1 /* Copyright (c) 2014, Intel Corporation.
2 *
3 * Permission to use, copy, modify, and/or distribute this software for any
4 * purpose with or without fee is hereby granted, provided that the above
5 * copyright notice and this permission notice appear in all copies.
6 *
7 * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
8 * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
9 * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY
10 * SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
11 * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION
12 * OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN
13 * CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. */
14
15 /* Developers and authors:
16 * Shay Gueron (1, 2), and Vlad Krasnov (1)
17 * (1) Intel Corporation, Israel Development Center
18 * (2) University of Haifa
19 * Reference:
20 * S.Gueron and V.Krasnov, "Fast Prime Field Elliptic Curve Cryptography with
21 * 256 Bit Primes" */
22
23 #include <openssl/ec.h>
24
25 #include <assert.h>
26 #include <stdint.h>
27 #include <string.h>
28
29 #include <openssl/bn.h>
30 #include <openssl/crypto.h>
31 #include <openssl/err.h>
32
33 #include "../bn/internal.h"
34 #include "../internal.h"
35 #include "internal.h"
36 #include "p256-x86_64.h"
37
38
39 #if !defined(OPENSSL_NO_ASM) && defined(OPENSSL_X86_64) && \
40 !defined(OPENSSL_SMALL)
41
42 typedef P256_POINT_AFFINE PRECOMP256_ROW[64];
43
44 /* One converted into the Montgomery domain */
45 static const BN_ULONG ONE[P256_LIMBS] = {
46 TOBN(0x00000000, 0x00000001), TOBN(0xffffffff, 0x00000000),
47 TOBN(0xffffffff, 0xffffffff), TOBN(0x00000000, 0xfffffffe),
48 };
49
50 /* Precomputed tables for the default generator */
51 #include "p256-x86_64-table.h"
52
53 /* Recode window to a signed digit, see util-64.c for details */
booth_recode_w5(unsigned in)54 static unsigned booth_recode_w5(unsigned in) {
55 unsigned s, d;
56
57 s = ~((in >> 5) - 1);
58 d = (1 << 6) - in - 1;
59 d = (d & s) | (in & ~s);
60 d = (d >> 1) + (d & 1);
61
62 return (d << 1) + (s & 1);
63 }
64
booth_recode_w7(unsigned in)65 static unsigned booth_recode_w7(unsigned in) {
66 unsigned s, d;
67
68 s = ~((in >> 7) - 1);
69 d = (1 << 8) - in - 1;
70 d = (d & s) | (in & ~s);
71 d = (d >> 1) + (d & 1);
72
73 return (d << 1) + (s & 1);
74 }
75
76 /* copy_conditional copies |src| to |dst| if |move| is one and leaves it as-is
77 * if |move| is zero.
78 *
79 * WARNING: this breaks the usual convention of constant-time functions
80 * returning masks. */
copy_conditional(BN_ULONG dst[P256_LIMBS],const BN_ULONG src[P256_LIMBS],BN_ULONG move)81 static void copy_conditional(BN_ULONG dst[P256_LIMBS],
82 const BN_ULONG src[P256_LIMBS], BN_ULONG move) {
83 BN_ULONG mask1 = ((BN_ULONG)0) - move;
84 BN_ULONG mask2 = ~mask1;
85
86 dst[0] = (src[0] & mask1) ^ (dst[0] & mask2);
87 dst[1] = (src[1] & mask1) ^ (dst[1] & mask2);
88 dst[2] = (src[2] & mask1) ^ (dst[2] & mask2);
89 dst[3] = (src[3] & mask1) ^ (dst[3] & mask2);
90 if (P256_LIMBS == 8) {
91 dst[4] = (src[4] & mask1) ^ (dst[4] & mask2);
92 dst[5] = (src[5] & mask1) ^ (dst[5] & mask2);
93 dst[6] = (src[6] & mask1) ^ (dst[6] & mask2);
94 dst[7] = (src[7] & mask1) ^ (dst[7] & mask2);
95 }
96 }
97
98 /* is_not_zero returns one iff in != 0 and zero otherwise.
99 *
100 * WARNING: this breaks the usual convention of constant-time functions
101 * returning masks.
