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aa6bb135 | 1 | /* |
48e82c8e | 2 | * Copyright 2014-2019 The OpenSSL Project Authors. All Rights Reserved. |
dcf6e50f | 3 | * Copyright (c) 2014, Intel Corporation. All Rights Reserved. |
eb791696 | 4 | * Copyright (c) 2015, CloudFlare, Inc. |
aa6bb135 RS |
5 | * |
6 | * Licensed under the OpenSSL license (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 | |
dcf6e50f | 10 | * |
eb791696 | 11 | * Originally written by Shay Gueron (1, 2), and Vlad Krasnov (1, 3) |
dcf6e50f RS |
12 | * (1) Intel Corporation, Israel Development Center, Haifa, Israel |
13 | * (2) University of Haifa, Israel | |
eb791696 | 14 | * (3) CloudFlare, Inc. |
dcf6e50f RS |
15 | * |
16 | * Reference: | |
17 | * S.Gueron and V.Krasnov, "Fast Prime Field Elliptic Curve Cryptography with | |
18 | * 256 Bit Primes" | |
aa6bb135 RS |
19 | */ |
20 | ||
4d3fa06f AP |
21 | #include <string.h> |
22 | ||
b39fc560 | 23 | #include "internal/cryptlib.h" |
0c994d54 | 24 | #include "crypto/bn.h" |
b5acbf91 | 25 | #include "ec_local.h" |
cd420b0b | 26 | #include "internal/refcount.h" |
4d3fa06f AP |
27 | |
28 | #if BN_BITS2 != 64 | |
58d47cf0 | 29 | # define TOBN(hi,lo) lo,hi |
4d3fa06f | 30 | #else |
58d47cf0 | 31 | # define TOBN(hi,lo) ((BN_ULONG)hi<<32|lo) |
4d3fa06f AP |
32 | #endif |
33 | ||
34 | #if defined(__GNUC__) | |
58d47cf0 | 35 | # define ALIGN32 __attribute((aligned(32))) |
4d3fa06f | 36 | #elif defined(_MSC_VER) |
58d47cf0 | 37 | # define ALIGN32 __declspec(align(32)) |
4d3fa06f AP |
38 | #else |
39 | # define ALIGN32 | |
40 | #endif | |
41 | ||
58d47cf0 AP |
42 | #define ALIGNPTR(p,N) ((unsigned char *)p+N-(size_t)p%N) |
43 | #define P256_LIMBS (256/BN_BITS2) | |
4d3fa06f AP |
44 | |
45 | typedef unsigned short u16; | |
46 | ||
47 | typedef struct { | |
48 | BN_ULONG X[P256_LIMBS]; | |
49 | BN_ULONG Y[P256_LIMBS]; | |
50 | BN_ULONG Z[P256_LIMBS]; | |
51 | } P256_POINT; | |
52 | ||
53 | typedef struct { | |
54 | BN_ULONG X[P256_LIMBS]; | |
55 | BN_ULONG Y[P256_LIMBS]; | |
56 | } P256_POINT_AFFINE; | |
57 | ||
58 | typedef P256_POINT_AFFINE PRECOMP256_ROW[64]; | |
59 | ||
60 | /* structure for precomputed multiples of the generator */ | |
3aef36ff | 61 | struct nistz256_pre_comp_st { |
4d3fa06f AP |
62 | const EC_GROUP *group; /* Parent EC_GROUP object */ |
63 | size_t w; /* Window size */ | |
20728adc AP |
64 | /* |
65 | * Constant time access to the X and Y coordinates of the pre-computed, | |
4d3fa06f | 66 | * generator multiplies, in the Montgomery domain. Pre-calculated |
20728adc AP |
67 | * multiplies are stored in affine form. |
68 | */ | |
4d3fa06f AP |
69 | PRECOMP256_ROW *precomp; |
70 | void *precomp_storage; | |
2f545ae4 | 71 | CRYPTO_REF_COUNT references; |
9b398ef2 | 72 | CRYPTO_RWLOCK *lock; |
3aef36ff | 73 | }; |
4d3fa06f AP |
74 | |
75 | /* Functions implemented in assembly */ | |
b62b2454 AP |
76 | /* |
77 | * Most of below mentioned functions *preserve* the property of inputs | |
78 | * being fully reduced, i.e. being in [0, modulus) range. Simply put if | |
79 | * inputs are fully reduced, then output is too. Note that reverse is | |
80 | * not true, in sense that given partially reduced inputs output can be | |
81 | * either, not unlikely reduced. And "most" in first sentence refers to | |
82 | * the fact that given the calculations flow one can tolerate that | |
83 | * addition, 1st function below, produces partially reduced result *if* | |
84 | * multiplications by 2 and 3, which customarily use addition, fully | |
85 | * reduce it. This effectively gives two options: a) addition produces | |
86 | * fully reduced result [as long as inputs are, just like remaining | |
87 | * functions]; b) addition is allowed to produce partially reduced | |
88 | * result, but multiplications by 2 and 3 perform additional reduction | |
89 | * step. Choice between the two can be platform-specific, but it was a) | |
90 | * in all cases so far... | |
91 | */ | |
92 | /* Modular add: res = a+b mod P */ | |
93 | void ecp_nistz256_add(BN_ULONG res[P256_LIMBS], | |
94 | const BN_ULONG a[P256_LIMBS], | |
95 | const BN_ULONG b[P256_LIMBS]); | |
4d3fa06f AP |
96 | /* Modular mul by 2: res = 2*a mod P */ |
97 | void ecp_nistz256_mul_by_2(BN_ULONG res[P256_LIMBS], | |
98 | const BN_ULONG a[P256_LIMBS]); | |
4d3fa06f AP |
99 | /* Modular mul by 3: res = 3*a mod P */ |
100 | void ecp_nistz256_mul_by_3(BN_ULONG res[P256_LIMBS], | |
101 | const BN_ULONG a[P256_LIMBS]); | |
b62b2454 AP |
102 | |
103 | /* Modular div by 2: res = a/2 mod P */ | |
104 | void ecp_nistz256_div_by_2(BN_ULONG res[P256_LIMBS], | |
105 | const BN_ULONG a[P256_LIMBS]); | |
20728adc | 106 | /* Modular sub: res = a-b mod P */ |
4d3fa06f AP |
107 | void ecp_nistz256_sub(BN_ULONG res[P256_LIMBS], |
108 | const BN_ULONG a[P256_LIMBS], | |
109 | const BN_ULONG b[P256_LIMBS]); | |
20728adc | 110 | /* Modular neg: res = -a mod P */ |
4d3fa06f AP |
111 | void ecp_nistz256_neg(BN_ULONG res[P256_LIMBS], const BN_ULONG a[P256_LIMBS]); |
112 | /* Montgomery mul: res = a*b*2^-256 mod P */ | |
113 | void ecp_nistz256_mul_mont(BN_ULONG res[P256_LIMBS], | |
114 | const BN_ULONG a[P256_LIMBS], | |
115 | const BN_ULONG b[P256_LIMBS]); | |
116 | /* Montgomery sqr: res = a*a*2^-256 mod P */ | |
117 | void ecp_nistz256_sqr_mont(BN_ULONG res[P256_LIMBS], | |
118 | const BN_ULONG a[P256_LIMBS]); | |
119 | /* Convert a number from Montgomery domain, by multiplying with 1 */ | |
120 | void ecp_nistz256_from_mont(BN_ULONG res[P256_LIMBS], | |
121 | const BN_ULONG in[P256_LIMBS]); | |
122 | /* Convert a number to Montgomery domain, by multiplying with 2^512 mod P*/ | |
123 | void ecp_nistz256_to_mont(BN_ULONG res[P256_LIMBS], | |
124 | const BN_ULONG in[P256_LIMBS]); | |
125 | /* Functions that perform constant time access to the precomputed tables */ | |
58d47cf0 | 126 | void ecp_nistz256_scatter_w5(P256_POINT *val, |
49b05c7d | 127 | const P256_POINT *in_t, int idx); |
20728adc | 128 | void ecp_nistz256_gather_w5(P256_POINT *val, |
49b05c7d | 129 | const P256_POINT *in_t, int idx); |
58d47cf0 | 130 | void ecp_nistz256_scatter_w7(P256_POINT_AFFINE *val, |
49b05c7d | 131 | const P256_POINT_AFFINE *in_t, int idx); |
58d47cf0 | 132 | void ecp_nistz256_gather_w7(P256_POINT_AFFINE *val, |
49b05c7d | 133 | const P256_POINT_AFFINE *in_t, int idx); |
4d3fa06f AP |
134 | |
135 | /* One converted into the Montgomery domain */ | |
136 | static const BN_ULONG ONE[P256_LIMBS] = { | |
137 | TOBN(0x00000000, 0x00000001), TOBN(0xffffffff, 0x00000000), | |
138 | TOBN(0xffffffff, 0xffffffff), TOBN(0x00000000, 0xfffffffe) | |
139 | }; | |
140 | ||
3aef36ff | 141 | static NISTZ256_PRE_COMP *ecp_nistz256_pre_comp_new(const EC_GROUP *group); |
4d3fa06f AP |
142 | |
143 | /* Precomputed tables for the default generator */ | |
3ff08e1d | 144 | extern const PRECOMP256_ROW ecp_nistz256_precomputed[37]; |
4d3fa06f AP |
145 | |
146 | /* Recode window to a signed digit, see ecp_nistputil.c for details */ | |
147 | static unsigned int _booth_recode_w5(unsigned int in) | |
148 | { | |
149 | unsigned int s, d; | |
150 | ||
151 | s = ~((in >> 5) - 1); | |
152 | d = (1 << 6) - in - 1; | |
153 | d = (d & s) | (in & ~s); | |
154 | d = (d >> 1) + (d & 1); | |
155 | ||
156 | return (d << 1) + (s & 1); | |
157 | } | |
158 | ||
159 | static unsigned int _booth_recode_w7(unsigned int in) | |
160 | { | |
161 | unsigned int s, d; | |
162 | ||
163 | s = ~((in >> 7) - 1); | |
164 | d = (1 << 8) - in - 1; | |
165 | d = (d & s) | (in & ~s); | |
166 | d = (d >> 1) + (d & 1); | |
167 | ||
168 | return (d << 1) + (s & 1); | |
169 | } | |
170 | ||
171 | static void copy_conditional(BN_ULONG dst[P256_LIMBS], | |
172 | const BN_ULONG src[P256_LIMBS], BN_ULONG move) | |
173 | { | |
5afc296a | 174 | BN_ULONG mask1 = 0-move; |
4d3fa06f AP |
175 | BN_ULONG mask2 = ~mask1; |
176 | ||
177 | dst[0] = (src[0] & mask1) ^ (dst[0] & mask2); | |
178 | dst[1] = (src[1] & mask1) ^ (dst[1] & mask2); | |
179 | dst[2] = (src[2] & mask1) ^ (dst[2] & mask2); | |
180 | dst[3] = (src[3] & mask1) ^ (dst[3] & mask2); | |
181 | if (P256_LIMBS == 8) { | |
182 | dst[4] = (src[4] & mask1) ^ (dst[4] & mask2); | |
183 | dst[5] = (src[5] & mask1) ^ (dst[5] & mask2); | |
184 | dst[6] = (src[6] & mask1) ^ (dst[6] & mask2); | |
185 | dst[7] = (src[7] & mask1) ^ (dst[7] & mask2); | |
186 | } | |
187 | } | |
188 | ||
189 | static BN_ULONG is_zero(BN_ULONG in) | |
190 | { | |
191 | in |= (0 - in); | |
192 | in = ~in; | |
4d3fa06f AP |
193 | in >>= BN_BITS2 - 1; |
194 | return in; | |
195 | } | |
196 | ||
197 | static BN_ULONG is_equal(const BN_ULONG a[P256_LIMBS], | |
198 | const BN_ULONG b[P256_LIMBS]) | |
199 | { | |
200 | BN_ULONG res; | |
201 | ||
202 | res = a[0] ^ b[0]; | |
203 | res |= a[1] ^ b[1]; | |
204 | res |= a[2] ^ b[2]; | |
205 | res |= a[3] ^ b[3]; | |
206 | if (P256_LIMBS == 8) { | |
207 | res |= a[4] ^ b[4]; | |
208 | res |= a[5] ^ b[5]; | |
209 | res |= a[6] ^ b[6]; | |
210 | res |= a[7] ^ b[7]; | |
