1 /*
2 * Copyright 2014-2024 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] |
469 in2_y[0] | in2_y[1] | in2_y[2] | in2_y[3]);
470 if (P256_LIMBS == 8)
471 in2infty |= (in2_x[4] | in2_x[5] | in2_x[6] | in2_x[7] |
472 in2_y[4] | in2_y[5] | in2_y[6] | in2_y[7]);
473
474 in1infty = is_zero(in1infty);
475 in2infty = is_zero(in2infty);
476
477 ecp_nistz256_sqr_mont(Z1sqr, in1_z); /* Z1^2 */
478
479 ecp_nistz256_mul_mont(U2, in2_x, Z1sqr); /* U2 = X2*Z1^2 */
480 ecp_nistz256_sub(H, U2, in1_x); /* H = U2 - U1 */
481
482 ecp_nistz256_mul_mont(S2, Z1sqr, in1_z); /* S2 = Z1^3 */
483
484 ecp_nistz256_mul_mont(res_z, H, in1_z); /* Z3 = H*Z1*Z2 */
485
486 ecp_nistz256_mul_mont(S2, S2, in2_y); /* S2 = Y2*Z1^3 */
487 ecp_nistz256_sub(R, S2, in1_y); /* R = S2 - S1 */
488
489 ecp_nistz256_sqr_mont(Hsqr, H); /* H^2 */
490 ecp_nistz256_sqr_mont(Rsqr, R); /* R^2 */
491 ecp_nistz256_mul_mont(Hcub, Hsqr, H); /* H^3 */
492
493 ecp_nistz256_mul_mont(U2, in1_x, Hsqr); /* U1*H^2 */
494 ecp_nistz256_mul_by_2(Hsqr, U2); /* 2*U1*H^2 */
495
496 ecp_nistz256_sub(res_x, Rsqr, Hsqr);
497 ecp_nistz256_sub(res_x, res_x, Hcub);
498 ecp_nistz256_sub(H, U2, res_x);
499
500 ecp_nistz256_mul_mont(S2, in1_y, Hcub);
501 ecp_nistz256_mul_mont(H, H, R);
502 ecp_nistz256_sub(res_y, H, S2);
503
504 copy_conditional(res_x, in2_x, in1infty);
505 copy_conditional(res_x, in1_x, in2infty);
506
507 copy_conditional(res_y, in2_y, in1infty);
508 copy_conditional(res_y, in1_y, in2infty);
509
510 copy_conditional(res_z, ONE, in1infty);
511 copy_conditional(res_z, in1_z, in2infty);
512
513 memcpy(r->X, res_x, sizeof(res_x));
514 memcpy(r->Y, res_y, sizeof(res_y));
515 memcpy(r->Z, res_z, sizeof(res_z));
516 }
517 #endif
518
519 /* r = in^-1 mod p */
ecp_nistz256_mod_inverse(BN_ULONG r[P256_LIMBS],const BN_ULONG in[P256_LIMBS])520 static void ecp_nistz256_mod_inverse(BN_ULONG r[P256_LIMBS],
521 const BN_ULONG in[P256_LIMBS])
522 {
523 /*
524 * The poly is ffffffff 00000001 00000000 00000000 00000000 ffffffff
525 * ffffffff ffffffff We use FLT and used poly-2 as exponent
526 */
527 BN_ULONG p2[P256_LIMBS];
528 BN_ULONG p4[P256_LIMBS];
529 BN_ULONG p8[P256_LIMBS];
530 BN_ULONG p16[P256_LIMBS];
531 BN_ULONG p32[P256_LIMBS];
532 BN_ULONG res[P256_LIMBS];
533 int i;
534
535 ecp_nistz256_sqr_mont(res, in);
536 ecp_nistz256_mul_mont(p2, res, in); /* 3*p */
537
538 ecp_nistz256_sqr_mont(res, p2);
539 ecp_nistz256_sqr_mont(res, res);
540 ecp_nistz256_mul_mont(p4, res, p2); /* f*p */
541
542 ecp_nistz256_sqr_mont(res, p4);
543 ecp_nistz256_sqr_mont(res, res);
544 ecp_nistz256_sqr_mont(res, res);
545 ecp_nistz256_sqr_mont(res, res);
546 ecp_nistz256_mul_mont(p8, res, p4); /* ff*p */
547
548 ecp_nistz256_sqr_mont(res, p8);
549 for (i = 0; i < 7; i++)
550 ecp_nistz256_sqr_mont(res, res);
551 ecp_nistz256_mul_mont(p16, res, p8); /* ffff*p */
552
553 ecp_nistz256_sqr_mont(res, p16);
554 for (i = 0; i < 15; i++)
555 ecp_nistz256_sqr_mont(res, res);
556 ecp_nistz256_mul_mont(p32, res, p16); /* ffffffff*p */
557
558 ecp_nistz256_sqr_mont(res, p32);
559 for (i = 0; i < 31; i++)
560 ecp_nistz256_sqr_mont(res, res);
561 ecp_nistz256_mul_mont(res, res, in);
562
563 for (i = 0; i < 32 * 4; i++)
564 ecp_nistz256_sqr_mont(res, res);
565 ecp_nistz256_mul_mont(res, res, p32);
566
567 for (i = 0; i < 32; i++)
568 ecp_nistz256_sqr_mont(res, res);
569 ecp_nistz256_mul_mont(res, res, p32);
570
571 for (i = 0; i < 16; i++)
572 ecp_nistz256_sqr_mont(res, res);
573 ecp_nistz256_mul_mont(res, res, p16);
574
575 for (i = 0; i < 8; i++)
576 ecp_nistz256_sqr_mont(res, res);
577 ecp_nistz256_mul_mont(res, res, p8);
578
579 ecp_nistz256_sqr_mont(res, res);
580 ecp_nistz256_sqr_mont(res, res);
581 ecp_nistz256_sqr_mont(res, res);
582 ecp_nistz256_sqr_mont(res, res);
583 ecp_nistz256_mul_mont(res, res, p4);
584
585 ecp_nistz256_sqr_mont(res, res);
586 ecp_nistz256_sqr_mont(res, res);
587 ecp_nistz256_mul_mont(res, res, p2);
588
589 ecp_nistz256_sqr_mont(res, res);
590 ecp_nistz256_sqr_mont(res, res);
591 ecp_nistz256_mul_mont(res, res, in);
592
593 memcpy(r, res, sizeof(res));
594 }
595
596 /*
597 * ecp_nistz256_bignum_to_field_elem copies the contents of |in| to |out| and
598 * returns one if it fits. Otherwise it returns zero.
