1 /*
2 * Copyright 2014-2025 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 /*
22 * ECDSA low level APIs are deprecated for public use, but still ok for
23 * internal use.
24 */
25 #include "internal/deprecated.h"
26
27 #include <string.h>
28
29 #include "internal/cryptlib.h"
30 #include "crypto/bn.h"
31 #include "ec_local.h"
32 #include "internal/refcount.h"
33
34 #if BN_BITS2 != 64
35 #define TOBN(hi, lo) lo, hi
36 #else
37 #define TOBN(hi, lo) ((BN_ULONG)hi << 32 | lo)
38 #endif
39
40 #define ALIGNPTR(p, N) ((unsigned char *)p + N - (size_t)p % N)
41 #define P256_LIMBS (256 / BN_BITS2)
42
43 typedef unsigned short u16;
44
45 typedef struct {
46 BN_ULONG X[P256_LIMBS];
47 BN_ULONG Y[P256_LIMBS];
48 BN_ULONG Z[P256_LIMBS];
49 } P256_POINT;
50
51 typedef struct {
52 BN_ULONG X[P256_LIMBS];
53 BN_ULONG Y[P256_LIMBS];
54 } P256_POINT_AFFINE;
55
56 typedef P256_POINT_AFFINE PRECOMP256_ROW[64];
57
58 /* structure for precomputed multiples of the generator */
59 struct nistz256_pre_comp_st {
60 const EC_GROUP *group; /* Parent EC_GROUP object */
61 size_t w; /* Window size */
62 /*
63 * Constant time access to the X and Y coordinates of the pre-computed,
64 * generator multiplies, in the Montgomery domain. Pre-calculated
65 * multiplies are stored in affine form.
66 */
67 PRECOMP256_ROW *precomp;
68 void *precomp_storage;
69 CRYPTO_REF_COUNT references;
70 };
71
72 /* Functions implemented in assembly */
73 /*
74 * Most of below mentioned functions *preserve* the property of inputs
75 * being fully reduced, i.e. being in [0, modulus) range. Simply put if
76 * inputs are fully reduced, then output is too. Note that reverse is
77 * not true, in sense that given partially reduced inputs output can be
78 * either, not unlikely reduced. And "most" in first sentence refers to
79 * the fact that given the calculations flow one can tolerate that
80 * addition, 1st function below, produces partially reduced result *if*
81 * multiplications by 2 and 3, which customarily use addition, fully
82 * reduce it. This effectively gives two options: a) addition produces
83 * fully reduced result [as long as inputs are, just like remaining
84 * functions]; b) addition is allowed to produce partially reduced
85 * result, but multiplications by 2 and 3 perform additional reduction
86 * step. Choice between the two can be platform-specific, but it was a)
87 * in all cases so far...
88 */
89 /* Modular add: res = a+b mod P */
90 void ecp_nistz256_add(BN_ULONG res[P256_LIMBS],
91 const BN_ULONG a[P256_LIMBS],
92 const BN_ULONG b[P256_LIMBS]);
93 /* Modular mul by 2: res = 2*a mod P */
94 void ecp_nistz256_mul_by_2(BN_ULONG res[P256_LIMBS],
95 const BN_ULONG a[P256_LIMBS]);
96 /* Modular mul by 3: res = 3*a mod P */
97 void ecp_nistz256_mul_by_3(BN_ULONG res[P256_LIMBS],
98 const BN_ULONG a[P256_LIMBS]);
99
100 /* Modular div by 2: res = a/2 mod P */
101 void ecp_nistz256_div_by_2(BN_ULONG res[P256_LIMBS],
102 const BN_ULONG a[P256_LIMBS]);
103 /* Modular sub: res = a-b mod P */
104 void ecp_nistz256_sub(BN_ULONG res[P256_LIMBS],
105 const BN_ULONG a[P256_LIMBS],
106 const BN_ULONG b[P256_LIMBS]);
107 /* Modular neg: res = -a mod P */
108 void ecp_nistz256_neg(BN_ULONG res[P256_LIMBS], const BN_ULONG a[P256_LIMBS]);
109 /* Montgomery mul: res = a*b*2^-256 mod P */
110 void ecp_nistz256_mul_mont(BN_ULONG res[P256_LIMBS],
111 const BN_ULONG a[P256_LIMBS],
112 const BN_ULONG b[P256_LIMBS]);
113 /* Montgomery sqr: res = a*a*2^-256 mod P */
114 void ecp_nistz256_sqr_mont(BN_ULONG res[P256_LIMBS],
115 const BN_ULONG a[P256_LIMBS]);
116 /* Convert a number from Montgomery domain, by multiplying with 1 */
117 void ecp_nistz256_from_mont(BN_ULONG res[P256_LIMBS],
118 const BN_ULONG in[P256_LIMBS]);
119 /* Convert a number to Montgomery domain, by multiplying with 2^512 mod P*/
120 void ecp_nistz256_to_mont(BN_ULONG res[P256_LIMBS],
121 const BN_ULONG in[P256_LIMBS]);
122 /* Functions that perform constant time access to the precomputed tables */
123 void ecp_nistz256_scatter_w5(P256_POINT *val,
124 const P256_POINT *in_t, int idx);
125 void ecp_nistz256_gather_w5(P256_POINT *val,
126 const P256_POINT *in_t, int idx);
127 void ecp_nistz256_scatter_w7(P256_POINT_AFFINE *val,
128 const P256_POINT_AFFINE *in_t, int idx);
129 void ecp_nistz256_gather_w7(P256_POINT_AFFINE *val,
130 const P256_POINT_AFFINE *in_t, int idx);
131
132 /* One converted into the Montgomery domain */
133 static const BN_ULONG ONE[P256_LIMBS] = {
134 TOBN(0x00000000, 0x00000001), TOBN(0xffffffff, 0x00000000),
135 TOBN(0xffffffff, 0xffffffff), TOBN(0x00000000, 0xfffffffe)
136 };
137
138 static NISTZ256_PRE_COMP *ecp_nistz256_pre_comp_new(const EC_GROUP *group);
139
140 /* Precomputed tables for the default generator */
141 extern const PRECOMP256_ROW ecp_nistz256_precomputed[37];
142
143 /* Recode window to a signed digit, see ecp_nistputil.c for details */
_booth_recode_w5(unsigned int in)144 static unsigned int _booth_recode_w5(unsigned int in)
145 {
146 unsigned int s, d;
147
148 s = ~((in >> 5) - 1);
149 d = (1 << 6) - in - 1;
150 d = (d & s) | (in & ~s);
151 d = (d >> 1) + (d & 1);
152
153 return (d << 1) + (s & 1);
154 }
155
_booth_recode_w7(unsigned int in)156 static unsigned int _booth_recode_w7(unsigned int in)
157 {
158 unsigned int s, d;
159
160 s = ~((in >> 7) - 1);
161 d = (1 << 8) - in - 1;
162 d = (d & s) | (in & ~s);
163 d = (d >> 1) + (d & 1);
164
165 return (d << 1) + (s & 1);
166 }
167
copy_conditional(BN_ULONG dst[P256_LIMBS],const BN_ULONG src[P256_LIMBS],BN_ULONG move)168 static void copy_conditional(BN_ULONG dst[P256_LIMBS],
169 const BN_ULONG src[P256_LIMBS], BN_ULONG move)
170 {
171 BN_ULONG mask1 = 0 - move;
172 BN_ULONG mask2 = ~mask1;
173
174 dst[0] = (src[0] & mask1) ^ (dst[0] & mask2);
175 dst[1] = (src[1] & mask1) ^ (dst[1] & mask2);
176 dst[2] = (src[2] & mask1) ^ (dst[2] & mask2);
177 dst[3] = (src[3] & mask1) ^ (dst[3] & mask2);
178 if (P256_LIMBS == 8) {
179 dst[4] = (src[4] & mask1) ^ (dst[4] & mask2);
180 dst[5] = (src[5] & mask1) ^ (dst[5] & mask2);
181 dst[6] = (src[6] & mask1) ^ (dst[6] & mask2);
182 dst[7] = (src[7] & mask1) ^ (dst[7] & mask2);
183 }
184 }
185
is_zero(BN_ULONG in)186 static BN_ULONG is_zero(BN_ULONG in)
187 {
188 in |= (0 - in);
189 in = ~in;
190 in >>= BN_BITS2 - 1;
191 return in;
192 }
193
is_equal(const BN_ULONG a[P256_LIMBS],const BN_ULONG b[P256_LIMBS])194 static BN_ULONG is_equal(const BN_ULONG a[P256_LIMBS],
195 const BN_ULONG b[P256_LIMBS])
196 {
197 BN_ULONG res;
198
199 res = a[0] ^ b[0];
200 res |= a[1] ^ b[1];
201 res |= a[2] ^ b[2];
202 res |= a[3] ^ b[3];
203 if (P256_LIMBS == 8) {
204 res |= a[4] ^ b[4];
205 res |= a[5] ^ b[5];
206 res |= a[6] ^ b[6];
207 res |= a[7] ^ b[7];
208 }
209
210 return is_zero(res);
211 }
212
is_one(const BIGNUM * z)213 static BN_ULONG is_one(const BIGNUM *z)
214 {
215 BN_ULONG res = 0;
216 BN_ULONG *a = bn_get_words(z);
217
218 if (bn_get_top(z) == (P256_LIMBS - P256_LIMBS / 8)) {
219 res = a[0] ^ ONE[0];
220 res |= a[1] ^ ONE[1];
221 res |= a[2] ^ ONE[2];
222 res |= a[3] ^ ONE[3];
223 if (P256_LIMBS == 8) {
224 res |= a[4] ^ ONE[4];
225 res |= a[5] ^ ONE[5];
226 res |= a[6] ^ ONE[6];
227 /*
228 * no check for a[7] (being zero) on 32-bit platforms,
229 * because value of "one" takes only 7 limbs.