211 | } | |
212 | ||
213 | return is_zero(res); | |
214 | } | |
215 | ||
2e929e53 | 216 | static BN_ULONG is_one(const BIGNUM *z) |
4d3fa06f | 217 | { |
2e929e53 AP |
218 | BN_ULONG res = 0; |
219 | BN_ULONG *a = bn_get_words(z); | |
220 | ||
221 | if (bn_get_top(z) == (P256_LIMBS - P256_LIMBS / 8)) { | |
222 | res = a[0] ^ ONE[0]; | |
223 | res |= a[1] ^ ONE[1]; | |
224 | res |= a[2] ^ ONE[2]; | |
225 | res |= a[3] ^ ONE[3]; | |
226 | if (P256_LIMBS == 8) { | |
227 | res |= a[4] ^ ONE[4]; | |
228 | res |= a[5] ^ ONE[5]; | |
229 | res |= a[6] ^ ONE[6]; | |
230 | /* | |
231 | * no check for a[7] (being zero) on 32-bit platforms, | |
232 | * because value of "one" takes only 7 limbs. | |
233 | */ | |
234 | } | |
235 | res = is_zero(res); | |
4d3fa06f AP |
236 | } |
237 | ||
2e929e53 | 238 | return res; |
4d3fa06f AP |
239 | } |
240 | ||
f3b3d7f0 RS |
241 | /* |
242 | * For reference, this macro is used only when new ecp_nistz256 assembly | |
243 | * module is being developed. For example, configure with | |
244 | * -DECP_NISTZ256_REFERENCE_IMPLEMENTATION and implement only functions | |
245 | * performing simplest arithmetic operations on 256-bit vectors. Then | |
246 | * work on implementation of higher-level functions performing point | |
247 | * operations. Then remove ECP_NISTZ256_REFERENCE_IMPLEMENTATION | |
248 | * and never define it again. (The correct macro denoting presence of | |
249 | * ecp_nistz256 module is ECP_NISTZ256_ASM.) | |
250 | */ | |
4d3fa06f | 251 | #ifndef ECP_NISTZ256_REFERENCE_IMPLEMENTATION |
58d47cf0 AP |
252 | void ecp_nistz256_point_double(P256_POINT *r, const P256_POINT *a); |
253 | void ecp_nistz256_point_add(P256_POINT *r, | |
254 | const P256_POINT *a, const P256_POINT *b); | |
255 | void ecp_nistz256_point_add_affine(P256_POINT *r, | |
256 | const P256_POINT *a, | |
257 | const P256_POINT_AFFINE *b); | |
4d3fa06f AP |
258 | #else |
259 | /* Point double: r = 2*a */ | |
58d47cf0 | 260 | static void ecp_nistz256_point_double(P256_POINT *r, const P256_POINT *a) |
4d3fa06f AP |
261 | { |
262 | BN_ULONG S[P256_LIMBS]; | |
263 | BN_ULONG M[P256_LIMBS]; | |
264 | BN_ULONG Zsqr[P256_LIMBS]; | |
265 | BN_ULONG tmp0[P256_LIMBS]; | |
266 | ||
267 | const BN_ULONG *in_x = a->X; | |
268 | const BN_ULONG *in_y = a->Y; | |
269 | const BN_ULONG *in_z = a->Z; | |
270 | ||
271 | BN_ULONG *res_x = r->X; | |
272 | BN_ULONG *res_y = r->Y; | |
273 | BN_ULONG *res_z = r->Z; | |
274 | ||
275 | ecp_nistz256_mul_by_2(S, in_y); | |
276 | ||
277 | ecp_nistz256_sqr_mont(Zsqr, in_z); | |
278 | ||
279 | ecp_nistz256_sqr_mont(S, S); | |
280 | ||
281 | ecp_nistz256_mul_mont(res_z, in_z, in_y); | |
282 | ecp_nistz256_mul_by_2(res_z, res_z); | |
283 | ||
284 | ecp_nistz256_add(M, in_x, Zsqr); | |
285 | ecp_nistz256_sub(Zsqr, in_x, Zsqr); | |
286 | ||
287 | ecp_nistz256_sqr_mont(res_y, S); | |
288 | ecp_nistz256_div_by_2(res_y, res_y); | |
289 | ||
290 | ecp_nistz256_mul_mont(M, M, Zsqr); | |
291 | ecp_nistz256_mul_by_3(M, M); | |
292 | ||
293 | ecp_nistz256_mul_mont(S, S, in_x); | |
294 | ecp_nistz256_mul_by_2(tmp0, S); | |
295 | ||
296 | ecp_nistz256_sqr_mont(res_x, M); | |
297 | ||
298 | ecp_nistz256_sub(res_x, res_x, tmp0); | |
299 | ecp_nistz256_sub(S, S, res_x); | |
300 | ||
301 | ecp_nistz256_mul_mont(S, S, M); | |
302 | ecp_nistz256_sub(res_y, S, res_y); | |
303 | } | |
304 | ||
305 | /* Point addition: r = a+b */ | |
20728adc AP |
306 | static void ecp_nistz256_point_add(P256_POINT *r, |
307 | const P256_POINT *a, const P256_POINT *b) | |
4d3fa06f AP |
308 | { |
309 | BN_ULONG U2[P256_LIMBS], S2[P256_LIMBS]; | |
310 | BN_ULONG U1[P256_LIMBS], S1[P256_LIMBS]; | |
311 | BN_ULONG Z1sqr[P256_LIMBS]; | |
312 | BN_ULONG Z2sqr[P256_LIMBS]; | |
313 | BN_ULONG H[P256_LIMBS], R[P256_LIMBS]; | |
314 | BN_ULONG Hsqr[P256_LIMBS]; | |
315 | BN_ULONG Rsqr[P256_LIMBS]; | |
316 | BN_ULONG Hcub[P256_LIMBS]; | |
317 | ||
318 | BN_ULONG res_x[P256_LIMBS]; | |
319 | BN_ULONG res_y[P256_LIMBS]; | |
320 | BN_ULONG res_z[P256_LIMBS]; | |
321 | ||
322 | BN_ULONG in1infty, in2infty; | |
323 | ||
324 | const BN_ULONG *in1_x = a->X; | |
325 | const BN_ULONG *in1_y = a->Y; | |
326 | const BN_ULONG *in1_z = a->Z; | |
327 | ||
328 | const BN_ULONG *in2_x = b->X; | |
329 | const BN_ULONG *in2_y = b->Y; | |
330 | const BN_ULONG *in2_z = b->Z; | |
331 | ||
e3057a57 AP |
332 | /* |
333 | * Infinity in encoded as (,,0) | |
334 | */ | |
335 | in1infty = (in1_z[0] | in1_z[1] | in1_z[2] | in1_z[3]); | |
4d3fa06f | 336 | if (P256_LIMBS == 8) |
e3057a57 | 337 | in1infty |= (in1_z[4] | in1_z[5] | in1_z[6] | in1_z[7]); |
4d3fa06f | 338 | |
e3057a57 | 339 | in2infty = (in2_z[0] | in2_z[1] | in2_z[2] | in2_z[3]); |
4d3fa06f | 340 | if (P256_LIMBS == 8) |
e3057a57 | 341 | in2infty |= (in2_z[4] | in2_z[5] | in2_z[6] | in2_z[7]); |
4d3fa06f AP |
342 | |
343 | in1infty = is_zero(in1infty); | |
344 | in2infty = is_zero(in2infty); | |
345 | ||
346 | ecp_nistz256_sqr_mont(Z2sqr, in2_z); /* Z2^2 */ | |
347 | ecp_nistz256_sqr_mont(Z1sqr, in1_z); /* Z1^2 */ | |
348 | ||
349 | ecp_nistz256_mul_mont(S1, Z2sqr, in2_z); /* S1 = Z2^3 */ | |
350 | ecp_nistz256_mul_mont(S2, Z1sqr, in1_z); /* S2 = Z1^3 */ | |
351 | ||
352 | ecp_nistz256_mul_mont(S1, S1, in1_y); /* S1 = Y1*Z2^3 */ | |
353 | ecp_nistz256_mul_mont(S2, S2, in2_y); /* S2 = Y2*Z1^3 */ | |
354 | ecp_nistz256_sub(R, S2, S1); /* R = S2 - S1 */ | |
355 | ||
356 | ecp_nistz256_mul_mont(U1, in1_x, Z2sqr); /* U1 = X1*Z2^2 */ | |
357 | ecp_nistz256_mul_mont(U2, in2_x, Z1sqr); /* U2 = X2*Z1^2 */ | |
358 | ecp_nistz256_sub(H, U2, U1); /* H = U2 - U1 */ | |
359 | ||
20728adc | 360 | /* |
38be93f6 BE |
361 | * The formulae are incorrect if the points are equal so we check for |
362 | * this and do doubling if this happens. | |
363 | * | |
364 | * Points here are in Jacobian projective coordinates (Xi, Yi, Zi) | |
365 | * that are bound to the affine coordinates (xi, yi) by the following | |
366 | * equations: | |
367 | * - xi = Xi / (Zi)^2 | |
368 | * - y1 = Yi / (Zi)^3 | |
369 | * | |
370 | * For the sake of optimization, the algorithm operates over | |
371 | * intermediate variables U1, U2 and S1, S2 that are derived from | |
372 | * the projective coordinates: | |
373 | * - U1 = X1 * (Z2)^2 ; U2 = X2 * (Z1)^2 | |
374 | * - S1 = Y1 * (Z2)^3 ; S2 = Y2 * (Z1)^3 | |
375 | * | |
376 | * It is easy to prove that is_equal(U1, U2) implies that the affine | |
377 | * x-coordinates are equal, or either point is at infinity. | |
378 | * Likewise is_equal(S1, S2) implies that the affine y-coordinates are | |
379 | * equal, or either point is at infinity. | |
380 | * | |
381 | * The special case of either point being the point at infinity (Z1 or Z2 | |
382 | * is zero), is handled separately later on in this function, so we avoid | |
383 | * jumping to point_double here in those special cases. | |
384 | * | |
385 | * When both points are inverse of each other, we know that the affine | |
386 | * x-coordinates are equal, and the y-coordinates have different sign. | |
387 | * Therefore since U1 = U2, we know H = 0, and therefore Z3 = H*Z1*Z2 | |
388 | * will equal 0, thus the result is infinity, if we simply let this | |
389 | * function continue normally. | |
390 | * | |
391 | * We use bitwise operations to avoid potential side-channels introduced by | |
392 | * the short-circuiting behaviour of boolean operators. | |
20728adc | 393 | */ |
38be93f6 BE |
394 | if (is_equal(U1, U2) & ~in1infty & ~in2infty & is_equal(S1, S2)) { |
395 | /* | |
396 | * This is obviously not constant-time but it should never happen during | |
397 | * single point multiplication, so there is no timing leak for ECDH or | |
398 | * ECDSA signing. | |
399 | */ | |
400 | ecp_nistz256_point_double(r, a); | |
401 | return; | |
4d3fa06f AP |
402 | } |
403 | ||
404 | ecp_nistz256_sqr_mont(Rsqr, R); /* R^2 */ | |
405 | ecp_nistz256_mul_mont(res_z, H, in1_z); /* Z3 = H*Z1*Z2 */ | |
406 | ecp_nistz256_sqr_mont(Hsqr, H); /* H^2 */ | |
407 | ecp_nistz256_mul_mont(res_z, res_z, in2_z); /* Z3 = H*Z1*Z2 */ | |
408 | ecp_nistz256_mul_mont(Hcub, Hsqr, H); /* H^3 */ | |
409 | ||
410 | ecp_nistz256_mul_mont(U2, U1, Hsqr); /* U1*H^2 */ | |
411 | ecp_nistz256_mul_by_2(Hsqr, U2); /* 2*U1*H^2 */ | |
412 | ||
413 | ecp_nistz256_sub(res_x, Rsqr, Hsqr); | |
414 | ecp_nistz256_sub(res_x, res_x, Hcub); | |
415 | ||
416 | ecp_nistz256_sub(res_y, U2, res_x); | |
417 | ||
418 | ecp_nistz256_mul_mont(S2, S1, Hcub); | |
419 | ecp_nistz256_mul_mont(res_y, R, res_y); | |
420 | ecp_nistz256_sub(res_y, res_y, S2); | |
421 | ||
422 | copy_conditional(res_x, in2_x, in1infty); | |
423 | copy_conditional(res_y, in2_y, in1infty); | |
424 | copy_conditional(res_z, in2_z, in1infty); | |
425 | ||
426 | copy_conditional(res_x, in1_x, in2infty); | |
427 | copy_conditional(res_y, in1_y, in2infty); | |
428 | copy_conditional(res_z, in1_z, in2infty); | |
429 | ||
430 | memcpy(r->X, res_x, sizeof(res_x)); | |
431 | memcpy(r->Y, res_y, sizeof(res_y)); | |