102 *
103 * (define-fun is_not_zero ((in (_ BitVec 64))) (_ BitVec 64)
104 * (bvlshr (bvor in (bvsub #x0000000000000000 in)) #x000000000000003f)
105 * )
106 *
107 * (declare-fun x () (_ BitVec 64))
108 *
109 * (assert (and (= x #x0000000000000000) (= (is_not_zero x) #x0000000000000001)))
110 * (check-sat)
111 *
112 * (assert (and (not (= x #x0000000000000000)) (= (is_not_zero x) #x0000000000000000)))
113 * (check-sat)
114 * */
is_not_zero(BN_ULONG in)115 static BN_ULONG is_not_zero(BN_ULONG in) {
116 in |= (0 - in);
117 in >>= BN_BITS2 - 1;
118 return in;
119 }
120
121 /* ecp_nistz256_mod_inverse_mont sets |r| to (|in| * 2^-256)^-1 * 2^256 mod p.
122 * That is, |r| is the modular inverse of |in| for input and output in the
123 * Montgomery domain. */
ecp_nistz256_mod_inverse_mont(BN_ULONG r[P256_LIMBS],const BN_ULONG in[P256_LIMBS])124 static void ecp_nistz256_mod_inverse_mont(BN_ULONG r[P256_LIMBS],
125 const BN_ULONG in[P256_LIMBS]) {
126 /* The poly is ffffffff 00000001 00000000 00000000 00000000 ffffffff ffffffff
127 ffffffff
128 We use FLT and used poly-2 as exponent */
129 BN_ULONG p2[P256_LIMBS];
130 BN_ULONG p4[P256_LIMBS];
131 BN_ULONG p8[P256_LIMBS];
132 BN_ULONG p16[P256_LIMBS];
133 BN_ULONG p32[P256_LIMBS];
134 BN_ULONG res[P256_LIMBS];
135 int i;
136
137 ecp_nistz256_sqr_mont(res, in);
138 ecp_nistz256_mul_mont(p2, res, in); /* 3*p */
139
140 ecp_nistz256_sqr_mont(res, p2);
141 ecp_nistz256_sqr_mont(res, res);
142 ecp_nistz256_mul_mont(p4, res, p2); /* f*p */
143
144 ecp_nistz256_sqr_mont(res, p4);
145 ecp_nistz256_sqr_mont(res, res);
146 ecp_nistz256_sqr_mont(res, res);
147 ecp_nistz256_sqr_mont(res, res);
148 ecp_nistz256_mul_mont(p8, res, p4); /* ff*p */
149
150 ecp_nistz256_sqr_mont(res, p8);
151 for (i = 0; i < 7; i++) {
152 ecp_nistz256_sqr_mont(res, res);
153 }
154 ecp_nistz256_mul_mont(p16, res, p8); /* ffff*p */
155
156 ecp_nistz256_sqr_mont(res, p16);
157 for (i = 0; i < 15; i++) {
158 ecp_nistz256_sqr_mont(res, res);
159 }
160 ecp_nistz256_mul_mont(p32, res, p16); /* ffffffff*p */
161
162 ecp_nistz256_sqr_mont(res, p32);
163 for (i = 0; i < 31; i++) {
164 ecp_nistz256_sqr_mont(res, res);
165 }
166 ecp_nistz256_mul_mont(res, res, in);
167
168 for (i = 0; i < 32 * 4; i++) {
169 ecp_nistz256_sqr_mont(res, res);
170 }
171 ecp_nistz256_mul_mont(res, res, p32);
172
173 for (i = 0; i < 32; i++) {
174 ecp_nistz256_sqr_mont(res, res);
175 }
176 ecp_nistz256_mul_mont(res, res, p32);
177
178 for (i = 0; i < 16; i++) {
179 ecp_nistz256_sqr_mont(res, res);
180 }
181 ecp_nistz256_mul_mont(res, res, p16);
182
183 for (i = 0; i < 8; i++) {
184 ecp_nistz256_sqr_mont(res, res);
185 }
186 ecp_nistz256_mul_mont(res, res, p8);
187
188 ecp_nistz256_sqr_mont(res, res);
189 ecp_nistz256_sqr_mont(res, res);
190 ecp_nistz256_sqr_mont(res, res);
191 ecp_nistz256_sqr_mont(res, res);
