1/*
2 * Copyright 2014-2018 The OpenSSL Project Authors. All Rights Reserved.
3 * Copyright (c) 2014, Intel Corporation. All Rights Reserved.
4 * Copyright (c) 2015, CloudFlare, Inc.
5 *
6 * Licensed under the Apache License 2.0 (the "License"). You may not use
7 * this file except in compliance with the License. You can obtain a copy
8 * in the file LICENSE in the source distribution or at
9 * https://www.openssl.org/source/license.html
10 *
11 * Originally written by Shay Gueron (1, 2), and Vlad Krasnov (1, 3)
12 * (1) Intel Corporation, Israel Development Center, Haifa, Israel
13 * (2) University of Haifa, Israel
14 * (3) CloudFlare, Inc.
15 *
16 * Reference:
17 * S.Gueron and V.Krasnov, "Fast Prime Field Elliptic Curve Cryptography with
18 * 256 Bit Primes"
19 */
20
21#include <string.h>
22
23#include "internal/cryptlib.h"
24#include "crypto/bn.h"
25#include "ec_local.h"
26#include "internal/refcount.h"
27
28#if BN_BITS2 != 64
29# define TOBN(hi,lo) lo,hi
30#else
31# define TOBN(hi,lo) ((BN_ULONG)hi<<32|lo)
32#endif
33
34#if defined(__GNUC__)
35# define ALIGN32 __attribute((aligned(32)))
36#elif defined(_MSC_VER)
37# define ALIGN32 __declspec(align(32))
38#else
39# define ALIGN32
40#endif
41
42#define ALIGNPTR(p,N) ((unsigned char *)p+N-(size_t)p%N)
43#define P256_LIMBS (256/BN_BITS2)
44
45typedef unsigned short u16;
46
47typedef struct {
48 BN_ULONG X[P256_LIMBS];
49 BN_ULONG Y[P256_LIMBS];
50 BN_ULONG Z[P256_LIMBS];
51} P256_POINT;
52
53typedef struct {
54 BN_ULONG X[P256_LIMBS];
55 BN_ULONG Y[P256_LIMBS];
56} P256_POINT_AFFINE;
57
58typedef P256_POINT_AFFINE PRECOMP256_ROW[64];
59
60/* structure for precomputed multiples of the generator */
61struct nistz256_pre_comp_st {
62 const EC_GROUP *group; /* Parent EC_GROUP object */
63 size_t w; /* Window size */
64 /*
65 * Constant time access to the X and Y coordinates of the pre-computed,
66 * generator multiplies, in the Montgomery domain. Pre-calculated
67 * multiplies are stored in affine form.
68 */
69 PRECOMP256_ROW *precomp;
70 void *precomp_storage;
71 CRYPTO_REF_COUNT references;
72 CRYPTO_RWLOCK *lock;
73};
74
75/* Functions implemented in assembly */
76/*
77 * Most of below mentioned functions *preserve* the property of inputs
78 * being fully reduced, i.e. being in [0, modulus) range. Simply put if
79 * inputs are fully reduced, then output is too. Note that reverse is
80 * not true, in sense that given partially reduced inputs output can be
81 * either, not unlikely reduced. And "most" in first sentence refers to
82 * the fact that given the calculations flow one can tolerate that
83 * addition, 1st function below, produces partially reduced result *if*
84 * multiplications by 2 and 3, which customarily use addition, fully
85 * reduce it. This effectively gives two options: a) addition produces
86 * fully reduced result [as long as inputs are, just like remaining
87 * functions]; b) addition is allowed to produce partially reduced
88 * result, but multiplications by 2 and 3 perform additional reduction
89 * step. Choice between the two can be platform-specific, but it was a)
90 * in all cases so far...
91 */
92/* Modular add: res = a+b mod P */
93void ecp_nistz256_add(BN_ULONG res[P256_LIMBS],
94 const BN_ULONG a[P256_LIMBS],
95 const BN_ULONG b[P256_LIMBS]);
96/* Modular mul by 2: res = 2*a mod P */
97void ecp_nistz256_mul_by_2(BN_ULONG res[P256_LIMBS],
98 const BN_ULONG a[P256_LIMBS]);
99/* Modular mul by 3: res = 3*a mod P */
100void ecp_nistz256_mul_by_3(BN_ULONG res[P256_LIMBS],
101 const BN_ULONG a[P256_LIMBS]);
102
103/* Modular div by 2: res = a/2 mod P */
104void ecp_nistz256_div_by_2(BN_ULONG res[P256_LIMBS],
105 const BN_ULONG a[P256_LIMBS]);
106/* Modular sub: res = a-b mod P */
107void ecp_nistz256_sub(BN_ULONG res[P256_LIMBS],
108 const BN_ULONG a[P256_LIMBS],
109 const BN_ULONG b[P256_LIMBS]);
110/* Modular neg: res = -a mod P */
111void ecp_nistz256_neg(BN_ULONG res[P256_LIMBS], const BN_ULONG a[P256_LIMBS]);
112/* Montgomery mul: res = a*b*2^-256 mod P */
113void ecp_nistz256_mul_mont(BN_ULONG res[P256_LIMBS],
114 const BN_ULONG a[P256_LIMBS],
115 const BN_ULONG b[P256_LIMBS]);
116/* Montgomery sqr: res = a*a*2^-256 mod P */
117void ecp_nistz256_sqr_mont(BN_ULONG res[P256_LIMBS],
118 const BN_ULONG a[P256_LIMBS]);
119/* Convert a number from Montgomery domain, by multiplying with 1 */
120void ecp_nistz256_from_mont(BN_ULONG res[P256_LIMBS],
121 const BN_ULONG in[P256_LIMBS]);
122/* Convert a number to Montgomery domain, by multiplying with 2^512 mod P*/
123void ecp_nistz256_to_mont(BN_ULONG res[P256_LIMBS],
124 const BN_ULONG in[P256_LIMBS]);
125/* Functions that perform constant time access to the precomputed tables */
126void ecp_nistz256_scatter_w5(P256_POINT *val,
127 const P256_POINT *in_t, int idx);
128void ecp_nistz256_gather_w5(P256_POINT *val,
129 const P256_POINT *in_t, int idx);
130void ecp_nistz256_scatter_w7(P256_POINT_AFFINE *val,
131 const P256_POINT_AFFINE *in_t, int idx);
132void ecp_nistz256_gather_w7(P256_POINT_AFFINE *val,
133 const P256_POINT_AFFINE *in_t, int idx);
134
135/* One converted into the Montgomery domain */
136static const BN_ULONG ONE[P256_LIMBS] = {
137 TOBN(0x00000000, 0x00000001), TOBN(0xffffffff, 0x00000000),
138 TOBN(0xffffffff, 0xffffffff), TOBN(0x00000000, 0xfffffffe)
139};
140
141static NISTZ256_PRE_COMP *ecp_nistz256_pre_comp_new(const EC_GROUP *group);
142
143/* Precomputed tables for the default generator */
144extern const PRECOMP256_ROW ecp_nistz256_precomputed[37];
145
146/* Recode window to a signed digit, see ecp_nistputil.c for details */
147static unsigned int _booth_recode_w5(unsigned int in)
148{
149 unsigned int s, d;
150
151 s = ~((in >> 5) - 1);
152 d = (1 << 6) - in - 1;
153 d = (d & s) | (in & ~s);
154 d = (d >> 1) + (d & 1);
155
156 return (d << 1) + (s & 1);
157}
158
159static unsigned int _booth_recode_w7(unsigned int in)
160{
161 unsigned int s, d;
162
163 s = ~((in >> 7) - 1);
164 d = (1 << 8) - in - 1;
165 d = (d & s) | (in & ~s);
166 d = (d >> 1) + (d & 1);
167
168 return (d << 1) + (s & 1);
169}
170
171static void copy_conditional(BN_ULONG dst[P256_LIMBS],
172 const BN_ULONG src[P256_LIMBS], BN_ULONG move)
173{
174 BN_ULONG mask1 = 0-move;
175 BN_ULONG mask2 = ~mask1;
176
177 dst[0] = (src[0] & mask1) ^ (dst[0] & mask2);
178 dst[1] = (src[1] & mask1) ^ (dst[1] & mask2);
179 dst[2] = (src[2] & mask1) ^ (dst[2] & mask2);
180 dst[3] = (src[3] & mask1) ^ (dst[3] & mask2);
181 if (P256_LIMBS == 8) {
182 dst[4] = (src[4] & mask1) ^ (dst[4] & mask2);
183 dst[5] = (src[5] & mask1) ^ (dst[5] & mask2);
184 dst[6] = (src[6] & mask1) ^ (dst[6] & mask2);
185 dst[7] = (src[7] & mask1) ^ (dst[7] & mask2);
186 }
187}
188
189static BN_ULONG is_zero(BN_ULONG in)
190{
191 in |= (0 - in);
192 in = ~in;
193 in >>= BN_BITS2 - 1;
194 return in;
195}
196
197static BN_ULONG is_equal(const BN_ULONG a[P256_LIMBS],
198 const BN_ULONG b[P256_LIMBS])
199{
200 BN_ULONG res;
201
202 res = a[0] ^ b[0];
203 res |= a[1] ^ b[1];
204 res |= a[2] ^ b[2];
205 res |= a[3] ^ b[3];
206 if (P256_LIMBS == 8) {
207 res |= a[4] ^ b[4];
208 res |= a[5] ^ b[5];
209 res |= a[6] ^ b[6];
210 res |= a[7] ^ b[7];
211 }
212
213 return is_zero(res);
214}
215
216static BN_ULONG is_one(const BIGNUM *z)
217{
218 BN_ULONG res = 0;
219 BN_ULONG *a = bn_get_words(z);
220
221 if (bn_get_top(z) == (P256_LIMBS - P256_LIMBS / 8)) {
222 res = a[0] ^ ONE[0];
223 res |= a[1] ^ ONE[1];
224 res |= a[2] ^ ONE[2];
225 res |= a[3] ^ ONE[3];
226 if (P256_LIMBS == 8) {
227 res |= a[4] ^ ONE[4];
228 res |= a[5] ^ ONE[5];
229 res |= a[6] ^ ONE[6];
230 /*
231 * no check for a[7] (being zero) on 32-bit platforms,
232 * because value of "one" takes only 7 limbs.