230 */
231 }
232 res = is_zero(res);
233 }
234
235 return res;
236 }
237
238 /*
239 * For reference, this macro is used only when new ecp_nistz256 assembly
240 * module is being developed. For example, configure with
241 * -DECP_NISTZ256_REFERENCE_IMPLEMENTATION and implement only functions
242 * performing simplest arithmetic operations on 256-bit vectors. Then
243 * work on implementation of higher-level functions performing point
244 * operations. Then remove ECP_NISTZ256_REFERENCE_IMPLEMENTATION
245 * and never define it again. (The correct macro denoting presence of
246 * ecp_nistz256 module is ECP_NISTZ256_ASM.)
247 */
248 #ifndef ECP_NISTZ256_REFERENCE_IMPLEMENTATION
249 void ecp_nistz256_point_double(P256_POINT *r, const P256_POINT *a);
250 void ecp_nistz256_point_add(P256_POINT *r,
251 const P256_POINT *a, const P256_POINT *b);
252 void ecp_nistz256_point_add_affine(P256_POINT *r,
253 const P256_POINT *a,
254 const P256_POINT_AFFINE *b);
255 #else
256 /* Point double: r = 2*a */
ecp_nistz256_point_double(P256_POINT * r,const P256_POINT * a)257 static void ecp_nistz256_point_double(P256_POINT *r, const P256_POINT *a)
258 {
259 BN_ULONG S[P256_LIMBS];
260 BN_ULONG M[P256_LIMBS];
261 BN_ULONG Zsqr[P256_LIMBS];
262 BN_ULONG tmp0[P256_LIMBS];
263
264 const BN_ULONG *in_x = a->X;
265 const BN_ULONG *in_y = a->Y;
266 const BN_ULONG *in_z = a->Z;
267
268 BN_ULONG *res_x = r->X;
269 BN_ULONG *res_y = r->Y;
270 BN_ULONG *res_z = r->Z;
271
272 ecp_nistz256_mul_by_2(S, in_y);
273
274 ecp_nistz256_sqr_mont(Zsqr, in_z);
275
276 ecp_nistz256_sqr_mont(S, S);
277
278 ecp_nistz256_mul_mont(res_z, in_z, in_y);
279 ecp_nistz256_mul_by_2(res_z, res_z);
280
281 ecp_nistz256_add(M, in_x, Zsqr);
282 ecp_nistz256_sub(Zsqr, in_x, Zsqr);
283
284 ecp_nistz256_sqr_mont(res_y, S);
285 ecp_nistz256_div_by_2(res_y, res_y);
286
287 ecp_nistz256_mul_mont(M, M, Zsqr);
288 ecp_nistz256_mul_by_3(M, M);
289
290 ecp_nistz256_mul_mont(S, S, in_x);
291 ecp_nistz256_mul_by_2(tmp0, S);
292
293 ecp_nistz256_sqr_mont(res_x, M);
294
295 ecp_nistz256_sub(res_x, res_x, tmp0);
296 ecp_nistz256_sub(S, S, res_x);
297
298 ecp_nistz256_mul_mont(S, S, M);
299 ecp_nistz256_sub(res_y, S, res_y);
300 }
301
302 /* Point addition: r = a+b */
ecp_nistz256_point_add(P256_POINT * r,const P256_POINT * a,const P256_POINT * b)303 static void ecp_nistz256_point_add(P256_POINT *r,
304 const P256_POINT *a, const P256_POINT *b)
305 {
306 BN_ULONG U2[P256_LIMBS], S2[P256_LIMBS];
307 BN_ULONG U1[P256_LIMBS], S1[P256_LIMBS];
308 BN_ULONG Z1sqr[P256_LIMBS];
309 BN_ULONG Z2sqr[P256_LIMBS];
310 BN_ULONG H[P256_LIMBS], R[P256_LIMBS];
311 BN_ULONG Hsqr[P256_LIMBS];
312 BN_ULONG Rsqr[P256_LIMBS];
313 BN_ULONG Hcub[P256_LIMBS];
314
315 BN_ULONG res_x[P256_LIMBS];
316 BN_ULONG res_y[P256_LIMBS];
317 BN_ULONG res_z[P256_LIMBS];
318
319 BN_ULONG in1infty, in2infty;
320
321 const BN_ULONG *in1_x = a->X;
322 const BN_ULONG *in1_y = a->Y;
323 const BN_ULONG *in1_z = a->Z;
324
325 const BN_ULONG *in2_x = b->X;
326 const BN_ULONG *in2_y = b->Y;
327 const BN_ULONG *in2_z = b->Z;
328
329 /*
330 * Infinity in encoded as (,,0)
331 */
332 in1infty = (in1_z[0] | in1_z[1] | in1_z[2] | in1_z[3]);
333 if (P256_LIMBS == 8)
334 in1infty |= (in1_z[4] | in1_z[5] | in1_z[6] | in1_z[7]);
335
336 in2infty = (in2_z[0] | in2_z[1] | in2_z[2] | in2_z[3]);
337 if (P256_LIMBS == 8)
338 in2infty |= (in2_z[4] | in2_z[5] | in2_z[6] | in2_z[7]);
339
340 in1infty = is_zero(in1infty);
341 in2infty = is_zero(in2infty);
342
343 ecp_nistz256_sqr_mont(Z2sqr, in2_z); /* Z2^2 */
344 ecp_nistz256_sqr_mont(Z1sqr, in1_z); /* Z1^2 */
345
346 ecp_nistz256_mul_mont(S1, Z2sqr, in2_z); /* S1 = Z2^3 */
347 ecp_nistz256_mul_mont(S2, Z1sqr, in1_z); /* S2 = Z1^3 */
348
349 ecp_nistz256_mul_mont(S1, S1, in1_y); /* S1 = Y1*Z2^3 */
350 ecp_nistz256_mul_mont(S2, S2, in2_y); /* S2 = Y2*Z1^3 */
351 ecp_nistz256_sub(R, S2, S1); /* R = S2 - S1 */
352
353 ecp_nistz256_mul_mont(U1, in1_x, Z2sqr); /* U1 = X1*Z2^2 */
354 ecp_nistz256_mul_mont(U2, in2_x, Z1sqr); /* U2 = X2*Z1^2 */
355 ecp_nistz256_sub(H, U2, U1); /* H = U2 - U1 */
356
357 /*
358 * The formulae are incorrect if the points are equal so we check for
359 * this and do doubling if this happens.
360 *
361 * Points here are in Jacobian projective coordinates (Xi, Yi, Zi)
362 * that are bound to the affine coordinates (xi, yi) by the following
363 * equations:
364 * - xi = Xi / (Zi)^2
365 * - y1 = Yi / (Zi)^3
366 *
367 * For the sake of optimization, the algorithm operates over
368 * intermediate variables U1, U2 and S1, S2 that are derived from
369 * the projective coordinates:
370 * - U1 = X1 * (Z2)^2 ; U2 = X2 * (Z1)^2
371 * - S1 = Y1 * (Z2)^3 ; S2 = Y2 * (Z1)^3
372 *
373 * It is easy to prove that is_equal(U1, U2) implies that the affine
374 * x-coordinates are equal, or either point is at infinity.
375 * Likewise is_equal(S1, S2) implies that the affine y-coordinates are
376 * equal, or either point is at infinity.
377 *
378 * The special case of either point being the point at infinity (Z1 or Z2
379 * is zero), is handled separately later on in this function, so we avoid
380 * jumping to point_double here in those special cases.
381 *
382 * When both points are inverse of each other, we know that the affine
383 * x-coordinates are equal, and the y-coordinates have different sign.
384 * Therefore since U1 = U2, we know H = 0, and therefore Z3 = H*Z1*Z2
385 * will equal 0, thus the result is infinity, if we simply let this
386 * function continue normally.
387 *
388 * We use bitwise operations to avoid potential side-channels introduced by
389 * the short-circuiting behaviour of boolean operators.
390 */
391 if (is_equal(U1, U2) & ~in1infty & ~in2infty & is_equal(S1, S2)) {
392 /*
393 * This is obviously not constant-time but it should never happen during
394 * single point multiplication, so there is no timing leak for ECDH or
395 * ECDSA signing.