599 */
ecp_nistz256_bignum_to_field_elem(BN_ULONG out[P256_LIMBS],const BIGNUM * in)600 __owur static int ecp_nistz256_bignum_to_field_elem(BN_ULONG out[P256_LIMBS],
601 const BIGNUM *in)
602 {
603 return bn_copy_words(out, in, P256_LIMBS);
604 }
605
606 /* 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)607 __owur static int ecp_nistz256_windowed_mul(const EC_GROUP *group,
608 P256_POINT *r,
609 const BIGNUM **scalar,
610 const EC_POINT **point,
611 size_t num, BN_CTX *ctx)
612 {
613 size_t i;
614 int j, ret = 0;
615 unsigned int idx;
616 unsigned char (*p_str)[33] = NULL;
617 const unsigned int window_size = 5;
618 const unsigned int mask = (1 << (window_size + 1)) - 1;
619 unsigned int wvalue;
620 P256_POINT *temp; /* place for 5 temporary points */
621 const BIGNUM **scalars = NULL;
622 P256_POINT (*table)[16] = NULL;
623 void *table_storage = NULL;
624
625 if ((num * 16 + 6) > OPENSSL_MALLOC_MAX_NELEMS(P256_POINT)
626 || (table_storage =
627 OPENSSL_malloc((num * 16 + 5) * sizeof(P256_POINT) + 64)) == NULL
628 || (p_str =
629 OPENSSL_malloc(num * 33 * sizeof(unsigned char))) == NULL
630 || (scalars = OPENSSL_malloc(num * sizeof(BIGNUM *))) == NULL)
631 goto err;
632
633 table = (void *)ALIGNPTR(table_storage, 64);
634 temp = (P256_POINT *)(table + num);
635
636 for (i = 0; i < num; i++) {
637 P256_POINT *row = table[i];
638
639 /* This is an unusual input, we don't guarantee constant-timeness. */
640 if ((BN_num_bits(scalar[i]) > 256) || BN_is_negative(scalar[i])) {
641 BIGNUM *mod;
642
643 if ((mod = BN_CTX_get(ctx)) == NULL)
644 goto err;
645 if (!BN_nnmod(mod, scalar[i], group->order, ctx)) {
646 ERR_raise(ERR_LIB_EC, ERR_R_BN_LIB);
647 goto err;
648 }
649 scalars[i] = mod;
650 } else
651 scalars[i] = scalar[i];
652
653 for (j = 0; j < bn_get_top(scalars[i]) * BN_BYTES; j += BN_BYTES) {
654 BN_ULONG d = bn_get_words(scalars[i])[j / BN_BYTES];
655
656 p_str[i][j + 0] = (unsigned char)d;
657 p_str[i][j + 1] = (unsigned char)(d >> 8);
658 p_str[i][j + 2] = (unsigned char)(d >> 16);
659 p_str[i][j + 3] = (unsigned char)(d >>= 24);
660 if (BN_BYTES == 8) {
661 d >>= 8;
662 p_str[i][j + 4] = (unsigned char)d;
663 p_str[i][j + 5] = (unsigned char)(d >> 8);
664 p_str[i][j + 6] = (unsigned char)(d >> 16);
665 p_str[i][j + 7] = (unsigned char)(d >> 24);
666 }
667 }
668 for (; j < 33; j++)
669 p_str[i][j] = 0;
670
671 if (!ecp_nistz256_bignum_to_field_elem(temp[0].X, point[i]->X)
672 || !ecp_nistz256_bignum_to_field_elem(temp[0].Y, point[i]->Y)
673 || !ecp_nistz256_bignum_to_field_elem(temp[0].Z, point[i]->Z)) {
674 ERR_raise(ERR_LIB_EC, EC_R_COORDINATES_OUT_OF_RANGE);
675 goto err;
676 }
677
678 /*
679 * row[0] is implicitly (0,0,0) (the point at infinity), therefore it
680 * is not stored. All other values are actually stored with an offset
681 * of -1 in table.
682 */
683
684 ecp_nistz256_scatter_w5 (row, &temp[0], 1);
685 ecp_nistz256_point_double(&temp[1], &temp[0]); /*1+1=2 */
686 ecp_nistz256_scatter_w5 (row, &temp[1], 2);
687 ecp_nistz256_point_add (&temp[2], &temp[1], &temp[0]); /*2+1=3 */
688 ecp_nistz256_scatter_w5 (row, &temp[2], 3);
689 ecp_nistz256_point_double(&temp[1], &temp[1]); /*2*2=4 */
690 ecp_nistz256_scatter_w5 (row, &temp[1], 4);
691 ecp_nistz256_point_double(&temp[2], &temp[2]); /*2*3=6 */
692 ecp_nistz256_scatter_w5 (row, &temp[2], 6);
693 ecp_nistz256_point_add (&temp[3], &temp[1], &temp[0]); /*4+1=5 */
694 ecp_nistz256_scatter_w5 (row, &temp[3], 5);
695 ecp_nistz256_point_add (&temp[4], &temp[2], &temp[0]); /*6+1=7 */
696 ecp_nistz256_scatter_w5 (row, &temp[4], 7);
697 ecp_nistz256_point_double(&temp[1], &temp[1]); /*2*4=8 */
698 ecp_nistz256_scatter_w5 (row, &temp[1], 8);
699 ecp_nistz256_point_double(&temp[2], &temp[2]); /*2*6=12 */
700 ecp_nistz256_scatter_w5 (row, &temp[2], 12);
701 ecp_nistz256_point_double(&temp[3], &temp[3]); /*2*5=10 */
702 ecp_nistz256_scatter_w5 (row, &temp[3], 10);
703 ecp_nistz256_point_double(&temp[4], &temp[4]); /*2*7=14 */
704 ecp_nistz256_scatter_w5 (row, &temp[4], 14);
705 ecp_nistz256_point_add (&temp[2], &temp[2], &temp[0]); /*12+1=13*/
706 ecp_nistz256_scatter_w5 (row, &temp[2], 13);
707 ecp_nistz256_point_add (&temp[3], &temp[3], &temp[0]); /*10+1=11*/
708 ecp_nistz256_scatter_w5 (row, &temp[3], 11);
709 ecp_nistz256_point_add (&temp[4], &temp[4], &temp[0]); /*14+1=15*/
710 ecp_nistz256_scatter_w5 (row, &temp[4], 15);
711 ecp_nistz256_point_add (&temp[2], &temp[1], &temp[0]); /*8+1=9 */
712 ecp_nistz256_scatter_w5 (row, &temp[2], 9);
713 ecp_nistz256_point_double(&temp[1], &temp[1]); /*2*8=16 */
714 ecp_nistz256_scatter_w5 (row, &temp[1], 16);
715 }
716
717 idx = 255;
718
719 wvalue = p_str[0][(idx - 1) / 8];
720 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