432 | memcpy(r->Z, res_z, sizeof(res_z)); | |
433 | } | |
434 | ||
435 | /* Point addition when b is known to be affine: r = a+b */ | |
58d47cf0 AP |
436 | static void ecp_nistz256_point_add_affine(P256_POINT *r, |
437 | const P256_POINT *a, | |
438 | const P256_POINT_AFFINE *b) | |
4d3fa06f AP |
439 | { |
440 | BN_ULONG U2[P256_LIMBS], S2[P256_LIMBS]; | |
441 | BN_ULONG Z1sqr[P256_LIMBS]; | |
442 | BN_ULONG H[P256_LIMBS], R[P256_LIMBS]; | |
443 | BN_ULONG Hsqr[P256_LIMBS]; | |
444 | BN_ULONG Rsqr[P256_LIMBS]; | |
445 | BN_ULONG Hcub[P256_LIMBS]; | |
446 | ||
447 | BN_ULONG res_x[P256_LIMBS]; | |
448 | BN_ULONG res_y[P256_LIMBS]; | |
449 | BN_ULONG res_z[P256_LIMBS]; | |
450 | ||
451 | BN_ULONG in1infty, in2infty; | |
452 | ||
453 | const BN_ULONG *in1_x = a->X; | |
454 | const BN_ULONG *in1_y = a->Y; | |
455 | const BN_ULONG *in1_z = a->Z; | |
456 | ||
457 | const BN_ULONG *in2_x = b->X; | |
458 | const BN_ULONG *in2_y = b->Y; | |
459 | ||
20728adc | 460 | /* |
e3057a57 | 461 | * Infinity in encoded as (,,0) |
20728adc | 462 | */ |
e3057a57 | 463 | in1infty = (in1_z[0] | in1_z[1] | in1_z[2] | in1_z[3]); |
4d3fa06f | 464 | if (P256_LIMBS == 8) |
e3057a57 | 465 | in1infty |= (in1_z[4] | in1_z[5] | in1_z[6] | in1_z[7]); |
4d3fa06f | 466 | |
e3057a57 AP |
467 | /* |
468 | * In affine representation we encode infinity as (0,0), which is | |
469 | * not on the curve, so it is OK | |
470 | */ | |
58d47cf0 AP |
471 | in2infty = (in2_x[0] | in2_x[1] | in2_x[2] | in2_x[3] | |
472 | in2_y[0] | in2_y[1] | in2_y[2] | in2_y[3]); | |
4d3fa06f | 473 | if (P256_LIMBS == 8) |
58d47cf0 AP |
474 | in2infty |= (in2_x[4] | in2_x[5] | in2_x[6] | in2_x[7] | |
475 | in2_y[4] | in2_y[5] | in2_y[6] | in2_y[7]); | |
4d3fa06f AP |
476 | |
477 | in1infty = is_zero(in1infty); | |
478 | in2infty = is_zero(in2infty); | |
479 | ||
480 | ecp_nistz256_sqr_mont(Z1sqr, in1_z); /* Z1^2 */ | |
481 | ||
482 | ecp_nistz256_mul_mont(U2, in2_x, Z1sqr); /* U2 = X2*Z1^2 */ | |
483 | ecp_nistz256_sub(H, U2, in1_x); /* H = U2 - U1 */ | |
484 | ||
485 | ecp_nistz256_mul_mont(S2, Z1sqr, in1_z); /* S2 = Z1^3 */ | |
486 | ||
487 | ecp_nistz256_mul_mont(res_z, H, in1_z); /* Z3 = H*Z1*Z2 */ | |
488 | ||
489 | ecp_nistz256_mul_mont(S2, S2, in2_y); /* S2 = Y2*Z1^3 */ | |
490 | ecp_nistz256_sub(R, S2, in1_y); /* R = S2 - S1 */ | |
491 | ||
492 | ecp_nistz256_sqr_mont(Hsqr, H); /* H^2 */ | |
493 | ecp_nistz256_sqr_mont(Rsqr, R); /* R^2 */ | |
494 | ecp_nistz256_mul_mont(Hcub, Hsqr, H); /* H^3 */ | |
495 | ||
496 | ecp_nistz256_mul_mont(U2, in1_x, Hsqr); /* U1*H^2 */ | |
497 | ecp_nistz256_mul_by_2(Hsqr, U2); /* 2*U1*H^2 */ | |
498 | ||
499 | ecp_nistz256_sub(res_x, Rsqr, Hsqr); | |
500 | ecp_nistz256_sub(res_x, res_x, Hcub); | |
501 | ecp_nistz256_sub(H, U2, res_x); | |
502 | ||
503 | ecp_nistz256_mul_mont(S2, in1_y, Hcub); | |
504 | ecp_nistz256_mul_mont(H, H, R); | |
505 | ecp_nistz256_sub(res_y, H, S2); | |
506 | ||
507 | copy_conditional(res_x, in2_x, in1infty); | |
508 | copy_conditional(res_x, in1_x, in2infty); | |
509 | ||
510 | copy_conditional(res_y, in2_y, in1infty); | |
511 | copy_conditional(res_y, in1_y, in2infty); | |
512 | ||
513 | copy_conditional(res_z, ONE, in1infty); | |
514 | copy_conditional(res_z, in1_z, in2infty); | |
515 | ||
516 | memcpy(r->X, res_x, sizeof(res_x)); | |
517 | memcpy(r->Y, res_y, sizeof(res_y)); | |
518 | memcpy(r->Z, res_z, sizeof(res_z)); | |
519 | } | |
520 | #endif | |
521 | ||
522 | /* r = in^-1 mod p */ | |
523 | static void ecp_nistz256_mod_inverse(BN_ULONG r[P256_LIMBS], | |
524 | const BN_ULONG in[P256_LIMBS]) | |
525 | { | |
20728adc AP |
526 | /* |
527 | * The poly is ffffffff 00000001 00000000 00000000 00000000 ffffffff | |
528 | * ffffffff ffffffff We use FLT and used poly-2 as exponent | |
529 | */ | |
4d3fa06f AP |
530 | BN_ULONG p2[P256_LIMBS]; |
531 | BN_ULONG p4[P256_LIMBS]; | |
532 | BN_ULONG p8[P256_LIMBS]; | |
533 | BN_ULONG p16[P256_LIMBS]; | |
534 | BN_ULONG p32[P256_LIMBS]; | |
535 | BN_ULONG res[P256_LIMBS]; | |
536 | int i; | |
537 | ||
538 | ecp_nistz256_sqr_mont(res, in); | |
539 | ecp_nistz256_mul_mont(p2, res, in); /* 3*p */ | |
540 | ||
541 | ecp_nistz256_sqr_mont(res, p2); | |
542 | ecp_nistz256_sqr_mont(res, res); | |
543 | ecp_nistz256_mul_mont(p4, res, p2); /* f*p */ | |
544 | ||
545 | ecp_nistz256_sqr_mont(res, p4); | |
546 | ecp_nistz256_sqr_mont(res, res); | |
547 | ecp_nistz256_sqr_mont(res, res); | |
548 | ecp_nistz256_sqr_mont(res, res); | |
549 | ecp_nistz256_mul_mont(p8, res, p4); /* ff*p */ | |
550 | ||
551 | ecp_nistz256_sqr_mont(res, p8); | |
552 | for (i = 0; i < 7; i++) | |
553 | ecp_nistz256_sqr_mont(res, res); | |
554 | ecp_nistz256_mul_mont(p16, res, p8); /* ffff*p */ | |
555 | ||
556 | ecp_nistz256_sqr_mont(res, p16); | |
557 | for (i = 0; i < 15; i++) | |
558 | ecp_nistz256_sqr_mont(res, res); | |
559 | ecp_nistz256_mul_mont(p32, res, p16); /* ffffffff*p */ | |
560 | ||
561 | ecp_nistz256_sqr_mont(res, p32); | |
562 | for (i = 0; i < 31; i++) | |
563 | ecp_nistz256_sqr_mont(res, res); | |
564 | ecp_nistz256_mul_mont(res, res, in); | |
565 | ||
566 | for (i = 0; i < 32 * 4; i++) | |
567 | ecp_nistz256_sqr_mont(res, res); | |
568 | ecp_nistz256_mul_mont(res, res, p32); | |
569 | ||
570 | for (i = 0; i < 32; i++) | |
571 | ecp_nistz256_sqr_mont(res, res); | |
572 | ecp_nistz256_mul_mont(res, res, p32); | |
573 | ||
574 | for (i = 0; i < 16; i++) | |
575 | ecp_nistz256_sqr_mont(res, res); | |
576 | ecp_nistz256_mul_mont(res, res, p16); | |
577 | ||
578 | for (i = 0; i < 8; i++) | |
579 | ecp_nistz256_sqr_mont(res, res); | |
580 | ecp_nistz256_mul_mont(res, res, p8); | |
581 | ||
582 | ecp_nistz256_sqr_mont(res, res); | |
583 | ecp_nistz256_sqr_mont(res, res); | |
584 | ecp_nistz256_sqr_mont(res, res); | |
585 | ecp_nistz256_sqr_mont(res, res); | |
586 | ecp_nistz256_mul_mont(res, res, p4); | |
587 | ||
588 | ecp_nistz256_sqr_mont(res, res); | |
589 | ecp_nistz256_sqr_mont(res, res); | |
590 | ecp_nistz256_mul_mont(res, res, p2); | |
591 | ||
592 | ecp_nistz256_sqr_mont(res, res); | |
593 | ecp_nistz256_sqr_mont(res, res); | |
594 | ecp_nistz256_mul_mont(res, res, in); | |
595 | ||
596 | memcpy(r, res, sizeof(res)); | |
597 | } | |
598 | ||
20728adc AP |
599 | /* |
600 | * ecp_nistz256_bignum_to_field_elem copies the contents of |in| to |out| and | |
601 | * returns one if it fits. Otherwise it returns zero. | |
602 | */ | |
5956b110 EK |
603 | __owur static int ecp_nistz256_bignum_to_field_elem(BN_ULONG out[P256_LIMBS], |
604 | const BIGNUM *in) | |
4d3fa06f | 605 | { |
5784a521 | 606 | return bn_copy_words(out, in, P256_LIMBS); |
4d3fa06f AP |
607 | } |
608 | ||
609 | /* r = sum(scalar[i]*point[i]) */ | |
5956b110 EK |
610 | __owur static int ecp_nistz256_windowed_mul(const EC_GROUP *group, |
611 | P256_POINT *r, | |
612 | const BIGNUM **scalar, | |
613 | const EC_POINT **point, | |
614 | size_t num, BN_CTX *ctx) | |
4d3fa06f | 615 | { |
5afc296a | 616 | size_t i; |
a4d5269e | 617 | int j, ret = 0; |
49b05c7d | 618 | unsigned int idx; |
4d3fa06f AP |
619 | unsigned char (*p_str)[33] = NULL; |
620 | const unsigned int window_size = 5; | |
621 | const unsigned int mask = (1 << (window_size + 1)) - 1; | |
622 | unsigned int wvalue; | |
20728adc | 623 | P256_POINT *temp; /* place for 5 temporary points */ |
4d3fa06f | 624 | const BIGNUM **scalars = NULL; |
20728adc | 625 | P256_POINT (*table)[16] = NULL; |
4d3fa06f AP |
626 | void *table_storage = NULL; |
627 | ||
5afc296a AP |
628 | if ((num * 16 + 6) > OPENSSL_MALLOC_MAX_NELEMS(P256_POINT) |
629 | || (table_storage = | |
630 | OPENSSL_malloc((num * 16 + 5) * sizeof(P256_POINT) + 64)) == NULL | |
4d3fa06f AP |
631 | || (p_str = |
632 | OPENSSL_malloc(num * 33 * sizeof(unsigned char))) == NULL | |
633 | || (scalars = OPENSSL_malloc(num * sizeof(BIGNUM *))) == NULL) { | |
be07ae9b | 634 | ECerr(EC_F_ECP_NISTZ256_WINDOWED_MUL, ERR_R_MALLOC_FAILURE); |
4d3fa06f | 635 | goto err; |
4d3fa06f AP |
636 | } |
637 | ||
3ff08e1d | 638 | table = (void *)ALIGNPTR(table_storage, 64); |
20728adc | 639 | temp = (P256_POINT *)(table + num); |
3ff08e1d | 640 | |
4d3fa06f AP |
641 | for (i = 0; i < num; i++) { |
642 | P256_POINT *row = table[i]; | |
643 | ||
c028254b | 644 | /* This is an unusual input, we don't guarantee constant-timeness. */ |
4d3fa06f AP |
645 | if ((BN_num_bits(scalar[i]) > 256) || BN_is_negative(scalar[i])) { |
646 | BIGNUM *mod; | |
647 | ||
648 | if ((mod = BN_CTX_get(ctx)) == NULL) | |
649 | goto err; | |
5784a521 | 650 | if (!BN_nnmod(mod, scalar[i], group->order, ctx)) { |
be07ae9b | 651 | ECerr(EC_F_ECP_NISTZ256_WINDOWED_MUL, ERR_R_BN_LIB); |
4d3fa06f AP |
652 | goto err; |
653 | } | |
654 | scalars[i] = mod; | |
655 | } else | |
656 | scalars[i] = scalar[i]; | |
657 | ||
5784a521 MC |
658 | for (j = 0; j < bn_get_top(scalars[i]) * BN_BYTES; j += BN_BYTES) { |
659 | BN_ULONG d = bn_get_words(scalars[i])[j / BN_BYTES]; | |
4d3fa06f | 660 | |
5afc296a AP |
661 | p_str[i][j + 0] = (unsigned char)d; |