233 */
234 }
235 res = is_zero(res);
236 }
237
238 return res;
239}
240
241/*
242 * For reference, this macro is used only when new ecp_nistz256 assembly
243 * module is being developed. For example, configure with
244 * -DECP_NISTZ256_REFERENCE_IMPLEMENTATION and implement only functions
245 * performing simplest arithmetic operations on 256-bit vectors. Then
246 * work on implementation of higher-level functions performing point
247 * operations. Then remove ECP_NISTZ256_REFERENCE_IMPLEMENTATION
248 * and never define it again. (The correct macro denoting presence of
249 * ecp_nistz256 module is ECP_NISTZ256_ASM.)
250 */
251#ifndef ECP_NISTZ256_REFERENCE_IMPLEMENTATION
252void ecp_nistz256_point_double(P256_POINT *r, const P256_POINT *a);
253void ecp_nistz256_point_add(P256_POINT *r,
254 const P256_POINT *a, const P256_POINT *b);
255void ecp_nistz256_point_add_affine(P256_POINT *r,
256 const P256_POINT *a,
257 const P256_POINT_AFFINE *b);
258#else
259/* Point double: r = 2*a */
260static void ecp_nistz256_point_double(P256_POINT *r, const P256_POINT *a)
261{
262 BN_ULONG S[P256_LIMBS];
263 BN_ULONG M[P256_LIMBS];
264 BN_ULONG Zsqr[P256_LIMBS];
265 BN_ULONG tmp0[P256_LIMBS];
266
267 const BN_ULONG *in_x = a->X;
268 const BN_ULONG *in_y = a->Y;
269 const BN_ULONG *in_z = a->Z;
270
271 BN_ULONG *res_x = r->X;
272 BN_ULONG *res_y = r->Y;
273 BN_ULONG *res_z = r->Z;
274
275 ecp_nistz256_mul_by_2(S, in_y);
276
277 ecp_nistz256_sqr_mont(Zsqr, in_z);
278
279 ecp_nistz256_sqr_mont(S, S);
280
281 ecp_nistz256_mul_mont(res_z, in_z, in_y);
282 ecp_nistz256_mul_by_2(res_z, res_z);
283
284 ecp_nistz256_add(M, in_x, Zsqr);
285 ecp_nistz256_sub(Zsqr, in_x, Zsqr);
286
287 ecp_nistz256_sqr_mont(res_y, S);
288 ecp_nistz256_div_by_2(res_y, res_y);
289
290 ecp_nistz256_mul_mont(M, M, Zsqr);
291 ecp_nistz256_mul_by_3(M, M);
292
293 ecp_nistz256_mul_mont(S, S, in_x);
294 ecp_nistz256_mul_by_2(tmp0, S);
295
296 ecp_nistz256_sqr_mont(res_x, M);
297
298 ecp_nistz256_sub(res_x, res_x, tmp0);
299 ecp_nistz256_sub(S, S, res_x);
300
301 ecp_nistz256_mul_mont(S, S, M);
302 ecp_nistz256_sub(res_y, S, res_y);
303}
304
305/* Point addition: r = a+b */
306static void ecp_nistz256_point_add(P256_POINT *r,
307 const P256_POINT *a, const P256_POINT *b)
308{
309 BN_ULONG U2[P256_LIMBS], S2[P256_LIMBS];
310 BN_ULONG U1[P256_LIMBS], S1[P256_LIMBS];
311 BN_ULONG Z1sqr[P256_LIMBS];
312 BN_ULONG Z2sqr[P256_LIMBS];
313 BN_ULONG H[P256_LIMBS], R[P256_LIMBS];
314 BN_ULONG Hsqr[P256_LIMBS];
315 BN_ULONG Rsqr[P256_LIMBS];
316 BN_ULONG Hcub[P256_LIMBS];
317
318 BN_ULONG res_x[P256_LIMBS];
319 BN_ULONG res_y[P256_LIMBS];
320 BN_ULONG res_z[P256_LIMBS];
321
322 BN_ULONG in1infty, in2infty;
323
324 const BN_ULONG *in1_x = a->X;
325 const BN_ULONG *in1_y = a->Y;
326 const BN_ULONG *in1_z = a->Z;
327
328 const BN_ULONG *in2_x = b->X;
329 const BN_ULONG *in2_y = b->Y;
330 const BN_ULONG *in2_z = b->Z;
331
332 /*
333 * Infinity in encoded as (,,0)
334 */
335 in1infty = (in1_z[0] | in1_z[1] | in1_z[2] | in1_z[3]);
336 if (P256_LIMBS == 8)
337 in1infty |= (in1_z[4] | in1_z[5] | in1_z[6] | in1_z[7]);
338
339 in2infty = (in2_z[0] | in2_z[1] | in2_z[2] | in2_z[3]);
340 if (P256_LIMBS == 8)
341 in2infty |= (in2_z[4] | in2_z[5] | in2_z[6] | in2_z[7]);
342
343 in1infty = is_zero(in1infty);
344 in2infty = is_zero(in2infty);
345
346 ecp_nistz256_sqr_mont(Z2sqr, in2_z); /* Z2^2 */
347 ecp_nistz256_sqr_mont(Z1sqr, in1_z); /* Z1^2 */
348
349 ecp_nistz256_mul_mont(S1, Z2sqr, in2_z); /* S1 = Z2^3 */
350 ecp_nistz256_mul_mont(S2, Z1sqr, in1_z); /* S2 = Z1^3 */
351
352 ecp_nistz256_mul_mont(S1, S1, in1_y); /* S1 = Y1*Z2^3 */
353 ecp_nistz256_mul_mont(S2, S2, in2_y); /* S2 = Y2*Z1^3 */
354 ecp_nistz256_sub(R, S2, S1); /* R = S2 - S1 */
355
356 ecp_nistz256_mul_mont(U1, in1_x, Z2sqr); /* U1 = X1*Z2^2 */
357 ecp_nistz256_mul_mont(U2, in2_x, Z1sqr); /* U2 = X2*Z1^2 */
358 ecp_nistz256_sub(H, U2, U1); /* H = U2 - U1 */
359
360 /*
361 * This should not happen during sign/ecdh, so no constant time violation
362 */
363 if (is_equal(U1, U2) && !in1infty && !in2infty) {
364 if (is_equal(S1, S2)) {
365 ecp_nistz256_point_double(r, a);
366 return;
367 } else {
368 memset(r, 0, sizeof(*r));
369 return;
370 }
371 }
372
373 ecp_nistz256_sqr_mont(Rsqr, R); /* R^2 */
374 ecp_nistz256_mul_mont(res_z, H, in1_z); /* Z3 = H*Z1*Z2 */
375 ecp_nistz256_sqr_mont(Hsqr, H); /* H^2 */
376 ecp_nistz256_mul_mont(res_z, res_z, in2_z); /* Z3 = H*Z1*Z2 */
377 ecp_nistz256_mul_mont(Hcub, Hsqr, H); /* H^3 */
378
379 ecp_nistz256_mul_mont(U2, U1, Hsqr); /* U1*H^2 */
380 ecp_nistz256_mul_by_2(Hsqr, U2); /* 2*U1*H^2 */
381
382 ecp_nistz256_sub(res_x, Rsqr, Hsqr);
383 ecp_nistz256_sub(res_x, res_x, Hcub);
384
385 ecp_nistz256_sub(res_y, U2, res_x);
386
387 ecp_nistz256_mul_mont(S2, S1, Hcub);
388 ecp_nistz256_mul_mont(res_y, R, res_y);
389 ecp_nistz256_sub(res_y, res_y, S2);
390
391 copy_conditional(res_x, in2_x, in1infty);
392 copy_conditional(res_y, in2_y, in1infty);
393 copy_conditional(res_z, in2_z, in1infty);
394
395 copy_conditional(res_x, in1_x, in2infty);
396 copy_conditional(res_y, in1_y, in2infty);
397 copy_conditional(res_z, in1_z, in2infty);
398
399 memcpy(r->X, res_x, sizeof(res_x));
400 memcpy(r->Y, res_y, sizeof(res_y));
401 memcpy(r->Z, res_z, sizeof(res_z));
402}
403
404/* Point addition when b is known to be affine: r = a+b */
405static void ecp_nistz256_point_add_affine(P256_POINT *r,
406 const P256_POINT *a,
407 const P256_POINT_AFFINE *b)
408{
409 BN_ULONG U2[P256_LIMBS], S2[P256_LIMBS];
410 BN_ULONG Z1sqr[P256_LIMBS];
411 BN_ULONG H[P256_LIMBS], R[P256_LIMBS];
412 BN_ULONG Hsqr[P256_LIMBS];
413 BN_ULONG Rsqr[P256_LIMBS];
414 BN_ULONG Hcub[P256_LIMBS];
415
416 BN_ULONG res_x[P256_LIMBS];
417 BN_ULONG res_y[P256_LIMBS];
418 BN_ULONG res_z[P256_LIMBS];
419
420 BN_ULONG in1infty, in2infty;
421
422 const BN_ULONG *in1_x = a->X;
423 const BN_ULONG *in1_y = a->Y;
424 const BN_ULONG *in1_z = a->Z;
425
426 const BN_ULONG *in2_x = b->X;
427 const BN_ULONG *in2_y = b->Y;
428
429 /*
430 * Infinity in encoded as (,,0)
431 */
432 in1infty = (in1_z[0] | in1_z[1] | in1_z[2] | in1_z[3]);
433 if (P256_LIMBS == 8)
434 in1infty |= (in1_z[4] | in1_z[5] | in1_z[6] | in1_z[7]);
435
436 /*
437 * In affine representation we encode infinity as (0,0), which is
438 * not on the curve, so it is OK
439 */
440 in2infty = (in2_x[0] | in2_x[1] | in2_x[2] | in2_x[3] |
441 in2_y[0] | in2_y[1] | in2_y[2] | in2_y[3]);
442 if (P256_LIMBS == 8)
443 in2infty |= (in2_x[4] | in2_x[5] | in2_x[6] | in2_x[7] |
444 in2_y[4] | in2_y[5] | in2_y[6] | in2_y[7]);
445
446 in1infty = is_zero(in1infty);
447 in2infty = is_zero(in2infty);