721
722 /*
723 * We gather to temp[0], because we know it's position relative
724 * to table
725 */
726 ecp_nistz256_gather_w5(&temp[0], table[0], _booth_recode_w5(wvalue) >> 1);
727 memcpy(r, &temp[0], sizeof(temp[0]));
728
729 while (idx >= 5) {
730 for (i = (idx == 255 ? 1 : 0); i < num; i++) {
731 unsigned int off = (idx - 1) / 8;
732
733 wvalue = p_str[i][off] | p_str[i][off + 1] << 8;
734 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
735
736 wvalue = _booth_recode_w5(wvalue);
737
738 ecp_nistz256_gather_w5(&temp[0], table[i], wvalue >> 1);
739
740 ecp_nistz256_neg(temp[1].Y, temp[0].Y);
741 copy_conditional(temp[0].Y, temp[1].Y, (wvalue & 1));
742
743 ecp_nistz256_point_add(r, r, &temp[0]);
744 }
745
746 idx -= window_size;
747
748 ecp_nistz256_point_double(r, r);
749 ecp_nistz256_point_double(r, r);
750 ecp_nistz256_point_double(r, r);
751 ecp_nistz256_point_double(r, r);
752 ecp_nistz256_point_double(r, r);
753 }
754
755 /* Final window */
756 for (i = 0; i < num; i++) {
757 wvalue = p_str[i][0];
758 wvalue = (wvalue << 1) & mask;
759
760 wvalue = _booth_recode_w5(wvalue);
761
762 ecp_nistz256_gather_w5(&temp[0], table[i], wvalue >> 1);
763
764 ecp_nistz256_neg(temp[1].Y, temp[0].Y);
765 copy_conditional(temp[0].Y, temp[1].Y, wvalue & 1);
766
767 ecp_nistz256_point_add(r, r, &temp[0]);
768 }
769
770 ret = 1;
771 err:
772 OPENSSL_free(table_storage);
773 OPENSSL_free(p_str);
774 OPENSSL_free(scalars);
775 return ret;
776 }
777
778 /* Coordinates of G, for which we have precomputed tables */
779 static const BN_ULONG def_xG[P256_LIMBS] = {
780 TOBN(0x79e730d4, 0x18a9143c), TOBN(0x75ba95fc, 0x5fedb601),
781 TOBN(0x79fb732b, 0x77622510), TOBN(0x18905f76, 0xa53755c6)
782 };
783
784 static const BN_ULONG def_yG[P256_LIMBS] = {
785 TOBN(0xddf25357, 0xce95560a), TOBN(0x8b4ab8e4, 0xba19e45c),
786 TOBN(0xd2e88688, 0xdd21f325), TOBN(0x8571ff18, 0x25885d85)
787 };
788
789 /*
790 * ecp_nistz256_is_affine_G returns one if |generator| is the standard, P-256
791 * generator.
792 */
ecp_nistz256_is_affine_G(const EC_POINT * generator)793 static int ecp_nistz256_is_affine_G(const EC_POINT *generator)
794 {
795 return (bn_get_top(generator->X) == P256_LIMBS) &&
796 (bn_get_top(generator->Y) == P256_LIMBS) &&
797 is_equal(bn_get_words(generator->X), def_xG) &&
798 is_equal(bn_get_words(generator->Y), def_yG) &&
799 is_one(generator->Z);
800 }
801
ecp_nistz256_mult_precompute(EC_GROUP * group,BN_CTX * ctx)802 __owur static int ecp_nistz256_mult_precompute(EC_GROUP *group, BN_CTX *ctx)
803 {
804 /*
805 * We precompute a table for a Booth encoded exponent (wNAF) based
806 * computation. Each table holds 64 values for safe access, with an
807 * implicit value of infinity at index zero. We use window of size 7, and
808 * therefore require ceil(256/7) = 37 tables.
809 */
810 const BIGNUM *order;
811 EC_POINT *P = NULL, *T = NULL;
812 const EC_POINT *generator;
813 NISTZ256_PRE_COMP *pre_comp;
814 BN_CTX *new_ctx = NULL;
815 int i, j, k, ret = 0;
816 size_t w;
817
818 PRECOMP256_ROW *preComputedTable = NULL;
819 unsigned char *precomp_storage = NULL;
820
821 /* if there is an old NISTZ256_PRE_COMP object, throw it away */
822 EC_pre_comp_free(group);
823 generator = EC_GROUP_get0_generator(group);
824 if (generator == NULL) {
825 ERR_raise(ERR_LIB_EC, EC_R_UNDEFINED_GENERATOR);
826 return 0;
827 }
828
829 if (ecp_nistz256_is_affine_G(generator)) {
830 /*
831 * No need to calculate tables for the standard generator because we
832 * have them statically.
833 */
834 return 1;
835 }
836
837 if ((pre_comp = ecp_nistz256_pre_comp_new(group)) == NULL)
838 return 0;
839
840 if (ctx == NULL) {
841 ctx = new_ctx = BN_CTX_new_ex(group->libctx);
842 if (ctx == NULL)
843 goto err;
844 }
845
846 BN_CTX_start(ctx);
847
848 order = EC_GROUP_get0_order(group);
849 if (order == NULL)
850 goto err;
851
852 if (BN_is_zero(order)) {
853 ERR_raise(ERR_LIB_EC, EC_R_UNKNOWN_ORDER);
854 goto err;
855 }
856
857 w = 7;
858
859 if ((precomp_storage =
860 OPENSSL_malloc(37 * 64 * sizeof(P256_POINT_AFFINE) + 64)) == NULL)
861 goto err;
862
863 preComputedTable = (void *)ALIGNPTR(precomp_storage, 64);
864
865 P = EC_POINT_new(group);
866 T = EC_POINT_new(group);
867 if (P == NULL || T == NULL)
868 goto err;
869
870 /*
871 * The zero entry is implicitly infinity, and we skip it, storing other
872 * values with -1 offset.
873 */
874 if (!EC_POINT_copy(T, generator))
875 goto err;
876
877 for (k = 0; k < 64; k++) {
878 if (!EC_POINT_copy(P, T))
879 goto err;
880 for (j = 0; j < 37; j++) {
881 P256_POINT_AFFINE temp;
882 /*
883 * It would be faster to use EC_POINTs_make_affine and
884 * make multiple points affine at the same time.