662 | p_str[i][j + 1] = (unsigned char)(d >> 8); | |
663 | p_str[i][j + 2] = (unsigned char)(d >> 16); | |
664 | p_str[i][j + 3] = (unsigned char)(d >>= 24); | |
4d3fa06f AP |
665 | if (BN_BYTES == 8) { |
666 | d >>= 8; | |
5afc296a AP |
667 | p_str[i][j + 4] = (unsigned char)d; |
668 | p_str[i][j + 5] = (unsigned char)(d >> 8); | |
669 | p_str[i][j + 6] = (unsigned char)(d >> 16); | |
670 | p_str[i][j + 7] = (unsigned char)(d >> 24); | |
4d3fa06f AP |
671 | } |
672 | } | |
673 | for (; j < 33; j++) | |
674 | p_str[i][j] = 0; | |
675 | ||
5784a521 MC |
676 | if (!ecp_nistz256_bignum_to_field_elem(temp[0].X, point[i]->X) |
677 | || !ecp_nistz256_bignum_to_field_elem(temp[0].Y, point[i]->Y) | |
678 | || !ecp_nistz256_bignum_to_field_elem(temp[0].Z, point[i]->Z)) { | |
58d47cf0 AP |
679 | ECerr(EC_F_ECP_NISTZ256_WINDOWED_MUL, |
680 | EC_R_COORDINATES_OUT_OF_RANGE); | |
4d3fa06f AP |
681 | goto err; |
682 | } | |
683 | ||
20728adc | 684 | /* |
dccd20d1 F |
685 | * row[0] is implicitly (0,0,0) (the point at infinity), therefore it |
686 | * is not stored. All other values are actually stored with an offset | |
687 | * of -1 in table. | |
3ff08e1d AP |
688 | */ |
689 | ||
690 | ecp_nistz256_scatter_w5 (row, &temp[0], 1); | |
691 | ecp_nistz256_point_double(&temp[1], &temp[0]); /*1+1=2 */ | |
692 | ecp_nistz256_scatter_w5 (row, &temp[1], 2); | |
693 | ecp_nistz256_point_add (&temp[2], &temp[1], &temp[0]); /*2+1=3 */ | |
694 | ecp_nistz256_scatter_w5 (row, &temp[2], 3); | |
695 | ecp_nistz256_point_double(&temp[1], &temp[1]); /*2*2=4 */ | |
696 | ecp_nistz256_scatter_w5 (row, &temp[1], 4); | |
697 | ecp_nistz256_point_double(&temp[2], &temp[2]); /*2*3=6 */ | |
698 | ecp_nistz256_scatter_w5 (row, &temp[2], 6); | |
699 | ecp_nistz256_point_add (&temp[3], &temp[1], &temp[0]); /*4+1=5 */ | |
700 | ecp_nistz256_scatter_w5 (row, &temp[3], 5); | |
701 | ecp_nistz256_point_add (&temp[4], &temp[2], &temp[0]); /*6+1=7 */ | |
702 | ecp_nistz256_scatter_w5 (row, &temp[4], 7); | |
703 | ecp_nistz256_point_double(&temp[1], &temp[1]); /*2*4=8 */ | |
704 | ecp_nistz256_scatter_w5 (row, &temp[1], 8); | |
705 | ecp_nistz256_point_double(&temp[2], &temp[2]); /*2*6=12 */ | |
706 | ecp_nistz256_scatter_w5 (row, &temp[2], 12); | |
707 | ecp_nistz256_point_double(&temp[3], &temp[3]); /*2*5=10 */ | |
708 | ecp_nistz256_scatter_w5 (row, &temp[3], 10); | |
709 | ecp_nistz256_point_double(&temp[4], &temp[4]); /*2*7=14 */ | |
710 | ecp_nistz256_scatter_w5 (row, &temp[4], 14); | |
711 | ecp_nistz256_point_add (&temp[2], &temp[2], &temp[0]); /*12+1=13*/ | |
712 | ecp_nistz256_scatter_w5 (row, &temp[2], 13); | |
713 | ecp_nistz256_point_add (&temp[3], &temp[3], &temp[0]); /*10+1=11*/ | |
714 | ecp_nistz256_scatter_w5 (row, &temp[3], 11); | |
715 | ecp_nistz256_point_add (&temp[4], &temp[4], &temp[0]); /*14+1=15*/ | |
716 | ecp_nistz256_scatter_w5 (row, &temp[4], 15); | |
717 | ecp_nistz256_point_add (&temp[2], &temp[1], &temp[0]); /*8+1=9 */ | |
718 | ecp_nistz256_scatter_w5 (row, &temp[2], 9); | |
719 | ecp_nistz256_point_double(&temp[1], &temp[1]); /*2*8=16 */ | |
720 | ecp_nistz256_scatter_w5 (row, &temp[1], 16); | |
4d3fa06f AP |
721 | } |
722 | ||
49b05c7d | 723 | idx = 255; |
4d3fa06f | 724 | |
49b05c7d RS |
725 | wvalue = p_str[0][(idx - 1) / 8]; |
726 | wvalue = (wvalue >> ((idx - 1) % 8)) & mask; | |
4d3fa06f | 727 | |
3ff08e1d AP |
728 | /* |
729 | * We gather to temp[0], because we know it's position relative | |
730 | * to table | |
731 | */ | |
732 | ecp_nistz256_gather_w5(&temp[0], table[0], _booth_recode_w5(wvalue) >> 1); | |
733 | memcpy(r, &temp[0], sizeof(temp[0])); | |
4d3fa06f | 734 | |
49b05c7d RS |
735 | while (idx >= 5) { |
736 | for (i = (idx == 255 ? 1 : 0); i < num; i++) { | |
737 | unsigned int off = (idx - 1) / 8; | |
4d3fa06f AP |
738 | |
739 | wvalue = p_str[i][off] | p_str[i][off + 1] << 8; | |
49b05c7d | 740 | wvalue = (wvalue >> ((idx - 1) % 8)) & mask; |
4d3fa06f AP |
741 | |
742 | wvalue = _booth_recode_w5(wvalue); | |
743 | ||
3ff08e1d | 744 | ecp_nistz256_gather_w5(&temp[0], table[i], wvalue >> 1); |
4d3fa06f | 745 | |
3ff08e1d AP |
746 | ecp_nistz256_neg(temp[1].Y, temp[0].Y); |
747 | copy_conditional(temp[0].Y, temp[1].Y, (wvalue & 1)); | |
4d3fa06f | 748 | |
3ff08e1d | 749 | ecp_nistz256_point_add(r, r, &temp[0]); |
4d3fa06f AP |
750 | } |
751 | ||
49b05c7d | 752 | idx -= window_size; |
4d3fa06f AP |
753 | |
754 | ecp_nistz256_point_double(r, r); | |
755 | ecp_nistz256_point_double(r, r); | |
756 | ecp_nistz256_point_double(r, r); | |
757 | ecp_nistz256_point_double(r, r); | |
758 | ecp_nistz256_point_double(r, r); | |
759 | } | |
760 | ||
761 | /* Final window */ | |
762 | for (i = 0; i < num; i++) { | |
763 | wvalue = p_str[i][0]; | |
764 | wvalue = (wvalue << 1) & mask; | |
765 | ||
766 | wvalue = _booth_recode_w5(wvalue); | |
767 | ||
3ff08e1d | 768 | ecp_nistz256_gather_w5(&temp[0], table[i], wvalue >> 1); |
4d3fa06f | 769 | |
3ff08e1d AP |
770 | ecp_nistz256_neg(temp[1].Y, temp[0].Y); |
771 | copy_conditional(temp[0].Y, temp[1].Y, wvalue & 1); | |
4d3fa06f | 772 | |
3ff08e1d | 773 | ecp_nistz256_point_add(r, r, &temp[0]); |
4d3fa06f AP |
774 | } |
775 | ||
a4d5269e | 776 | ret = 1; |
58d47cf0 | 777 | err: |
b548a1f1 RS |
778 | OPENSSL_free(table_storage); |
779 | OPENSSL_free(p_str); | |
780 | OPENSSL_free(scalars); | |
a4d5269e | 781 | return ret; |
4d3fa06f AP |
782 | } |
783 | ||
784 | /* Coordinates of G, for which we have precomputed tables */ | |
f44903a4 | 785 | static const BN_ULONG def_xG[P256_LIMBS] = { |
4d3fa06f AP |
786 | TOBN(0x79e730d4, 0x18a9143c), TOBN(0x75ba95fc, 0x5fedb601), |
787 | TOBN(0x79fb732b, 0x77622510), TOBN(0x18905f76, 0xa53755c6) | |
788 | }; | |
789 | ||
f44903a4 | 790 | static const BN_ULONG def_yG[P256_LIMBS] = { |
4d3fa06f AP |
791 | TOBN(0xddf25357, 0xce95560a), TOBN(0x8b4ab8e4, 0xba19e45c), |
792 | TOBN(0xd2e88688, 0xdd21f325), TOBN(0x8571ff18, 0x25885d85) | |
793 | }; | |
794 | ||
20728adc AP |
795 | /* |
796 | * ecp_nistz256_is_affine_G returns one if |generator| is the standard, P-256 | |
797 | * generator. | |
798 | */ | |
58d47cf0 | 799 | static int ecp_nistz256_is_affine_G(const EC_POINT *generator) |
4d3fa06f | 800 | { |
5784a521 MC |
801 | return (bn_get_top(generator->X) == P256_LIMBS) && |
802 | (bn_get_top(generator->Y) == P256_LIMBS) && | |
5784a521 MC |
803 | is_equal(bn_get_words(generator->X), def_xG) && |
804 | is_equal(bn_get_words(generator->Y), def_yG) && | |
2e929e53 | 805 | is_one(generator->Z); |
4d3fa06f AP |
806 | } |
807 | ||
5956b110 | 808 | __owur static int ecp_nistz256_mult_precompute(EC_GROUP *group, BN_CTX *ctx) |
4d3fa06f | 809 | { |
20728adc AP |
810 | /* |
811 | * We precompute a table for a Booth encoded exponent (wNAF) based | |
4d3fa06f | 812 | * computation. Each table holds 64 values for safe access, with an |
20728adc AP |
813 | * implicit value of infinity at index zero. We use window of size 7, and |
814 | * therefore require ceil(256/7) = 37 tables. | |
815 | */ | |
be2e334f | 816 | const BIGNUM *order; |
4d3fa06f AP |
817 | EC_POINT *P = NULL, *T = NULL; |
818 | const EC_POINT *generator; | |
3aef36ff | 819 | NISTZ256_PRE_COMP *pre_comp; |
53dd4ddf | 820 | BN_CTX *new_ctx = NULL; |
4d3fa06f AP |
821 | int i, j, k, ret = 0; |
822 | size_t w; | |
823 | ||
824 | PRECOMP256_ROW *preComputedTable = NULL; | |
825 | unsigned char *precomp_storage = NULL; | |
826 | ||
3aef36ff | 827 | /* if there is an old NISTZ256_PRE_COMP object, throw it away */ |
2c52ac9b | 828 | EC_pre_comp_free(group); |
4d3fa06f AP |
829 | generator = EC_GROUP_get0_generator(group); |
830 | if (generator == NULL) { | |
be07ae9b | 831 | ECerr(EC_F_ECP_NISTZ256_MULT_PRECOMPUTE, EC_R_UNDEFINED_GENERATOR); |
4d3fa06f AP |
832 | return 0; |
833 | } | |
834 | ||
835 | if (ecp_nistz256_is_affine_G(generator)) { | |
20728adc AP |
836 | /* |
837 | * No need to calculate tables for the standard generator because we | |
838 | * have them statically. | |
839 | */ | |
4d3fa06f AP |
840 | return 1; |
841 | } | |
842 | ||
be07ae9b | 843 | if ((pre_comp = ecp_nistz256_pre_comp_new(group)) == NULL) |
4d3fa06f AP |
844 | return 0; |
845 | ||
846 | if (ctx == NULL) { | |
53dd4ddf | 847 | ctx = new_ctx = BN_CTX_new(); |
4d3fa06f AP |
848 | if (ctx == NULL) |
849 | goto err; | |
850 | } | |
851 | ||
852 | BN_CTX_start(ctx); | |
4d3fa06f | 853 | |
be2e334f | 854 | order = EC_GROUP_get0_order(group); |
4d3fa06f AP |
855 | if (order == NULL) |
856 | goto err; | |
857 | ||
4d3fa06f | 858 | if (BN_is_zero(order)) { |
be07ae9b | 859 | ECerr(EC_F_ECP_NISTZ256_MULT_PRECOMPUTE, EC_R_UNKNOWN_ORDER); |
4d3fa06f AP |
860 | goto err; |
861 | } | |
862 | ||
863 | w = 7; | |
864 | ||
865 | if ((precomp_storage = | |
866 | OPENSSL_malloc(37 * 64 * sizeof(P256_POINT_AFFINE) + 64)) == NULL) { | |
be07ae9b | 867 | ECerr(EC_F_ECP_NISTZ256_MULT_PRECOMPUTE, ERR_R_MALLOC_FAILURE); |
4d3fa06f | 868 | goto err; |
4d3fa06f AP |
869 | } |
870 | ||
3ff08e1d AP |
871 | preComputedTable = (void *)ALIGNPTR(precomp_storage, 64); |