448
449 ecp_nistz256_sqr_mont(Z1sqr, in1_z); /* Z1^2 */
450
451 ecp_nistz256_mul_mont(U2, in2_x, Z1sqr); /* U2 = X2*Z1^2 */
452 ecp_nistz256_sub(H, U2, in1_x); /* H = U2 - U1 */
453
454 ecp_nistz256_mul_mont(S2, Z1sqr, in1_z); /* S2 = Z1^3 */
455
456 ecp_nistz256_mul_mont(res_z, H, in1_z); /* Z3 = H*Z1*Z2 */
457
458 ecp_nistz256_mul_mont(S2, S2, in2_y); /* S2 = Y2*Z1^3 */
459 ecp_nistz256_sub(R, S2, in1_y); /* R = S2 - S1 */
460
461 ecp_nistz256_sqr_mont(Hsqr, H); /* H^2 */
462 ecp_nistz256_sqr_mont(Rsqr, R); /* R^2 */
463 ecp_nistz256_mul_mont(Hcub, Hsqr, H); /* H^3 */
464
465 ecp_nistz256_mul_mont(U2, in1_x, Hsqr); /* U1*H^2 */
466 ecp_nistz256_mul_by_2(Hsqr, U2); /* 2*U1*H^2 */
467
468 ecp_nistz256_sub(res_x, Rsqr, Hsqr);
469 ecp_nistz256_sub(res_x, res_x, Hcub);
470 ecp_nistz256_sub(H, U2, res_x);
471
472 ecp_nistz256_mul_mont(S2, in1_y, Hcub);
473 ecp_nistz256_mul_mont(H, H, R);
474 ecp_nistz256_sub(res_y, H, S2);
475
476 copy_conditional(res_x, in2_x, in1infty);
477 copy_conditional(res_x, in1_x, in2infty);
478
479 copy_conditional(res_y, in2_y, in1infty);
480 copy_conditional(res_y, in1_y, in2infty);
481
482 copy_conditional(res_z, ONE, in1infty);
483 copy_conditional(res_z, in1_z, in2infty);
484
485 memcpy(r->X, res_x, sizeof(res_x));
486 memcpy(r->Y, res_y, sizeof(res_y));
487 memcpy(r->Z, res_z, sizeof(res_z));
488}
489#endif
490
491/* r = in^-1 mod p */
492static void ecp_nistz256_mod_inverse(BN_ULONG r[P256_LIMBS],
493 const BN_ULONG in[P256_LIMBS])
494{
495 /*
496 * The poly is ffffffff 00000001 00000000 00000000 00000000 ffffffff
497 * ffffffff ffffffff We use FLT and used poly-2 as exponent
498 */
499 BN_ULONG p2[P256_LIMBS];
500 BN_ULONG p4[P256_LIMBS];
501 BN_ULONG p8[P256_LIMBS];
502 BN_ULONG p16[P256_LIMBS];
503 BN_ULONG p32[P256_LIMBS];
504 BN_ULONG res[P256_LIMBS];
505 int i;
506
507 ecp_nistz256_sqr_mont(res, in);
508 ecp_nistz256_mul_mont(p2, res, in); /* 3*p */
509
510 ecp_nistz256_sqr_mont(res, p2);
511 ecp_nistz256_sqr_mont(res, res);
512 ecp_nistz256_mul_mont(p4, res, p2); /* f*p */
513
514 ecp_nistz256_sqr_mont(res, p4);
515 ecp_nistz256_sqr_mont(res, res);
516 ecp_nistz256_sqr_mont(res, res);
517 ecp_nistz256_sqr_mont(res, res);
518 ecp_nistz256_mul_mont(p8, res, p4); /* ff*p */
519
520 ecp_nistz256_sqr_mont(res, p8);
521 for (i = 0; i < 7; i++)
522 ecp_nistz256_sqr_mont(res, res);
523 ecp_nistz256_mul_mont(p16, res, p8); /* ffff*p */
524
525 ecp_nistz256_sqr_mont(res, p16);
526 for (i = 0; i < 15; i++)
527 ecp_nistz256_sqr_mont(res, res);
528 ecp_nistz256_mul_mont(p32, res, p16); /* ffffffff*p */
529
530 ecp_nistz256_sqr_mont(res, p32);
531 for (i = 0; i < 31; i++)
532 ecp_nistz256_sqr_mont(res, res);
533 ecp_nistz256_mul_mont(res, res, in);
534
535 for (i = 0; i < 32 * 4; i++)
536 ecp_nistz256_sqr_mont(res, res);
537 ecp_nistz256_mul_mont(res, res, p32);
538
539 for (i = 0; i < 32; i++)
540 ecp_nistz256_sqr_mont(res, res);
541 ecp_nistz256_mul_mont(res, res, p32);
542
543 for (i = 0; i < 16; i++)
544 ecp_nistz256_sqr_mont(res, res);
545 ecp_nistz256_mul_mont(res, res, p16);
546
547 for (i = 0; i < 8; i++)
548 ecp_nistz256_sqr_mont(res, res);
549 ecp_nistz256_mul_mont(res, res, p8);
550
551 ecp_nistz256_sqr_mont(res, res);
552 ecp_nistz256_sqr_mont(res, res);
553 ecp_nistz256_sqr_mont(res, res);
554 ecp_nistz256_sqr_mont(res, res);
555 ecp_nistz256_mul_mont(res, res, p4);
556
557 ecp_nistz256_sqr_mont(res, res);
558 ecp_nistz256_sqr_mont(res, res);
559 ecp_nistz256_mul_mont(res, res, p2);
560
561 ecp_nistz256_sqr_mont(res, res);
562 ecp_nistz256_sqr_mont(res, res);
563 ecp_nistz256_mul_mont(res, res, in);
564
565 memcpy(r, res, sizeof(res));
566}
567
568/*
569 * ecp_nistz256_bignum_to_field_elem copies the contents of |in| to |out| and
570 * returns one if it fits. Otherwise it returns zero.
571 */
572__owur static int ecp_nistz256_bignum_to_field_elem(BN_ULONG out[P256_LIMBS],
573 const BIGNUM *in)
574{
575 return bn_copy_words(out, in, P256_LIMBS);
576}
577
578/* r = sum(scalar[i]*point[i]) */
579__owur static int ecp_nistz256_windowed_mul(const EC_GROUP *group,
580 P256_POINT *r,
581 const BIGNUM **scalar,
582 const EC_POINT **point,
583 size_t num, BN_CTX *ctx)
584{
585 size_t i;
586 int j, ret = 0;
587 unsigned int idx;
588 unsigned char (*p_str)[33] = NULL;
589 const unsigned int window_size = 5;
590 const unsigned int mask = (1 << (window_size + 1)) - 1;
591 unsigned int wvalue;
592 P256_POINT *temp; /* place for 5 temporary points */
593 const BIGNUM **scalars = NULL;
594 P256_POINT (*table)[16] = NULL;
595 void *table_storage = NULL;
596
597 if ((num * 16 + 6) > OPENSSL_MALLOC_MAX_NELEMS(P256_POINT)
598 || (table_storage =
599 OPENSSL_malloc((num * 16 + 5) * sizeof(P256_POINT) + 64)) == NULL
600 || (p_str =
601 OPENSSL_malloc(num * 33 * sizeof(unsigned char))) == NULL
602 || (scalars = OPENSSL_malloc(num * sizeof(BIGNUM *))) == NULL) {
603 ECerr(EC_F_ECP_NISTZ256_WINDOWED_MUL, ERR_R_MALLOC_FAILURE);
604 goto err;
605 }
606
607 table = (void *)ALIGNPTR(table_storage, 64);
608 temp = (P256_POINT *)(table + num);
609
610 for (i = 0; i < num; i++) {
611 P256_POINT *row = table[i];
612
613 /* This is an unusual input, we don't guarantee constant-timeness. */
614 if ((BN_num_bits(scalar[i]) > 256) || BN_is_negative(scalar[i])) {
615 BIGNUM *mod;
616
617 if ((mod = BN_CTX_get(ctx)) == NULL)
618 goto err;
619 if (!BN_nnmod(mod, scalar[i], group->order, ctx)) {
620 ECerr(EC_F_ECP_NISTZ256_WINDOWED_MUL, ERR_R_BN_LIB);
621 goto err;
622 }
623 scalars[i] = mod;
624 } else
625 scalars[i] = scalar[i];
626
627 for (j = 0; j < bn_get_top(scalars[i]) * BN_BYTES; j += BN_BYTES) {
628 BN_ULONG d = bn_get_words(scalars[i])[j / BN_BYTES];
629
630 p_str[i][j + 0] = (unsigned char)d;
631 p_str[i][j + 1] = (unsigned char)(d >> 8);
632 p_str[i][j + 2] = (unsigned char)(d >> 16);
633 p_str[i][j + 3] = (unsigned char)(d >>= 24);
634 if (BN_BYTES == 8) {
635 d >>= 8;
636 p_str[i][j + 4] = (unsigned char)d;
637 p_str[i][j + 5] = (unsigned char)(d >> 8);
638 p_str[i][j + 6] = (unsigned char)(d >> 16);
639 p_str[i][j + 7] = (unsigned char)(d >> 24);
640 }
641 }
642 for (; j < 33; j++)
643 p_str[i][j] = 0;
644
645 if (!ecp_nistz256_bignum_to_field_elem(temp[0].X, point[i]->X)
646 || !ecp_nistz256_bignum_to_field_elem(temp[0].Y, point[i]->Y)
647 || !ecp_nistz256_bignum_to_field_elem(temp[0].Z, point[i]->Z)) {
648 ECerr(EC_F_ECP_NISTZ256_WINDOWED_MUL,
649 EC_R_COORDINATES_OUT_OF_RANGE);
650 goto err;
651 }
652
653 /*
654 * row[0] is implicitly (0,0,0) (the point at infinity), therefore it
655 * is not stored. All other values are actually stored with an offset
656 * of -1 in table.
