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aa6bb135 | 1 | /* |
8020d79b | 2 | * Copyright 2014-2021 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 | 5 | * |
a7f182b7 | 6 | * Licensed under the Apache License 2.0 (the "License"). You may not use |
aa6bb135 RS |
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 | ||
579422c8 P |
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 | ||
4d3fa06f AP |
27 | #include <string.h> |
28 | ||
b39fc560 | 29 | #include "internal/cryptlib.h" |
25f2138b | 30 | #include "crypto/bn.h" |
706457b7 | 31 | #include "ec_local.h" |
cd420b0b | 32 | #include "internal/refcount.h" |
4d3fa06f AP |
33 | |
34 | #if BN_BITS2 != 64 | |
58d47cf0 | 35 | # define TOBN(hi,lo) lo,hi |
4d3fa06f | 36 | #else |
58d47cf0 | 37 | # define TOBN(hi,lo) ((BN_ULONG)hi<<32|lo) |
4d3fa06f AP |
38 | #endif |
39 | ||
40 | #if defined(__GNUC__) | |
58d47cf0 | 41 | # define ALIGN32 __attribute((aligned(32))) |
4d3fa06f | 42 | #elif defined(_MSC_VER) |
58d47cf0 | 43 | # define ALIGN32 __declspec(align(32)) |
4d3fa06f AP |
44 | #else |
45 | # define ALIGN32 | |
46 | #endif | |
47 | ||
58d47cf0 AP |
48 | #define ALIGNPTR(p,N) ((unsigned char *)p+N-(size_t)p%N) |
49 | #define P256_LIMBS (256/BN_BITS2) | |
4d3fa06f AP |
50 | |
51 | typedef unsigned short u16; | |
52 | ||
53 | typedef struct { | |
54 | BN_ULONG X[P256_LIMBS]; | |
55 | BN_ULONG Y[P256_LIMBS]; | |
56 | BN_ULONG Z[P256_LIMBS]; | |
57 | } P256_POINT; | |
58 | ||
59 | typedef struct { | |
60 | BN_ULONG X[P256_LIMBS]; | |
61 | BN_ULONG Y[P256_LIMBS]; | |
62 | } P256_POINT_AFFINE; | |
63 | ||
64 | typedef P256_POINT_AFFINE PRECOMP256_ROW[64]; | |
65 | ||
66 | /* structure for precomputed multiples of the generator */ | |
3aef36ff | 67 | struct nistz256_pre_comp_st { |
4d3fa06f AP |
68 | const EC_GROUP *group; /* Parent EC_GROUP object */ |
69 | size_t w; /* Window size */ | |
20728adc AP |
70 | /* |
71 | * Constant time access to the X and Y coordinates of the pre-computed, | |
4d3fa06f | 72 | * generator multiplies, in the Montgomery domain. Pre-calculated |
20728adc AP |
73 | * multiplies are stored in affine form. |
74 | */ | |
4d3fa06f AP |
75 | PRECOMP256_ROW *precomp; |
76 | void *precomp_storage; | |
2f545ae4 | 77 | CRYPTO_REF_COUNT references; |
9b398ef2 | 78 | CRYPTO_RWLOCK *lock; |
3aef36ff | 79 | }; |
4d3fa06f AP |
80 | |
81 | /* Functions implemented in assembly */ | |
b62b2454 AP |
82 | /* |
83 | * Most of below mentioned functions *preserve* the property of inputs | |
84 | * being fully reduced, i.e. being in [0, modulus) range. Simply put if | |
85 | * inputs are fully reduced, then output is too. Note that reverse is | |