872 | ||
4d3fa06f AP |
873 | P = EC_POINT_new(group); |
874 | T = EC_POINT_new(group); | |
53dd4ddf EK |
875 | if (P == NULL || T == NULL) |
876 | goto err; | |
4d3fa06f | 877 | |
20728adc AP |
878 | /* |
879 | * The zero entry is implicitly infinity, and we skip it, storing other | |
880 | * values with -1 offset. | |
881 | */ | |
53dd4ddf EK |
882 | if (!EC_POINT_copy(T, generator)) |
883 | goto err; | |
4d3fa06f AP |
884 | |
885 | for (k = 0; k < 64; k++) { | |
53dd4ddf EK |
886 | if (!EC_POINT_copy(P, T)) |
887 | goto err; | |
4d3fa06f | 888 | for (j = 0; j < 37; j++) { |
3ff08e1d | 889 | P256_POINT_AFFINE temp; |
20728adc | 890 | /* |
6038354c | 891 | * It would be faster to use EC_POINTs_make_affine and |
20728adc AP |
892 | * make multiple points affine at the same time. |
893 | */ | |
6038354c EK |
894 | if (!EC_POINT_make_affine(group, P, ctx)) |
895 | goto err; | |
896 | if (!ecp_nistz256_bignum_to_field_elem(temp.X, P->X) || | |
897 | !ecp_nistz256_bignum_to_field_elem(temp.Y, P->Y)) { | |
898 | ECerr(EC_F_ECP_NISTZ256_MULT_PRECOMPUTE, | |
899 | EC_R_COORDINATES_OUT_OF_RANGE); | |
900 | goto err; | |
901 | } | |
3ff08e1d | 902 | ecp_nistz256_scatter_w7(preComputedTable[j], &temp, k); |
6038354c EK |
903 | for (i = 0; i < 7; i++) { |
904 | if (!EC_POINT_dbl(group, P, P, ctx)) | |
905 | goto err; | |
906 | } | |
4d3fa06f | 907 | } |
6038354c EK |
908 | if (!EC_POINT_add(group, T, T, generator, ctx)) |
909 | goto err; | |
4d3fa06f AP |
910 | } |
911 | ||
912 | pre_comp->group = group; | |
913 | pre_comp->w = w; | |
914 | pre_comp->precomp = preComputedTable; | |
915 | pre_comp->precomp_storage = precomp_storage; | |
4d3fa06f | 916 | precomp_storage = NULL; |
3aef36ff | 917 | SETPRECOMP(group, nistz256, pre_comp); |
4d3fa06f | 918 | pre_comp = NULL; |
4d3fa06f AP |
919 | ret = 1; |
920 | ||
58d47cf0 | 921 | err: |
c8a9fa69 | 922 | BN_CTX_end(ctx); |
53dd4ddf EK |
923 | BN_CTX_free(new_ctx); |
924 | ||
3aef36ff | 925 | EC_nistz256_pre_comp_free(pre_comp); |
b548a1f1 | 926 | OPENSSL_free(precomp_storage); |
8fdc3734 RS |
927 | EC_POINT_free(P); |
928 | EC_POINT_free(T); | |
4d3fa06f AP |
929 | return ret; |
930 | } | |
931 | ||
932 | /* | |
933 | * Note that by default ECP_NISTZ256_AVX2 is undefined. While it's great | |
934 | * code processing 4 points in parallel, corresponding serial operation | |
935 | * is several times slower, because it uses 29x29=58-bit multiplication | |
936 | * as opposite to 64x64=128-bit in integer-only scalar case. As result | |
937 | * it doesn't provide *significant* performance improvement. Note that | |
938 | * just defining ECP_NISTZ256_AVX2 is not sufficient to make it work, | |
939 | * you'd need to compile even asm/ecp_nistz256-avx.pl module. | |
940 | */ | |
941 | #if defined(ECP_NISTZ256_AVX2) | |
3ff08e1d | 942 | # if !(defined(__x86_64) || defined(__x86_64__) || \ |
eb791696 | 943 | defined(_M_AMD64) || defined(_M_X64)) || \ |
4d3fa06f AP |
944 | !(defined(__GNUC__) || defined(_MSC_VER)) /* this is for ALIGN32 */ |
945 | # undef ECP_NISTZ256_AVX2 | |
946 | # else | |
947 | /* Constant time access, loading four values, from four consecutive tables */ | |
58d47cf0 AP |
948 | void ecp_nistz256_avx2_multi_gather_w7(void *result, const void *in, |
949 | int index0, int index1, int index2, | |
950 | int index3); | |
4d3fa06f AP |
951 | void ecp_nistz256_avx2_transpose_convert(void *RESULTx4, const void *in); |
952 | void ecp_nistz256_avx2_convert_transpose_back(void *result, const void *Ax4); | |
953 | void ecp_nistz256_avx2_point_add_affine_x4(void *RESULTx4, const void *Ax4, | |
954 | const void *Bx4); | |
955 | void ecp_nistz256_avx2_point_add_affines_x4(void *RESULTx4, const void *Ax4, | |
956 | const void *Bx4); | |
957 | void ecp_nistz256_avx2_to_mont(void *RESULTx4, const void *Ax4); | |
958 | void ecp_nistz256_avx2_from_mont(void *RESULTx4, const void *Ax4); | |
959 | void ecp_nistz256_avx2_set1(void *RESULTx4); | |
960 | int ecp_nistz_avx2_eligible(void); | |
961 | ||
962 | static void booth_recode_w7(unsigned char *sign, | |
963 | unsigned char *digit, unsigned char in) | |
964 | { | |
965 | unsigned char s, d; | |
966 | ||
967 | s = ~((in >> 7) - 1); | |
968 | d = (1 << 8) - in - 1; | |
969 | d = (d & s) | (in & ~s); | |
970 | d = (d >> 1) + (d & 1); | |
971 | ||
972 | *sign = s & 1; | |
973 | *digit = d; | |
974 | } | |
975 | ||
20728adc AP |
976 | /* |
977 | * ecp_nistz256_avx2_mul_g performs multiplication by G, using only the | |
4d3fa06f | 978 | * precomputed table. It does 4 affine point additions in parallel, |
20728adc AP |
979 | * significantly speeding up point multiplication for a fixed value. |
980 | */ | |
58d47cf0 | 981 | static void ecp_nistz256_avx2_mul_g(P256_POINT *r, |
4d3fa06f | 982 | unsigned char p_str[33], |
58d47cf0 | 983 | const P256_POINT_AFFINE(*preComputedTable)[64]) |
4d3fa06f AP |
984 | { |
985 | const unsigned int window_size = 7; | |
986 | const unsigned int mask = (1 << (window_size + 1)) - 1; | |
987 | unsigned int wvalue; | |
988 | /* Using 4 windows at a time */ | |
989 | unsigned char sign0, digit0; | |
990 | unsigned char sign1, digit1; | |
991 | unsigned char sign2, digit2; | |
992 | unsigned char sign3, digit3; | |
49b05c7d | 993 | unsigned int idx = 0; |
4d3fa06f AP |
994 | BN_ULONG tmp[P256_LIMBS]; |
995 | int i; | |
996 | ||
997 | ALIGN32 BN_ULONG aX4[4 * 9 * 3] = { 0 }; | |
998 | ALIGN32 BN_ULONG bX4[4 * 9 * 2] = { 0 }; | |
3ff08e1d AP |
999 | ALIGN32 P256_POINT_AFFINE point_arr[4]; |
1000 | ALIGN32 P256_POINT res_point_arr[4]; | |
4d3fa06f AP |
1001 | |
1002 | /* Initial four windows */ | |
1003 | wvalue = *((u16 *) & p_str[0]); | |
1004 | wvalue = (wvalue << 1) & mask; | |
49b05c7d | 1005 | idx += window_size; |
4d3fa06f | 1006 | booth_recode_w7(&sign0, &digit0, wvalue); |
49b05c7d RS |
1007 | wvalue = *((u16 *) & p_str[(idx - 1) / 8]); |
1008 | wvalue = (wvalue >> ((idx - 1) % 8)) & mask; | |
1009 | idx += window_size; | |
4d3fa06f | 1010 | booth_recode_w7(&sign1, &digit1, wvalue); |
49b05c7d RS |
1011 | wvalue = *((u16 *) & p_str[(idx - 1) / 8]); |
1012 | wvalue = (wvalue >> ((idx - 1) % 8)) & mask; | |
1013 | idx += window_size; | |
4d3fa06f | 1014 | booth_recode_w7(&sign2, &digit2, wvalue); |
49b05c7d RS |
1015 | wvalue = *((u16 *) & p_str[(idx - 1) / 8]); |
1016 | wvalue = (wvalue >> ((idx - 1) % 8)) & mask; | |
1017 | idx += window_size; | |
4d3fa06f AP |
1018 | booth_recode_w7(&sign3, &digit3, wvalue); |
1019 | ||
3ff08e1d | 1020 | ecp_nistz256_avx2_multi_gather_w7(point_arr, preComputedTable[0], |
4d3fa06f AP |
1021 | digit0, digit1, digit2, digit3); |
1022 | ||
1023 | ecp_nistz256_neg(tmp, point_arr[0].Y); | |
1024 | copy_conditional(point_arr[0].Y, tmp, sign0); | |
1025 | ecp_nistz256_neg(tmp, point_arr[1].Y); | |
1026 | copy_conditional(point_arr[1].Y, tmp, sign1); | |
1027 | ecp_nistz256_neg(tmp, point_arr[2].Y); | |
1028 | copy_conditional(point_arr[2].Y, tmp, sign2); | |
1029 | ecp_nistz256_neg(tmp, point_arr[3].Y); | |
1030 | copy_conditional(point_arr[3].Y, tmp, sign3); | |
1031 | ||
1032 | ecp_nistz256_avx2_transpose_convert(aX4, point_arr); | |
1033 | ecp_nistz256_avx2_to_mont(aX4, aX4); | |
1034 | ecp_nistz256_avx2_to_mont(&aX4[4 * 9], &aX4[4 * 9]); | |
1035 | ecp_nistz256_avx2_set1(&aX4[4 * 9 * 2]); | |
1036 | ||
49b05c7d RS |
1037 | wvalue = *((u16 *) & p_str[(idx - 1) / 8]); |
1038 | wvalue = (wvalue >> ((idx - 1) % 8)) & mask; | |
1039 | idx += window_size; | |
4d3fa06f | 1040 | booth_recode_w7(&sign0, &digit0, wvalue); |
49b05c7d RS |
1041 | wvalue = *((u16 *) & p_str[(idx - 1) / 8]); |
1042 | wvalue = (wvalue >> ((idx - 1) % 8)) & mask; | |
1043 | idx += window_size; | |
4d3fa06f | 1044 | booth_recode_w7(&sign1, &digit1, wvalue); |
49b05c7d RS |
1045 | wvalue = *((u16 *) & p_str[(idx - 1) / 8]); |
1046 | wvalue = (wvalue >> ((idx - 1) % 8)) & mask; | |
1047 | idx += window_size; | |
4d3fa06f | 1048 | booth_recode_w7(&sign2, &digit2, wvalue); |
49b05c7d RS |
1049 | wvalue = *((u16 *) & p_str[(idx - 1) / 8]); |
1050 | wvalue = (wvalue >> ((idx - 1) % 8)) & mask; | |
1051 | idx += window_size; | |
4d3fa06f AP |
1052 | booth_recode_w7(&sign3, &digit3, wvalue); |
1053 | ||
3ff08e1d | 1054 | ecp_nistz256_avx2_multi_gather_w7(point_arr, preComputedTable[4 * 1], |
4d3fa06f AP |
1055 | digit0, digit1, digit2, digit3); |
1056 | ||
1057 | ecp_nistz256_neg(tmp, point_arr[0].Y); | |
1058 | copy_conditional(point_arr[0].Y, tmp, sign0); | |
1059 | ecp_nistz256_neg(tmp, point_arr[1].Y); | |
1060 | copy_conditional(point_arr[1].Y, tmp, sign1); | |
1061 | ecp_nistz256_neg(tmp, point_arr[2].Y); | |
1062 | copy_conditional(point_arr[2].Y, tmp, sign2); | |
1063 | ecp_nistz256_neg(tmp, point_arr[3].Y); | |
1064 | copy_conditional(point_arr[3].Y, tmp, sign3); | |
1065 | ||
1066 | ecp_nistz256_avx2_transpose_convert(bX4, point_arr); | |
1067 | ecp_nistz256_avx2_to_mont(bX4, bX4); | |
1068 | ecp_nistz256_avx2_to_mont(&bX4[4 * 9], &bX4[4 * 9]); | |