657 */
658
659 ecp_nistz256_scatter_w5 (row, &temp[0], 1);
660 ecp_nistz256_point_double(&temp[1], &temp[0]); /*1+1=2 */
661 ecp_nistz256_scatter_w5 (row, &temp[1], 2);
662 ecp_nistz256_point_add (&temp[2], &temp[1], &temp[0]); /*2+1=3 */
663 ecp_nistz256_scatter_w5 (row, &temp[2], 3);
664 ecp_nistz256_point_double(&temp[1], &temp[1]); /*2*2=4 */
665 ecp_nistz256_scatter_w5 (row, &temp[1], 4);
666 ecp_nistz256_point_double(&temp[2], &temp[2]); /*2*3=6 */
667 ecp_nistz256_scatter_w5 (row, &temp[2], 6);
668 ecp_nistz256_point_add (&temp[3], &temp[1], &temp[0]); /*4+1=5 */
669 ecp_nistz256_scatter_w5 (row, &temp[3], 5);
670 ecp_nistz256_point_add (&temp[4], &temp[2], &temp[0]); /*6+1=7 */
671 ecp_nistz256_scatter_w5 (row, &temp[4], 7);
672 ecp_nistz256_point_double(&temp[1], &temp[1]); /*2*4=8 */
673 ecp_nistz256_scatter_w5 (row, &temp[1], 8);
674 ecp_nistz256_point_double(&temp[2], &temp[2]); /*2*6=12 */
675 ecp_nistz256_scatter_w5 (row, &temp[2], 12);
676 ecp_nistz256_point_double(&temp[3], &temp[3]); /*2*5=10 */
677 ecp_nistz256_scatter_w5 (row, &temp[3], 10);
678 ecp_nistz256_point_double(&temp[4], &temp[4]); /*2*7=14 */
679 ecp_nistz256_scatter_w5 (row, &temp[4], 14);
680 ecp_nistz256_point_add (&temp[2], &temp[2], &temp[0]); /*12+1=13*/
681 ecp_nistz256_scatter_w5 (row, &temp[2], 13);
682 ecp_nistz256_point_add (&temp[3], &temp[3], &temp[0]); /*10+1=11*/
683 ecp_nistz256_scatter_w5 (row, &temp[3], 11);
684 ecp_nistz256_point_add (&temp[4], &temp[4], &temp[0]); /*14+1=15*/
685 ecp_nistz256_scatter_w5 (row, &temp[4], 15);
686 ecp_nistz256_point_add (&temp[2], &temp[1], &temp[0]); /*8+1=9 */
687 ecp_nistz256_scatter_w5 (row, &temp[2], 9);
688 ecp_nistz256_point_double(&temp[1], &temp[1]); /*2*8=16 */
689 ecp_nistz256_scatter_w5 (row, &temp[1], 16);
690 }
691
692 idx = 255;
693
694 wvalue = p_str[0][(idx - 1) / 8];
695 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
696
697 /*
698 * We gather to temp[0], because we know it's position relative
699 * to table
700 */
701 ecp_nistz256_gather_w5(&temp[0], table[0], _booth_recode_w5(wvalue) >> 1);
702 memcpy(r, &temp[0], sizeof(temp[0]));
703
704 while (idx >= 5) {
705 for (i = (idx == 255 ? 1 : 0); i < num; i++) {
706 unsigned int off = (idx - 1) / 8;
707
708 wvalue = p_str[i][off] | p_str[i][off + 1] << 8;
709 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
710
711 wvalue = _booth_recode_w5(wvalue);
712
713 ecp_nistz256_gather_w5(&temp[0], table[i], wvalue >> 1);
714
715 ecp_nistz256_neg(temp[1].Y, temp[0].Y);
716 copy_conditional(temp[0].Y, temp[1].Y, (wvalue & 1));
717
718 ecp_nistz256_point_add(r, r, &temp[0]);
719 }
720
721 idx -= window_size;
722
723 ecp_nistz256_point_double(r, r);
724 ecp_nistz256_point_double(r, r);
725 ecp_nistz256_point_double(r, r);
726 ecp_nistz256_point_double(r, r);
727 ecp_nistz256_point_double(r, r);
728 }
729
730 /* Final window */
731 for (i = 0; i < num; i++) {
732 wvalue = p_str[i][0];
733 wvalue = (wvalue << 1) & mask;
734
735 wvalue = _booth_recode_w5(wvalue);
736
737 ecp_nistz256_gather_w5(&temp[0], table[i], wvalue >> 1);
738
739 ecp_nistz256_neg(temp[1].Y, temp[0].Y);
740 copy_conditional(temp[0].Y, temp[1].Y, wvalue & 1);
741
742 ecp_nistz256_point_add(r, r, &temp[0]);
743 }
744
745 ret = 1;
746 err:
747 OPENSSL_free(table_storage);
748 OPENSSL_free(p_str);
749 OPENSSL_free(scalars);
750 return ret;
751}
752
753/* Coordinates of G, for which we have precomputed tables */
754static const BN_ULONG def_xG[P256_LIMBS] = {
755 TOBN(0x79e730d4, 0x18a9143c), TOBN(0x75ba95fc, 0x5fedb601),
756 TOBN(0x79fb732b, 0x77622510), TOBN(0x18905f76, 0xa53755c6)
757};
758
759static const BN_ULONG def_yG[P256_LIMBS] = {
760 TOBN(0xddf25357, 0xce95560a), TOBN(0x8b4ab8e4, 0xba19e45c),
761 TOBN(0xd2e88688, 0xdd21f325), TOBN(0x8571ff18, 0x25885d85)
762};
763
764/*
765 * ecp_nistz256_is_affine_G returns one if |generator| is the standard, P-256
766 * generator.
767 */
768static int ecp_nistz256_is_affine_G(const EC_POINT *generator)
769{
770 return (bn_get_top(generator->X) == P256_LIMBS) &&
771 (bn_get_top(generator->Y) == P256_LIMBS) &&
772 is_equal(bn_get_words(generator->X), def_xG) &&
773 is_equal(bn_get_words(generator->Y), def_yG) &&
774 is_one(generator->Z);
775}
776
777__owur static int ecp_nistz256_mult_precompute(EC_GROUP *group, BN_CTX *ctx)
778{
779 /*
780 * We precompute a table for a Booth encoded exponent (wNAF) based
781 * computation. Each table holds 64 values for safe access, with an
782 * implicit value of infinity at index zero. We use window of size 7, and
783 * therefore require ceil(256/7) = 37 tables.
784 */
785 const BIGNUM *order;
786 EC_POINT *P = NULL, *T = NULL;
787 const EC_POINT *generator;
788 NISTZ256_PRE_COMP *pre_comp;
789 BN_CTX *new_ctx = NULL;
790 int i, j, k, ret = 0;
791 size_t w;
792
793 PRECOMP256_ROW *preComputedTable = NULL;
794 unsigned char *precomp_storage = NULL;
795
796 /* if there is an old NISTZ256_PRE_COMP object, throw it away */
797 EC_pre_comp_free(group);
798 generator = EC_GROUP_get0_generator(group);
799 if (generator == NULL) {
800 ECerr(EC_F_ECP_NISTZ256_MULT_PRECOMPUTE, EC_R_UNDEFINED_GENERATOR);
801 return 0;
802 }
803
804 if (ecp_nistz256_is_affine_G(generator)) {
805 /*
806 * No need to calculate tables for the standard generator because we
807 * have them statically.
808 */
809 return 1;
810 }
811
812 if ((pre_comp = ecp_nistz256_pre_comp_new(group)) == NULL)
813 return 0;
814
815 if (ctx == NULL) {
816 ctx = new_ctx = BN_CTX_new_ex(group->libctx);
817 if (ctx == NULL)
818 goto err;
819 }
820
821 BN_CTX_start(ctx);
822
823 order = EC_GROUP_get0_order(group);
824 if (order == NULL)
825 goto err;
826
827 if (BN_is_zero(order)) {
828 ECerr(EC_F_ECP_NISTZ256_MULT_PRECOMPUTE, EC_R_UNKNOWN_ORDER);
829 goto err;
830 }
831
832 w = 7;
833
834 if ((precomp_storage =
835 OPENSSL_malloc(37 * 64 * sizeof(P256_POINT_AFFINE) + 64)) == NULL) {
836 ECerr(EC_F_ECP_NISTZ256_MULT_PRECOMPUTE, ERR_R_MALLOC_FAILURE);
837 goto err;
838 }
839
840 preComputedTable = (void *)ALIGNPTR(precomp_storage, 64);
841
842 P = EC_POINT_new(group);
843 T = EC_POINT_new(group);
844 if (P == NULL || T == NULL)
845 goto err;
846
847 /*
848 * The zero entry is implicitly infinity, and we skip it, storing other
849 * values with -1 offset.