396 */
397 ecp_nistz256_point_double(r, a);
398 return;
399 }
400
401 ecp_nistz256_sqr_mont(Rsqr, R); /* R^2 */
402 ecp_nistz256_mul_mont(res_z, H, in1_z); /* Z3 = H*Z1*Z2 */
403 ecp_nistz256_sqr_mont(Hsqr, H); /* H^2 */
404 ecp_nistz256_mul_mont(res_z, res_z, in2_z); /* Z3 = H*Z1*Z2 */
405 ecp_nistz256_mul_mont(Hcub, Hsqr, H); /* H^3 */
406
407 ecp_nistz256_mul_mont(U2, U1, Hsqr); /* U1*H^2 */
408 ecp_nistz256_mul_by_2(Hsqr, U2); /* 2*U1*H^2 */
409
410 ecp_nistz256_sub(res_x, Rsqr, Hsqr);
411 ecp_nistz256_sub(res_x, res_x, Hcub);
412
413 ecp_nistz256_sub(res_y, U2, res_x);
414
415 ecp_nistz256_mul_mont(S2, S1, Hcub);
416 ecp_nistz256_mul_mont(res_y, R, res_y);
417 ecp_nistz256_sub(res_y, res_y, S2);
418
419 copy_conditional(res_x, in2_x, in1infty);
420 copy_conditional(res_y, in2_y, in1infty);
421 copy_conditional(res_z, in2_z, in1infty);
422
423 copy_conditional(res_x, in1_x, in2infty);
424 copy_conditional(res_y, in1_y, in2infty);
425 copy_conditional(res_z, in1_z, in2infty);
426
427 memcpy(r->X, res_x, sizeof(res_x));
428 memcpy(r->Y, res_y, sizeof(res_y));
429 memcpy(r->Z, res_z, sizeof(res_z));
430 }
431
432 /* Point addition when b is known to be affine: r = a+b */
ecp_nistz256_point_add_affine(P256_POINT * r,const P256_POINT * a,const P256_POINT_AFFINE * b)433 static void ecp_nistz256_point_add_affine(P256_POINT *r,
434 const P256_POINT *a,
435 const P256_POINT_AFFINE *b)
436 {
437 BN_ULONG U2[P256_LIMBS], S2[P256_LIMBS];
438 BN_ULONG Z1sqr[P256_LIMBS];
439 BN_ULONG H[P256_LIMBS], R[P256_LIMBS];
440 BN_ULONG Hsqr[P256_LIMBS];
441 BN_ULONG Rsqr[P256_LIMBS];
442 BN_ULONG Hcub[P256_LIMBS];
443
444 BN_ULONG res_x[P256_LIMBS];
445 BN_ULONG res_y[P256_LIMBS];
446 BN_ULONG res_z[P256_LIMBS];
447
448 BN_ULONG in1infty, in2infty;
449
450 const BN_ULONG *in1_x = a->X;
451 const BN_ULONG *in1_y = a->Y;
452 const BN_ULONG *in1_z = a->Z;
453
454 const BN_ULONG *in2_x = b->X;
455 const BN_ULONG *in2_y = b->Y;
456
457 /*
458 * Infinity in encoded as (,,0)
459 */
460 in1infty = (in1_z[0] | in1_z[1] | in1_z[2] | in1_z[3]);
461 if (P256_LIMBS == 8)
462 in1infty |= (in1_z[4] | in1_z[5] | in1_z[6] | in1_z[7]);
463
464 /*
465 * In affine representation we encode infinity as (0,0), which is
466 * not on the curve, so it is OK
467 */
468 in2infty = (in2_x[0] | in2_x[1] | in2_x[2] | in2_x[3] | in2_y[0] | in2_y[1] | in2_y[2] | in2_y[3]);
469 if (P256_LIMBS == 8)
470 in2infty |= (in2_x[4] | in2_x[5] | in2_x[6] | in2_x[7] | in2_y[4] | in2_y[5] | in2_y[6] | in2_y[7]);
471
472 in1infty = is_zero(in1infty);
473 in2infty = is_zero(in2infty);
474
475 ecp_nistz256_sqr_mont(Z1sqr, in1_z); /* Z1^2 */
476
477 ecp_nistz256_mul_mont(U2, in2_x, Z1sqr); /* U2 = X2*Z1^2 */
478 ecp_nistz256_sub(H, U2, in1_x); /* H = U2 - U1 */
479
480 ecp_nistz256_mul_mont(S2, Z1sqr, in1_z); /* S2 = Z1^3 */
481
482 ecp_nistz256_mul_mont(res_z, H, in1_z); /* Z3 = H*Z1*Z2 */
483
484 ecp_nistz256_mul_mont(S2, S2, in2_y); /* S2 = Y2*Z1^3 */
485 ecp_nistz256_sub(R, S2, in1_y); /* R = S2 - S1 */
486
487 ecp_nistz256_sqr_mont(Hsqr, H); /* H^2 */
488 ecp_nistz256_sqr_mont(Rsqr, R); /* R^2 */
489 ecp_nistz256_mul_mont(Hcub, Hsqr, H); /* H^3 */
490
491 ecp_nistz256_mul_mont(U2, in1_x, Hsqr); /* U1*H^2 */
492 ecp_nistz256_mul_by_2(Hsqr, U2); /* 2*U1*H^2 */
493
494 ecp_nistz256_sub(res_x, Rsqr, Hsqr);
495 ecp_nistz256_sub(res_x, res_x, Hcub);
496 ecp_nistz256_sub(H, U2, res_x);
497
498 ecp_nistz256_mul_mont(S2, in1_y, Hcub);
499 ecp_nistz256_mul_mont(H, H, R);
500 ecp_nistz256_sub(res_y, H, S2);
501
502 copy_conditional(res_x, in2_x, in1infty);
503 copy_conditional(res_x, in1_x, in2infty);
504
505 copy_conditional(res_y, in2_y, in1infty);
506 copy_conditional(res_y, in1_y, in2infty);
507
508 copy_conditional(res_z, ONE, in1infty);
509 copy_conditional(res_z, in1_z, in2infty);
510
511 memcpy(r->X, res_x, sizeof(res_x));
512 memcpy(r->Y, res_y, sizeof(res_y));
513 memcpy(r->Z, res_z, sizeof(res_z));
514 }
515 #endif
516
517 /* r = in^-1 mod p */
ecp_nistz256_mod_inverse(BN_ULONG r[P256_LIMBS],const BN_ULONG in[P256_LIMBS])518 static void ecp_nistz256_mod_inverse(BN_ULONG r[P256_LIMBS],
519 const BN_ULONG in[P256_LIMBS])
520 {
521 /*
522 * The poly is ffffffff 00000001 00000000 00000000 00000000 ffffffff
523 * ffffffff ffffffff We use FLT and used poly-2 as exponent
524 */
525 BN_ULONG p2[P256_LIMBS];
526 BN_ULONG p4[P256_LIMBS];
527 BN_ULONG p8[P256_LIMBS];
528 BN_ULONG p16[P256_LIMBS];
529 BN_ULONG p32[P256_LIMBS];
530 BN_ULONG res[P256_LIMBS];
531 int i;
532
533 ecp_nistz256_sqr_mont(res, in);
534 ecp_nistz256_mul_mont(p2, res, in); /* 3*p */
535
536 ecp_nistz256_sqr_mont(res, p2);
537 ecp_nistz256_sqr_mont(res, res);
538 ecp_nistz256_mul_mont(p4, res, p2); /* f*p */
539
540 ecp_nistz256_sqr_mont(res, p4);
541 ecp_nistz256_sqr_mont(res, res);
542 ecp_nistz256_sqr_mont(res, res);
543 ecp_nistz256_sqr_mont(res, res);
544 ecp_nistz256_mul_mont(p8, res, p4); /* ff*p */
545
546 ecp_nistz256_sqr_mont(res, p8);
547 for (i = 0; i < 7; i++)
548 ecp_nistz256_sqr_mont(res, res);
549 ecp_nistz256_mul_mont(p16, res, p8); /* ffff*p */
550
551 ecp_nistz256_sqr_mont(res, p16);
552 for (i = 0; i < 15; i++)
553 ecp_nistz256_sqr_mont(res, res);
554 ecp_nistz256_mul_mont(p32, res, p16); /* ffffffff*p */
555
556 ecp_nistz256_sqr_mont(res, p32);
557 for (i = 0; i < 31; i++)
558 ecp_nistz256_sqr_mont(res, res);
559 ecp_nistz256_mul_mont(res, res, in);
560
561 for (i = 0; i < 32 * 4; i++)
562 ecp_nistz256_sqr_mont(res, res);
563 ecp_nistz256_mul_mont(res, res, p32);
564
565 for (i = 0; i < 32; i++)
566 ecp_nistz256_sqr_mont(res, res);
567 ecp_nistz256_mul_mont(res, res, p32);
568
569 for (i = 0; i < 16; i++)
570 ecp_nistz256_sqr_mont(res, res);
571 ecp_nistz256_mul_mont(res, res, p16);
572
573 for (i = 0; i < 8; i++)
574 ecp_nistz256_sqr_mont(res, res);
575 ecp_nistz256_mul_mont(res, res, p8);
576
577 ecp_nistz256_sqr_mont(res, res);
578 ecp_nistz256_sqr_mont(res, res);
579 ecp_nistz256_sqr_mont(res, res);
580 ecp_nistz256_sqr_mont(res, res);
581 ecp_nistz256_mul_mont(res, res, p4);
582
583 ecp_nistz256_sqr_mont(res, res);
584 ecp_nistz256_sqr_mont(res, res);
585 ecp_nistz256_mul_mont(res, res, p2);
586
587 ecp_nistz256_sqr_mont(res, res);
588 ecp_nistz256_sqr_mont(res, res);
589 ecp_nistz256_mul_mont(res, res, in);
590
591 memcpy(r, res, sizeof(res));
592 }
593
594 /*
595 * ecp_nistz256_bignum_to_field_elem copies the contents of |in| to |out| and
596 * returns one if it fits. Otherwise it returns zero.