192 ecp_nistz256_mul_mont(res, res, p4);
193
194 ecp_nistz256_sqr_mont(res, res);
195 ecp_nistz256_sqr_mont(res, res);
196 ecp_nistz256_mul_mont(res, res, p2);
197
198 ecp_nistz256_sqr_mont(res, res);
199 ecp_nistz256_sqr_mont(res, res);
200 ecp_nistz256_mul_mont(r, res, in);
201 }
202
203 /* ecp_nistz256_bignum_to_field_elem copies the contents of |in| to |out| and
204 * returns one if it fits. Otherwise it returns zero. */
ecp_nistz256_bignum_to_field_elem(BN_ULONG out[P256_LIMBS],const BIGNUM * in)205 static int ecp_nistz256_bignum_to_field_elem(BN_ULONG out[P256_LIMBS],
206 const BIGNUM *in) {
207 if (in->top > P256_LIMBS) {
208 return 0;
209 }
210
211 OPENSSL_memset(out, 0, sizeof(BN_ULONG) * P256_LIMBS);
212 OPENSSL_memcpy(out, in->d, sizeof(BN_ULONG) * in->top);
213 return 1;
214 }
215
216 /* r = p * p_scalar */
ecp_nistz256_windowed_mul(const EC_GROUP * group,P256_POINT * r,const EC_POINT * p,const BIGNUM * p_scalar,BN_CTX * ctx)217 static int ecp_nistz256_windowed_mul(const EC_GROUP *group, P256_POINT *r,
218 const EC_POINT *p, const BIGNUM *p_scalar,
219 BN_CTX *ctx) {
220 assert(p != NULL);
221 assert(p_scalar != NULL);
222
223 static const unsigned kWindowSize = 5;
224 static const unsigned kMask = (1 << (5 /* kWindowSize */ + 1)) - 1;
225
226 /* A |P256_POINT| is (3 * 32) = 96 bytes, and the 64-byte alignment should
227 * add no more than 63 bytes of overhead. Thus, |table| should require
228 * ~1599 ((96 * 16) + 63) bytes of stack space. */
229 alignas(64) P256_POINT table[16];
230 uint8_t p_str[33];
231
232
233 int ret = 0;
234 BN_CTX *new_ctx = NULL;
235 int ctx_started = 0;
236
237 if (BN_num_bits(p_scalar) > 256 || BN_is_negative(p_scalar)) {
238 if (ctx == NULL) {
239 new_ctx = BN_CTX_new();
240 if (new_ctx == NULL) {
241 OPENSSL_PUT_ERROR(EC, ERR_R_MALLOC_FAILURE);
242 goto err;
243 }
244 ctx = new_ctx;
245 }
246 BN_CTX_start(ctx);
247 ctx_started = 1;
248 BIGNUM *mod = BN_CTX_get(ctx);
249 if (mod == NULL) {
250 OPENSSL_PUT_ERROR(EC, ERR_R_MALLOC_FAILURE);
251 goto err;
252 }
253 if (!BN_nnmod(mod, p_scalar, &group->order, ctx)) {
254 OPENSSL_PUT_ERROR(EC, ERR_R_BN_LIB);
255 goto err;
256 }
257 p_scalar = mod;
258 }
259
260 int j;
261 for (j = 0; j < p_scalar->top * BN_BYTES; j += BN_BYTES) {
262 BN_ULONG d = p_scalar->d[j / BN_BYTES];
263
264 p_str[j + 0] = d & 0xff;
265 p_str[j + 1] = (d >> 8) & 0xff;
266 p_str[j + 2] = (d >> 16) & 0xff;
267 p_str[j + 3] = (d >>= 24) & 0xff;
268 if (BN_BYTES == 8) {
269 d >>= 8;
270 p_str[j + 4] = d & 0xff;
271 p_str[j + 5] = (d >> 8) & 0xff;
272 p_str[j + 6] = (d >> 16) & 0xff;
273 p_str[j + 7] = (d >> 24) & 0xff;
274 }
275 }
276
277 for (; j < 33; j++) {
278 p_str[j] = 0;
279 }
280
281 /* table[0] is implicitly (0,0,0) (the point at infinity), therefore it is