86 | * not true, in sense that given partially reduced inputs output can be | |
87 | * either, not unlikely reduced. And "most" in first sentence refers to | |
88 | * the fact that given the calculations flow one can tolerate that | |
89 | * addition, 1st function below, produces partially reduced result *if* | |
90 | * multiplications by 2 and 3, which customarily use addition, fully | |
91 | * reduce it. This effectively gives two options: a) addition produces | |
92 | * fully reduced result [as long as inputs are, just like remaining | |
93 | * functions]; b) addition is allowed to produce partially reduced | |
94 | * result, but multiplications by 2 and 3 perform additional reduction | |
95 | * step. Choice between the two can be platform-specific, but it was a) | |
96 | * in all cases so far... | |
97 | */ | |
98 | /* Modular add: res = a+b mod P */ | |
99 | void ecp_nistz256_add(BN_ULONG res[P256_LIMBS], | |
100 | const BN_ULONG a[P256_LIMBS], | |
101 | const BN_ULONG b[P256_LIMBS]); | |
4d3fa06f AP |
102 | /* Modular mul by 2: res = 2*a mod P */ |
103 | void ecp_nistz256_mul_by_2(BN_ULONG res[P256_LIMBS], | |
104 | const BN_ULONG a[P256_LIMBS]); | |
4d3fa06f AP |
105 | /* Modular mul by 3: res = 3*a mod P */ |
106 | void ecp_nistz256_mul_by_3(BN_ULONG res[P256_LIMBS], | |
107 | const BN_ULONG a[P256_LIMBS]); | |
b62b2454 AP |
108 | |
109 | /* Modular div by 2: res = a/2 mod P */ | |
110 | void ecp_nistz256_div_by_2(BN_ULONG res[P256_LIMBS], | |
111 | const BN_ULONG a[P256_LIMBS]); | |
20728adc | 112 | /* Modular sub: res = a-b mod P */ |
4d3fa06f AP |
113 | void ecp_nistz256_sub(BN_ULONG res[P256_LIMBS], |
114 | const BN_ULONG a[P256_LIMBS], | |
115 | const BN_ULONG b[P256_LIMBS]); | |
20728adc | 116 | /* Modular neg: res = -a mod P */ |
4d3fa06f AP |
117 | void ecp_nistz256_neg(BN_ULONG res[P256_LIMBS], const BN_ULONG a[P256_LIMBS]); |
118 | /* Montgomery mul: res = a*b*2^-256 mod P */ | |
119 | void ecp_nistz256_mul_mont(BN_ULONG res[P256_LIMBS], | |
120 | const BN_ULONG a[P256_LIMBS], | |
121 | const BN_ULONG b[P256_LIMBS]); | |
122 | /* Montgomery sqr: res = a*a*2^-256 mod P */ | |
123 | void ecp_nistz256_sqr_mont(BN_ULONG res[P256_LIMBS], | |
124 | const BN_ULONG a[P256_LIMBS]); | |
125 | /* Convert a number from Montgomery domain, by multiplying with 1 */ | |
126 | void ecp_nistz256_from_mont(BN_ULONG res[P256_LIMBS], | |
127 | const BN_ULONG in[P256_LIMBS]); | |
128 | /* Convert a number to Montgomery domain, by multiplying with 2^512 mod P*/ | |
129 | void ecp_nistz256_to_mont(BN_ULONG res[P256_LIMBS], | |
130 | const BN_ULONG in[P256_LIMBS]); | |
131 | /* Functions that perform constant time access to the precomputed tables */ | |