597 */
ecp_nistz256_bignum_to_field_elem(BN_ULONG out[P256_LIMBS],const BIGNUM * in)598 __owur static int ecp_nistz256_bignum_to_field_elem(BN_ULONG out[P256_LIMBS],
599 const BIGNUM *in)
600 {
601 return bn_copy_words(out, in, P256_LIMBS);
602 }
603
604 /* r = sum(scalar[i]*point[i]) */
ecp_nistz256_windowed_mul(const EC_GROUP * group,P256_POINT * r,const BIGNUM ** scalar,const EC_POINT ** point,size_t num,BN_CTX * ctx)605 __owur static int ecp_nistz256_windowed_mul(const EC_GROUP *group,
606 P256_POINT *r,
607 const BIGNUM **scalar,
608 const EC_POINT **point,
609 size_t num, BN_CTX *ctx)
610 {
611 size_t i;
612 int j, ret = 0;
613 unsigned int idx;
614 unsigned char (*p_str)[33] = NULL;
615 const unsigned int window_size = 5;
616 const unsigned int mask = (1 << (window_size + 1)) - 1;
617 unsigned int wvalue;
618 P256_POINT *temp; /* place for 5 temporary points */
619 const BIGNUM **scalars = NULL;
620 P256_POINT(*table)
621 [16] = NULL;
622 void *table_storage = NULL;
623
624 if ((num * 16 + 6) > OPENSSL_MALLOC_MAX_NELEMS(P256_POINT)
625 || (table_storage = OPENSSL_malloc((num * 16 + 5) * sizeof(P256_POINT) + 64)) == NULL
626 || (p_str = OPENSSL_malloc(num * 33 * sizeof(unsigned char))) == NULL
627 || (scalars = OPENSSL_malloc(num * sizeof(BIGNUM *))) == NULL)
628 goto err;
629
630 table = (void *)ALIGNPTR(table_storage, 64);
631 temp = (P256_POINT *)(table + num);
632
633 for (i = 0; i < num; i++) {
634 P256_POINT *row = table[i];
635
636 /* This is an unusual input, we don't guarantee constant-timeness. */
637 if ((BN_num_bits(scalar[i]) > 256) || BN_is_negative(scalar[i])) {
638 BIGNUM *mod;
639
640 if ((mod = BN_CTX_get(ctx)) == NULL)
641 goto err;
642 if (!BN_nnmod(mod, scalar[i], group->order, ctx)) {
643 ERR_raise(ERR_LIB_EC, ERR_R_BN_LIB);
644 goto err;
645 }
646 scalars[i] = mod;
647 } else
648 scalars[i] = scalar[i];
649
650 for (j = 0; j < bn_get_top(scalars[i]) * BN_BYTES; j += BN_BYTES) {
651 BN_ULONG d = bn_get_words(scalars[i])[j / BN_BYTES];
652
653 p_str[i][j + 0] = (unsigned char)d;
654 p_str[i][j + 1] = (unsigned char)(d >> 8);
655 p_str[i][j + 2] = (unsigned char)(d >> 16);
656 p_str[i][j + 3] = (unsigned char)(d >>= 24);
657 if (BN_BYTES == 8) {
658 d >>= 8;
659 p_str[i][j + 4] = (unsigned char)d;
660 p_str[i][j + 5] = (unsigned char)(d >> 8);
661 p_str[i][j + 6] = (unsigned char)(d >> 16);
662 p_str[i][j + 7] = (unsigned char)(d >> 24);
663 }
664 }
665 for (; j < 33; j++)
666 p_str[i][j] = 0;
667
668 if (!ecp_nistz256_bignum_to_field_elem(temp[0].X, point[i]->X)
669 || !ecp_nistz256_bignum_to_field_elem(temp[0].Y, point[i]->Y)
670 || !ecp_nistz256_bignum_to_field_elem(temp[0].Z, point[i]->Z)) {
671 ERR_raise(ERR_LIB_EC, EC_R_COORDINATES_OUT_OF_RANGE);
672 goto err;
673 }
674
675 /*
676 * row[0] is implicitly (0,0,0) (the point at infinity), therefore it
677 * is not stored. All other values are actually stored with an offset
678 * of -1 in table.
679 */
680
681 ecp_nistz256_scatter_w5(row, &temp[0], 1);
682 ecp_nistz256_point_double(&temp[1], &temp[0]); /*1+1=2 */
683 ecp_nistz256_scatter_w5(row, &temp[1], 2);
684 ecp_nistz256_point_add(&temp[2], &temp[1], &temp[0]); /*2+1=3 */
685 ecp_nistz256_scatter_w5(row, &temp[2], 3);
686 ecp_nistz256_point_double(&temp[1], &temp[1]); /*2*2=4 */
687 ecp_nistz256_scatter_w5(row, &temp[1], 4);
688 ecp_nistz256_point_double(&temp[2], &temp[2]); /*2*3=6 */
689 ecp_nistz256_scatter_w5(row, &temp[2], 6);
690 ecp_nistz256_point_add(&temp[3], &temp[1], &temp[0]); /*4+1=5 */
691 ecp_nistz256_scatter_w5(row, &temp[3], 5);
692 ecp_nistz256_point_add(&temp[4], &temp[2], &temp[0]); /*6+1=7 */
693 ecp_nistz256_scatter_w5(row, &temp[4], 7);
694 ecp_nistz256_point_double(&temp[1], &temp[1]); /*2*4=8 */
695 ecp_nistz256_scatter_w5(row, &temp[1], 8);
696 ecp_nistz256_point_double(&temp[2], &temp[2]); /*2*6=12 */
697 ecp_nistz256_scatter_w5(row, &temp[2], 12);
698 ecp_nistz256_point_double(&temp[3], &temp[3]); /*2*5=10 */
699 ecp_nistz256_scatter_w5(row, &temp[3], 10);
700 ecp_nistz256_point_double(&temp[4], &temp[4]); /*2*7=14 */
701 ecp_nistz256_scatter_w5(row, &temp[4], 14);
702 ecp_nistz256_point_add(&temp[2], &temp[2], &temp[0]); /*12+1=13*/
703 ecp_nistz256_scatter_w5(row, &temp[2], 13);
704 ecp_nistz256_point_add(&temp[3], &temp[3], &temp[0]); /*10+1=11*/
705 ecp_nistz256_scatter_w5(row, &temp[3], 11);
706 ecp_nistz256_point_add(&temp[4], &temp[4], &temp[0]); /*14+1=15*/
707 ecp_nistz256_scatter_w5(row, &temp[4], 15);
708 ecp_nistz256_point_add(&temp[2], &temp[1], &temp[0]); /*8+1=9 */
709 ecp_nistz256_scatter_w5(row, &temp[2], 9);
710 ecp_nistz256_point_double(&temp[1], &temp[1]); /*2*8=16 */
711 ecp_nistz256_scatter_w5(row, &temp[1], 16);
712 }
713
714 idx = 255;
715
716 wvalue = p_str[0][(idx - 1) / 8];
717 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
718
719 /*
720 * We gather to temp[0], because we know it's position relative
721 * to table
722 */
723 ecp_nistz256_gather_w5(&temp[0], table[0], _booth_recode_w5(wvalue) >> 1);
724 memcpy(r, &temp[0], sizeof(temp[0]));
725
726 while (idx >= 5) {
727 for (i = (idx == 255 ? 1 : 0); i < num; i++) {
728 unsigned int off = (idx - 1) / 8;
729
730 wvalue = p_str[i][off] | p_str[i][off + 1] << 8;
731 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
732
733 wvalue = _booth_recode_w5(wvalue);
734
735 ecp_nistz256_gather_w5(&temp[0], table[i], wvalue >> 1);
736
737 ecp_nistz256_neg(temp[1].Y, temp[0].Y);
738 copy_conditional(temp[0].Y, temp[1].Y, (wvalue & 1));
739
740 ecp_nistz256_point_add(r, r, &temp[0]);
741 }
742
743 idx -= window_size;
744
745 ecp_nistz256_point_double(r, r);
746 ecp_nistz256_point_double(r, r);
747 ecp_nistz256_point_double(r, r);
748 ecp_nistz256_point_double(r, r);
749 ecp_nistz256_point_double(r, r);
750 }
751
752 /* Final window */
753 for (i = 0; i < num; i++) {
754 wvalue = p_str[i][0];
755 wvalue = (wvalue << 1) & mask;
756
757 wvalue = _booth_recode_w5(wvalue);
758
759 ecp_nistz256_gather_w5(&temp[0], table[i], wvalue >> 1);
760
761 ecp_nistz256_neg(temp[1].Y, temp[0].Y);
762 copy_conditional(temp[0].Y, temp[1].Y, wvalue & 1);
763
764 ecp_nistz256_point_add(r, r, &temp[0]);
765 }
766
767 ret = 1;
768 err:
769 OPENSSL_free(table_storage);
770 OPENSSL_free(p_str);
771 OPENSSL_free(scalars);
772 return ret;
773 }
774
775 /* Coordinates of G, for which we have precomputed tables */
776 static const BN_ULONG def_xG[P256_LIMBS] = {
777 TOBN(0x79e730d4, 0x18a9143c), TOBN(0x75ba95fc, 0x5fedb601),
778 TOBN(0x79fb732b, 0x77622510), TOBN(0x18905f76, 0xa53755c6)
779 };
780
781 static const BN_ULONG def_yG[P256_LIMBS] = {
782 TOBN(0xddf25357, 0xce95560a), TOBN(0x8b4ab8e4, 0xba19e45c),
783 TOBN(0xd2e88688, 0xdd21f325), TOBN(0x8571ff18, 0x25885d85)
784 };
785
786 /*
787 * ecp_nistz256_is_affine_G returns one if |generator| is the standard, P-256
788 * generator.