282 * not stored. All other values are actually stored with an offset of -1 in
283 * table. */
284 P256_POINT *row = table;
285
286 if (!ecp_nistz256_bignum_to_field_elem(row[1 - 1].X, &p->X) ||
287 !ecp_nistz256_bignum_to_field_elem(row[1 - 1].Y, &p->Y) ||
288 !ecp_nistz256_bignum_to_field_elem(row[1 - 1].Z, &p->Z)) {
289 OPENSSL_PUT_ERROR(EC, EC_R_COORDINATES_OUT_OF_RANGE);
290 goto err;
291 }
292
293 ecp_nistz256_point_double(&row[2 - 1], &row[1 - 1]);
294 ecp_nistz256_point_add(&row[3 - 1], &row[2 - 1], &row[1 - 1]);
295 ecp_nistz256_point_double(&row[4 - 1], &row[2 - 1]);
296 ecp_nistz256_point_double(&row[6 - 1], &row[3 - 1]);
297 ecp_nistz256_point_double(&row[8 - 1], &row[4 - 1]);
298 ecp_nistz256_point_double(&row[12 - 1], &row[6 - 1]);
299 ecp_nistz256_point_add(&row[5 - 1], &row[4 - 1], &row[1 - 1]);
300 ecp_nistz256_point_add(&row[7 - 1], &row[6 - 1], &row[1 - 1]);
301 ecp_nistz256_point_add(&row[9 - 1], &row[8 - 1], &row[1 - 1]);
302 ecp_nistz256_point_add(&row[13 - 1], &row[12 - 1], &row[1 - 1]);
303 ecp_nistz256_point_double(&row[14 - 1], &row[7 - 1]);
304 ecp_nistz256_point_double(&row[10 - 1], &row[5 - 1]);
305 ecp_nistz256_point_add(&row[15 - 1], &row[14 - 1], &row[1 - 1]);
306 ecp_nistz256_point_add(&row[11 - 1], &row[10 - 1], &row[1 - 1]);
307 ecp_nistz256_point_double(&row[16 - 1], &row[8 - 1]);
308
309 BN_ULONG tmp[P256_LIMBS];
310 alignas(32) P256_POINT h;
311 unsigned index = 255;
312 unsigned wvalue = p_str[(index - 1) / 8];
313 wvalue = (wvalue >> ((index - 1) % 8)) & kMask;
314
315 ecp_nistz256_select_w5(r, table, booth_recode_w5(wvalue) >> 1);
316
317 while (index >= 5) {
318 if (index != 255) {
319 unsigned off = (index - 1) / 8;
320
321 wvalue = p_str[off] | p_str[off + 1] << 8;
322 wvalue = (wvalue >> ((index - 1) % 8)) & kMask;
323
324 wvalue = booth_recode_w5(wvalue);
325
326 ecp_nistz256_select_w5(&h, table, wvalue >> 1);
327
328 ecp_nistz256_neg(tmp, h.Y);
329 copy_conditional(h.Y, tmp, (wvalue & 1));
330
331 ecp_nistz256_point_add(r, r, &h);
332 }
333
334 index -= kWindowSize;
335
336 ecp_nistz256_point_double(r, r);
337 ecp_nistz256_point_double(r, r);
338 ecp_nistz256_point_double(r, r);
339 ecp_nistz256_point_double(r, r);
340 ecp_nistz256_point_double(r, r);
341 }
342
343 /* Final window */
344 wvalue = p_str[0];
345 wvalue = (wvalue << 1) & kMask;
346
347 wvalue = booth_recode_w5(wvalue);
348
349 ecp_nistz256_select_w5(&h, table, wvalue >> 1);
350
351 ecp_nistz256_neg(tmp, h.Y);
352 copy_conditional(h.Y, tmp, wvalue & 1);
353
354 ecp_nistz256_point_add(r, r, &h);
355
356 ret = 1;
357
358 err:
359 if (ctx_started) {
360 BN_CTX_end(ctx);
361 }
362 BN_CTX_free(new_ctx);
363 return ret;
364 }
365
ecp_nistz256_points_mul(const EC_GROUP * group,EC_POINT * r,const BIGNUM * g_scalar,const EC_POINT * p_,const BIGNUM * p_scalar,BN_CTX * ctx)366 static int ecp_nistz256_points_mul(