58d47cf0 | 132 | void ecp_nistz256_scatter_w5(P256_POINT *val, |
49b05c7d | 133 | const P256_POINT *in_t, int idx); |
20728adc | 134 | void ecp_nistz256_gather_w5(P256_POINT *val, |
49b05c7d | 135 | const P256_POINT *in_t, int idx); |
58d47cf0 | 136 | void ecp_nistz256_scatter_w7(P256_POINT_AFFINE *val, |
49b05c7d | 137 | const P256_POINT_AFFINE *in_t, int idx); |
58d47cf0 | 138 | void ecp_nistz256_gather_w7(P256_POINT_AFFINE *val, |
49b05c7d | 139 | const P256_POINT_AFFINE *in_t, int idx); |
4d3fa06f AP |
140 | |
141 | /* One converted into the Montgomery domain */ | |
142 | static const BN_ULONG ONE[P256_LIMBS] = { | |
143 | TOBN(0x00000000, 0x00000001), TOBN(0xffffffff, 0x00000000), | |
144 | TOBN(0xffffffff, 0xffffffff), TOBN(0x00000000, 0xfffffffe) | |
145 | }; | |
146 | ||
3aef36ff | 147 | static NISTZ256_PRE_COMP *ecp_nistz256_pre_comp_new(const EC_GROUP *group); |
4d3fa06f AP |
148 | |
149 | /* Precomputed tables for the default generator */ | |
3ff08e1d | 150 | extern const PRECOMP256_ROW ecp_nistz256_precomputed[37]; |
4d3fa06f AP |
151 | |
152 | /* Recode window to a signed digit, see ecp_nistputil.c for details */ | |
153 | static unsigned int _booth_recode_w5(unsigned int in) | |
154 | { | |
155 | unsigned int s, d; | |
156 | ||
157 | s = ~((in >> 5) - 1); | |
158 | d = (1 << 6) - in - 1; | |
159 | d = (d & s) | (in & ~s); | |
160 | d = (d >> 1) + (d & 1); | |
161 | ||
162 | return (d << 1) + (s & 1); | |
163 | } | |
164 | ||
165 | static unsigned int _booth_recode_w7(unsigned int in) | |
166 | { | |
167 | unsigned int s, d; | |
168 | ||
169 | s = ~((in >> 7) - 1); | |
170 | d = (1 << 8) - in - 1; | |
171 | d = (d & s) | (in & ~s); | |
172 | d = (d >> 1) + (d & 1); | |
173 | ||
174 | return (d << 1) + (s & 1); | |
175 | } | |
176 | ||
177 | static void copy_conditional(BN_ULONG dst[P256_LIMBS], | |
178 | const BN_ULONG src[P256_LIMBS], BN_ULONG move) | |
179 | { | |
5afc296a | 180 | BN_ULONG mask1 = 0-move; |
4d3fa06f AP |
181 | BN_ULONG mask2 = ~mask1; |
182 | ||
183 | dst[0] = (src[0] & mask1) ^ (dst[0] & mask2); | |
184 | dst[1] = (src[1] & mask1) ^ (dst[1] & mask2); | |
185 | dst[2] = (src[2] & mask1) ^ (dst[2] & mask2); | |
186 | dst[3] = (src[3] & mask1) ^ (dst[3] & mask2); | |
187 | if (P256_LIMBS == 8) { | |
188 | dst[4] = (src[4] & mask1) ^ (dst[4] & mask2); | |
189 | dst[5] = (src[5] & mask1) ^ (dst[5] & mask2); | |
190 | dst[6] = (src[6] & mask1) ^ (dst[6] & mask2); | |
191 | dst[7] = (src[7] & mask1) ^ (dst[7] & mask2); | |
192 | } | |
193 | } | |
194 | ||
195 | static BN_ULONG is_zero(BN_ULONG in) | |
196 | { | |
197 | in |= (0 - in); | |
198 | in = ~in; | |
4d3fa06f AP |
199 | in >>= BN_BITS2 - 1; |