885 */
886 if (group->meth->make_affine == NULL
887 || !group->meth->make_affine(group, P, ctx))
888 goto err;
889 if (!ecp_nistz256_bignum_to_field_elem(temp.X, P->X) ||
890 !ecp_nistz256_bignum_to_field_elem(temp.Y, P->Y)) {
891 ERR_raise(ERR_LIB_EC, EC_R_COORDINATES_OUT_OF_RANGE);
892 goto err;
893 }
894 ecp_nistz256_scatter_w7(preComputedTable[j], &temp, k);
895 for (i = 0; i < 7; i++) {
896 if (!EC_POINT_dbl(group, P, P, ctx))
897 goto err;
898 }
899 }
900 if (!EC_POINT_add(group, T, T, generator, ctx))
901 goto err;
902 }
903
904 pre_comp->group = group;
905 pre_comp->w = w;
906 pre_comp->precomp = preComputedTable;
907 pre_comp->precomp_storage = precomp_storage;
908 precomp_storage = NULL;
909 SETPRECOMP(group, nistz256, pre_comp);
910 pre_comp = NULL;
911 ret = 1;
912
913 err:
914 BN_CTX_end(ctx);
915 BN_CTX_free(new_ctx);
916
917 EC_nistz256_pre_comp_free(pre_comp);
918 OPENSSL_free(precomp_storage);
919 EC_POINT_free(P);
920 EC_POINT_free(T);
921 return ret;
922 }
923
ecp_nistz256_set_from_affine(EC_POINT * out,const EC_GROUP * group,const P256_POINT_AFFINE * in,BN_CTX * ctx)924 __owur static int ecp_nistz256_set_from_affine(EC_POINT *out, const EC_GROUP *group,
925 const P256_POINT_AFFINE *in,
926 BN_CTX *ctx)
927 {
928 int ret = 0;
929
930 if ((ret = bn_set_words(out->X, in->X, P256_LIMBS))
931 && (ret = bn_set_words(out->Y, in->Y, P256_LIMBS))
932 && (ret = bn_set_words(out->Z, ONE, P256_LIMBS)))
933 out->Z_is_one = 1;
934
935 return ret;
936 }
937
938 /* 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)939 __owur static int ecp_nistz256_points_mul(const EC_GROUP *group,
940 EC_POINT *r,
941 const BIGNUM *scalar,
942 size_t num,
943 const EC_POINT *points[],
944 const BIGNUM *scalars[], BN_CTX *ctx)
945 {
946 int i = 0, ret = 0, no_precomp_for_generator = 0, p_is_infinity = 0;
947 unsigned char p_str[33] = { 0 };
948 const PRECOMP256_ROW *preComputedTable = NULL;
949 const NISTZ256_PRE_COMP *pre_comp = NULL;
950 const EC_POINT *generator = NULL;
951 const BIGNUM **new_scalars = NULL;
952 const EC_POINT **new_points = NULL;
953 unsigned int idx = 0;
954 const unsigned int window_size = 7;
955 const unsigned int mask = (1 << (window_size + 1)) - 1;
956 unsigned int wvalue;
957 ALIGN32 union {
958 P256_POINT p;
959 P256_POINT_AFFINE a;
960 } t, p;
961 BIGNUM *tmp_scalar;
962
963 if ((num + 1) == 0 || (num + 1) > OPENSSL_MALLOC_MAX_NELEMS(void *)) {
964 ERR_raise(ERR_LIB_EC, ERR_R_PASSED_INVALID_ARGUMENT);
965 return 0;
966 }
967
968 memset(&p, 0, sizeof(p));
969 BN_CTX_start(ctx);
970
971 if (scalar) {
972 generator = EC_GROUP_get0_generator(group);
973 if (generator == NULL) {
974 ERR_raise(ERR_LIB_EC, EC_R_UNDEFINED_GENERATOR);
975 goto err;
976 }
977
978 /* look if we can use precomputed multiples of generator */
979 pre_comp = group->pre_comp.nistz256;
980
981 if (pre_comp) {
982 /*
983 * If there is a precomputed table for the generator, check that
984 * it was generated with the same generator.
985 */
986 EC_POINT *pre_comp_generator = EC_POINT_new(group);
987 if (pre_comp_generator == NULL)
988 goto err;
989
990 ecp_nistz256_gather_w7(&p.a, pre_comp->precomp[0], 1);
991 if (!ecp_nistz256_set_from_affine(pre_comp_generator,
992 group, &p.a, ctx)) {
993 EC_POINT_free(pre_comp_generator);
994 goto err;
995 }
996
997 if (0 == EC_POINT_cmp(group, generator, pre_comp_generator, ctx))
998 preComputedTable = (const PRECOMP256_ROW *)pre_comp->precomp;
999
1000 EC_POINT_free(pre_comp_generator);
1001 }
1002
1003 if (preComputedTable == NULL && ecp_nistz256_is_affine_G(generator)) {
1004 /*
1005 * If there is no precomputed data, but the generator is the
1006 * default, a hardcoded table of precomputed data is used. This
1007 * is because applications, such as Apache, do not use
1008 * EC_KEY_precompute_mult.
1009 */
1010 preComputedTable = ecp_nistz256_precomputed;
1011 }
1012
1013 if (preComputedTable) {
1014 BN_ULONG infty;
1015
1016 if ((BN_num_bits(scalar) > 256)
1017 || BN_is_negative(scalar)) {
1018 if ((tmp_scalar = BN_CTX_get(ctx)) == NULL)
1019 goto err;
1020
1021 if (!BN_nnmod(tmp_scalar, scalar, group->order, ctx)) {
1022 ERR_raise(ERR_LIB_EC, ERR_R_BN_LIB);
1023 goto err;
1024 }
1025 scalar = tmp_scalar;
1026 }
1027
1028 for (i = 0; i < bn_get_top(scalar) * BN_BYTES; i += BN_BYTES) {
1029 BN_ULONG d = bn_get_words(scalar)[i / BN_BYTES];
1030
1031 p_str[i + 0] = (unsigned char)d;
1032 p_str[i + 1] = (unsigned char)(d >> 8);
1033 p_str[i + 2] = (unsigned char)(d >> 16);
1034 p_str[i + 3] = (unsigned char)(d >>= 24);
1035 if (BN_BYTES == 8) {
1036 d >>= 8;
1037 p_str[i + 4] = (unsigned char)d;
1038 p_str[i + 5] = (unsigned char)(d >> 8);
1039 p_str[i + 6] = (unsigned char)(d >> 16);
1040 p_str[i + 7] = (unsigned char)(d >> 24);
1041 }
1042 }
1043
1044 for (; i < 33; i++)
1045 p_str[i] = 0;
1046
1047 /* First window */
1048 wvalue = (p_str[0] << 1) & mask;
1049 idx += window_size;
1050
1051 wvalue = _booth_recode_w7(wvalue);
1052
1053 ecp_nistz256_gather_w7(&p.a, preComputedTable[0],
1054 wvalue >> 1);
1055
1056 ecp_nistz256_neg(p.p.Z, p.p.Y);
1057 copy_conditional(p.p.Y, p.p.Z, wvalue & 1);
1058
1059 /*
1060 * Since affine infinity is encoded as (0,0) and
1061 * Jacobian is (,,0), we need to harmonize them
1062 * by assigning "one" or zero to Z.