367 const EC_GROUP *group, EC_POINT *r, const BIGNUM *g_scalar,
368 const EC_POINT *p_, const BIGNUM *p_scalar, BN_CTX *ctx) {
369 assert((p_ != NULL) == (p_scalar != NULL));
370
371 static const unsigned kWindowSize = 7;
372 static const unsigned kMask = (1 << (7 /* kWindowSize */ + 1)) - 1;
373
374 alignas(32) union {
375 P256_POINT p;
376 P256_POINT_AFFINE a;
377 } t, p;
378
379 int ret = 0;
380 BN_CTX *new_ctx = NULL;
381 int ctx_started = 0;
382
383 if (g_scalar != NULL) {
384 if (BN_num_bits(g_scalar) > 256 || BN_is_negative(g_scalar)) {
385 if (ctx == NULL) {
386 new_ctx = BN_CTX_new();
387 if (new_ctx == NULL) {
388 goto err;
389 }
390 ctx = new_ctx;
391 }
392 BN_CTX_start(ctx);
393 ctx_started = 1;
394 BIGNUM *tmp_scalar = BN_CTX_get(ctx);
395 if (tmp_scalar == NULL) {
396 goto err;
397 }
398
399 if (!BN_nnmod(tmp_scalar, g_scalar, &group->order, ctx)) {
400 OPENSSL_PUT_ERROR(EC, ERR_R_BN_LIB);
401 goto err;
402 }
403 g_scalar = tmp_scalar;
404 }
405
406 uint8_t p_str[33] = {0};
407 int i;
408 for (i = 0; i < g_scalar->top * BN_BYTES; i += BN_BYTES) {
409 BN_ULONG d = g_scalar->d[i / BN_BYTES];
410
411 p_str[i + 0] = d & 0xff;
412 p_str[i + 1] = (d >> 8) & 0xff;
413 p_str[i + 2] = (d >> 16) & 0xff;
414 p_str[i + 3] = (d >>= 24) & 0xff;
415 if (BN_BYTES == 8) {
416 d >>= 8;
417 p_str[i + 4] = d & 0xff;
418 p_str[i + 5] = (d >> 8) & 0xff;
419 p_str[i + 6] = (d >> 16) & 0xff;
420 p_str[i + 7] = (d >> 24) & 0xff;
421 }
422 }
423
424 for (; i < (int) sizeof(p_str); i++) {
425 p_str[i] = 0;
426 }
427
428 /* First window */
429 unsigned wvalue = (p_str[0] << 1) & kMask;
430 unsigned index = kWindowSize;
431
432 wvalue = booth_recode_w7(wvalue);
433
434 const PRECOMP256_ROW *const precomputed_table =
435 (const PRECOMP256_ROW *)ecp_nistz256_precomputed;
436 ecp_nistz256_select_w7(&p.a, precomputed_table[0], wvalue >> 1);
437
438 ecp_nistz256_neg(p.p.Z, p.p.Y);
439 copy_conditional(p.p.Y, p.p.Z, wvalue & 1);
440
441 /* Convert |p| from affine to Jacobian coordinates. We set Z to zero if |p|
442 * is infinity and |ONE| otherwise. |p| was computed from the table, so it
443 * is infinity iff |wvalue >> 1| is zero. */
444 OPENSSL_memset(p.p.Z, 0, sizeof(p.p.Z));
445 copy_conditional(p.p.Z, ONE, is_not_zero(wvalue >> 1));
446
447 for (i = 1; i < 37; i++) {
448 unsigned off = (index - 1) / 8;
449 wvalue = p_str[off] | p_str[off + 1] << 8;
450 wvalue = (wvalue >> ((index - 1) % 8)) & kMask;
451 index += kWindowSize;
452
453 wvalue = booth_recode_w7(wvalue);
454
455 ecp_nistz256_select_w7(&t.a, precomputed_table[i], wvalue >> 1);
456
457 ecp_nistz256_neg(t.p.Z, t.a.Y);
458 copy_conditional(t.a.Y, t.p.Z, wvalue & 1);
459
460 ecp_nistz256_point_add_affine(&p.p, &p.p, &t.a);
461 }
462 }
463
464 const int p_is_infinity = g_scalar == NULL;