200 | return in; | |
201 | } | |
202 | ||
203 | static BN_ULONG is_equal(const BN_ULONG a[P256_LIMBS], | |
204 | const BN_ULONG b[P256_LIMBS]) | |
205 | { | |
206 | BN_ULONG res; | |
207 | ||
208 | res = a[0] ^ b[0]; | |
209 | res |= a[1] ^ b[1]; | |
210 | res |= a[2] ^ b[2]; | |
211 | res |= a[3] ^ b[3]; | |
212 | if (P256_LIMBS == 8) { | |
213 | res |= a[4] ^ b[4]; | |
214 | res |= a[5] ^ b[5]; | |
215 | res |= a[6] ^ b[6]; | |
216 | res |= a[7] ^ b[7]; | |
217 | } | |
218 | ||
219 | return is_zero(res); | |
220 | } | |
221 | ||
2e929e53 | 222 | static BN_ULONG is_one(const BIGNUM *z) |
4d3fa06f | 223 | { |
2e929e53 AP |
224 | BN_ULONG res = 0; |
225 | BN_ULONG *a = bn_get_words(z); | |
226 | ||
227 | if (bn_get_top(z) == (P256_LIMBS - P256_LIMBS / 8)) { | |
228 | res = a[0] ^ ONE[0]; | |
229 | res |= a[1] ^ ONE[1]; | |
230 | res |= a[2] ^ ONE[2]; | |
231 | res |= a[3] ^ ONE[3]; | |
232 | if (P256_LIMBS == 8) { | |
233 | res |= a[4] ^ ONE[4]; | |
234 | res |= a[5] ^ ONE[5]; | |
235 | res |= a[6] ^ ONE[6]; | |
236 | /* | |
237 | * no check for a[7] (being zero) on 32-bit platforms, | |
238 | * because value of "one" takes only 7 limbs. | |
239 | */ | |
240 | } | |
241 | res = is_zero(res); | |
4d3fa06f AP |
242 | } |
243 | ||
2e929e53 | 244 | return res; |
4d3fa06f AP |
245 | } |
246 | ||
f3b3d7f0 RS |
247 | /* |
248 | * For reference, this macro is used only when new ecp_nistz256 assembly | |
249 | * module is being developed. For example, configure with | |
250 | * -DECP_NISTZ256_REFERENCE_IMPLEMENTATION and implement only functions | |
251 | * performing simplest arithmetic operations on 256-bit vectors. Then | |
252 | * work on implementation of higher-level functions performing point | |
253 | * operations. Then remove ECP_NISTZ256_REFERENCE_IMPLEMENTATION | |
254 | * and never define it again. (The correct macro denoting presence of | |
255 | * ecp_nistz256 module is ECP_NISTZ256_ASM.) | |
256 | */ | |
4d3fa06f | 257 | #ifndef ECP_NISTZ256_REFERENCE_IMPLEMENTATION |
58d47cf0 AP |
258 | void ecp_nistz256_point_double(P256_POINT *r, const P256_POINT *a); |
259 | void ecp_nistz256_point_add(P256_POINT *r, | |
260 | const P256_POINT *a, const P256_POINT *b); | |
261 | void ecp_nistz256_point_add_affine(P256_POINT *r, | |
262 | const P256_POINT *a, | |
263 | const P256_POINT_AFFINE *b); | |
4d3fa06f AP |
264 | #else |
265 | /* Point double: r = 2*a */ | |
58d47cf0 | 266 | static void ecp_nistz256_point_double(P256_POINT *r, const P256_POINT *a) |
4d3fa06f AP |
267 | { |
268 | BN_ULONG S[P256_LIMBS]; | |
269 | BN_ULONG M[P256_LIMBS]; | |
270 | BN_ULONG Zsqr[P256_LIMBS]; | |
271 | BN_ULONG tmp0[P256_LIMBS]; | |
272 | ||
