = P256_LIMBS;
1086 y.flags = BN_FLG_STATIC_DATA;
1088 ret = EC_POINT_set_affine_coordinates_GFp(group, out, &x, &y, ctx);
1093 /* r = scalar*G + sum(scalars[i]*points[i]) */
1094 static int ecp_nistz256_points_mul(const EC_GROUP * group,
1096 const BIGNUM * scalar,
1098 const EC_POINT * points[],
1099 const BIGNUM * scalars[], BN_CTX * ctx)
1101 int i = 0, ret = 0, no_precomp_for_generator = 0, p_is_infinity = 0;
1103 unsigned char p_str[33] = { 0 };
1104 const PRECOMP256_ROW *preComputedTable = NULL;
1105 const EC_PRE_COMP *pre_comp = NULL;
1106 const EC_POINT *generator = NULL;
1107 unsigned int index = 0;
1108 const unsigned int window_size = 7;
1109 const unsigned int mask = (1 << (window_size + 1)) - 1;
1110 unsigned int wvalue;
1113 P256_POINT_AFFINE a;
1117 if ((num+1) == 0 || (num+1) > OPENSSL_MALLOC_MAX_NELEMS(void *)) {
1118 ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, ERR_R_MALLOC_FAILURE);
1122 if (group->meth != r->meth) {
1123 ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, EC_R_INCOMPATIBLE_OBJECTS);
1126 if ((scalar == NULL) && (num == 0))
1127 return EC_POINT_set_to_infinity(group, r);
1129 for (j = 0; j < num; j++) {
1130 if (group->meth != points[j]->meth) {
1131 ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, EC_R_INCOMPATIBLE_OBJECTS);
1136 /* Need 256 bits for space for all coordinates. */
1137 bn_wexpand(&r->X, P256_LIMBS);
1138 bn_wexpand(&r->Y, P256_LIMBS);
1139 bn_wexpand(&r->Z, P256_LIMBS);
1140 r->X.top = P256_LIMBS;
1141 r->Y.top = P256_LIMBS;
1142 r->Z.top = P256_LIMBS;
1145 generator = EC_GROUP_get0_generator(group);
1146 if (generator == NULL) {
1147 ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, EC_R_UNDEFINED_GENERATOR);
1151 /* look if we can use precomputed multiples of generator */
1153 EC_EX_DATA_get_data(group->extra_data, ecp_nistz256_pre_comp_dup,
1154 ecp_nistz256_pre_comp_free,
1155 ecp_nistz256_pre_comp_clear_free);
1158 /* If there is a precomputed table for the generator,
1159 * check that it was generated with the same
1161 EC_POINT *pre_comp_generator = EC_POINT_new(group);
1162 if (pre_comp_generator == NULL)
1165 if (!ecp_nistz256_set_from_affine(pre_comp_generator,
1166 group, pre_comp->precomp[0],
1170 if (0 == EC_POINT_cmp(group, generator, pre_comp_generator, ctx))
1171 preComputedTable = (const PRECOMP256_ROW *)pre_comp->precomp;
1173 EC_POINT_free(pre_comp_generator);
1176 if (preComputedTable == NULL && ecp_nistz256_is_affine_G(generator)) {
1177 /* If there is no precomputed data, but the generator
1178 * is the default, a hardcoded table of precomputed
1179 * data is used. This is because applications, such as
1180 * Apache, do not use EC_KEY_precompute_mult. */
1181 preComputedTable = ecp_nistz256_precomputed;
1184 if (preComputedTable) {
1185 if ((BN_num_bits(scalar) > 256)
1186 || BN_is_negative(scalar)) {
1187 if ((tmp_scalar = BN_CTX_get(ctx)) == NULL)
1190 if (!BN_nnmod(tmp_scalar, scalar, &group->order, ctx)) {
1191 ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, ERR_R_BN_LIB);
1194 scalar = tmp_scalar;
1197 for (i = 0; i < scalar->top * BN_BYTES; i += BN_BYTES) {
1198 BN_ULONG d = scalar->d[i / BN_BYTES];
1200 p_str[i + 0] = d & 0xff;
1201 p_str[i + 1] = (d >> 8) & 0xff;