1069 | /* Optimized when both inputs are affine */ | |
1070 | ecp_nistz256_avx2_point_add_affines_x4(aX4, aX4, bX4); | |
1071 | ||
1072 | for (i = 2; i < 9; i++) { | |
49b05c7d RS |
1073 | wvalue = *((u16 *) & p_str[(idx - 1) / 8]); |
1074 | wvalue = (wvalue >> ((idx - 1) % 8)) & mask; | |
1075 | idx += window_size; | |
4d3fa06f | 1076 | booth_recode_w7(&sign0, &digit0, wvalue); |
49b05c7d RS |
1077 | wvalue = *((u16 *) & p_str[(idx - 1) / 8]); |
1078 | wvalue = (wvalue >> ((idx - 1) % 8)) & mask; | |
1079 | idx += window_size; | |
4d3fa06f | 1080 | booth_recode_w7(&sign1, &digit1, wvalue); |
49b05c7d RS |
1081 | wvalue = *((u16 *) & p_str[(idx - 1) / 8]); |
1082 | wvalue = (wvalue >> ((idx - 1) % 8)) & mask; | |
1083 | idx += window_size; | |
4d3fa06f | 1084 | booth_recode_w7(&sign2, &digit2, wvalue); |
49b05c7d RS |
1085 | wvalue = *((u16 *) & p_str[(idx - 1) / 8]); |
1086 | wvalue = (wvalue >> ((idx - 1) % 8)) & mask; | |
1087 | idx += window_size; | |
4d3fa06f AP |
1088 | booth_recode_w7(&sign3, &digit3, wvalue); |
1089 | ||
3ff08e1d | 1090 | ecp_nistz256_avx2_multi_gather_w7(point_arr, |
4d3fa06f AP |
1091 | preComputedTable[4 * i], |
1092 | digit0, digit1, digit2, digit3); | |
1093 | ||
1094 | ecp_nistz256_neg(tmp, point_arr[0].Y); | |
1095 | copy_conditional(point_arr[0].Y, tmp, sign0); | |
1096 | ecp_nistz256_neg(tmp, point_arr[1].Y); | |
1097 | copy_conditional(point_arr[1].Y, tmp, sign1); | |
1098 | ecp_nistz256_neg(tmp, point_arr[2].Y); | |
1099 | copy_conditional(point_arr[2].Y, tmp, sign2); | |
1100 | ecp_nistz256_neg(tmp, point_arr[3].Y); | |
1101 | copy_conditional(point_arr[3].Y, tmp, sign3); | |
1102 | ||
1103 | ecp_nistz256_avx2_transpose_convert(bX4, point_arr); | |
1104 | ecp_nistz256_avx2_to_mont(bX4, bX4); | |
1105 | ecp_nistz256_avx2_to_mont(&bX4[4 * 9], &bX4[4 * 9]); | |
1106 | ||
1107 | ecp_nistz256_avx2_point_add_affine_x4(aX4, aX4, bX4); | |
1108 | } | |
1109 | ||
1110 | ecp_nistz256_avx2_from_mont(&aX4[4 * 9 * 0], &aX4[4 * 9 * 0]); | |
1111 | ecp_nistz256_avx2_from_mont(&aX4[4 * 9 * 1], &aX4[4 * 9 * 1]); | |
1112 | ecp_nistz256_avx2_from_mont(&aX4[4 * 9 * 2], &aX4[4 * 9 * 2]); | |
1113 | ||
1114 | ecp_nistz256_avx2_convert_transpose_back(res_point_arr, aX4); | |
1115 | /* Last window is performed serially */ | |
49b05c7d RS |
1116 | wvalue = *((u16 *) & p_str[(idx - 1) / 8]); |
1117 | wvalue = (wvalue >> ((idx - 1) % 8)) & mask; | |
4d3fa06f | 1118 | booth_recode_w7(&sign0, &digit0, wvalue); |
58d47cf0 AP |
1119 | ecp_nistz256_gather_w7((P256_POINT_AFFINE *)r, |
1120 | preComputedTable[36], digit0); | |
4d3fa06f AP |
1121 | ecp_nistz256_neg(tmp, r->Y); |
1122 | copy_conditional(r->Y, tmp, sign0); | |
1123 | memcpy(r->Z, ONE, sizeof(ONE)); | |
1124 | /* Sum the four windows */ | |
1125 | ecp_nistz256_point_add(r, r, &res_point_arr[0]); | |
1126 | ecp_nistz256_point_add(r, r, &res_point_arr[1]); | |
1127 | ecp_nistz256_point_add(r, r, &res_point_arr[2]); | |
1128 | ecp_nistz256_point_add(r, r, &res_point_arr[3]); | |
1129 | } | |
1130 | # endif | |
1131 | #endif | |
1132 | ||
5956b110 EK |
1133 | __owur static int ecp_nistz256_set_from_affine(EC_POINT *out, const EC_GROUP *group, |
1134 | const P256_POINT_AFFINE *in, | |
1135 | BN_CTX *ctx) | |
4d3fa06f | 1136 | { |
4d3fa06f AP |
1137 | int ret = 0; |
1138 | ||
8fc4aeb9 AP |
1139 | if ((ret = bn_set_words(out->X, in->X, P256_LIMBS)) |
1140 | && (ret = bn_set_words(out->Y, in->Y, P256_LIMBS)) | |
1141 | && (ret = bn_set_words(out->Z, ONE, P256_LIMBS))) | |
1142 | out->Z_is_one = 1; | |
4d3fa06f AP |
1143 | |
1144 | return ret; | |
1145 | } | |
1146 | ||
1147 | /* r = scalar*G + sum(scalars[i]*points[i]) */ | |
5956b110 EK |
1148 | __owur static int ecp_nistz256_points_mul(const EC_GROUP *group, |
1149 | EC_POINT *r, | |
1150 | const BIGNUM *scalar, | |
1151 | size_t num, | |
1152 | const EC_POINT *points[], | |
1153 | const BIGNUM *scalars[], BN_CTX *ctx) | |
4d3fa06f AP |
1154 | { |
1155 | int i = 0, ret = 0, no_precomp_for_generator = 0, p_is_infinity = 0; | |
1156 | unsigned char p_str[33] = { 0 }; | |
1157 | const PRECOMP256_ROW *preComputedTable = NULL; | |
3aef36ff | 1158 | const NISTZ256_PRE_COMP *pre_comp = NULL; |
4d3fa06f | 1159 | const EC_POINT *generator = NULL; |
a4d5269e EK |
1160 | const BIGNUM **new_scalars = NULL; |
1161 | const EC_POINT **new_points = NULL; | |
49b05c7d | 1162 | unsigned int idx = 0; |
4d3fa06f AP |
1163 | const unsigned int window_size = 7; |
1164 | const unsigned int mask = (1 << (window_size + 1)) - 1; | |
1165 | unsigned int wvalue; | |
1166 | ALIGN32 union { | |
1167 | P256_POINT p; | |
1168 | P256_POINT_AFFINE a; | |
1169 | } t, p; | |
1170 | BIGNUM *tmp_scalar; | |
1171 | ||
58d47cf0 | 1172 | if ((num + 1) == 0 || (num + 1) > OPENSSL_MALLOC_MAX_NELEMS(void *)) { |
3ff08e1d AP |
1173 | ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, ERR_R_MALLOC_FAILURE); |
1174 | return 0; | |
1175 | } | |
1176 | ||
e22d2199 | 1177 | BN_CTX_start(ctx); |
4d3fa06f AP |
1178 | |
1179 | if (scalar) { | |
1180 | generator = EC_GROUP_get0_generator(group); | |
1181 | if (generator == NULL) { | |
be07ae9b | 1182 | ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, EC_R_UNDEFINED_GENERATOR); |
4d3fa06f AP |
1183 | goto err; |
1184 | } | |
1185 | ||
1186 | /* look if we can use precomputed multiples of generator */ | |
3aef36ff | 1187 | pre_comp = group->pre_comp.nistz256; |
4d3fa06f AP |
1188 | |
1189 | if (pre_comp) { | |
20728adc AP |
1190 | /* |
1191 | * If there is a precomputed table for the generator, check that | |
1192 | * it was generated with the same generator. | |
1193 | */ | |
4d3fa06f AP |
1194 | EC_POINT *pre_comp_generator = EC_POINT_new(group); |
1195 | if (pre_comp_generator == NULL) | |
1196 | goto err; | |
1197 | ||
8fc4aeb9 | 1198 | ecp_nistz256_gather_w7(&p.a, pre_comp->precomp[0], 1); |
3ff08e1d | 1199 | if (!ecp_nistz256_set_from_affine(pre_comp_generator, |
8fc4aeb9 | 1200 | group, &p.a, ctx)) { |
e22d2199 | 1201 | EC_POINT_free(pre_comp_generator); |
4d3fa06f | 1202 | goto err; |
e22d2199 | 1203 | } |
4d3fa06f AP |
1204 | |
1205 | if (0 == EC_POINT_cmp(group, generator, pre_comp_generator, ctx)) | |
1206 | preComputedTable = (const PRECOMP256_ROW *)pre_comp->precomp; | |
1207 | ||
1208 | EC_POINT_free(pre_comp_generator); | |
1209 | } | |
1210 | ||
1211 | if (preComputedTable == NULL && ecp_nistz256_is_affine_G(generator)) { | |
20728adc AP |
1212 | /* |
1213 | * If there is no precomputed data, but the generator is the | |
1214 | * default, a hardcoded table of precomputed data is used. This | |
1215 | * is because applications, such as Apache, do not use | |
1216 | * EC_KEY_precompute_mult. | |
1217 | */ | |
3ff08e1d | 1218 | preComputedTable = ecp_nistz256_precomputed; |
4d3fa06f AP |
1219 | } |
1220 | ||
1221 | if (preComputedTable) { | |
1222 | if ((BN_num_bits(scalar) > 256) | |
1223 | || BN_is_negative(scalar)) { | |
1224 | if ((tmp_scalar = BN_CTX_get(ctx)) == NULL) | |
1225 | goto err; | |
1226 | ||
5784a521 | 1227 | if (!BN_nnmod(tmp_scalar, scalar, group->order, ctx)) { |
be07ae9b | 1228 | ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, ERR_R_BN_LIB); |
4d3fa06f AP |
1229 | goto err; |
1230 | } | |
1231 | scalar = tmp_scalar; | |
1232 | } | |
1233 | ||
5784a521 MC |
1234 | for (i = 0; i < bn_get_top(scalar) * BN_BYTES; i += BN_BYTES) { |
1235 | BN_ULONG d = bn_get_words(scalar)[i / BN_BYTES]; | |
4d3fa06f | 1236 | |
5afc296a AP |
1237 | p_str[i + 0] = (unsigned char)d; |
1238 | p_str[i + 1] = (unsigned char)(d >> 8); | |
1239 | p_str[i + 2] = (unsigned char)(d >> 16); | |
1240 | p_str[i + 3] = (unsigned char)(d >>= 24); | |
4d3fa06f AP |
1241 | if (BN_BYTES == 8) { |
1242 | d >>= 8; | |
5afc296a AP |
1243 | p_str[i + 4] = (unsigned char)d; |
1244 | p_str[i + 5] = (unsigned char)(d >> 8); | |
1245 | p_str[i + 6] = (unsigned char)(d >> 16); | |
1246 | p_str[i + 7] = (unsigned char)(d >> 24); | |
4d3fa06f AP |
1247 | } |
1248 | } | |
1249 | ||
1250 | for (; i < 33; i++) | |
1251 | p_str[i] = 0; | |
1252 | ||
1253 | #if defined(ECP_NISTZ256_AVX2) | |
1254 | if (ecp_nistz_avx2_eligible()) { | |
1255 | ecp_nistz256_avx2_mul_g(&p.p, p_str, preComputedTable); | |
1256 | } else | |
1257 | #endif | |
1258 | { | |
e3057a57 AP |
1259 | BN_ULONG infty; |
1260 | ||
4d3fa06f AP |
1261 | /* First window */ |
1262 | wvalue = (p_str[0] << 1) & mask; | |
49b05c7d | 1263 | idx += window_size; |
4d3fa06f AP |
1264 | |
1265 | wvalue = _booth_recode_w7(wvalue); | |
1266 | ||
58d47cf0 AP |
1267 | ecp_nistz256_gather_w7(&p.a, preComputedTable[0], |
1268 | wvalue >> 1); | |
4d3fa06f AP |
1269 | |
1270 | ecp_nistz256_neg(p.p.Z, p.p.Y); | |
1271 | copy_conditional(p.p.Y, p.p.Z, wvalue & 1); | |
1272 | ||
e3057a57 AP |
1273 | /* |
1274 | * Since affine infinity is encoded as (0,0) and | |
1275 | * Jacobian ias (,,0), we need to harmonize them | |
1276 | * by assigning "one" or zero to Z. | |
1277 | */ | |
1278 | infty = (p.p.X[0] | p.p.X[1] | p.p.X[2] | p.p.X[3] | | |