273 | const BN_ULONG *in_x = a->X; | |
274 | const BN_ULONG *in_y = a->Y; | |
275 | const BN_ULONG *in_z = a->Z; | |
276 | ||
277 | BN_ULONG *res_x = r->X; | |
278 | BN_ULONG *res_y = r->Y; | |
279 | BN_ULONG *res_z = r->Z; | |
280 | ||
281 | ecp_nistz256_mul_by_2(S, in_y); | |
282 | ||
283 | ecp_nistz256_sqr_mont(Zsqr, in_z); | |
284 | ||
285 | ecp_nistz256_sqr_mont(S, S); | |
286 | ||
287 | ecp_nistz256_mul_mont(res_z, in_z, in_y); | |
288 | ecp_nistz256_mul_by_2(res_z, res_z); | |
289 | ||
290 | ecp_nistz256_add(M, in_x, Zsqr); | |
291 | ecp_nistz256_sub(Zsqr, in_x, Zsqr); | |
292 | ||
293 | ecp_nistz256_sqr_mont(res_y, S); | |
294 | ecp_nistz256_div_by_2(res_y, res_y); | |
295 | ||
296 | ecp_nistz256_mul_mont(M, M, Zsqr); | |
297 | ecp_nistz256_mul_by_3(M, M); | |
298 | ||
299 | ecp_nistz256_mul_mont(S, S, in_x); | |
300 | ecp_nistz256_mul_by_2(tmp0, S); | |
301 | ||
302 | ecp_nistz256_sqr_mont(res_x, M); | |
303 | ||
304 | ecp_nistz256_sub(res_x, res_x, tmp0); | |
305 | ecp_nistz256_sub(S, S, res_x); | |
306 | ||
307 | ecp_nistz256_mul_mont(S, S, M); | |
308 | ecp_nistz256_sub(res_y, S, res_y); | |
309 | } | |
310 | ||
311 | /* Point addition: r = a+b */ | |
20728adc AP |
312 | static void ecp_nistz256_point_add(P256_POINT *r, |
313 | const P256_POINT *a, const P256_POINT *b) | |
4d3fa06f AP |
314 | { |
315 | BN_ULONG U2[P256_LIMBS], S2[P256_LIMBS]; | |
316 | BN_ULONG U1[P256_LIMBS], S1[P256_LIMBS]; | |
317 | BN_ULONG Z1sqr[P256_LIMBS]; | |
318 | BN_ULONG Z2sqr[P256_LIMBS]; | |
319 | BN_ULONG H[P256_LIMBS], R[P256_LIMBS]; | |
320 | BN_ULONG Hsqr[P256_LIMBS]; | |
321 | BN_ULONG Rsqr[P256_LIMBS]; | |
322 | BN_ULONG Hcub[P256_LIMBS]; | |
323 | ||
324 | BN_ULONG res_x[P256_LIMBS]; | |
325 | BN_ULONG res_y[P256_LIMBS]; | |
326 | BN_ULONG res_z[P256_LIMBS]; | |
327 | ||
328 | BN_ULONG in1infty, in2infty; | |
329 | ||
330 | const BN_ULONG *in1_x = a->X; | |
331 | const BN_ULONG *in1_y = a->Y; | |
332 | const BN_ULONG *in1_z = a->Z; | |
333 | ||
334 | const BN_ULONG *in2_x = b->X; | |
335 | const BN_ULONG *in2_y = b->Y; | |
336 | const BN_ULONG *in2_z = b->Z; | |
337 | ||
e3057a57 AP |
338 | /* |
339 | * Infinity in encoded as (,,0) | |
340 | */ | |
341 | in1infty = (in1_z[0] | in1_z[1] | in1_z[2] | in1_z[3]); | |
4d3fa06f | 342 | if (P256_LIMBS == 8) |
e3057a57 | 343 | in1infty |= (in1_z[4] | in1_z[5] | in1_z[6] | in1_z[7]); |
4d3fa06f | 344 | |
e3057a57 | 345 | in2infty = (in2_z[0] | in2_z[1] | in2_z[2] | in2_z[3]); |
4d3fa06f | 346 | if (P256_LIMBS == 8) |
e3057a57 | 347 | in2infty |= (in2_z[4] | in2_z[5] | in2_z[6] | in2_z[7]); |
4d3fa06f AP |
348 | |
349 | in1infty = is_zero(in1infty); | |
350 | in2infty = is_zero(in2infty); | |
351 | ||