1202 p_str[i + 2] = (d >> 16) & 0xff;
1203 p_str[i + 3] = (d >>= 24) & 0xff;
1204 if (BN_BYTES == 8) {
1206 p_str[i + 4] = d & 0xff;
1207 p_str[i + 5] = (d >> 8) & 0xff;
1208 p_str[i + 6] = (d >> 16) & 0xff;
1209 p_str[i + 7] = (d >> 24) & 0xff;
1216 #if defined(ECP_NISTZ256_AVX2)
1217 if (ecp_nistz_avx2_eligible()) {
1218 ecp_nistz256_avx2_mul_g(&p.p, p_str, preComputedTable);
1223 wvalue = (p_str[0] << 1) & mask;
1224 index += window_size;
1226 wvalue = _booth_recode_w7(wvalue);
1228 ecp_nistz256_gather_w7(&p.a, preComputedTable[0], wvalue >> 1);
1230 ecp_nistz256_neg(p.p.Z, p.p.Y);
1231 copy_conditional(p.p.Y, p.p.Z, wvalue & 1);
1233 memcpy(p.p.Z, ONE, sizeof(ONE));
1235 for (i = 1; i < 37; i++) {
1236 unsigned int off = (index - 1) / 8;
1237 wvalue = p_str[off] | p_str[off + 1] << 8;
1238 wvalue = (wvalue >> ((index - 1) % 8)) & mask;
1239 index += window_size;
1241 wvalue = _booth_recode_w7(wvalue);
1243 ecp_nistz256_gather_w7(&t.a,
1244 preComputedTable[i], wvalue >> 1);
1246 ecp_nistz256_neg(t.p.Z, t.a.Y);
1247 copy_conditional(t.a.Y, t.p.Z, wvalue & 1);
1249 ecp_nistz256_point_add_affine(&p.p, &p.p, &t.a);
1254 no_precomp_for_generator = 1;
1259 if (no_precomp_for_generator) {
1260 /* Without a precomputed table for the generator, it has to be
1261 * handled like a normal point. */
1262 const BIGNUM **new_scalars;
1263 const EC_POINT **new_points;
1265 new_scalars = OPENSSL_malloc((num + 1) * sizeof(BIGNUM *));
1267 ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, ERR_R_MALLOC_FAILURE);
1271 new_points = OPENSSL_malloc((num + 1) * sizeof(EC_POINT *));
1273 OPENSSL_free(new_scalars);
1274 ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, ERR_R_MALLOC_FAILURE);
1278 memcpy(new_scalars, scalars, num * sizeof(BIGNUM *));
1279 new_scalars[num] = scalar;
1280 memcpy(new_points, points, num * sizeof(EC_POINT *));
1281 new_points[num] = generator;
1283 scalars = new_scalars;
1284 points = new_points;
1289 P256_POINT *out = &t.p;
1293 ecp_nistz256_windowed_mul(group, out, scalars, points, num, ctx);
1296 ecp_nistz256_point_add(&p.p, &p.p, out);
1299 if (no_precomp_for_generator) {
1300 OPENSSL_free(points);
1301 OPENSSL_free(scalars);
1304 memcpy(r->X.d, p.p.X, sizeof(p.p.X));
1305 memcpy(r->Y.d, p.p.Y, sizeof(p.p.Y));
1306 memcpy(r->Z.d, p.p.Z, sizeof(p.p.Z));
1307 bn_correct_top(&r->X);
1308 bn_correct_top(&r->Y);
1309 bn_correct_top(&r->Z);
1317 static int ecp_nistz256_get_affine(const EC_GROUP * group,
1318 const EC_POINT * point,
1319 BIGNUM * x, BIGNUM * y, BN_CTX * ctx)
1321 BN_ULONG z_inv2[P256_LIMBS];
1322 BN_ULONG z_inv3[P256_LIMBS];
1323 BN_ULONG x_aff[P256_LIMBS];
1324 BN_ULONG y_aff[P256_LIMBS];
1325 BN_ULONG point_x[P256_LIMBS], point_y[P256_LIMBS], point_z[P256_LIMBS];
1327 if (EC_POINT_is_at_infinity(group, point)) {
1328 ECerr(EC_F_ECP_NISTZ256_GET_AFFINE, EC_R_POINT_AT_INFINITY);
1332 if (!ecp_nistz256_bignum_to_field_elem(point_x, &point->X) ||
1333 !ecp_nistz256_bignum_to_field_elem(point_y, &point->Y) ||
1334 !ecp_nistz256_bignum_to_field_elem(point_z, &point->Z)) {
1335 ECerr(EC_F_ECP_NISTZ256_GET_AFFINE, EC_R_COORDINATES_OUT_OF_RANGE);
1339 ecp_nistz256_mod_inverse(z_inv3, point_z);
1340 ecp_nistz256_sqr_mont(z_inv2, z_inv3);
1341 ecp_nistz256_mul_mont(x_aff, z_inv2, point_x);