1279 | p.p.Y[0] | p.p.Y[1] | p.p.Y[2] | p.p.Y[3]); | |
1280 | if (P256_LIMBS == 8) | |
1281 | infty |= (p.p.X[4] | p.p.X[5] | p.p.X[6] | p.p.X[7] | | |
1282 | p.p.Y[4] | p.p.Y[5] | p.p.Y[6] | p.p.Y[7]); | |
1283 | ||
1284 | infty = 0 - is_zero(infty); | |
1285 | infty = ~infty; | |
1286 | ||
1287 | p.p.Z[0] = ONE[0] & infty; | |
1288 | p.p.Z[1] = ONE[1] & infty; | |
1289 | p.p.Z[2] = ONE[2] & infty; | |
1290 | p.p.Z[3] = ONE[3] & infty; | |
1291 | if (P256_LIMBS == 8) { | |
1292 | p.p.Z[4] = ONE[4] & infty; | |
1293 | p.p.Z[5] = ONE[5] & infty; | |
1294 | p.p.Z[6] = ONE[6] & infty; | |
1295 | p.p.Z[7] = ONE[7] & infty; | |
1296 | } | |
4d3fa06f AP |
1297 | |
1298 | for (i = 1; i < 37; i++) { | |
49b05c7d | 1299 | unsigned int off = (idx - 1) / 8; |
4d3fa06f | 1300 | wvalue = p_str[off] | p_str[off + 1] << 8; |
49b05c7d RS |
1301 | wvalue = (wvalue >> ((idx - 1) % 8)) & mask; |
1302 | idx += window_size; | |
4d3fa06f AP |
1303 | |
1304 | wvalue = _booth_recode_w7(wvalue); | |
1305 | ||
3ff08e1d | 1306 | ecp_nistz256_gather_w7(&t.a, |
4d3fa06f AP |
1307 | preComputedTable[i], wvalue >> 1); |
1308 | ||
1309 | ecp_nistz256_neg(t.p.Z, t.a.Y); | |
1310 | copy_conditional(t.a.Y, t.p.Z, wvalue & 1); | |
1311 | ||
1312 | ecp_nistz256_point_add_affine(&p.p, &p.p, &t.a); | |
1313 | } | |
1314 | } | |
1315 | } else { | |
1316 | p_is_infinity = 1; | |
1317 | no_precomp_for_generator = 1; | |
1318 | } | |
1319 | } else | |
1320 | p_is_infinity = 1; | |
1321 | ||
1322 | if (no_precomp_for_generator) { | |
20728adc AP |
1323 | /* |
1324 | * Without a precomputed table for the generator, it has to be | |
1325 | * handled like a normal point. | |
1326 | */ | |
4d3fa06f | 1327 | new_scalars = OPENSSL_malloc((num + 1) * sizeof(BIGNUM *)); |
90945fa3 | 1328 | if (new_scalars == NULL) { |
be07ae9b | 1329 | ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, ERR_R_MALLOC_FAILURE); |
e22d2199 | 1330 | goto err; |
4d3fa06f AP |
1331 | } |
1332 | ||
1333 | new_points = OPENSSL_malloc((num + 1) * sizeof(EC_POINT *)); | |
90945fa3 | 1334 | if (new_points == NULL) { |
be07ae9b | 1335 | ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, ERR_R_MALLOC_FAILURE); |
e22d2199 | 1336 | goto err; |
4d3fa06f AP |
1337 | } |
1338 | ||
1339 | memcpy(new_scalars, scalars, num * sizeof(BIGNUM *)); | |
1340 | new_scalars[num] = scalar; | |
1341 | memcpy(new_points, points, num * sizeof(EC_POINT *)); | |
1342 | new_points[num] = generator; | |
1343 | ||
1344 | scalars = new_scalars; | |
1345 | points = new_points; | |
1346 | num++; | |
1347 | } | |
1348 | ||
1349 | if (num) { | |
1350 | P256_POINT *out = &t.p; | |
1351 | if (p_is_infinity) | |
1352 | out = &p.p; | |
1353 | ||
a4d5269e EK |
1354 | if (!ecp_nistz256_windowed_mul(group, out, scalars, points, num, ctx)) |
1355 | goto err; | |
4d3fa06f AP |
1356 | |
1357 | if (!p_is_infinity) | |
1358 | ecp_nistz256_point_add(&p.p, &p.p, out); | |
1359 | } | |
1360 | ||
c028254b | 1361 | /* Not constant-time, but we're only operating on the public output. */ |
e22d2199 EK |
1362 | if (!bn_set_words(r->X, p.p.X, P256_LIMBS) || |
1363 | !bn_set_words(r->Y, p.p.Y, P256_LIMBS) || | |
1364 | !bn_set_words(r->Z, p.p.Z, P256_LIMBS)) { | |
1365 | goto err; | |
1366 | } | |
2e929e53 | 1367 | r->Z_is_one = is_one(r->Z) & 1; |
4d3fa06f AP |
1368 | |
1369 | ret = 1; | |
1370 | ||
e22d2199 | 1371 | err: |
7b953da4 | 1372 | BN_CTX_end(ctx); |
b548a1f1 RS |
1373 | OPENSSL_free(new_points); |
1374 | OPENSSL_free(new_scalars); | |
4d3fa06f AP |
1375 | return ret; |
1376 | } | |
1377 | ||
5956b110 EK |
1378 | __owur static int ecp_nistz256_get_affine(const EC_GROUP *group, |
1379 | const EC_POINT *point, | |
1380 | BIGNUM *x, BIGNUM *y, BN_CTX *ctx) | |
4d3fa06f AP |
1381 | { |
1382 | BN_ULONG z_inv2[P256_LIMBS]; | |
1383 | BN_ULONG z_inv3[P256_LIMBS]; | |
1384 | BN_ULONG x_aff[P256_LIMBS]; | |
1385 | BN_ULONG y_aff[P256_LIMBS]; | |
1386 | BN_ULONG point_x[P256_LIMBS], point_y[P256_LIMBS], point_z[P256_LIMBS]; | |
e22d2199 | 1387 | BN_ULONG x_ret[P256_LIMBS], y_ret[P256_LIMBS]; |
4d3fa06f AP |
1388 | |
1389 | if (EC_POINT_is_at_infinity(group, point)) { | |
be07ae9b | 1390 | ECerr(EC_F_ECP_NISTZ256_GET_AFFINE, EC_R_POINT_AT_INFINITY); |
4d3fa06f AP |
1391 | return 0; |
1392 | } | |
1393 | ||
5784a521 MC |
1394 | if (!ecp_nistz256_bignum_to_field_elem(point_x, point->X) || |
1395 | !ecp_nistz256_bignum_to_field_elem(point_y, point->Y) || | |
1396 | !ecp_nistz256_bignum_to_field_elem(point_z, point->Z)) { | |
be07ae9b | 1397 | ECerr(EC_F_ECP_NISTZ256_GET_AFFINE, EC_R_COORDINATES_OUT_OF_RANGE); |
4d3fa06f AP |
1398 | return 0; |
1399 | } | |
1400 | ||
1401 | ecp_nistz256_mod_inverse(z_inv3, point_z); | |
1402 | ecp_nistz256_sqr_mont(z_inv2, z_inv3); | |
1403 | ecp_nistz256_mul_mont(x_aff, z_inv2, point_x); | |
1404 | ||
1405 | if (x != NULL) { | |
e22d2199 EK |
1406 | ecp_nistz256_from_mont(x_ret, x_aff); |
1407 | if (!bn_set_words(x, x_ret, P256_LIMBS)) | |
1408 | return 0; | |
4d3fa06f AP |
1409 | } |
1410 | ||
1411 | if (y != NULL) { | |
1412 | ecp_nistz256_mul_mont(z_inv3, z_inv3, z_inv2); | |
1413 | ecp_nistz256_mul_mont(y_aff, z_inv3, point_y); | |
e22d2199 EK |
1414 | ecp_nistz256_from_mont(y_ret, y_aff); |
1415 | if (!bn_set_words(y, y_ret, P256_LIMBS)) | |
1416 | return 0; | |
4d3fa06f AP |
1417 | } |
1418 | ||
1419 | return 1; | |
1420 | } | |
1421 | ||
3aef36ff | 1422 | static NISTZ256_PRE_COMP *ecp_nistz256_pre_comp_new(const EC_GROUP *group) |
4d3fa06f | 1423 | { |
3aef36ff | 1424 | NISTZ256_PRE_COMP *ret = NULL; |
4d3fa06f AP |
1425 | |
1426 | if (!group) | |
1427 | return NULL; | |
1428 | ||
3aef36ff | 1429 | ret = OPENSSL_zalloc(sizeof(*ret)); |
4d3fa06f | 1430 | |
90945fa3 | 1431 | if (ret == NULL) { |
be07ae9b | 1432 | ECerr(EC_F_ECP_NISTZ256_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE); |
4d3fa06f AP |
1433 | return ret; |
1434 | } | |
1435 | ||
1436 | ret->group = group; | |
1437 | ret->w = 6; /* default */ | |
4d3fa06f | 1438 | ret->references = 1; |
9b398ef2 AG |
1439 | |
1440 | ret->lock = CRYPTO_THREAD_lock_new(); | |
1441 | if (ret->lock == NULL) { | |
1442 | ECerr(EC_F_ECP_NISTZ256_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE); | |
1443 | OPENSSL_free(ret); | |
1444 | return NULL; | |
1445 | } | |
4d3fa06f AP |
1446 | return ret; |
1447 | } | |
1448 | ||
3aef36ff | 1449 | NISTZ256_PRE_COMP *EC_nistz256_pre_comp_dup(NISTZ256_PRE_COMP *p) |
4d3fa06f | 1450 | { |
9b398ef2 | 1451 | int i; |
3aef36ff | 1452 | if (p != NULL) |
2f545ae4 | 1453 | CRYPTO_UP_REF(&p->references, &i, p->lock); |
3aef36ff | 1454 | return p; |
4d3fa06f AP |
1455 | } |
1456 | ||
3aef36ff | 1457 | void EC_nistz256_pre_comp_free(NISTZ256_PRE_COMP *pre) |
4d3fa06f | 1458 | { |
9b398ef2 AG |
1459 | int i; |
1460 | ||
1461 | if (pre == NULL) | |
4d3fa06f | 1462 | return; |
9b398ef2 | 1463 | |
2f545ae4 | 1464 | CRYPTO_DOWN_REF(&pre->references, &i, pre->lock); |
9b398ef2 AG |
1465 | REF_PRINT_COUNT("EC_nistz256", x); |
1466 | if (i > 0) | |
1467 | return; | |
1468 | REF_ASSERT_ISNT(i < 0); | |
1469 | ||
b548a1f1 | 1470 | OPENSSL_free(pre->precomp_storage); |
9b398ef2 | 1471 | CRYPTO_THREAD_lock_free(pre->lock); |
4d3fa06f AP |
1472 | OPENSSL_free(pre); |
1473 | } | |
1474 | ||
4d3fa06f | 1475 | |
58d47cf0 | 1476 | static int ecp_nistz256_window_have_precompute_mult(const EC_GROUP *group) |
4d3fa06f AP |
1477 | { |
1478 | /* There is a hard-coded table for the default generator. */ | |
1479 | const EC_POINT *generator = EC_GROUP_get0_generator(group); | |
3aef36ff | 1480 | |
4d3fa06f AP |
1481 | if (generator != NULL && ecp_nistz256_is_affine_G(generator)) { |
1482 | /* There is a hard-coded table for the default generator. */ | |
1483 | return 1; | |
1484 | } | |
1485 | ||
3aef36ff | 1486 | return HAVEPRECOMP(group, nistz256); |
4d3fa06f AP |
1487 | } |
1488 | ||
eb791696 AP |
1489 | #if defined(__x86_64) || defined(__x86_64__) || \ |
1490 | defined(_M_AMD64) || defined(_M_X64) || \ | |
ab4f2026 AP |
1491 | defined(__powerpc64__) || defined(_ARCH_PP64) || \ |
1492 | defined(__aarch64__) | |
eb791696 AP |
1493 | /* |
1494 | * Montgomery mul modulo Order(P): res = a*b*2^-256 mod Order(P) | |
1495 | */ | |
1496 | void ecp_nistz256_ord_mul_mont(BN_ULONG res[P256_LIMBS], | |
1497 | const BN_ULONG a[P256_LIMBS], | |
1498 | const BN_ULONG b[P256_LIMBS]); | |
1499 | void ecp_nistz256_ord_sqr_mont(BN_ULONG res[P256_LIMBS], | |
1500 | const BN_ULONG a[P256_LIMBS], | |
1501 | int rep); | |
1502 | ||
1503 | static int ecp_nistz256_inv_mod_ord(const EC_GROUP *group, BIGNUM *r, | |
792546eb | 1504 | const BIGNUM *x, BN_CTX *ctx) |
eb791696 AP |
1505 | { |
1506 | /* RR = 2^512 mod ord(p256) */ | |
10bc3409 AP |
1507 | static const BN_ULONG RR[P256_LIMBS] = { |
1508 | TOBN(0x83244c95,0xbe79eea2), TOBN(0x4699799c,0x49bd6fa6), | |
1509 | TOBN(0x2845b239,0x2b6bec59), TOBN(0x66e12d94,0xf3d95620) | |
1510 | }; | |
eb791696 | 1511 | /* The constant 1 (unlike ONE that is one in Montgomery representation) */ |
10bc3409 AP |