352 | ecp_nistz256_sqr_mont(Z2sqr, in2_z); /* Z2^2 */ | |
353 | ecp_nistz256_sqr_mont(Z1sqr, in1_z); /* Z1^2 */ | |
354 | ||
355 | ecp_nistz256_mul_mont(S1, Z2sqr, in2_z); /* S1 = Z2^3 */ | |
356 | ecp_nistz256_mul_mont(S2, Z1sqr, in1_z); /* S2 = Z1^3 */ | |
357 | ||
358 | ecp_nistz256_mul_mont(S1, S1, in1_y); /* S1 = Y1*Z2^3 */ | |
359 | ecp_nistz256_mul_mont(S2, S2, in2_y); /* S2 = Y2*Z1^3 */ | |
360 | ecp_nistz256_sub(R, S2, S1); /* R = S2 - S1 */ | |
361 | ||
362 | ecp_nistz256_mul_mont(U1, in1_x, Z2sqr); /* U1 = X1*Z2^2 */ | |
363 | ecp_nistz256_mul_mont(U2, in2_x, Z1sqr); /* U2 = X2*Z1^2 */ | |
364 | ecp_nistz256_sub(H, U2, U1); /* H = U2 - U1 */ | |
365 | ||
20728adc | 366 | /* |
45a40538 BE |
367 | * The formulae are incorrect if the points are equal so we check for |
368 | * this and do doubling if this happens. | |
369 | * | |
370 | * Points here are in Jacobian projective coordinates (Xi, Yi, Zi) | |
371 | * that are bound to the affine coordinates (xi, yi) by the following | |
372 | * equations: | |
373 | * - xi = Xi / (Zi)^2 | |
374 | * - y1 = Yi / (Zi)^3 | |
375 | * | |
376 | * For the sake of optimization, the algorithm operates over | |
377 | * intermediate variables U1, U2 and S1, S2 that are derived from | |
378 | * the projective coordinates: | |
379 | * - U1 = X1 * (Z2)^2 ; U2 = X2 * (Z1)^2 | |
380 | * - S1 = Y1 * (Z2)^3 ; S2 = Y2 * (Z1)^3 | |
381 | * | |
382 | * It is easy to prove that is_equal(U1, U2) implies that the affine | |
383 | * x-coordinates are equal, or either point is at infinity. | |
384 | * Likewise is_equal(S1, S2) implies that the affine y-coordinates are | |
385 | * equal, or either point is at infinity. | |
386 | * | |
387 | * The special case of either point being the point at infinity (Z1 or Z2 | |
388 | * is zero), is handled separately later on in this function, so we avoid | |
389 | * jumping to point_double here in those special cases. | |
390 | * | |
391 | * When both points are inverse of each other, we know that the affine | |
392 | * x-coordinates are equal, and the y-coordinates have different sign. | |
393 | * Therefore since U1 = U2, we know H = 0, and therefore Z3 = H*Z1*Z2 | |
394 | * will equal 0, thus the result is infinity, if we simply let this | |
395 | * function continue normally. | |
396 | * | |
397 | * We use bitwise operations to avoid potential side-channels introduced by | |
398 | * the short-circuiting behaviour of boolean operators. | |
20728adc | 399 | */ |
45a40538 BE |
400 | if (is_equal(U1, U2) & ~in1infty & ~in2infty & is_equal(S1, S2)) { |
401 | /* | |
402 | * This is obviously not constant-time but it should never happen during | |