850 */
851 if (!EC_POINT_copy(T, generator))
852 goto err;
853
854 for (k = 0; k < 64; k++) {
855 if (!EC_POINT_copy(P, T))
856 goto err;
857 for (j = 0; j < 37; j++) {
858 P256_POINT_AFFINE temp;
859 /*
860 * It would be faster to use EC_POINTs_make_affine and
861 * make multiple points affine at the same time.
862 */
863 if (!EC_POINT_make_affine(group, P, ctx))
864 goto err;
865 if (!ecp_nistz256_bignum_to_field_elem(temp.X, P->X) ||
866 !ecp_nistz256_bignum_to_field_elem(temp.Y, P->Y)) {
867 ECerr(EC_F_ECP_NISTZ256_MULT_PRECOMPUTE,
868 EC_R_COORDINATES_OUT_OF_RANGE);
869 goto err;
870 }
871 ecp_nistz256_scatter_w7(preComputedTable[j], &temp, k);
872 for (i = 0; i < 7; i++) {
873 if (!EC_POINT_dbl(group, P, P, ctx))
874 goto err;
875 }
876 }
877 if (!EC_POINT_add(group, T, T, generator, ctx))
878 goto err;
879 }
880
881 pre_comp->group = group;
882 pre_comp->w = w;
883 pre_comp->precomp = preComputedTable;
884 pre_comp->precomp_storage = precomp_storage;
885 precomp_storage = NULL;
886 SETPRECOMP(group, nistz256, pre_comp);
887 pre_comp = NULL;
888 ret = 1;
889
890 err:
891 BN_CTX_end(ctx);
892 BN_CTX_free(new_ctx);
893
894 EC_nistz256_pre_comp_free(pre_comp);
895 OPENSSL_free(precomp_storage);
896 EC_POINT_free(P);
897 EC_POINT_free(T);
898 return ret;
899}
900
901/*
902 * Note that by default ECP_NISTZ256_AVX2 is undefined. While it's great
903 * code processing 4 points in parallel, corresponding serial operation
904 * is several times slower, because it uses 29x29=58-bit multiplication
905 * as opposite to 64x64=128-bit in integer-only scalar case. As result
906 * it doesn't provide *significant* performance improvement. Note that
907 * just defining ECP_NISTZ256_AVX2 is not sufficient to make it work,
908 * you'd need to compile even asm/ecp_nistz256-avx.pl module.
909 */
910#if defined(ECP_NISTZ256_AVX2)
911# if !(defined(__x86_64) || defined(__x86_64__) || \
912 defined(_M_AMD64) || defined(_M_X64)) || \
913 !(defined(__GNUC__) || defined(_MSC_VER)) /* this is for ALIGN32 */
914# undef ECP_NISTZ256_AVX2
915# else
916/* Constant time access, loading four values, from four consecutive tables */
917void ecp_nistz256_avx2_multi_gather_w7(void *result, const void *in,
918 int index0, int index1, int index2,
919 int index3);
920void ecp_nistz256_avx2_transpose_convert(void *RESULTx4, const void *in);
921void ecp_nistz256_avx2_convert_transpose_back(void *result, const void *Ax4);
922void ecp_nistz256_avx2_point_add_affine_x4(void *RESULTx4, const void *Ax4,
923 const void *Bx4);
924void ecp_nistz256_avx2_point_add_affines_x4(void *RESULTx4, const void *Ax4,
925 const void *Bx4);
926void ecp_nistz256_avx2_to_mont(void *RESULTx4, const void *Ax4);
927void ecp_nistz256_avx2_from_mont(void *RESULTx4, const void *Ax4);
928void ecp_nistz256_avx2_set1(void *RESULTx4);
929int ecp_nistz_avx2_eligible(void);
930
931static void booth_recode_w7(unsigned char *sign,
932 unsigned char *digit, unsigned char in)
933{
934 unsigned char s, d;
935
936 s = ~((in >> 7) - 1);
937 d = (1 << 8) - in - 1;
938 d = (d & s) | (in & ~s);
939 d = (d >> 1) + (d & 1);
940
941 *sign = s & 1;
942 *digit = d;
943}
944
945/*
946 * ecp_nistz256_avx2_mul_g performs multiplication by G, using only the
947 * precomputed table. It does 4 affine point additions in parallel,
948 * significantly speeding up point multiplication for a fixed value.
949 */
950static void ecp_nistz256_avx2_mul_g(P256_POINT *r,
951 unsigned char p_str[33],
952 const P256_POINT_AFFINE(*preComputedTable)[64])
953{
954 const unsigned int window_size = 7;
955 const unsigned int mask = (1 << (window_size + 1)) - 1;
956 unsigned int wvalue;
957 /* Using 4 windows at a time */
958 unsigned char sign0, digit0;
959 unsigned char sign1, digit1;
960 unsigned char sign2, digit2;
961 unsigned char sign3, digit3;
962 unsigned int idx = 0;
963 BN_ULONG tmp[P256_LIMBS];
964 int i;
965
966 ALIGN32 BN_ULONG aX4[4 * 9 * 3] = { 0 };
967 ALIGN32 BN_ULONG bX4[4 * 9 * 2] = { 0 };
968 ALIGN32 P256_POINT_AFFINE point_arr[4];
969 ALIGN32 P256_POINT res_point_arr[4];
970
971 /* Initial four windows */
972 wvalue = *((u16 *) & p_str[0]);
973 wvalue = (wvalue << 1) & mask;
974 idx += window_size;
975 booth_recode_w7(&sign0, &digit0, wvalue);
976 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
977 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
978 idx += window_size;
979 booth_recode_w7(&sign1, &digit1, wvalue);
980 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
981 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
982 idx += window_size;
983 booth_recode_w7(&sign2, &digit2, wvalue);
984 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
985 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
986 idx += window_size;
987 booth_recode_w7(&sign3, &digit3, wvalue);
988
989 ecp_nistz256_avx2_multi_gather_w7(point_arr, preComputedTable[0],
990 digit0, digit1, digit2, digit3);
991
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);
1000
1001 ecp_nistz256_avx2_transpose_convert(aX4, point_arr);
1002 ecp_nistz256_avx2_to_mont(aX4, aX4);
1003 ecp_nistz256_avx2_to_mont(&aX4[4 * 9], &aX4[4 * 9]);
1004 ecp_nistz256_avx2_set1(&aX4[4 * 9 * 2]);
1005
1006 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
1007 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
1008 idx += window_size;
1009 booth_recode_w7(&sign0, &digit0, wvalue);
1010 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
1011 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
1012 idx += window_size;
1013 booth_recode_w7(&sign1, &digit1, wvalue);
1014 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
1015 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
1016 idx += window_size;
1017 booth_recode_w7(&sign2, &digit2, wvalue);
1018 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
1019 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
1020 idx += window_size;
1021 booth_recode_w7(&sign3, &digit3, wvalue);
1022
1023 ecp_nistz256_avx2_multi_gather_w7(point_arr, preComputedTable[4 * 1],
1024 digit0, digit1, digit2, digit3);
1025
1026 ecp_nistz256_neg(tmp, point_arr[0].Y);
1027 copy_conditional(point_arr[0].Y, tmp, sign0);
1028 ecp_nistz256_neg(tmp, point_arr[1].Y);
1029 copy_conditional(point_arr[1].Y, tmp, sign1);
1030 ecp_nistz256_neg(tmp, point_arr[2].Y);
1031 copy_conditional(point_arr[2].Y, tmp, sign2);
1032 ecp_nistz256_neg(tmp, point_arr[3].Y);
1033 copy_conditional(point_arr[3].Y, tmp, sign3);
1034
1035 ecp_nistz256_avx2_transpose_convert(bX4, point_arr);
1036 ecp_nistz256_avx2_to_mont(bX4, bX4);
1037 ecp_nistz256_avx2_to_mont(&bX4[4 * 9], &bX4[4 * 9]);
1038 /* Optimized when both inputs are affine */
1039 ecp_nistz256_avx2_point_add_affines_x4(aX4, aX4, bX4);
1040
1041 for (i = 2; i < 9; i++) {
1042 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
1043 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
1044 idx += window_size;
1045 booth_recode_w7(&sign0, &digit0, wvalue);
1046 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
1047 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
1048 idx += window_size;
1049 booth_recode_w7(&sign1, &digit1, wvalue);
1050 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
1051 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
1052 idx += window_size;
1053 booth_recode_w7(&sign2, &digit2, wvalue);
1054 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
1055 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
1056 idx += window_size;
1057 booth_recode_w7(&sign3, &digit3, wvalue);
1058