1063 */
1064 infty = (p.p.X[0] | p.p.X[1] | p.p.X[2] | p.p.X[3] |
1065 p.p.Y[0] | p.p.Y[1] | p.p.Y[2] | p.p.Y[3]);
1066 if (P256_LIMBS == 8)
1067 infty |= (p.p.X[4] | p.p.X[5] | p.p.X[6] | p.p.X[7] |
1068 p.p.Y[4] | p.p.Y[5] | p.p.Y[6] | p.p.Y[7]);
1069
1070 infty = 0 - is_zero(infty);
1071 infty = ~infty;
1072
1073 p.p.Z[0] = ONE[0] & infty;
1074 p.p.Z[1] = ONE[1] & infty;
1075 p.p.Z[2] = ONE[2] & infty;
1076 p.p.Z[3] = ONE[3] & infty;
1077 if (P256_LIMBS == 8) {
1078 p.p.Z[4] = ONE[4] & infty;
1079 p.p.Z[5] = ONE[5] & infty;
1080 p.p.Z[6] = ONE[6] & infty;
1081 p.p.Z[7] = ONE[7] & infty;
1082 }
1083
1084 for (i = 1; i < 37; i++) {
1085 unsigned int off = (idx - 1) / 8;
1086 wvalue = p_str[off] | p_str[off + 1] << 8;
1087 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
1088 idx += window_size;
1089
1090 wvalue = _booth_recode_w7(wvalue);
1091
1092 ecp_nistz256_gather_w7(&t.a,
1093 preComputedTable[i], wvalue >> 1);
1094
1095 ecp_nistz256_neg(t.p.Z, t.a.Y);
1096 copy_conditional(t.a.Y, t.p.Z, wvalue & 1);
1097
1098 ecp_nistz256_point_add_affine(&p.p, &p.p, &t.a);
1099 }
1100 } else {
1101 p_is_infinity = 1;
1102 no_precomp_for_generator = 1;
1103 }
1104 } else
1105 p_is_infinity = 1;
1106
1107 if (no_precomp_for_generator) {
1108 /*
1109 * Without a precomputed table for the generator, it has to be
1110 * handled like a normal point.
1111 */
1112 new_scalars = OPENSSL_malloc((num + 1) * sizeof(BIGNUM *));
1113 if (new_scalars == NULL)
1114 goto err;
1115
1116 new_points = OPENSSL_malloc((num + 1) * sizeof(EC_POINT *));
1117 if (new_points == NULL)
1118 goto err;
1119
1120 memcpy(new_scalars, scalars, num * sizeof(BIGNUM *));
1121 new_scalars[num] = scalar;
1122 memcpy(new_points, points, num * sizeof(EC_POINT *));
1123 new_points[num] = generator;
1124
1125 scalars = new_scalars;
1126 points = new_points;
1127 num++;
1128 }
1129
1130 if (num) {
1131 P256_POINT *out = &t.p;
1132 if (p_is_infinity)
1133 out = &p.p;
1134
1135 if (!ecp_nistz256_windowed_mul(group, out, scalars, points, num, ctx))
1136 goto err;
1137
1138 if (!p_is_infinity)
1139 ecp_nistz256_point_add(&p.p, &p.p, out);
1140 }
1141
1142 /* Not constant-time, but we're only operating on the public output. */
1143 if (!bn_set_words(r->X, p.p.X, P256_LIMBS) ||
1144 !bn_set_words(r->Y, p.p.Y, P256_LIMBS) ||
1145 !bn_set_words(r->Z, p.p.Z, P256_LIMBS)) {
1146 goto err;
1147 }
1148 r->Z_is_one = is_one(r->Z) & 1;
1149
1150 ret = 1;
1151
1152 err:
1153 BN_CTX_end(ctx);
1154 OPENSSL_free(new_points);
1155 OPENSSL_free(new_scalars);
1156 return ret;
1157 }
1158
ecp_nistz256_get_affine(const EC_GROUP * group,const EC_POINT * point,BIGNUM * x,BIGNUM * y,BN_CTX * ctx)1159 __owur static int ecp_nistz256_get_affine(const EC_GROUP *group,
1160 const EC_POINT *point,
1161 BIGNUM *x, BIGNUM *y, BN_CTX *ctx)
1162 {
1163 BN_ULONG z_inv2[P256_LIMBS];
1164 BN_ULONG z_inv3[P256_LIMBS];
1165 BN_ULONG x_aff[P256_LIMBS];
1166 BN_ULONG y_aff[P256_LIMBS];
1167 BN_ULONG point_x[P256_LIMBS], point_y[P256_LIMBS], point_z[P256_LIMBS];
1168 BN_ULONG x_ret[P256_LIMBS], y_ret[P256_LIMBS];
1169
1170 if (EC_POINT_is_at_infinity(group, point)) {
1171 ERR_raise(ERR_LIB_EC, EC_R_POINT_AT_INFINITY);
1172 return 0;
1173 }
1174
1175 if (!ecp_nistz256_bignum_to_field_elem(point_x, point->X) ||
1176 !ecp_nistz256_bignum_to_field_elem(point_y, point->Y) ||
1177 !ecp_nistz256_bignum_to_field_elem(point_z, point->Z)) {
1178 ERR_raise(ERR_LIB_EC, EC_R_COORDINATES_OUT_OF_RANGE);
1179 return 0;
1180 }
1181
1182 ecp_nistz256_mod_inverse(z_inv3, point_z);
1183 ecp_nistz256_sqr_mont(z_inv2, z_inv3);
1184 ecp_nistz256_mul_mont(x_aff, z_inv2, point_x);
1185
1186 if (x != NULL) {
1187 ecp_nistz256_from_mont(x_ret, x_aff);
1188 if (!bn_set_words(x, x_ret, P256_LIMBS))
1189 return 0;
1190 }
1191
1192 if (y != NULL) {
1193 ecp_nistz256_mul_mont(z_inv3, z_inv3, z_inv2);
1194 ecp_nistz256_mul_mont(y_aff, z_inv3, point_y);
1195 ecp_nistz256_from_mont(y_ret, y_aff);