403 | * single point multiplication, so there is no timing leak for ECDH or | |
404 | * ECDSA signing. | |
405 | */ | |
406 | ecp_nistz256_point_double(r, a); | |
407 | return; | |
4d3fa06f AP |
408 | } |
409 | ||
410 | ecp_nistz256_sqr_mont(Rsqr, R); /* R^2 */ | |
411 | ecp_nistz256_mul_mont(res_z, H, in1_z); /* Z3 = H*Z1*Z2 */ | |
412 | ecp_nistz256_sqr_mont(Hsqr, H); /* H^2 */ | |
413 | ecp_nistz256_mul_mont(res_z, res_z, in2_z); /* Z3 = H*Z1*Z2 */ | |
414 | ecp_nistz256_mul_mont(Hcub, Hsqr, H); /* H^3 */ | |
415 | ||
416 | ecp_nistz256_mul_mont(U2, U1, Hsqr); /* U1*H^2 */ | |
417 | ecp_nistz256_mul_by_2(Hsqr, U2); /* 2*U1*H^2 */ | |
418 | ||
419 | ecp_nistz256_sub(res_x, Rsqr, Hsqr); | |
420 | ecp_nistz256_sub(res_x, res_x, Hcub); | |
421 | ||
422 | ecp_nistz256_sub(res_y, U2, res_x); | |
423 | ||
424 | ecp_nistz256_mul_mont(S2, S1, Hcub); | |
425 | ecp_nistz256_mul_mont(res_y, R, res_y); | |
426 | ecp_nistz256_sub(res_y, res_y, S2); | |
427 | ||
428 | copy_conditional(res_x, in2_x, in1infty); | |
429 | copy_conditional(res_y, in2_y, in1infty); | |
430 | copy_conditional(res_z, in2_z, in1infty); | |
431 | ||
432 | copy_conditional(res_x, in1_x, in2infty); | |
433 | copy_conditional(res_y, in1_y, in2infty); | |
434 | copy_conditional(res_z, in1_z, in2infty); | |
435 | ||
436 | memcpy(r->X, res_x, sizeof(res_x)); | |
437 | memcpy(r->Y, res_y, sizeof(res_y)); | |
438 | memcpy(r->Z, res_z, sizeof(res_z)); | |
439 | } | |
440 | ||
441 | /* Point addition when b is known to be affine: r = a+b */ | |
58d47cf0 AP |
442 | static void ecp_nistz256_point_add_affine(P256_POINT *r, |
443 | const P256_POINT *a, | |
444 | const P256_POINT_AFFINE *b) | |
4d3fa06f AP |
445 | { |
446 | BN_ULONG U2[P256_LIMBS], S2[P256_LIMBS]; | |
447 | BN_ULONG Z1sqr[P256_LIMBS]; | |
448 | BN_ULONG H[P256_LIMBS], R[P256_LIMBS]; | |
449 | BN_ULONG Hsqr[P256_LIMBS]; | |
450 | BN_ULONG Rsqr[P256_LIMBS]; | |
451 | BN_ULONG Hcub[P256_LIMBS]; | |
452 | ||
453 | BN_ULONG res_x[P256_LIMBS]; | |
454 | BN_ULONG res_y[P256_LIMBS]; | |
455 | BN_ULONG res_z[P256_LIMBS]; | |
456 | ||
457 | BN_ULONG in1infty, in2infty; | |
458 | ||
459 | const BN_ULONG *in1_x = a->X; | |
460 | const BN_ULONG *in1_y = a->Y; | |
461 | const BN_ULONG *in1_z = a->Z; | |
462 | ||
463 | const BN_ULONG *in2_x = b->X; | |
464 | const BN_ULONG *in2_y = b->Y; | |
465 | ||
20728adc | 466 | /* |
e3057a57 | 467 | * Infinity in encoded as (,,0) |
20728adc | 468 | */ |
e3057a57 | 469 | in1infty = (in1_z[0] | in1_z[1] | in1_z[2] | in1_z[3]); |
4d3fa06f | 470 | if (P256_LIMBS == 8) |
e3057a57 | 471 | in1infty |= (in1_z[4] | in1_z[5] | in1_z[6] | in1_z[7]); |
4d3fa06f | 472 | |
e3057a57 AP |
473 | /* |