1344 bn_wexpand(x, P256_LIMBS);
1345 x->top = P256_LIMBS;
1346 ecp_nistz256_from_mont(x->d, x_aff);
1351 ecp_nistz256_mul_mont(z_inv3, z_inv3, z_inv2);
1352 ecp_nistz256_mul_mont(y_aff, z_inv3, point_y);
1353 bn_wexpand(y, P256_LIMBS);
1354 y->top = P256_LIMBS;
1355 ecp_nistz256_from_mont(y->d, y_aff);
1362 static EC_PRE_COMP *ecp_nistz256_pre_comp_new(const EC_GROUP * group)
1364 EC_PRE_COMP *ret = NULL;
1369 ret = (EC_PRE_COMP *) OPENSSL_malloc(sizeof(EC_PRE_COMP));
1372 ECerr(EC_F_ECP_NISTZ256_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE);
1377 ret->w = 6; /* default */
1378 ret->precomp = NULL;
1379 ret->precomp_storage = NULL;
1380 ret->references = 1;
1384 static void *ecp_nistz256_pre_comp_dup(void *src_)
1386 EC_PRE_COMP *src = src_;
1388 /* no need to actually copy, these objects never change! */
1389 CRYPTO_add(&src->references, 1, CRYPTO_LOCK_EC_PRE_COMP);
1394 static void ecp_nistz256_pre_comp_free(void *pre_)
1397 EC_PRE_COMP *pre = pre_;
1402 i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP);
1406 if (pre->precomp_storage)
1407 OPENSSL_free(pre->precomp_storage);
1412 static void ecp_nistz256_pre_comp_clear_free(void *pre_)
1415 EC_PRE_COMP *pre = pre_;
1420 i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP);
1424 if (pre->precomp_storage) {
1425 OPENSSL_cleanse(pre->precomp,
1426 32 * sizeof(unsigned char) * (1 << pre->w) * 2 * 37);
1427 OPENSSL_free(pre->precomp_storage);
1429 OPENSSL_cleanse(pre, sizeof *pre);
1433 static int ecp_nistz256_window_have_precompute_mult(const EC_GROUP * group)
1435 /* There is a hard-coded table for the default generator. */
1436 const EC_POINT *generator = EC_GROUP_get0_generator(group);
1437 if (generator != NULL && ecp_nistz256_is_affine_G(generator)) {
1438 /* There is a hard-coded table for the default generator. */
1442 return EC_EX_DATA_get_data(group->extra_data, ecp_nistz256_pre_comp_dup,
1443 ecp_nistz256_pre_comp_free,
1444 ecp_nistz256_pre_comp_clear_free) != NULL;
1447 const EC_METHOD *EC_GFp_nistz256_method(void)
1449 static const EC_METHOD ret = {
1450 EC_FLAGS_DEFAULT_OCT,
1451 NID_X9_62_prime_field,
1452 ec_GFp_mont_group_init,
1453 ec_GFp_mont_group_finish,
1454 ec_GFp_mont_group_clear_finish,
1455 ec_GFp_mont_group_copy,
1456 ec_GFp_mont_group_set_curve,
1457 ec_GFp_simple_group_get_curve,
1458 ec_GFp_simple_group_get_degree,
1459 ec_GFp_simple_group_check_discriminant,
1460 ec_GFp_simple_point_init,
1461 ec_GFp_simple_point_finish,
1462 ec_GFp_simple_point_clear_finish,
1463 ec_GFp_simple_point_copy,
1464 ec_GFp_simple_point_set_to_infinity,
1465 ec_GFp_simple_set_Jprojective_coordinates_GFp,
1466 ec_GFp_simple_get_Jprojective_coordinates_GFp,
1467 ec_GFp_simple_point_set_affine_coordinates,
1468 ecp_nistz256_get_affine,
1472 ec_GFp_simple_invert,
1473 ec_GFp_simple_is_at_infinity,
1474 ec_GFp_simple_is_on_curve,
1476 ec_GFp_simple_make_affine,
1477 ec_GFp_simple_points_make_affine,
1478 ecp_nistz256_points_mul, /* mul */
1479 ecp_nistz256_mult_precompute, /* precompute_mult */
1480 ecp_nistz256_window_have_precompute_mult, /* have_precompute_mult */
1481 ec_GFp_mont_field_mul,
1482 ec_GFp_mont_field_sqr,
1484 ec_GFp_mont_field_encode,
1485 ec_GFp_mont_field_decode,
1486 ec_GFp_mont_field_set_to_one