1059 ecp_nistz256_avx2_multi_gather_w7(point_arr,
1060 preComputedTable[4 * i],
1061 digit0, digit1, digit2, digit3);
1062
1063 ecp_nistz256_neg(tmp, point_arr[0].Y);
1064 copy_conditional(point_arr[0].Y, tmp, sign0);
1065 ecp_nistz256_neg(tmp, point_arr[1].Y);
1066 copy_conditional(point_arr[1].Y, tmp, sign1);
1067 ecp_nistz256_neg(tmp, point_arr[2].Y);
1068 copy_conditional(point_arr[2].Y, tmp, sign2);
1069 ecp_nistz256_neg(tmp, point_arr[3].Y);
1070 copy_conditional(point_arr[3].Y, tmp, sign3);
1071
1072 ecp_nistz256_avx2_transpose_convert(bX4, point_arr);
1073 ecp_nistz256_avx2_to_mont(bX4, bX4);
1074 ecp_nistz256_avx2_to_mont(&bX4[4 * 9], &bX4[4 * 9]);
1075
1076 ecp_nistz256_avx2_point_add_affine_x4(aX4, aX4, bX4);
1077 }
1078
1079 ecp_nistz256_avx2_from_mont(&aX4[4 * 9 * 0], &aX4[4 * 9 * 0]);
1080 ecp_nistz256_avx2_from_mont(&aX4[4 * 9 * 1], &aX4[4 * 9 * 1]);
1081 ecp_nistz256_avx2_from_mont(&aX4[4 * 9 * 2], &aX4[4 * 9 * 2]);
1082
1083 ecp_nistz256_avx2_convert_transpose_back(res_point_arr, aX4);
1084 /* Last window is performed serially */
1085 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
1086 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
1087 booth_recode_w7(&sign0, &digit0, wvalue);
1088 ecp_nistz256_gather_w7((P256_POINT_AFFINE *)r,
1089 preComputedTable[36], digit0);
1090 ecp_nistz256_neg(tmp, r->Y);
1091 copy_conditional(r->Y, tmp, sign0);
1092 memcpy(r->Z, ONE, sizeof(ONE));
1093 /* Sum the four windows */
1094 ecp_nistz256_point_add(r, r, &res_point_arr[0]);
1095 ecp_nistz256_point_add(r, r, &res_point_arr[1]);
1096 ecp_nistz256_point_add(r, r, &res_point_arr[2]);
1097 ecp_nistz256_point_add(r, r, &res_point_arr[3]);
1098}
1099# endif
1100#endif
1101
1102__owur static int ecp_nistz256_set_from_affine(EC_POINT *out, const EC_GROUP *group,
1103 const P256_POINT_AFFINE *in,
1104 BN_CTX *ctx)
1105{
1106 int ret = 0;
1107
1108 if ((ret = bn_set_words(out->X, in->X, P256_LIMBS))
1109 && (ret = bn_set_words(out->Y, in->Y, P256_LIMBS))
1110 && (ret = bn_set_words(out->Z, ONE, P256_LIMBS)))
1111 out->Z_is_one = 1;
1112
1113 return ret;
1114}
1115
1116/* r = scalar*G + sum(scalars[i]*points[i]) */
1117__owur static int ecp_nistz256_points_mul(const EC_GROUP *group,
1118 EC_POINT *r,
1119 const BIGNUM *scalar,
1120 size_t num,
1121 const EC_POINT *points[],
1122 const BIGNUM *scalars[], BN_CTX *ctx)
1123{
1124 int i = 0, ret = 0, no_precomp_for_generator = 0, p_is_infinity = 0;
1125 unsigned char p_str[33] = { 0 };
1126 const PRECOMP256_ROW *preComputedTable = NULL;
1127 const NISTZ256_PRE_COMP *pre_comp = NULL;
1128 const EC_POINT *generator = NULL;
1129 const BIGNUM **new_scalars = NULL;
1130 const EC_POINT **new_points = NULL;
1131 unsigned int idx = 0;
1132 const unsigned int window_size = 7;
1133 const unsigned int mask = (1 << (window_size + 1)) - 1;
1134 unsigned int wvalue;
1135 ALIGN32 union {
1136 P256_POINT p;
1137 P256_POINT_AFFINE a;
1138 } t, p;
1139 BIGNUM *tmp_scalar;
1140
1141 if ((num + 1) == 0 || (num + 1) > OPENSSL_MALLOC_MAX_NELEMS(void *)) {
1142 ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, ERR_R_MALLOC_FAILURE);
1143 return 0;
1144 }
1145
1146 BN_CTX_start(ctx);
1147
1148 if (scalar) {
1149 generator = EC_GROUP_get0_generator(group);
1150 if (generator == NULL) {
1151 ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, EC_R_UNDEFINED_GENERATOR);
1152 goto err;
1153 }
1154
1155 /* look if we can use precomputed multiples of generator */
1156 pre_comp = group->pre_comp.nistz256;
1157
1158 if (pre_comp) {
1159 /*
1160 * If there is a precomputed table for the generator, check that
1161 * it was generated with the same generator.
1162 */
1163 EC_POINT *pre_comp_generator = EC_POINT_new(group);
1164 if (pre_comp_generator == NULL)
1165 goto err;
1166
1167 ecp_nistz256_gather_w7(&p.a, pre_comp->precomp[0], 1);
1168 if (!ecp_nistz256_set_from_affine(pre_comp_generator,
1169 group, &p.a, ctx)) {
1170 EC_POINT_free(pre_comp_generator);
1171 goto err;
1172 }
1173
1174 if (0 == EC_POINT_cmp(group, generator, pre_comp_generator, ctx))
1175 preComputedTable = (const PRECOMP256_ROW *)pre_comp->precomp;
1176
1177 EC_POINT_free(pre_comp_generator);
1178 }
1179
1180 if (preComputedTable == NULL && ecp_nistz256_is_affine_G(generator)) {
1181 /*
1182 * If there is no precomputed data, but the generator is the
1183 * default, a hardcoded table of precomputed data is used. This
1184 * is because applications, such as Apache, do not use
1185 * EC_KEY_precompute_mult.
1186 */
1187 preComputedTable = ecp_nistz256_precomputed;
1188 }
1189
1190 if (preComputedTable) {
1191 if ((BN_num_bits(scalar) > 256)
1192 || BN_is_negative(scalar)) {
1193 if ((tmp_scalar = BN_CTX_get(ctx)) == NULL)
1194 goto err;
1195
1196 if (!BN_nnmod(tmp_scalar, scalar, group->order, ctx)) {
1197 ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, ERR_R_BN_LIB);
1198 goto err;
1199 }
1200 scalar = tmp_scalar;
1201 }
1202
1203 for (i = 0; i < bn_get_top(scalar) * BN_BYTES; i += BN_BYTES) {
1204 BN_ULONG d = bn_get_words(scalar)[i / BN_BYTES];
1205
1206 p_str[i + 0] = (unsigned char)d;
1207 p_str[i + 1] = (unsigned char)(d >> 8);
1208 p_str[i + 2] = (unsigned char)(d >> 16);
1209 p_str[i + 3] = (unsigned char)(d >>= 24);
1210 if (BN_BYTES == 8) {
1211 d >>= 8;
1212 p_str[i + 4] = (unsigned char)d;
1213 p_str[i + 5] = (unsigned char)(d >> 8);
1214 p_str[i + 6] = (unsigned char)(d >> 16);
1215 p_str[i + 7] = (unsigned char)(d >> 24);
1216 }
1217 }
1218
1219 for (; i < 33; i++)
1220 p_str[i] = 0;
1221
1222#if defined(ECP_NISTZ256_AVX2)
1223 if (ecp_nistz_avx2_eligible()) {
1224 ecp_nistz256_avx2_mul_g(&p.p, p_str, preComputedTable);
1225 } else
1226#endif
1227 {
1228 BN_ULONG infty;
1229
1230 /* First window */
1231 wvalue = (p_str[0] << 1) & mask;
1232 idx += window_size;
1233
1234 wvalue = _booth_recode_w7(wvalue);
1235
1236 ecp_nistz256_gather_w7(&p.a, preComputedTable[0],
1237 wvalue >> 1);
1238
1239 ecp_nistz256_neg(p.p.Z, p.p.Y);
1240 copy_conditional(p.p.Y, p.p.Z, wvalue & 1);
1241
1242 /*
1243 * Since affine infinity is encoded as (0,0) and
1244 * Jacobian ias (,,0), we need to harmonize them
1245 * by assigning "one" or zero to Z.
1246 */
1247 infty = (p.p.X[0] | p.p.X[1] | p.p.X[2] | p.p.X[3] |
1248 p.p.Y[0] | p.p.Y[1] | p.p.Y[2] | p.p.Y[3]);
1249 if (P256_LIMBS == 8)
1250 infty |= (p.p.X[4] | p.p.X[5] | p.p.X[6] | p.p.X[7] |
1251 p.p.Y[4] | p.p.Y[5] | p.p.Y[6] | p.p.Y[7]);
1252
1253 infty = 0 - is_zero(infty);
1254 infty = ~infty;
1255
1256 p.p.Z[0] = ONE[0] & infty;
1257 p.p.Z[1] = ONE[1] & infty;
1258 p.p.Z[2] = ONE[2] & infty;
1259 p.p.Z[3] = ONE[3] & infty;
1260 if (P256_LIMBS == 8) {
1261 p.p.Z[4] = ONE[4] & infty;
1262 p.p.Z[5] = ONE[5] & infty;
1263 p.p.Z[6] = ONE[6] & infty;
1264 p.p.Z[7] = ONE[7] & infty;
1265 }
1266
1267 for (i = 1; i < 37; i++) {
1268 unsigned int off = (idx - 1) / 8;
1269 wvalue = p_str[off] | p_str[off + 1] << 8;
1270 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
1271 idx += window_size;
1272
1273 wvalue = _booth_recode_w7(wvalue);
1274
1275 ecp_nistz256_gather_w7(&t.a,
1276 preComputedTable[i], wvalue >> 1);
1277
1278 ecp_nistz256_neg(t.p.Z, t.a.Y);
1279 copy_conditional(t.a.Y, t.p.Z, wvalue & 1);
1280
1281 ecp_nistz256_point_add_affine(&p.p, &p.p, &t.a);
1282 }
1283 }
1284 } else {
1285 p_is_infinity = 1;
1286 no_precomp_for_generator = 1;
1287 }
1288 } else
1289 p_is_infinity = 1;
1290
1291 if (no_precomp_for_generator) {
1292 /*
1293 * Without a precomputed table for the generator, it has to be
1294 * handled like a normal point.