789 */
ecp_nistz256_is_affine_G(const EC_POINT * generator)790 static int ecp_nistz256_is_affine_G(const EC_POINT *generator)
791 {
792 return (bn_get_top(generator->X) == P256_LIMBS) && (bn_get_top(generator->Y) == P256_LIMBS) && is_equal(bn_get_words(generator->X), def_xG) && is_equal(bn_get_words(generator->Y), def_yG) && is_one(generator->Z);
793 }
794
ecp_nistz256_mult_precompute(EC_GROUP * group,BN_CTX * ctx)795 __owur static int ecp_nistz256_mult_precompute(EC_GROUP *group, BN_CTX *ctx)
796 {
797 /*
798 * We precompute a table for a Booth encoded exponent (wNAF) based
799 * computation. Each table holds 64 values for safe access, with an
800 * implicit value of infinity at index zero. We use window of size 7, and
801 * therefore require ceil(256/7) = 37 tables.
802 */
803 const BIGNUM *order;
804 EC_POINT *P = NULL, *T = NULL;
805 const EC_POINT *generator;
806 NISTZ256_PRE_COMP *pre_comp;
807 BN_CTX *new_ctx = NULL;
808 int i, j, k, ret = 0;
809 size_t w;
810
811 PRECOMP256_ROW *preComputedTable = NULL;
812 unsigned char *precomp_storage = NULL;
813
814 /* if there is an old NISTZ256_PRE_COMP object, throw it away */
815 EC_pre_comp_free(group);
816 generator = EC_GROUP_get0_generator(group);
817 if (generator == NULL) {
818 ERR_raise(ERR_LIB_EC, EC_R_UNDEFINED_GENERATOR);
819 return 0;
820 }
821
822 if (ecp_nistz256_is_affine_G(generator)) {
823 /*
824 * No need to calculate tables for the standard generator because we
825 * have them statically.
826 */
827 return 1;
828 }
829
830 if ((pre_comp = ecp_nistz256_pre_comp_new(group)) == NULL)
831 return 0;
832
833 if (ctx == NULL) {
834 ctx = new_ctx = BN_CTX_new_ex(group->libctx);
835 if (ctx == NULL)
836 goto err;
837 }
838
839 BN_CTX_start(ctx);
840
841 order = EC_GROUP_get0_order(group);
842 if (order == NULL)
843 goto err;
844
845 if (BN_is_zero(order)) {
846 ERR_raise(ERR_LIB_EC, EC_R_UNKNOWN_ORDER);
847 goto err;
848 }
849
850 w = 7;
851
852 if ((precomp_storage = OPENSSL_malloc(37 * 64 * sizeof(P256_POINT_AFFINE) + 64)) == NULL)
853 goto err;
854
855 preComputedTable = (void *)ALIGNPTR(precomp_storage, 64);
856
857 P = EC_POINT_new(group);
858 T = EC_POINT_new(group);
859 if (P == NULL || T == NULL)
860 goto err;
861
862 /*
863 * The zero entry is implicitly infinity, and we skip it, storing other
864 * values with -1 offset.
865 */
866 if (!EC_POINT_copy(T, generator))
867 goto err;
868
869 for (k = 0; k < 64; k++) {
870 if (!EC_POINT_copy(P, T))
871 goto err;
872 for (j = 0; j < 37; j++) {
873 P256_POINT_AFFINE temp;
874 /*
875 * It would be faster to use EC_POINTs_make_affine and
876 * make multiple points affine at the same time.
877 */
878 if (group->meth->make_affine == NULL
879 || !group->meth->make_affine(group, P, ctx))
880 goto err;
881 if (!ecp_nistz256_bignum_to_field_elem(temp.X, P->X) || !ecp_nistz256_bignum_to_field_elem(temp.Y, P->Y)) {
882 ERR_raise(ERR_LIB_EC, EC_R_COORDINATES_OUT_OF_RANGE);
883 goto err;
884 }
885 ecp_nistz256_scatter_w7(preComputedTable[j], &temp, k);
886 for (i = 0; i < 7; i++) {
887 if (!EC_POINT_dbl(group, P, P, ctx))
888 goto err;
889 }
890 }
891 if (!EC_POINT_add(group, T, T, generator, ctx))
892 goto err;
893 }
894
895 pre_comp->group = group;
896 pre_comp->w = w;
897 pre_comp->precomp = preComputedTable;
898 pre_comp->precomp_storage = precomp_storage;
899 precomp_storage = NULL;
900 SETPRECOMP(group, nistz256, pre_comp);
901 pre_comp = NULL;
902 ret = 1;
903
904 err:
905 BN_CTX_end(ctx);
906 BN_CTX_free(new_ctx);
907
908 EC_nistz256_pre_comp_free(pre_comp);
909 OPENSSL_free(precomp_storage);
910 EC_POINT_free(P);
911 EC_POINT_free(T);
912 return ret;
913 }
914
ecp_nistz256_set_from_affine(EC_POINT * out,const EC_GROUP * group,const P256_POINT_AFFINE * in,BN_CTX * ctx)915 __owur static int ecp_nistz256_set_from_affine(EC_POINT *out, const EC_GROUP *group,
916 const P256_POINT_AFFINE *in,
917 BN_CTX *ctx)
918 {
919 int ret = 0;
920
921 if ((ret = bn_set_words(out->X, in->X, P256_LIMBS))
922 && (ret = bn_set_words(out->Y, in->Y, P256_LIMBS))
923 && (ret = bn_set_words(out->Z, ONE, P256_LIMBS)))
924 out->Z_is_one = 1;
925
926 return ret;
927 }
928
929 /* r = scalar*G + sum(scalars[i]*points[i]) */
ecp_nistz256_points_mul(const EC_GROUP * group,EC_POINT * r,const BIGNUM * scalar,size_t num,const EC_POINT * points[],const BIGNUM * scalars[],BN_CTX * ctx)930 __owur static int ecp_nistz256_points_mul(const EC_GROUP *group,
931 EC_POINT *r,
932 const BIGNUM *scalar,
933 size_t num,
934 const EC_POINT *points[],
935 const BIGNUM *scalars[], BN_CTX *ctx)
936 {
937 int i = 0, ret = 0, no_precomp_for_generator = 0, p_is_infinity = 0;
938 unsigned char p_str[33] = { 0 };
939 const PRECOMP256_ROW *preComputedTable = NULL;
940 const NISTZ256_PRE_COMP *pre_comp = NULL;
941 const EC_POINT *generator = NULL;
942 const BIGNUM **new_scalars = NULL;
943 const EC_POINT **new_points = NULL;
944 unsigned int idx = 0;
945 const unsigned int window_size = 7;
946 const unsigned int mask = (1 << (window_size + 1)) - 1;
947 unsigned int wvalue;
948 ALIGN32 union {
949 P256_POINT p;
950 P256_POINT_AFFINE a;
951 } t, p;
952 BIGNUM *tmp_scalar;
953
954 if ((num + 1) == 0 || (num + 1) > OPENSSL_MALLOC_MAX_NELEMS(void *)) {
955 ERR_raise(ERR_LIB_EC, ERR_R_PASSED_INVALID_ARGUMENT);
956 return 0;
957 }
958
959 memset(&p, 0, sizeof(p));
960 BN_CTX_start(ctx);
961
962 if (scalar) {
963 generator = EC_GROUP_get0_generator(group);
964 if (generator == NULL) {
965 ERR_raise(ERR_LIB_EC, EC_R_UNDEFINED_GENERATOR);
966 goto err;
967 }
968
969 /* look if we can use precomputed multiples of generator */
970 pre_comp = group->pre_comp.nistz256;
971
972 if (pre_comp) {
973 /*
974 * If there is a precomputed table for the generator, check that
975 * it was generated with the same generator.
976 */
977 EC_POINT *pre_comp_generator = EC_POINT_new(group);
978 if (pre_comp_generator == NULL)
979 goto err;
980
981 ecp_nistz256_gather_w7(&p.a, pre_comp->precomp[0], 1);
982 if (!ecp_nistz256_set_from_affine(pre_comp_generator,
983 group, &p.a, ctx)) {
984 EC_POINT_free(pre_comp_generator);
985 goto err;
986 }
987
988 if (0 == EC_POINT_cmp(group, generator, pre_comp_generator, ctx))
989 preComputedTable = (const PRECOMP256_ROW *)pre_comp->precomp;
990
991 EC_POINT_free(pre_comp_generator);
992 }
993
994 if (preComputedTable == NULL && ecp_nistz256_is_affine_G(generator)) {
995 /*
996 * If there is no precomputed data, but the generator is the
997 * default, a hardcoded table of precomputed data is used. This
998 * is because applications, such as Apache, do not use
999 * EC_KEY_precompute_mult.