1196 if (!bn_set_words(y, y_ret, P256_LIMBS))
1197 return 0;
1198 }
1199
1200 return 1;
1201 }
1202
ecp_nistz256_pre_comp_new(const EC_GROUP * group)1203 static NISTZ256_PRE_COMP *ecp_nistz256_pre_comp_new(const EC_GROUP *group)
1204 {
1205 NISTZ256_PRE_COMP *ret = NULL;
1206
1207 if (!group)
1208 return NULL;
1209
1210 ret = OPENSSL_zalloc(sizeof(*ret));
1211
1212 if (ret == NULL)
1213 return ret;
1214
1215 ret->group = group;
1216 ret->w = 6; /* default */
1217
1218 if (!CRYPTO_NEW_REF(&ret->references, 1)) {
1219 OPENSSL_free(ret);
1220 return NULL;
1221 }
1222 return ret;
1223 }
1224
EC_nistz256_pre_comp_dup(NISTZ256_PRE_COMP * p)1225 NISTZ256_PRE_COMP *EC_nistz256_pre_comp_dup(NISTZ256_PRE_COMP *p)
1226 {
1227 int i;
1228 if (p != NULL)
1229 CRYPTO_UP_REF(&p->references, &i);
1230 return p;
1231 }
1232
EC_nistz256_pre_comp_free(NISTZ256_PRE_COMP * pre)1233 void EC_nistz256_pre_comp_free(NISTZ256_PRE_COMP *pre)
1234 {
1235 int i;
1236
1237 if (pre == NULL)
1238 return;
1239
1240 CRYPTO_DOWN_REF(&pre->references, &i);
1241 REF_PRINT_COUNT("EC_nistz256", pre);
1242 if (i > 0)
1243 return;
1244 REF_ASSERT_ISNT(i < 0);
1245
1246 OPENSSL_free(pre->precomp_storage);
1247 CRYPTO_FREE_REF(&pre->references);
1248 OPENSSL_free(pre);
1249 }
1250
1251
ecp_nistz256_window_have_precompute_mult(const EC_GROUP * group)1252 static int ecp_nistz256_window_have_precompute_mult(const EC_GROUP *group)
1253 {
1254 /* There is a hard-coded table for the default generator. */
1255 const EC_POINT *generator = EC_GROUP_get0_generator(group);
1256
1257 if (generator != NULL && ecp_nistz256_is_affine_G(generator)) {
1258 /* There is a hard-coded table for the default generator. */
1259 return 1;
1260 }
1261
1262 return HAVEPRECOMP(group, nistz256);
1263 }
1264
1265 #if defined(__x86_64) || defined(__x86_64__) || \
1266 defined(_M_AMD64) || defined(_M_X64) || \
1267 defined(__powerpc64__) || defined(_ARCH_PP64) || \
1268 defined(__aarch64__)
1269 /*
1270 * Montgomery mul modulo Order(P): res = a*b*2^-256 mod Order(P)
1271 */
1272 void ecp_nistz256_ord_mul_mont(BN_ULONG res[P256_LIMBS],
1273 const BN_ULONG a[P256_LIMBS],
1274 const BN_ULONG b[P256_LIMBS]);
1275 void ecp_nistz256_ord_sqr_mont(BN_ULONG res[P256_LIMBS],
1276 const BN_ULONG a[P256_LIMBS],
1277 BN_ULONG rep);
1278
ecp_nistz256_inv_mod_ord(const EC_GROUP * group,BIGNUM * r,const BIGNUM * x,BN_CTX * ctx)1279 static int ecp_nistz256_inv_mod_ord(const EC_GROUP *group, BIGNUM *r,
1280 const BIGNUM *x, BN_CTX *ctx)
1281 {
1282 /* RR = 2^512 mod ord(p256) */
1283 static const BN_ULONG RR[P256_LIMBS] = {
1284 TOBN(0x83244c95,0xbe79eea2), TOBN(0x4699799c,0x49bd6fa6),
1285 TOBN(0x2845b239,0x2b6bec59), TOBN(0x66e12d94,0xf3d95620)
1286 };
1287 /* The constant 1 (unlike ONE that is one in Montgomery representation) */
1288 static const BN_ULONG one[P256_LIMBS] = {
1289 TOBN(0,1), TOBN(0,0), TOBN(0,0), TOBN(0,0)
1290 };
1291 /*
1292 * We don't use entry 0 in the table, so we omit it and address
1293 * with -1 offset.
1294 */
1295 BN_ULONG table[15][P256_LIMBS];
1296 BN_ULONG out[P256_LIMBS], t[P256_LIMBS];
1297 int i, ret = 0;
1298 enum {
1299 i_1 = 0, i_10, i_11, i_101, i_111, i_1010, i_1111,
1300 i_10101, i_101010, i_101111, i_x6, i_x8, i_x16, i_x32
1301 };
1302
1303 /*
1304 * Catch allocation failure early.
1305 */
1306 if (bn_wexpand(r, P256_LIMBS) == NULL) {
1307 ERR_raise(ERR_LIB_EC, ERR_R_BN_LIB);
1308 goto err;
1309 }
1310
1311 if ((BN_num_bits(x) > 256) || BN_is_negative(x)) {
1312 BIGNUM *tmp;
1313
1314 if ((tmp = BN_CTX_get(ctx)) == NULL
1315 || !BN_nnmod(tmp, x, group->order, ctx)) {
1316 ERR_raise(ERR_LIB_EC, ERR_R_BN_LIB);
1317 goto err;
1318 }
1319 x = tmp;
1320 }
1321
1322 if (!ecp_nistz256_bignum_to_field_elem(t, x)) {
1323 ERR_raise(ERR_LIB_EC, EC_R_COORDINATES_OUT_OF_RANGE);
1324 goto err;
1325 }
1326
1327 ecp_nistz256_ord_mul_mont(table[0], t, RR);
1328 #if 0
1329 /*
1330 * Original sparse-then-fixed-window algorithm, retained for reference.