1295 */
1296 new_scalars = OPENSSL_malloc((num + 1) * sizeof(BIGNUM *));
1297 if (new_scalars == NULL) {
1298 ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, ERR_R_MALLOC_FAILURE);
1299 goto err;
1300 }
1301
1302 new_points = OPENSSL_malloc((num + 1) * sizeof(EC_POINT *));
1303 if (new_points == NULL) {
1304 ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, ERR_R_MALLOC_FAILURE);
1305 goto err;
1306 }
1307
1308 memcpy(new_scalars, scalars, num * sizeof(BIGNUM *));
1309 new_scalars[num] = scalar;
1310 memcpy(new_points, points, num * sizeof(EC_POINT *));
1311 new_points[num] = generator;
1312
1313 scalars = new_scalars;
1314 points = new_points;
1315 num++;
1316 }
1317
1318 if (num) {
1319 P256_POINT *out = &t.p;
1320 if (p_is_infinity)
1321 out = &p.p;
1322
1323 if (!ecp_nistz256_windowed_mul(group, out, scalars, points, num, ctx))
1324 goto err;
1325
1326 if (!p_is_infinity)
1327 ecp_nistz256_point_add(&p.p, &p.p, out);
1328 }
1329
1330 /* Not constant-time, but we're only operating on the public output. */
1331 if (!bn_set_words(r->X, p.p.X, P256_LIMBS) ||
1332 !bn_set_words(r->Y, p.p.Y, P256_LIMBS) ||
1333 !bn_set_words(r->Z, p.p.Z, P256_LIMBS)) {
1334 goto err;
1335 }
1336 r->Z_is_one = is_one(r->Z) & 1;
1337
1338 ret = 1;
1339
1340err:
1341 BN_CTX_end(ctx);
1342 OPENSSL_free(new_points);
1343 OPENSSL_free(new_scalars);
1344 return ret;
1345}
1346
1347__owur static int ecp_nistz256_get_affine(const EC_GROUP *group,
1348 const EC_POINT *point,
1349 BIGNUM *x, BIGNUM *y, BN_CTX *ctx)
1350{
1351 BN_ULONG z_inv2[P256_LIMBS];
1352 BN_ULONG z_inv3[P256_LIMBS];
1353 BN_ULONG x_aff[P256_LIMBS];
1354 BN_ULONG y_aff[P256_LIMBS];
1355 BN_ULONG point_x[P256_LIMBS], point_y[P256_LIMBS], point_z[P256_LIMBS];
1356 BN_ULONG x_ret[P256_LIMBS], y_ret[P256_LIMBS];
1357
1358 if (EC_POINT_is_at_infinity(group, point)) {
1359 ECerr(EC_F_ECP_NISTZ256_GET_AFFINE, EC_R_POINT_AT_INFINITY);
1360 return 0;
1361 }
1362
1363 if (!ecp_nistz256_bignum_to_field_elem(point_x, point->X) ||
1364 !ecp_nistz256_bignum_to_field_elem(point_y, point->Y) ||
1365 !ecp_nistz256_bignum_to_field_elem(point_z, point->Z)) {
1366 ECerr(EC_F_ECP_NISTZ256_GET_AFFINE, EC_R_COORDINATES_OUT_OF_RANGE);
1367 return 0;
1368 }
1369
1370 ecp_nistz256_mod_inverse(z_inv3, point_z);
1371 ecp_nistz256_sqr_mont(z_inv2, z_inv3);
1372 ecp_nistz256_mul_mont(x_aff, z_inv2, point_x);
1373
1374 if (x != NULL) {
1375 ecp_nistz256_from_mont(x_ret, x_aff);
1376 if (!bn_set_words(x, x_ret, P256_LIMBS))
1377 return 0;
1378 }
1379
1380 if (y != NULL) {
1381 ecp_nistz256_mul_mont(z_inv3, z_inv3, z_inv2);
1382 ecp_nistz256_mul_mont(y_aff, z_inv3, point_y);
1383 ecp_nistz256_from_mont(y_ret, y_aff);
1384 if (!bn_set_words(y, y_ret, P256_LIMBS))
1385 return 0;
1386 }
1387
1388 return 1;
1389}
1390
1391static NISTZ256_PRE_COMP *ecp_nistz256_pre_comp_new(const EC_GROUP *group)
1392{
1393 NISTZ256_PRE_COMP *ret = NULL;
1394
1395 if (!group)
1396 return NULL;
1397
1398 ret = OPENSSL_zalloc(sizeof(*ret));
1399
1400 if (ret == NULL) {
1401 ECerr(EC_F_ECP_NISTZ256_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE);
1402 return ret;
1403 }
1404
1405 ret->group = group;
1406 ret->w = 6; /* default */
1407 ret->references = 1;
1408
1409 ret->lock = CRYPTO_THREAD_lock_new();
1410 if (ret->lock == NULL) {
1411 ECerr(EC_F_ECP_NISTZ256_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE);
1412 OPENSSL_free(ret);
1413 return NULL;
1414 }
1415 return ret;
1416}
1417
1418NISTZ256_PRE_COMP *EC_nistz256_pre_comp_dup(NISTZ256_PRE_COMP *p)
1419{
1420 int i;
1421 if (p != NULL)
1422 CRYPTO_UP_REF(&p->references, &i, p->lock);
1423 return p;
1424}
1425
1426void EC_nistz256_pre_comp_free(NISTZ256_PRE_COMP *pre)
1427{
1428 int i;
1429
1430 if (pre == NULL)
1431 return;
1432
1433 CRYPTO_DOWN_REF(&pre->references, &i, pre->lock);
1434 REF_PRINT_COUNT("EC_nistz256", pre);
1435 if (i > 0)
1436 return;
1437 REF_ASSERT_ISNT(i < 0);
1438
1439 OPENSSL_free(pre->precomp_storage);
1440 CRYPTO_THREAD_lock_free(pre->lock);
1441 OPENSSL_free(pre);
1442}
1443
1444
1445static int ecp_nistz256_window_have_precompute_mult(const EC_GROUP *group)
1446{
1447 /* There is a hard-coded table for the default generator. */
1448 const EC_POINT *generator = EC_GROUP_get0_generator(group);
1449
1450 if (generator != NULL && ecp_nistz256_is_affine_G(generator)) {
1451 /* There is a hard-coded table for the default generator. */
1452 return 1;
1453 }
1454
1455 return HAVEPRECOMP(group, nistz256);
1456}
1457
1458#if defined(__x86_64) || defined(__x86_64__) || \
1459 defined(_M_AMD64) || defined(_M_X64) || \
1460 defined(__powerpc64__) || defined(_ARCH_PP64) || \
1461 defined(__aarch64__)
1462/*
1463 * Montgomery mul modulo Order(P): res = a*b*2^-256 mod Order(P)
1464 */
1465void ecp_nistz256_ord_mul_mont(BN_ULONG res[P256_LIMBS],
1466 const BN_ULONG a[P256_LIMBS],
1467 const BN_ULONG b[P256_LIMBS]);
1468void ecp_nistz256_ord_sqr_mont(BN_ULONG res[P256_LIMBS],
1469 const BN_ULONG a[P256_LIMBS],
1470 BN_ULONG rep);
1471
1472static int ecp_nistz256_inv_mod_ord(const EC_GROUP *group, BIGNUM *r,
1473 const BIGNUM *x, BN_CTX *ctx)
1474{
1475 /* RR = 2^512 mod ord(p256) */
1476 static const BN_ULONG RR[P256_LIMBS] = {
1477 TOBN(0x83244c95,0xbe79eea2), TOBN(0x4699799c,0x49bd6fa6),
1478 TOBN(0x2845b239,0x2b6bec59), TOBN(0x66e12d94,0xf3d95620)
1479 };
1480 /* The constant 1 (unlike ONE that is one in Montgomery representation) */
1481 static const BN_ULONG one[P256_LIMBS] = {
1482 TOBN(0,1), TOBN(0,0), TOBN(0,0), TOBN(0,0)
1483 };
1484 /*
1485 * We don't use entry 0 in the table, so we omit it and address
1486 * with -1 offset.
1487 */
1488 BN_ULONG table[15][P256_LIMBS];
1489 BN_ULONG out[P256_LIMBS], t[P256_LIMBS];
1490 int i, ret = 0;
1491 enum {
1492 i_1 = 0, i_10, i_11, i_101, i_111, i_1010, i_1111,
1493 i_10101, i_101010, i_101111, i_x6, i_x8, i_x16, i_x32
1494 };
1495
1496 /*
1497 * Catch allocation failure early.
1498 */
1499 if (bn_wexpand(r, P256_LIMBS) == NULL) {
1500 ECerr(EC_F_ECP_NISTZ256_INV_MOD_ORD, ERR_R_BN_LIB);
1501 goto err;
1502 }
1503
1504 if ((BN_num_bits(x) > 256) || BN_is_negative(x)) {
1505 BIGNUM *tmp;
1506
1507 if ((tmp = BN_CTX_get(ctx)) == NULL
1508 || !BN_nnmod(tmp, x, group->order, ctx)) {
1509 ECerr(EC_F_ECP_NISTZ256_INV_MOD_ORD, ERR_R_BN_LIB);
1510 goto err;
1511 }
1512 x = tmp;
1513 }
1514
1515 if (!ecp_nistz256_bignum_to_field_elem(t, x)) {
1516 ECerr(EC_F_ECP_NISTZ256_INV_MOD_ORD, EC_R_COORDINATES_OUT_OF_RANGE);
1517 goto err;
1518 }
1519
1520 ecp_nistz256_ord_mul_mont(table[0], t, RR);
1521#if 0
1522 /*
1523 * Original sparse-then-fixed-window algorithm, retained for reference.