1000 */
1001 preComputedTable = ecp_nistz256_precomputed;
1002 }
1003
1004 if (preComputedTable) {
1005 BN_ULONG infty;
1006
1007 if ((BN_num_bits(scalar) > 256)
1008 || BN_is_negative(scalar)) {
1009 if ((tmp_scalar = BN_CTX_get(ctx)) == NULL)
1010 goto err;
1011
1012 if (!BN_nnmod(tmp_scalar, scalar, group->order, ctx)) {
1013 ERR_raise(ERR_LIB_EC, ERR_R_BN_LIB);
1014 goto err;
1015 }
1016 scalar = tmp_scalar;
1017 }
1018
1019 for (i = 0; i < bn_get_top(scalar) * BN_BYTES; i += BN_BYTES) {
1020 BN_ULONG d = bn_get_words(scalar)[i / BN_BYTES];
1021
1022 p_str[i + 0] = (unsigned char)d;
1023 p_str[i + 1] = (unsigned char)(d >> 8);
1024 p_str[i + 2] = (unsigned char)(d >> 16);
1025 p_str[i + 3] = (unsigned char)(d >>= 24);
1026 if (BN_BYTES == 8) {
1027 d >>= 8;
1028 p_str[i + 4] = (unsigned char)d;
1029 p_str[i + 5] = (unsigned char)(d >> 8);
1030 p_str[i + 6] = (unsigned char)(d >> 16);
1031 p_str[i + 7] = (unsigned char)(d >> 24);
1032 }
1033 }
1034
1035 for (; i < 33; i++)
1036 p_str[i] = 0;
1037
1038 /* First window */
1039 wvalue = (p_str[0] << 1) & mask;
1040 idx += window_size;
1041
1042 wvalue = _booth_recode_w7(wvalue);
1043
1044 ecp_nistz256_gather_w7(&p.a, preComputedTable[0],
1045 wvalue >> 1);
1046
1047 ecp_nistz256_neg(p.p.Z, p.p.Y);
1048 copy_conditional(p.p.Y, p.p.Z, wvalue & 1);
1049
1050 /*
1051 * Since affine infinity is encoded as (0,0) and
1052 * Jacobian is (,,0), we need to harmonize them
1053 * by assigning "one" or zero to Z.
1054 */
1055 infty = (p.p.X[0] | p.p.X[1] | p.p.X[2] | p.p.X[3] | p.p.Y[0] | p.p.Y[1] | p.p.Y[2] | p.p.Y[3]);
1056 if (P256_LIMBS == 8)
1057 infty |= (p.p.X[4] | p.p.X[5] | p.p.X[6] | p.p.X[7] | p.p.Y[4] | p.p.Y[5] | p.p.Y[6] | p.p.Y[7]);
1058
1059 infty = 0 - is_zero(infty);
1060 infty = ~infty;
1061
1062 p.p.Z[0] = ONE[0] & infty;
1063 p.p.Z[1] = ONE[1] & infty;
1064 p.p.Z[2] = ONE[2] & infty;
1065 p.p.Z[3] = ONE[3] & infty;
1066 if (P256_LIMBS == 8) {
1067 p.p.Z[4] = ONE[4] & infty;
1068 p.p.Z[5] = ONE[5] & infty;
1069 p.p.Z[6] = ONE[6] & infty;
1070 p.p.Z[7] = ONE[7] & infty;
1071 }
1072
1073 for (i = 1; i < 37; i++) {
1074 unsigned int off = (idx - 1) / 8;
1075 wvalue = p_str[off] | p_str[off + 1] << 8;
1076 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
1077 idx += window_size;
1078
1079 wvalue = _booth_recode_w7(wvalue);
1080
1081 ecp_nistz256_gather_w7(&t.a,
1082 preComputedTable[i], wvalue >> 1);
1083
1084 ecp_nistz256_neg(t.p.Z, t.a.Y);
1085 copy_conditional(t.a.Y, t.p.Z, wvalue & 1);
1086
1087 ecp_nistz256_point_add_affine(&p.p, &p.p, &t.a);
1088 }
1089 } else {
1090 p_is_infinity = 1;
1091 no_precomp_for_generator = 1;
1092 }
1093 } else
1094 p_is_infinity = 1;
1095
1096 if (no_precomp_for_generator) {
1097 /*
1098 * Without a precomputed table for the generator, it has to be
1099 * handled like a normal point.
1100 */
1101 new_scalars = OPENSSL_malloc((num + 1) * sizeof(BIGNUM *));
1102 if (new_scalars == NULL)
1103 goto err;
1104
1105 new_points = OPENSSL_malloc((num + 1) * sizeof(EC_POINT *));
1106 if (new_points == NULL)
1107 goto err;
1108
1109 memcpy(new_scalars, scalars, num * sizeof(BIGNUM *));
1110 new_scalars[num] = scalar;
1111 memcpy(new_points, points, num * sizeof(EC_POINT *));
1112 new_points[num] = generator;
1113
1114 scalars = new_scalars;
1115 points = new_points;
1116 num++;
1117 }
1118
1119 if (num) {
1120 P256_POINT *out = &t.p;
1121 if (p_is_infinity)
1122 out = &p.p;
1123
1124 if (!ecp_nistz256_windowed_mul(group, out, scalars, points, num, ctx))
1125 goto err;
1126
1127 if (!p_is_infinity)
1128 ecp_nistz256_point_add(&p.p, &p.p, out);
1129 }
1130
1131 /* Not constant-time, but we're only operating on the public output. */
1132 if (!bn_set_words(r->X, p.p.X, P256_LIMBS) || !bn_set_words(r->Y, p.p.Y, P256_LIMBS) || !bn_set_words(r->Z, p.p.Z, P256_LIMBS)) {
1133 goto err;
1134 }
1135 r->Z_is_one = is_one(r->Z) & 1;
1136
1137 ret = 1;
1138
1139 err:
1140 BN_CTX_end(ctx);
1141 OPENSSL_free(new_points);
1142 OPENSSL_free(new_scalars);
1143 return ret;
1144 }
1145
ecp_nistz256_get_affine(const EC_GROUP * group,const EC_POINT * point,BIGNUM * x,BIGNUM * y,BN_CTX * ctx)1146 __owur static int ecp_nistz256_get_affine(const EC_GROUP *group,
1147 const EC_POINT *point,
1148 BIGNUM *x, BIGNUM *y, BN_CTX *ctx)
1149 {
1150 BN_ULONG z_inv2[P256_LIMBS];
1151 BN_ULONG z_inv3[P256_LIMBS];
1152 BN_ULONG x_aff[P256_LIMBS];
1153 BN_ULONG y_aff[P256_LIMBS];
1154 BN_ULONG point_x[P256_LIMBS], point_y[P256_LIMBS], point_z[P256_LIMBS];
1155 BN_ULONG x_ret[P256_LIMBS], y_ret[P256_LIMBS];
1156
1157 if (EC_POINT_is_at_infinity(group, point)) {
1158 ERR_raise(ERR_LIB_EC, EC_R_POINT_AT_INFINITY);
1159 return 0;
1160 }
1161
1162 if (!ecp_nistz256_bignum_to_field_elem(point_x, point->X) || !ecp_nistz256_bignum_to_field_elem(point_y, point->Y) || !ecp_nistz256_bignum_to_field_elem(point_z, point->Z)) {
1163 ERR_raise(ERR_LIB_EC, EC_R_COORDINATES_OUT_OF_RANGE);
1164 return 0;
1165 }
1166
1167 ecp_nistz256_mod_inverse(z_inv3, point_z);
1168 ecp_nistz256_sqr_mont(z_inv2, z_inv3);
1169 ecp_nistz256_mul_mont(x_aff, z_inv2, point_x);
1170
1171 if (x != NULL) {
1172 ecp_nistz256_from_mont(x_ret, x_aff);
1173 if (!bn_set_words(x, x_ret, P256_LIMBS))
1174 return 0;
1175 }
1176
1177 if (y != NULL) {
1178 ecp_nistz256_mul_mont(z_inv3, z_inv3, z_inv2);
1179 ecp_nistz256_mul_mont(y_aff, z_inv3, point_y);
1180 ecp_nistz256_from_mont(y_ret, y_aff);
1181 if (!bn_set_words(y, y_ret, P256_LIMBS))
1182 return 0;
1183 }
1184
1185 return 1;
1186 }
1187
ecp_nistz256_pre_comp_new(const EC_GROUP * group)1188 static NISTZ256_PRE_COMP *ecp_nistz256_pre_comp_new(const EC_GROUP *group)
1189 {
1190 NISTZ256_PRE_COMP *ret = NULL;
1191
1192 if (!group)
1193 return NULL;
1194
1195 ret = OPENSSL_zalloc(sizeof(*ret));
1196
1197 if (ret == NULL)
1198 return ret;
1199
1200 ret->group = group;
1201 ret->w = 6; /* default */
1202
1203 if (!CRYPTO_NEW_REF(&ret->references, 1)) {
1204 OPENSSL_free(ret);
1205 return NULL;
1206 }
1207 return ret;
1208 }
1209
EC_nistz256_pre_comp_dup(NISTZ256_PRE_COMP * p)1210 NISTZ256_PRE_COMP *EC_nistz256_pre_comp_dup(NISTZ256_PRE_COMP *p)
1211 {
1212 int i;
1213 if (p != NULL)
1214 CRYPTO_UP_REF(&p->references, &i);
1215 return p;
1216 }
1217
EC_nistz256_pre_comp_free(NISTZ256_PRE_COMP * pre)1218 void EC_nistz256_pre_comp_free(NISTZ256_PRE_COMP *pre)
1219 {
1220 int i;
1221
1222 if (pre == NULL)
1223 return;
1224
1225 CRYPTO_DOWN_REF(&pre->references, &i);
1226 REF_PRINT_COUNT("EC_nistz256", i, pre);
1227 if (i > 0)
1228 return;
1229 REF_ASSERT_ISNT(i < 0);
1230
1231 OPENSSL_free(pre->precomp_storage);
1232 CRYPTO_FREE_REF(&pre->references);
1233 OPENSSL_free(pre);
1234 }
1235
ecp_nistz256_window_have_precompute_mult(const EC_GROUP * group)1236 static int ecp_nistz256_window_have_precompute_mult(const EC_GROUP *group)
1237 {
1238 /* There is a hard-coded table for the default generator. */
1239 const EC_POINT *generator = EC_GROUP_get0_generator(group);
1240
1241 if (generator != NULL && ecp_nistz256_is_affine_G(generator)) {
1242 /* There is a hard-coded table for the default generator. */
1243 return 1;
1244 }
1245
1246 return HAVEPRECOMP(group, nistz256);
1247 }
1248
1249 #if defined(__x86_64) || defined(__x86_64__) || defined(_M_AMD64) || defined(_M_X64) || defined(__powerpc64__) || defined(_ARCH_PP64) || defined(__aarch64__)
1250 /*
1251 * Montgomery mul modulo Order(P): res = a*b*2^-256 mod Order(P)
1252 */
1253 void ecp_nistz256_ord_mul_mont(BN_ULONG res[P256_LIMBS],
1254 const BN_ULONG a[P256_LIMBS],
1255 const BN_ULONG b[P256_LIMBS]);
1256 void ecp_nistz256_ord_sqr_mont(BN_ULONG res[P256_LIMBS],
1257 const BN_ULONG a[P256_LIMBS],
1258 BN_ULONG rep);
1259
ecp_nistz256_inv_mod_ord(const EC_GROUP * group,BIGNUM * r,const BIGNUM * x,BN_CTX * ctx)1260 static int ecp_nistz256_inv_mod_ord(const EC_GROUP *group, BIGNUM *r,
1261 const BIGNUM *x, BN_CTX *ctx)
1262 {
1263 /* RR = 2^512 mod ord(p256) */
1264 static const BN_ULONG RR[P256_LIMBS] = {
1265 TOBN(0x83244c95, 0xbe79eea2), TOBN(0x4699799c, 0x49bd6fa6),
1266 TOBN(0x2845b239, 0x2b6bec59), TOBN(0x66e12d94, 0xf3d95620)
1267 };
1268 /* The constant 1 (unlike ONE that is one in Montgomery representation) */
1269 static const BN_ULONG one[P256_LIMBS] = {
1270 TOBN(0, 1), TOBN(0, 0), TOBN(0, 0), TOBN(0, 0)
1271 };
1272 /*
1273 * We don't use entry 0 in the table, so we omit it and address
1274 * with -1 offset.