1512 | static const BN_ULONG one[P256_LIMBS] = { |
1513 | TOBN(0,1), TOBN(0,0), TOBN(0,0), TOBN(0,0) | |
1514 | }; | |
eb791696 AP |
1515 | /* |
1516 | * We don't use entry 0 in the table, so we omit it and address | |
1517 | * with -1 offset. | |
1518 | */ | |
1519 | BN_ULONG table[15][P256_LIMBS]; | |
1520 | BN_ULONG out[P256_LIMBS], t[P256_LIMBS]; | |
1521 | int i, ret = 0; | |
8e403a79 TS |
1522 | enum { |
1523 | i_1 = 0, i_10, i_11, i_101, i_111, i_1010, i_1111, | |
1524 | i_10101, i_101010, i_101111, i_x6, i_x8, i_x16, i_x32 | |
1525 | }; | |
eb791696 AP |
1526 | |
1527 | /* | |
1528 | * Catch allocation failure early. | |
1529 | */ | |
1530 | if (bn_wexpand(r, P256_LIMBS) == NULL) { | |
1531 | ECerr(EC_F_ECP_NISTZ256_INV_MOD_ORD, ERR_R_BN_LIB); | |
1532 | goto err; | |
1533 | } | |
1534 | ||
1535 | if ((BN_num_bits(x) > 256) || BN_is_negative(x)) { | |
1536 | BIGNUM *tmp; | |
1537 | ||
1538 | if ((tmp = BN_CTX_get(ctx)) == NULL | |
1539 | || !BN_nnmod(tmp, x, group->order, ctx)) { | |
1540 | ECerr(EC_F_ECP_NISTZ256_INV_MOD_ORD, ERR_R_BN_LIB); | |
1541 | goto err; | |
1542 | } | |
1543 | x = tmp; | |
1544 | } | |
1545 | ||
1546 | if (!ecp_nistz256_bignum_to_field_elem(t, x)) { | |
1547 | ECerr(EC_F_ECP_NISTZ256_INV_MOD_ORD, EC_R_COORDINATES_OUT_OF_RANGE); | |
1548 | goto err; | |
1549 | } | |
1550 | ||
1551 | ecp_nistz256_ord_mul_mont(table[0], t, RR); | |
10bc3409 AP |
1552 | #if 0 |
1553 | /* | |
1554 | * Original sparse-then-fixed-window algorithm, retained for reference. | |
1555 | */ | |
eb791696 AP |
1556 | for (i = 2; i < 16; i += 2) { |
1557 | ecp_nistz256_ord_sqr_mont(table[i-1], table[i/2-1], 1); | |
1558 | ecp_nistz256_ord_mul_mont(table[i], table[i-1], table[0]); | |
1559 | } | |
1560 | ||
1561 | /* | |
1562 | * The top 128bit of the exponent are highly redudndant, so we | |
1563 | * perform an optimized flow | |
1564 | */ | |
1565 | ecp_nistz256_ord_sqr_mont(t, table[15-1], 4); /* f0 */ | |
1566 | ecp_nistz256_ord_mul_mont(t, t, table[15-1]); /* ff */ | |
1567 | ||
1568 | ecp_nistz256_ord_sqr_mont(out, t, 8); /* ff00 */ | |
1569 | ecp_nistz256_ord_mul_mont(out, out, t); /* ffff */ | |
1570 | ||
1571 | ecp_nistz256_ord_sqr_mont(t, out, 16); /* ffff0000 */ | |
1572 | ecp_nistz256_ord_mul_mont(t, t, out); /* ffffffff */ | |
1573 | ||
1574 | ecp_nistz256_ord_sqr_mont(out, t, 64); /* ffffffff0000000000000000 */ | |
1575 | ecp_nistz256_ord_mul_mont(out, out, t); /* ffffffff00000000ffffffff */ | |
1576 | ||
1577 | ecp_nistz256_ord_sqr_mont(out, out, 32); /* ffffffff00000000ffffffff00000000 */ | |
1578 | ecp_nistz256_ord_mul_mont(out, out, t); /* ffffffff00000000ffffffffffffffff */ | |
1579 | ||
1580 | /* | |
10bc3409 | 1581 | * The bottom 128 bit of the exponent are processed with fixed 4-bit window |
eb791696 AP |
1582 | */ |
1583 | for(i = 0; i < 32; i++) { | |
10bc3409 AP |
1584 | /* expLo - the low 128 bits of the exponent we use (ord(p256) - 2), |
1585 | * split into nibbles */ | |
1586 | static const unsigned char expLo[32] = { | |
1587 | 0xb,0xc,0xe,0x6,0xf,0xa,0xa,0xd,0xa,0x7,0x1,0x7,0x9,0xe,0x8,0x4, | |
1588 | 0xf,0x3,0xb,0x9,0xc,0xa,0xc,0x2,0xf,0xc,0x6,0x3,0x2,0x5,0x4,0xf | |
1589 | }; | |
1590 | ||
eb791696 AP |
1591 | ecp_nistz256_ord_sqr_mont(out, out, 4); |
1592 | /* The exponent is public, no need in constant-time access */ | |
1593 | ecp_nistz256_ord_mul_mont(out, out, table[expLo[i]-1]); | |
1594 | } | |
10bc3409 AP |
1595 | #else |
1596 | /* | |
1597 | * https://briansmith.org/ecc-inversion-addition-chains-01#p256_scalar_inversion | |
1598 | * | |
1599 | * Even though this code path spares 12 squarings, 4.5%, and 13 | |
1600 | * multiplications, 25%, on grand scale sign operation is not that | |
1601 | * much faster, not more that 2%... | |
1602 | */ | |
10bc3409 AP |
1603 | |
1604 | /* pre-calculate powers */ | |
1605 | ecp_nistz256_ord_sqr_mont(table[i_10], table[i_1], 1); | |
1606 | ||
1607 | ecp_nistz256_ord_mul_mont(table[i_11], table[i_1], table[i_10]); | |
1608 | ||
1609 | ecp_nistz256_ord_mul_mont(table[i_101], table[i_11], table[i_10]); | |
1610 | ||
1611 | ecp_nistz256_ord_mul_mont(table[i_111], table[i_101], table[i_10]); | |
1612 | ||
1613 | ecp_nistz256_ord_sqr_mont(table[i_1010], table[i_101], 1); | |
1614 | ||
1615 | ecp_nistz256_ord_mul_mont(table[i_1111], table[i_1010], table[i_101]); | |
1616 | ||
1617 | ecp_nistz256_ord_sqr_mont(table[i_10101], table[i_1010], 1); | |
1618 | ecp_nistz256_ord_mul_mont(table[i_10101], table[i_10101], table[i_1]); | |
1619 | ||
1620 | ecp_nistz256_ord_sqr_mont(table[i_101010], table[i_10101], 1); | |
1621 | ||
1622 | ecp_nistz256_ord_mul_mont(table[i_101111], table[i_101010], table[i_101]); | |
1623 | ||
1624 | ecp_nistz256_ord_mul_mont(table[i_x6], table[i_101010], table[i_10101]); | |
1625 | ||
1626 | ecp_nistz256_ord_sqr_mont(table[i_x8], table[i_x6], 2); | |
1627 | ecp_nistz256_ord_mul_mont(table[i_x8], table[i_x8], table[i_11]); | |
1628 | ||
1629 | ecp_nistz256_ord_sqr_mont(table[i_x16], table[i_x8], 8); | |
1630 | ecp_nistz256_ord_mul_mont(table[i_x16], table[i_x16], table[i_x8]); | |
1631 | ||
1632 | ecp_nistz256_ord_sqr_mont(table[i_x32], table[i_x16], 16); | |
1633 | ecp_nistz256_ord_mul_mont(table[i_x32], table[i_x32], table[i_x16]); | |
1634 | ||
1635 | /* calculations */ | |
1636 | ecp_nistz256_ord_sqr_mont(out, table[i_x32], 64); | |
1637 | ecp_nistz256_ord_mul_mont(out, out, table[i_x32]); | |
1638 | ||
1639 | for (i = 0; i < 27; i++) { | |
1640 | static const struct { unsigned char p, i; } chain[27] = { | |
1641 | { 32, i_x32 }, { 6, i_101111 }, { 5, i_111 }, | |
1642 | { 4, i_11 }, { 5, i_1111 }, { 5, i_10101 }, | |
1643 | { 4, i_101 }, { 3, i_101 }, { 3, i_101 }, | |
1644 | { 5, i_111 }, { 9, i_101111 }, { 6, i_1111 }, | |
1645 | { 2, i_1 }, { 5, i_1 }, { 6, i_1111 }, | |
1646 | { 5, i_111 }, { 4, i_111 }, { 5, i_111 }, | |
1647 | { 5, i_101 }, { 3, i_11 }, { 10, i_101111 }, | |
1648 | { 2, i_11 }, { 5, i_11 }, { 5, i_11 }, | |
1649 | { 3, i_1 }, { 7, i_10101 }, { 6, i_1111 } | |
1650 | }; | |
1651 | ||
1652 | ecp_nistz256_ord_sqr_mont(out, out, chain[i].p); | |
1653 | ecp_nistz256_ord_mul_mont(out, out, table[chain[i].i]); | |
1654 | } | |
1655 | #endif | |
eb791696 AP |
1656 | ecp_nistz256_ord_mul_mont(out, out, one); |
1657 | ||
1658 | /* | |
1659 | * Can't fail, but check return code to be consistent anyway. | |
1660 | */ | |
1661 | if (!bn_set_words(r, out, P256_LIMBS)) | |
1662 | goto err; | |
1663 | ||
1664 | ret = 1; | |
1665 | err: | |
1666 | return ret; | |
1667 | } | |
1668 | #else | |
1669 | # define ecp_nistz256_inv_mod_ord NULL | |
1670 | #endif | |
1671 | ||
4d3fa06f AP |
1672 | const EC_METHOD *EC_GFp_nistz256_method(void) |
1673 | { | |
1674 | static const EC_METHOD ret = { | |
1675 | EC_FLAGS_DEFAULT_OCT, | |
1676 | NID_X9_62_prime_field, | |
1677 | ec_GFp_mont_group_init, | |
1678 | ec_GFp_mont_group_finish, | |
1679 | ec_GFp_mont_group_clear_finish, | |
1680 | ec_GFp_mont_group_copy, | |
1681 | ec_GFp_mont_group_set_curve, | |
1682 | ec_GFp_simple_group_get_curve, | |
1683 | ec_GFp_simple_group_get_degree, | |
9ff9bccc | 1684 | ec_group_simple_order_bits, |
4d3fa06f AP |
1685 | ec_GFp_simple_group_check_discriminant, |
1686 | ec_GFp_simple_point_init, | |
1687 | ec_GFp_simple_point_finish, | |
1688 | ec_GFp_simple_point_clear_finish, | |
1689 | ec_GFp_simple_point_copy, | |
1690 | ec_GFp_simple_point_set_to_infinity, | |
1691 | ec_GFp_simple_set_Jprojective_coordinates_GFp, | |
1692 | ec_GFp_simple_get_Jprojective_coordinates_GFp, | |
1693 | ec_GFp_simple_point_set_affine_coordinates, | |
1694 | ecp_nistz256_get_affine, | |
1695 | 0, 0, 0, | |
1696 | ec_GFp_simple_add, | |
1697 | ec_GFp_simple_dbl, | |
1698 | ec_GFp_simple_invert, | |
1699 | ec_GFp_simple_is_at_infinity, | |
1700 | ec_GFp_simple_is_on_curve, | |
1701 | ec_GFp_simple_cmp, | |
1702 | ec_GFp_simple_make_affine, | |
1703 | ec_GFp_simple_points_make_affine, | |
1704 | ecp_nistz256_points_mul, /* mul */ | |
1705 | ecp_nistz256_mult_precompute, /* precompute_mult */ | |
1706 | ecp_nistz256_window_have_precompute_mult, /* have_precompute_mult */ | |
1707 | ec_GFp_mont_field_mul, | |
1708 | ec_GFp_mont_field_sqr, | |
1709 | 0, /* field_div */ | |
48e82c8e | 1710 | ec_GFp_mont_field_inv, |
4d3fa06f AP |
1711 | ec_GFp_mont_field_encode, |
1712 | ec_GFp_mont_field_decode, | |
9ff9bccc DSH |
1713 | ec_GFp_mont_field_set_to_one, |
1714 | ec_key_simple_priv2oct, | |
1715 | ec_key_simple_oct2priv, | |
1716 | 0, /* set private */ | |
1717 | ec_key_simple_generate_key, | |
1718 | ec_key_simple_check_key, | |
1719 | ec_key_simple_generate_public_key, | |
1720 | 0, /* keycopy */ | |
1721 | 0, /* keyfinish */ | |
eb791696 | 1722 | ecdh_simple_compute_key, |
f667820c | 1723 | ecp_nistz256_inv_mod_ord, /* can be #define-d NULL */ |
37124360 NT |
1724 | 0, /* blind_coordinates */ |
1725 | 0, /* ladder_pre */ | |
1726 | 0, /* ladder_step */ | |
1727 | 0 /* ladder_post */ | |
4d3fa06f AP |
1728 | }; |
1729 | ||
1730 | return &ret; | |
1731 | } |