465 if (p_scalar != NULL) {
466 P256_POINT *out = &t.p;
467 if (p_is_infinity) {
468 out = &p.p;
469 }
470
471 if (!ecp_nistz256_windowed_mul(group, out, p_, p_scalar, ctx)) {
472 goto err;
473 }
474
475 if (!p_is_infinity) {
476 ecp_nistz256_point_add(&p.p, &p.p, out);
477 }
478 }
479
480 /* Not constant-time, but we're only operating on the public output. */
481 if (!bn_set_words(&r->X, p.p.X, P256_LIMBS) ||
482 !bn_set_words(&r->Y, p.p.Y, P256_LIMBS) ||
483 !bn_set_words(&r->Z, p.p.Z, P256_LIMBS)) {
484 return 0;
485 }
486
487 ret = 1;
488
489 err:
490 if (ctx_started) {
491 BN_CTX_end(ctx);
492 }
493 BN_CTX_free(new_ctx);
494 return ret;
495 }
496
ecp_nistz256_get_affine(const EC_GROUP * group,const EC_POINT * point,BIGNUM * x,BIGNUM * y,BN_CTX * ctx)497 static int ecp_nistz256_get_affine(const EC_GROUP *group, const EC_POINT *point,
498 BIGNUM *x, BIGNUM *y, BN_CTX *ctx) {
499 BN_ULONG z_inv2[P256_LIMBS];
500 BN_ULONG z_inv3[P256_LIMBS];
501 BN_ULONG point_x[P256_LIMBS], point_y[P256_LIMBS], point_z[P256_LIMBS];
502
503 if (EC_POINT_is_at_infinity(group, point)) {
504 OPENSSL_PUT_ERROR(EC, EC_R_POINT_AT_INFINITY);
505 return 0;
506 }
507
508 if (!ecp_nistz256_bignum_to_field_elem(point_x, &point->X) ||
509 !ecp_nistz256_bignum_to_field_elem(point_y, &point->Y) ||
510 !ecp_nistz256_bignum_to_field_elem(point_z, &point->Z)) {
511 OPENSSL_PUT_ERROR(EC, EC_R_COORDINATES_OUT_OF_RANGE);
512 return 0;
513 }
514
515 ecp_nistz256_mod_inverse_mont(z_inv3, point_z);
516 ecp_nistz256_sqr_mont(z_inv2, z_inv3);
517
518 /* Instead of using |ecp_nistz256_from_mont| to convert the |x| coordinate
519 * and then calling |ecp_nistz256_from_mont| again to convert the |y|
520 * coordinate below, convert the common factor |z_inv2| once now, saving one
521 * reduction. */
522 ecp_nistz256_from_mont(z_inv2, z_inv2);
523
524 if (x != NULL) {
525 BN_ULONG x_aff[P256_LIMBS];
526 ecp_nistz256_mul_mont(x_aff, z_inv2, point_x);
527 if (!bn_set_words(x, x_aff, P256_LIMBS)) {
528 OPENSSL_PUT_ERROR(EC, ERR_R_MALLOC_FAILURE);
529 return 0;
530 }
531 }
532
533 if (y != NULL) {
534 BN_ULONG y_aff[P256_LIMBS];
535 ecp_nistz256_mul_mont(z_inv3, z_inv3, z_inv2);
536 ecp_nistz256_mul_mont(y_aff, z_inv3, point_y);
537 if (!bn_set_words(y, y_aff, P256_LIMBS)) {
538 OPENSSL_PUT_ERROR(EC, ERR_R_MALLOC_FAILURE);
539 return 0;
540 }
541 }
542
543 return 1;
544 }
545
546
547 const EC_METHOD EC_GFp_nistz256_method = {
548 ec_GFp_mont_group_init,
549 ec_GFp_mont_group_finish,
550 ec_GFp_mont_group_copy,
551 ec_GFp_mont_group_set_curve,
552 ecp_nistz256_get_affine,
553 ecp_nistz256_points_mul,
554 ec_GFp_mont_field_mul,
555 ec_GFp_mont_field_sqr,
556 ec_GFp_mont_field_encode,
557 ec_GFp_mont_field_decode,
558 };
559
560 #endif /* !defined(OPENSSL_NO_ASM) && defined(OPENSSL_X86_64) && \
561 !defined(OPENSSL_SMALL) */
562