1275 */
1276 BN_ULONG table[15][P256_LIMBS];
1277 BN_ULONG out[P256_LIMBS], t[P256_LIMBS];
1278 int i, ret = 0;
1279 enum {
1280 i_1 = 0,
1281 i_10,
1282 i_11,
1283 i_101,
1284 i_111,
1285 i_1010,
1286 i_1111,
1287 i_10101,
1288 i_101010,
1289 i_101111,
1290 i_x6,
1291 i_x8,
1292 i_x16,
1293 i_x32
1294 };
1295
1296 /*
1297 * Catch allocation failure early.
1298 */
1299 if (bn_wexpand(r, P256_LIMBS) == NULL) {
1300 ERR_raise(ERR_LIB_EC, ERR_R_BN_LIB);
1301 goto err;
1302 }
1303
1304 if ((BN_num_bits(x) > 256) || BN_is_negative(x)) {
1305 BIGNUM *tmp;
1306
1307 if ((tmp = BN_CTX_get(ctx)) == NULL
1308 || !BN_nnmod(tmp, x, group->order, ctx)) {
1309 ERR_raise(ERR_LIB_EC, ERR_R_BN_LIB);
1310 goto err;
1311 }
1312 x = tmp;
1313 }
1314
1315 if (!ecp_nistz256_bignum_to_field_elem(t, x)) {
1316 ERR_raise(ERR_LIB_EC, EC_R_COORDINATES_OUT_OF_RANGE);
1317 goto err;
1318 }
1319
1320 ecp_nistz256_ord_mul_mont(table[0], t, RR);
1321 #if 0
1322 /*
1323 * Original sparse-then-fixed-window algorithm, retained for reference.
1324 */
1325 for (i = 2; i < 16; i += 2) {
1326 ecp_nistz256_ord_sqr_mont(table[i-1], table[i/2-1], 1);
1327 ecp_nistz256_ord_mul_mont(table[i], table[i-1], table[0]);
1328 }
1329
1330 /*
1331 * The top 128bit of the exponent are highly redudndant, so we
1332 * perform an optimized flow
1333 */
1334 ecp_nistz256_ord_sqr_mont(t, table[15-1], 4); /* f0 */
1335 ecp_nistz256_ord_mul_mont(t, t, table[15-1]); /* ff */
1336
1337 ecp_nistz256_ord_sqr_mont(out, t, 8); /* ff00 */
1338 ecp_nistz256_ord_mul_mont(out, out, t); /* ffff */
1339
1340 ecp_nistz256_ord_sqr_mont(t, out, 16); /* ffff0000 */
1341 ecp_nistz256_ord_mul_mont(t, t, out); /* ffffffff */
1342
1343 ecp_nistz256_ord_sqr_mont(out, t, 64); /* ffffffff0000000000000000 */
1344 ecp_nistz256_ord_mul_mont(out, out, t); /* ffffffff00000000ffffffff */
1345
1346 ecp_nistz256_ord_sqr_mont(out, out, 32); /* ffffffff00000000ffffffff00000000 */
1347 ecp_nistz256_ord_mul_mont(out, out, t); /* ffffffff00000000ffffffffffffffff */
1348
1349 /*
1350 * The bottom 128 bit of the exponent are processed with fixed 4-bit window
1351 */
1352 for (i = 0; i < 32; i++) {
1353 /* expLo - the low 128 bits of the exponent we use (ord(p256) - 2),
1354 * split into nibbles */
1355 static const unsigned char expLo[32] = {
1356 0xb,0xc,0xe,0x6,0xf,0xa,0xa,0xd,0xa,0x7,0x1,0x7,0x9,0xe,0x8,0x4,
1357 0xf,0x3,0xb,0x9,0xc,0xa,0xc,0x2,0xf,0xc,0x6,0x3,0x2,0x5,0x4,0xf
1358 };
1359
1360 ecp_nistz256_ord_sqr_mont(out, out, 4);
1361 /* The exponent is public, no need in constant-time access */
1362 ecp_nistz256_ord_mul_mont(out, out, table[expLo[i]-1]);
1363 }
1364 #else
1365 /*
1366 * https://briansmith.org/ecc-inversion-addition-chains-01#p256_scalar_inversion
1367 *
1368 * Even though this code path spares 12 squarings, 4.5%, and 13
1369 * multiplications, 25%, on grand scale sign operation is not that
1370 * much faster, not more that 2%...
1371 */
1372
1373 /* pre-calculate powers */
1374 ecp_nistz256_ord_sqr_mont(table[i_10], table[i_1], 1);
1375
1376 ecp_nistz256_ord_mul_mont(table[i_11], table[i_1], table[i_10]);
1377
1378 ecp_nistz256_ord_mul_mont(table[i_101], table[i_11], table[i_10]);
1379
1380 ecp_nistz256_ord_mul_mont(table[i_111], table[i_101], table[i_10]);
1381
1382 ecp_nistz256_ord_sqr_mont(table[i_1010], table[i_101], 1);
1383
1384 ecp_nistz256_ord_mul_mont(table[i_1111], table[i_1010], table[i_101]);
1385
1386 ecp_nistz256_ord_sqr_mont(table[i_10101], table[i_1010], 1);
1387 ecp_nistz256_ord_mul_mont(table[i_10101], table[i_10101], table[i_1]);
1388
1389 ecp_nistz256_ord_sqr_mont(table[i_101010], table[i_10101], 1);
1390
1391 ecp_nistz256_ord_mul_mont(table[i_101111], table[i_101010], table[i_101]);
1392
1393 ecp_nistz256_ord_mul_mont(table[i_x6], table[i_101010], table[i_10101]);
1394
1395 ecp_nistz256_ord_sqr_mont(table[i_x8], table[i_x6], 2);
1396 ecp_nistz256_ord_mul_mont(table[i_x8], table[i_x8], table[i_11]);
1397
1398 ecp_nistz256_ord_sqr_mont(table[i_x16], table[i_x8], 8);
1399 ecp_nistz256_ord_mul_mont(table[i_x16], table[i_x16], table[i_x8]);
1400
1401 ecp_nistz256_ord_sqr_mont(table[i_x32], table[i_x16], 16);
1402 ecp_nistz256_ord_mul_mont(table[i_x32], table[i_x32], table[i_x16]);
1403
1404 /* calculations */
1405 ecp_nistz256_ord_sqr_mont(out, table[i_x32], 64);
1406 ecp_nistz256_ord_mul_mont(out, out, table[i_x32]);
1407
1408 for (i = 0; i < 27; i++) {
1409 static const struct {
1410 unsigned char p, i;
1411 } chain[27] = {
1412 { 32, i_x32 }, { 6, i_101111 }, { 5, i_111 },
1413 { 4, i_11 }, { 5, i_1111 }, { 5, i_10101 },
1414 { 4, i_101 }, { 3, i_101 }, { 3, i_101 },
1415 { 5, i_111 }, { 9, i_101111 }, { 6, i_1111 },
1416 { 2, i_1 }, { 5, i_1 }, { 6, i_1111 },
1417 { 5, i_111 }, { 4, i_111 }, { 5, i_111 },
1418 { 5, i_101 }, { 3, i_11 }, { 10, i_101111 },
1419 { 2, i_11 }, { 5, i_11 }, { 5, i_11 },
1420 { 3, i_1 }, { 7, i_10101 }, { 6, i_1111 }
1421 };
1422
1423 ecp_nistz256_ord_sqr_mont(out, out, chain[i].p);
1424 ecp_nistz256_ord_mul_mont(out, out, table[chain[i].i]);
1425 }
1426 #endif
1427 ecp_nistz256_ord_mul_mont(out, out, one);
1428
1429 /*
1430 * Can't fail, but check return code to be consistent anyway.