1331 */
1332 for (i = 2; i < 16; i += 2) {
1333 ecp_nistz256_ord_sqr_mont(table[i-1], table[i/2-1], 1);
1334 ecp_nistz256_ord_mul_mont(table[i], table[i-1], table[0]);
1335 }
1336
1337 /*
1338 * The top 128bit of the exponent are highly redudndant, so we
1339 * perform an optimized flow
1340 */
1341 ecp_nistz256_ord_sqr_mont(t, table[15-1], 4); /* f0 */
1342 ecp_nistz256_ord_mul_mont(t, t, table[15-1]); /* ff */
1343
1344 ecp_nistz256_ord_sqr_mont(out, t, 8); /* ff00 */
1345 ecp_nistz256_ord_mul_mont(out, out, t); /* ffff */
1346
1347 ecp_nistz256_ord_sqr_mont(t, out, 16); /* ffff0000 */
1348 ecp_nistz256_ord_mul_mont(t, t, out); /* ffffffff */
1349
1350 ecp_nistz256_ord_sqr_mont(out, t, 64); /* ffffffff0000000000000000 */
1351 ecp_nistz256_ord_mul_mont(out, out, t); /* ffffffff00000000ffffffff */
1352
1353 ecp_nistz256_ord_sqr_mont(out, out, 32); /* ffffffff00000000ffffffff00000000 */
1354 ecp_nistz256_ord_mul_mont(out, out, t); /* ffffffff00000000ffffffffffffffff */
1355
1356 /*
1357 * The bottom 128 bit of the exponent are processed with fixed 4-bit window
1358 */
1359 for (i = 0; i < 32; i++) {
1360 /* expLo - the low 128 bits of the exponent we use (ord(p256) - 2),
1361 * split into nibbles */
1362 static const unsigned char expLo[32] = {
1363 0xb,0xc,0xe,0x6,0xf,0xa,0xa,0xd,0xa,0x7,0x1,0x7,0x9,0xe,0x8,0x4,
1364 0xf,0x3,0xb,0x9,0xc,0xa,0xc,0x2,0xf,0xc,0x6,0x3,0x2,0x5,0x4,0xf
1365 };
1366
1367 ecp_nistz256_ord_sqr_mont(out, out, 4);
1368 /* The exponent is public, no need in constant-time access */
1369 ecp_nistz256_ord_mul_mont(out, out, table[expLo[i]-1]);
1370 }
1371 #else
1372 /*
1373 * https://briansmith.org/ecc-inversion-addition-chains-01#p256_scalar_inversion
1374 *
1375 * Even though this code path spares 12 squarings, 4.5%, and 13
1376 * multiplications, 25%, on grand scale sign operation is not that
1377 * much faster, not more that 2%...
1378 */
1379
1380 /* pre-calculate powers */
1381 ecp_nistz256_ord_sqr_mont(table[i_10], table[i_1], 1);
1382
1383 ecp_nistz256_ord_mul_mont(table[i_11], table[i_1], table[i_10]);
1384
1385 ecp_nistz256_ord_mul_mont(table[i_101], table[i_11], table[i_10]);
1386
1387 ecp_nistz256_ord_mul_mont(table[i_111], table[i_101], table[i_10]);
1388
1389 ecp_nistz256_ord_sqr_mont(table[i_1010], table[i_101], 1);
1390
1391 ecp_nistz256_ord_mul_mont(table[i_1111], table[i_1010], table[i_101]);
1392
1393 ecp_nistz256_ord_sqr_mont(table[i_10101], table[i_1010], 1);
1394 ecp_nistz256_ord_mul_mont(table[i_10101], table[i_10101], table[i_1]);
1395
1396 ecp_nistz256_ord_sqr_mont(table[i_101010], table[i_10101], 1);
1397
1398 ecp_nistz256_ord_mul_mont(table[i_101111], table[i_101010], table[i_101]);
1399
1400 ecp_nistz256_ord_mul_mont(table[i_x6], table[i_101010], table[i_10101]);
1401
1402 ecp_nistz256_ord_sqr_mont(table[i_x8], table[i_x6], 2);
1403 ecp_nistz256_ord_mul_mont(table[i_x8], table[i_x8], table[i_11]);
1404
1405 ecp_nistz256_ord_sqr_mont(table[i_x16], table[i_x8], 8);
1406 ecp_nistz256_ord_mul_mont(table[i_x16], table[i_x16], table[i_x8]);
1407
1408 ecp_nistz256_ord_sqr_mont(table[i_x32], table[i_x16], 16);
1409 ecp_nistz256_ord_mul_mont(table[i_x32], table[i_x32], table[i_x16]);
1410
1411 /* calculations */
1412 ecp_nistz256_ord_sqr_mont(out, table[i_x32], 64);
1413 ecp_nistz256_ord_mul_mont(out, out, table[i_x32]);
1414
1415 for (i = 0; i < 27; i++) {
1416 static const struct { unsigned char p, i; } chain[27] = {
1417 { 32, i_x32 }, { 6, i_101111 }, { 5, i_111 },
1418 { 4, i_11 }, { 5, i_1111 }, { 5, i_10101 },
1419 { 4, i_101 }, { 3, i_101 }, { 3, i_101 },
1420 { 5, i_111 }, { 9, i_101111 }, { 6, i_1111 },
1421 { 2, i_1 }, { 5, i_1 }, { 6, i_1111 },
1422 { 5, i_111 }, { 4, i_111 }, { 5, i_111 },
1423 { 5, i_101 }, { 3, i_11 }, { 10, i_101111 },
1424 { 2, i_11 }, { 5, i_11 }, { 5, i_11 },
1425 { 3, i_1 }, { 7, i_10101 }, { 6, i_1111 }
1426 };
1427
1428 ecp_nistz256_ord_sqr_mont(out, out, chain[i].p);
1429 ecp_nistz256_ord_mul_mont(out, out, table[chain[i].i]);
1430 }
1431 #endif
1432 ecp_nistz256_ord_mul_mont(out, out, one);
1433
1434 /*
1435 * Can't fail, but check return code to be consistent anyway.