1524 */
1525 for (i = 2; i < 16; i += 2) {
1526 ecp_nistz256_ord_sqr_mont(table[i-1], table[i/2-1], 1);
1527 ecp_nistz256_ord_mul_mont(table[i], table[i-1], table[0]);
1528 }
1529
1530 /*
1531 * The top 128bit of the exponent are highly redudndant, so we
1532 * perform an optimized flow
1533 */
1534 ecp_nistz256_ord_sqr_mont(t, table[15-1], 4); /* f0 */
1535 ecp_nistz256_ord_mul_mont(t, t, table[15-1]); /* ff */
1536
1537 ecp_nistz256_ord_sqr_mont(out, t, 8); /* ff00 */
1538 ecp_nistz256_ord_mul_mont(out, out, t); /* ffff */
1539
1540 ecp_nistz256_ord_sqr_mont(t, out, 16); /* ffff0000 */
1541 ecp_nistz256_ord_mul_mont(t, t, out); /* ffffffff */
1542
1543 ecp_nistz256_ord_sqr_mont(out, t, 64); /* ffffffff0000000000000000 */
1544 ecp_nistz256_ord_mul_mont(out, out, t); /* ffffffff00000000ffffffff */
1545
1546 ecp_nistz256_ord_sqr_mont(out, out, 32); /* ffffffff00000000ffffffff00000000 */
1547 ecp_nistz256_ord_mul_mont(out, out, t); /* ffffffff00000000ffffffffffffffff */
1548
1549 /*
1550 * The bottom 128 bit of the exponent are processed with fixed 4-bit window
1551 */
1552 for(i = 0; i < 32; i++) {
1553 /* expLo - the low 128 bits of the exponent we use (ord(p256) - 2),
1554 * split into nibbles */
1555 static const unsigned char expLo[32] = {
1556 0xb,0xc,0xe,0x6,0xf,0xa,0xa,0xd,0xa,0x7,0x1,0x7,0x9,0xe,0x8,0x4,
1557 0xf,0x3,0xb,0x9,0xc,0xa,0xc,0x2,0xf,0xc,0x6,0x3,0x2,0x5,0x4,0xf
1558 };
1559
1560 ecp_nistz256_ord_sqr_mont(out, out, 4);
1561 /* The exponent is public, no need in constant-time access */
1562 ecp_nistz256_ord_mul_mont(out, out, table[expLo[i]-1]);
1563 }
1564#else
1565 /*
1566 * https://briansmith.org/ecc-inversion-addition-chains-01#p256_scalar_inversion
1567 *
1568 * Even though this code path spares 12 squarings, 4.5%, and 13
1569 * multiplications, 25%, on grand scale sign operation is not that
1570 * much faster, not more that 2%...
1571 */
1572
1573 /* pre-calculate powers */
1574 ecp_nistz256_ord_sqr_mont(table[i_10], table[i_1], 1);
1575
1576 ecp_nistz256_ord_mul_mont(table[i_11], table[i_1], table[i_10]);
1577
1578 ecp_nistz256_ord_mul_mont(table[i_101], table[i_11], table[i_10]);
1579
1580 ecp_nistz256_ord_mul_mont(table[i_111], table[i_101], table[i_10]);
1581
1582 ecp_nistz256_ord_sqr_mont(table[i_1010], table[i_101], 1);
1583
1584 ecp_nistz256_ord_mul_mont(table[i_1111], table[i_1010], table[i_101]);
1585
1586 ecp_nistz256_ord_sqr_mont(table[i_10101], table[i_1010], 1);
1587 ecp_nistz256_ord_mul_mont(table[i_10101], table[i_10101], table[i_1]);
1588
1589 ecp_nistz256_ord_sqr_mont(table[i_101010], table[i_10101], 1);
1590
1591 ecp_nistz256_ord_mul_mont(table[i_101111], table[i_101010], table[i_101]);
1592
1593 ecp_nistz256_ord_mul_mont(table[i_x6], table[i_101010], table[i_10101]);
1594
1595 ecp_nistz256_ord_sqr_mont(table[i_x8], table[i_x6], 2);
1596 ecp_nistz256_ord_mul_mont(table[i_x8], table[i_x8], table[i_11]);
1597
1598 ecp_nistz256_ord_sqr_mont(table[i_x16], table[i_x8], 8);
1599 ecp_nistz256_ord_mul_mont(table[i_x16], table[i_x16], table[i_x8]);
1600
1601 ecp_nistz256_ord_sqr_mont(table[i_x32], table[i_x16], 16);
1602 ecp_nistz256_ord_mul_mont(table[i_x32], table[i_x32], table[i_x16]);
1603
1604 /* calculations */
1605 ecp_nistz256_ord_sqr_mont(out, table[i_x32], 64);
1606 ecp_nistz256_ord_mul_mont(out, out, table[i_x32]);
1607
1608 for (i = 0; i < 27; i++) {
1609 static const struct { unsigned char p, i; } chain[27] = {
1610 { 32, i_x32 }, { 6, i_101111 }, { 5, i_111 },
1611 { 4, i_11 }, { 5, i_1111 }, { 5, i_10101 },
1612 { 4, i_101 }, { 3, i_101 }, { 3, i_101 },
1613 { 5, i_111 }, { 9, i_101111 }, { 6, i_1111 },
1614 { 2, i_1 }, { 5, i_1 }, { 6, i_1111 },
1615 { 5, i_111 }, { 4, i_111 }, { 5, i_111 },
1616 { 5, i_101 }, { 3, i_11 }, { 10, i_101111 },
1617 { 2, i_11 }, { 5, i_11 }, { 5, i_11 },
1618 { 3, i_1 }, { 7, i_10101 }, { 6, i_1111 }
1619 };
1620
1621 ecp_nistz256_ord_sqr_mont(out, out, chain[i].p);
1622 ecp_nistz256_ord_mul_mont(out, out, table[chain[i].i]);
1623 }
1624#endif
1625 ecp_nistz256_ord_mul_mont(out, out, one);
1626
1627 /*
1628 * Can't fail, but check return code to be consistent anyway.
1629 */
1630 if (!bn_set_words(r, out, P256_LIMBS))
1631 goto err;
1632
1633 ret = 1;
1634err:
1635 return ret;
1636}
1637#else
1638# define ecp_nistz256_inv_mod_ord NULL
1639#endif
1640
1641const EC_METHOD *EC_GFp_nistz256_method(void)
1642{
1643 static const EC_METHOD ret = {
1644 EC_FLAGS_DEFAULT_OCT,
1645 NID_X9_62_prime_field,
1646 ec_GFp_mont_group_init,
1647 ec_GFp_mont_group_finish,
1648 ec_GFp_mont_group_clear_finish,
1649 ec_GFp_mont_group_copy,
1650 ec_GFp_mont_group_set_curve,
1651 ec_GFp_simple_group_get_curve,
1652 ec_GFp_simple_group_get_degree,
1653 ec_group_simple_order_bits,
1654 ec_GFp_simple_group_check_discriminant,
1655 ec_GFp_simple_point_init,
1656 ec_GFp_simple_point_finish,
1657 ec_GFp_simple_point_clear_finish,
1658 ec_GFp_simple_point_copy,
1659 ec_GFp_simple_point_set_to_infinity,
1660 ec_GFp_simple_set_Jprojective_coordinates_GFp,
1661 ec_GFp_simple_get_Jprojective_coordinates_GFp,
1662 ec_GFp_simple_point_set_affine_coordinates,
1663 ecp_nistz256_get_affine,
1664 0, 0, 0,
1665 ec_GFp_simple_add,
1666 ec_GFp_simple_dbl,
1667 ec_GFp_simple_invert,
1668 ec_GFp_simple_is_at_infinity,
1669 ec_GFp_simple_is_on_curve,
1670 ec_GFp_simple_cmp,
1671 ec_GFp_simple_make_affine,
1672 ec_GFp_simple_points_make_affine,
1673 ecp_nistz256_points_mul, /* mul */
1674 ecp_nistz256_mult_precompute, /* precompute_mult */
1675 ecp_nistz256_window_have_precompute_mult, /* have_precompute_mult */
1676 ec_GFp_mont_field_mul,
1677 ec_GFp_mont_field_sqr,
1678 0, /* field_div */
1679 ec_GFp_mont_field_inv,
1680 ec_GFp_mont_field_encode,
1681 ec_GFp_mont_field_decode,
1682 ec_GFp_mont_field_set_to_one,
1683 ec_key_simple_priv2oct,
1684 ec_key_simple_oct2priv,
1685 0, /* set private */
1686 ec_key_simple_generate_key,
1687 ec_key_simple_check_key,
1688 ec_key_simple_generate_public_key,
1689 0, /* keycopy */
1690 0, /* keyfinish */
1691 ecdh_simple_compute_key,
1692 ecdsa_simple_sign_setup,
1693 ecdsa_simple_sign_sig,
1694 ecdsa_simple_verify_sig,
1695 ecp_nistz256_inv_mod_ord, /* can be #define-d NULL */
1696 0, /* blind_coordinates */
1697 0, /* ladder_pre */
1698 0, /* ladder_step */
1699 0 /* ladder_post */
1700 };
1701
1702 return &ret;
1703}
1704