1431 */
1432 if (!bn_set_words(r, out, P256_LIMBS))
1433 goto err;
1434
1435 ret = 1;
1436 err:
1437 return ret;
1438 }
1439 #else
1440 #define ecp_nistz256_inv_mod_ord NULL
1441 #endif
1442
ecp_nistz256group_full_init(EC_GROUP * group,const unsigned char * params)1443 static int ecp_nistz256group_full_init(EC_GROUP *group,
1444 const unsigned char *params)
1445 {
1446 BN_CTX *ctx = NULL;
1447 BN_MONT_CTX *mont = NULL, *ordmont = NULL;
1448 const int param_len = 32;
1449 const int seed_len = 20;
1450 int ok = 0;
1451 uint32_t hi_order_n = 0xccd1c8aa;
1452 uint32_t lo_order_n = 0xee00bc4f;
1453 BIGNUM *p = NULL, *a = NULL, *b = NULL, *x = NULL, *y = NULL, *one = NULL,
1454 *order = NULL;
1455 EC_POINT *P = NULL;
1456
1457 if ((ctx = BN_CTX_new_ex(group->libctx)) == NULL) {
1458 ERR_raise(ERR_LIB_EC, ERR_R_MALLOC_FAILURE);
1459 return 0;
1460 }
1461
1462 if (!EC_GROUP_set_seed(group, params, seed_len)) {
1463 ERR_raise(ERR_LIB_EC, ERR_R_EC_LIB);
1464 goto err;
1465 }
1466 params += seed_len;
1467
1468 if ((p = BN_bin2bn(params + 0 * param_len, param_len, NULL)) == NULL
1469 || (a = BN_bin2bn(params + 1 * param_len, param_len, NULL)) == NULL
1470 || (b = BN_bin2bn(params + 2 * param_len, param_len, NULL)) == NULL) {
1471 ERR_raise(ERR_LIB_EC, ERR_R_BN_LIB);
1472 goto err;
1473 }
1474
1475 /*
1476 * Set up curve params and montgomery for field
1477 * Start by setting up montgomery and one
1478 */
1479 mont = BN_MONT_CTX_new();
1480 if (mont == NULL)
1481 goto err;
1482
1483 if (!ossl_bn_mont_ctx_set(mont, p, 256, params + 6 * param_len, param_len,
1484 1, 0))
1485 goto err;
1486
1487 one = BN_new();
1488 if (one == NULL) {
1489 ERR_raise(ERR_LIB_EC, ERR_R_BN_LIB);
1490 goto err;
1491 }
1492 if (!BN_to_montgomery(one, BN_value_one(), mont, ctx)) {
1493 ERR_raise(ERR_LIB_EC, ERR_R_BN_LIB);
1494 goto err;
1495 }
1496 group->field_data1 = mont;
1497 mont = NULL;
1498 group->field_data2 = one;
1499 one = NULL;
1500
1501 if (!ossl_ec_GFp_simple_group_set_curve(group, p, a, b, ctx)) {
1502 ERR_raise(ERR_LIB_EC, ERR_R_EC_LIB);
1503 goto err;
1504 }
1505
1506 if ((P = EC_POINT_new(group)) == NULL) {
1507 ERR_raise(ERR_LIB_EC, ERR_R_EC_LIB);
1508 goto err;
1509 }
1510
1511 if ((x = BN_bin2bn(params + 3 * param_len, param_len, NULL)) == NULL
1512 || (y = BN_bin2bn(params + 4 * param_len, param_len, NULL)) == NULL) {
1513 ERR_raise(ERR_LIB_EC, ERR_R_BN_LIB);
1514 goto err;
1515 }
1516 if (!EC_POINT_set_affine_coordinates(group, P, x, y, ctx)) {
1517 ERR_raise(ERR_LIB_EC, ERR_R_EC_LIB);
1518 goto err;
1519 }
1520 if ((order = BN_bin2bn(params + 5 * param_len, param_len, NULL)) == NULL
1521 || !BN_set_word(x, (BN_ULONG)1)) { /* cofactor is 1 */
1522 ERR_raise(ERR_LIB_EC, ERR_R_BN_LIB);
1523 goto err;
1524 }
1525
1526 /*
1527 * Set up generator and order and montgomery data
1528 */
1529 group->generator = EC_POINT_new(group);
1530 if (group->generator == NULL) {
1531 ERR_raise(ERR_LIB_EC, ERR_R_EC_LIB);
1532 goto err;
1533 }
1534 if (!EC_POINT_copy(group->generator, P))
1535 goto err;
1536 if (!BN_copy(group->order, order))
1537 goto err;
1538 if (!BN_set_word(group->cofactor, 1))
1539 goto err;
1540
1541 ordmont = BN_MONT_CTX_new();
1542 if (ordmont == NULL)
1543 goto err;
1544 if (!ossl_bn_mont_ctx_set(ordmont, order, 256, params + 7 * param_len,
1545 param_len, lo_order_n, hi_order_n))
1546 goto err;
1547
1548 group->mont_data = ordmont;
1549 ordmont = NULL;
1550
1551 ok = 1;
1552
1553 err:
1554 EC_POINT_free(P);
1555 BN_CTX_free(ctx);
1556 BN_MONT_CTX_free(mont);
1557 BN_MONT_CTX_free(ordmont);
1558 BN_free(p);
1559 BN_free(one);
1560 BN_free(a);
1561 BN_free(b);
1562 BN_free(order);
1563 BN_free(x);
1564 BN_free(y);
1565
1566 return ok;
1567 }
1568
EC_GFp_nistz256_method(void)1569 const EC_METHOD *EC_GFp_nistz256_method(void)
1570 {
1571 static const EC_METHOD ret = {
1572 EC_FLAGS_DEFAULT_OCT,
1573 NID_X9_62_prime_field,
1574 ossl_ec_GFp_mont_group_init,
1575 ossl_ec_GFp_mont_group_finish,
1576 ossl_ec_GFp_mont_group_clear_finish,
1577 ossl_ec_GFp_mont_group_copy,
1578 ossl_ec_GFp_mont_group_set_curve,
1579 ossl_ec_GFp_simple_group_get_curve,
1580 ossl_ec_GFp_simple_group_get_degree,
1581 ossl_ec_group_simple_order_bits,
1582 ossl_ec_GFp_simple_group_check_discriminant,
1583 ossl_ec_GFp_simple_point_init,
1584 ossl_ec_GFp_simple_point_finish,
1585 ossl_ec_GFp_simple_point_clear_finish,
1586 ossl_ec_GFp_simple_point_copy,
1587 ossl_ec_GFp_simple_point_set_to_infinity,
1588 ossl_ec_GFp_simple_point_set_affine_coordinates,
1589 ecp_nistz256_get_affine,
1590 0, 0, 0,
1591 ossl_ec_GFp_simple_add,
1592 ossl_ec_GFp_simple_dbl,
1593 ossl_ec_GFp_simple_invert,
1594 ossl_ec_GFp_simple_is_at_infinity,
1595 ossl_ec_GFp_simple_is_on_curve,
1596 ossl_ec_GFp_simple_cmp,
1597 ossl_ec_GFp_simple_make_affine,
1598 ossl_ec_GFp_simple_points_make_affine,
1599 ecp_nistz256_points_mul, /* mul */
1600 ecp_nistz256_mult_precompute, /* precompute_mult */
1601 ecp_nistz256_window_have_precompute_mult, /* have_precompute_mult */
1602 ossl_ec_GFp_mont_field_mul,
1603 ossl_ec_GFp_mont_field_sqr,
1604 0, /* field_div */
1605 ossl_ec_GFp_mont_field_inv,
1606 ossl_ec_GFp_mont_field_encode,
1607 ossl_ec_GFp_mont_field_decode,
1608 ossl_ec_GFp_mont_field_set_to_one,
1609 ossl_ec_key_simple_priv2oct,
1610 ossl_ec_key_simple_oct2priv,
1611 0, /* set private */
1612 ossl_ec_key_simple_generate_key,
1613 ossl_ec_key_simple_check_key,
1614 ossl_ec_key_simple_generate_public_key,
1615 0, /* keycopy */
1616 0, /* keyfinish */
1617 ossl_ecdh_simple_compute_key,
1618 ossl_ecdsa_simple_sign_setup,
1619 ossl_ecdsa_simple_sign_sig,
1620 ossl_ecdsa_simple_verify_sig,
1621 ecp_nistz256_inv_mod_ord, /* can be #define-d NULL */
1622 0, /* blind_coordinates */
1623 0, /* ladder_pre */
1624 0, /* ladder_step */
1625 0, /* ladder_post */
1626 ecp_nistz256group_full_init
1627 };
1628
1629 return &ret;
1630 }
1631