1436 */
1437 if (!bn_set_words(r, out, P256_LIMBS))
1438 goto err;
1439
1440 ret = 1;
1441 err:
1442 return ret;
1443 }
1444 #else
1445 # define ecp_nistz256_inv_mod_ord NULL
1446 #endif
1447
ecp_nistz256group_full_init(EC_GROUP * group,const unsigned char * params)1448 static int ecp_nistz256group_full_init(EC_GROUP *group,
1449 const unsigned char *params) {
1450 BN_CTX *ctx = NULL;
1451 BN_MONT_CTX *mont = NULL, *ordmont = NULL;
1452 const int param_len = 32;
1453 const int seed_len = 20;
1454 int ok = 0;
1455 uint32_t hi_order_n = 0xccd1c8aa;
1456 uint32_t lo_order_n = 0xee00bc4f;
1457 BIGNUM *p = NULL, *a = NULL, *b = NULL, *x = NULL, *y = NULL, *one = NULL,
1458 *order = NULL;
1459 EC_POINT *P = NULL;
1460
1461 if ((ctx = BN_CTX_new_ex(group->libctx)) == NULL) {
1462 ERR_raise(ERR_LIB_EC, ERR_R_MALLOC_FAILURE);
1463 return 0;
1464 }
1465
1466 if (!EC_GROUP_set_seed(group, params, seed_len)) {
1467 ERR_raise(ERR_LIB_EC, ERR_R_EC_LIB);
1468 goto err;
1469 }
1470 params += seed_len;
1471
1472 if ((p = BN_bin2bn(params + 0 * param_len, param_len, NULL)) == NULL
1473 || (a = BN_bin2bn(params + 1 * param_len, param_len, NULL)) == NULL
1474 || (b = BN_bin2bn(params + 2 * param_len, param_len, NULL)) == NULL) {
1475 ERR_raise(ERR_LIB_EC, ERR_R_BN_LIB);
1476 goto err;
1477 }
1478
1479 /*
1480 * Set up curve params and montgomery for field
1481 * Start by setting up montgomery and one
1482 */
1483 mont = BN_MONT_CTX_new();
1484 if (mont == NULL)
1485 goto err;
1486
1487 if (!ossl_bn_mont_ctx_set(mont, p, 256, params + 6 * param_len, param_len,
1488 1, 0))
1489 goto err;
1490
1491 one = BN_new();
1492 if (one == NULL) {
1493 ERR_raise(ERR_LIB_EC, ERR_R_BN_LIB);
1494 goto err;
1495 }
1496 if (!BN_to_montgomery(one, BN_value_one(), mont, ctx)){
1497 ERR_raise(ERR_LIB_EC, ERR_R_BN_LIB);
1498 goto err;
1499 }
1500 group->field_data1 = mont;
1501 mont = NULL;
1502 group->field_data2 = one;
1503 one = NULL;
1504
1505 if (!ossl_ec_GFp_simple_group_set_curve(group, p, a, b, ctx)) {
1506 ERR_raise(ERR_LIB_EC, ERR_R_EC_LIB);
1507 goto err;
1508 }
1509
1510 if ((P = EC_POINT_new(group)) == NULL) {
1511 ERR_raise(ERR_LIB_EC, ERR_R_EC_LIB);
1512 goto err;
1513 }
1514
1515 if ((x = BN_bin2bn(params + 3 * param_len, param_len, NULL)) == NULL
1516 || (y = BN_bin2bn(params + 4 * param_len, param_len, NULL)) == NULL) {
1517 ERR_raise(ERR_LIB_EC, ERR_R_BN_LIB);
1518 goto err;
1519 }
1520 if (!EC_POINT_set_affine_coordinates(group, P, x, y, ctx)) {
1521 ERR_raise(ERR_LIB_EC, ERR_R_EC_LIB);
1522 goto err;
1523 }
1524 if ((order = BN_bin2bn(params + 5 * param_len, param_len, NULL)) == NULL
1525 || !BN_set_word(x, (BN_ULONG)1)) { // cofactor is 1
1526 ERR_raise(ERR_LIB_EC, ERR_R_BN_LIB);
1527 goto err;
1528 }
1529
1530 /*
1531 * Set up generator and order and montgomery data
1532 */
1533 group->generator = EC_POINT_new(group);
1534 if (group->generator == NULL){
1535 ERR_raise(ERR_LIB_EC, ERR_R_EC_LIB);
1536 goto err;
1537 }
1538 if (!EC_POINT_copy(group->generator, P))
1539 goto err;
1540 if (!BN_copy(group->order, order))
1541 goto err;
1542 if (!BN_set_word(group->cofactor, 1))
1543 goto err;
1544
1545 ordmont = BN_MONT_CTX_new();
1546 if (ordmont == NULL)
1547 goto err;
1548 if (!ossl_bn_mont_ctx_set(ordmont, order, 256, params + 7 * param_len,
1549 param_len, lo_order_n, hi_order_n))
1550 goto err;
1551
1552 group->mont_data = ordmont;
1553 ordmont = NULL;
1554
1555 ok = 1;
1556
1557 err:
1558 EC_POINT_free(P);
1559 BN_CTX_free(ctx);
1560 BN_MONT_CTX_free(mont);
1561 BN_MONT_CTX_free(ordmont);
1562 BN_free(p);
1563 BN_free(one);
1564 BN_free(a);
1565 BN_free(b);
1566 BN_free(order);
1567 BN_free(x);
1568 BN_free(y);
1569
1570 return ok;
1571 }
1572
EC_GFp_nistz256_method(void)1573 const EC_METHOD *EC_GFp_nistz256_method(void)
1574 {
1575 static const EC_METHOD ret = {
1576 EC_FLAGS_DEFAULT_OCT,
1577 NID_X9_62_prime_field,
1578 ossl_ec_GFp_mont_group_init,
1579 ossl_ec_GFp_mont_group_finish,
1580 ossl_ec_GFp_mont_group_clear_finish,
1581 ossl_ec_GFp_mont_group_copy,
1582 ossl_ec_GFp_mont_group_set_curve,
1583 ossl_ec_GFp_simple_group_get_curve,
1584 ossl_ec_GFp_simple_group_get_degree,
1585 ossl_ec_group_simple_order_bits,
1586 ossl_ec_GFp_simple_group_check_discriminant,
1587 ossl_ec_GFp_simple_point_init,
1588 ossl_ec_GFp_simple_point_finish,
1589 ossl_ec_GFp_simple_point_clear_finish,
1590 ossl_ec_GFp_simple_point_copy,
1591 ossl_ec_GFp_simple_point_set_to_infinity,
1592 ossl_ec_GFp_simple_point_set_affine_coordinates,
1593 ecp_nistz256_get_affine,
1594 0, 0, 0,
1595 ossl_ec_GFp_simple_add,
1596 ossl_ec_GFp_simple_dbl,
1597 ossl_ec_GFp_simple_invert,
1598 ossl_ec_GFp_simple_is_at_infinity,
1599 ossl_ec_GFp_simple_is_on_curve,
1600 ossl_ec_GFp_simple_cmp,
1601 ossl_ec_GFp_simple_make_affine,
1602 ossl_ec_GFp_simple_points_make_affine,
1603 ecp_nistz256_points_mul, /* mul */
1604 ecp_nistz256_mult_precompute, /* precompute_mult */
1605 ecp_nistz256_window_have_precompute_mult, /* have_precompute_mult */
1606 ossl_ec_GFp_mont_field_mul,
1607 ossl_ec_GFp_mont_field_sqr,
1608 0, /* field_div */
1609 ossl_ec_GFp_mont_field_inv,
1610 ossl_ec_GFp_mont_field_encode,
1611 ossl_ec_GFp_mont_field_decode,
1612 ossl_ec_GFp_mont_field_set_to_one,
1613 ossl_ec_key_simple_priv2oct,
1614 ossl_ec_key_simple_oct2priv,
1615 0, /* set private */
1616 ossl_ec_key_simple_generate_key,
1617 ossl_ec_key_simple_check_key,
1618 ossl_ec_key_simple_generate_public_key,
1619 0, /* keycopy */
1620 0, /* keyfinish */
1621 ossl_ecdh_simple_compute_key,
1622 ossl_ecdsa_simple_sign_setup,
1623 ossl_ecdsa_simple_sign_sig,
1624 ossl_ecdsa_simple_verify_sig,
1625 ecp_nistz256_inv_mod_ord, /* can be #define-d NULL */
1626 0, /* blind_coordinates */
1627 0, /* ladder_pre */
1628 0, /* ladder_step */
1629 0, /* ladder_post */
1630 ecp_nistz256group_full_init
1631 };
1632
1633 return &ret;
1634 }
1635