474 | * In affine representation we encode infinity as (0,0), which is | |
475 | * not on the curve, so it is OK | |
476 | */ | |
58d47cf0 AP |
477 | in2infty = (in2_x[0] | in2_x[1] | in2_x[2] | in2_x[3] | |
478 | in2_y[0] | in2_y[1] | in2_y[2] | in2_y[3]); | |
4d3fa06f | 479 | if (P256_LIMBS == 8) |
58d47cf0 AP |
480 | in2infty |= (in2_x[4] | in2_x[5] | in2_x[6] | in2_x[7] | |
481 | in2_y[4] | in2_y[5] | in2_y[6] | in2_y[7]); | |
4d3fa06f AP |
482 | |
483 | in1infty = is_zero(in1infty); | |
484 | in2infty = is_zero(in2infty); | |
485 | ||
486 | ecp_nistz256_sqr_mont(Z1sqr, in1_z); /* Z1^2 */ | |
487 | ||
488 | ecp_nistz256_mul_mont(U2, in2_x, Z1sqr); /* U2 = X2*Z1^2 */ | |
489 | ecp_nistz256_sub(H, U2, in1_x); /* H = U2 - U1 */ | |
490 | ||
491 | ecp_nistz256_mul_mont(S2, Z1sqr, in1_z); /* S2 = Z1^3 */ | |
492 | ||
493 | ecp_nistz256_mul_mont(res_z, H, in1_z); /* Z3 = H*Z1*Z2 */ | |
494 | ||
495 | ecp_nistz256_mul_mont(S2, S2, in2_y); /* S2 = Y2*Z1^3 */ | |
496 | ecp_nistz256_sub(R, S2, in1_y); /* R = S2 - S1 */ | |
497 | ||
498 | ecp_nistz256_sqr_mont(Hsqr, H); /* H^2 */ | |
499 | ecp_nistz256_sqr_mont(Rsqr, R); /* R^2 */ | |
500 | ecp_nistz256_mul_mont(Hcub, Hsqr, H); /* H^3 */ | |
501 | ||
502 | ecp_nistz256_mul_mont(U2, in1_x, Hsqr); /* U1*H^2 */ | |
503 | ecp_nistz256_mul_by_2(Hsqr, U2); /* 2*U1*H^2 */ | |
504 | ||
505 | ecp_nistz256_sub(res_x, Rsqr, Hsqr); | |
506 | ecp_nistz256_sub(res_x, res_x, Hcub); | |
507 | ecp_nistz256_sub(H, U2, res_x); | |
508 | ||
509 | ecp_nistz256_mul_mont(S2, in1_y, Hcub); | |
510 | ecp_nistz256_mul_mont(H, H, R); | |
511 | ecp_nistz256_sub(res_y, H, S2); | |
512 | ||
513 | copy_conditional(res_x, in2_x, in1infty); | |
514 | copy_conditional(res_x, in1_x, in2infty); | |
515 | ||
516 | copy_conditional(res_y, in2_y, in1infty); | |
517 | copy_conditional(res_y, in1_y, in2infty); | |
518 | ||
519 | copy_conditional(res_z, ONE, in1infty); | |
520 | copy_conditional(res_z, in1_z, in2infty); | |
521 | ||
522 | memcpy(r->X, res_x, sizeof(res_x)); | |
523 | memcpy(r->Y, res_y, sizeof(res_y)); | |
524 | memcpy(r->Z, res_z, sizeof(res_z)); | |
525 | } | |
526 | #endif | |
527 | ||
528 | /* r = in^-1 mod p */ | |
529 | static void ecp_nistz256_mod_inverse(BN_ULONG r[P256_LIMBS], | |
530 | const BN_ULONG in[P256_LIMBS]) | |
531 | { | |
20728adc AP |
532 | /* |
533 | * The poly is ffffffff 00000001 00000000 00000000 00000000 ffffffff | |
534 | * ffffffff ffffffff We use FLT and used poly-2 as exponent | |
535 | */ | |
4d3fa06f AP |
536 | BN_ULONG p2[P256_LIMBS]; |
537 | BN_ULONG p4[P256_LIMBS]; | |
538 | BN_ULONG p8[P256_LIMBS]; | |
539 | BN_ULONG p16[P256_LIMBS]; | |
540 | BN_ULONG p32[P256_LIMBS]; | |
541 | BN_ULONG res[P256_LIMBS]; | |
542 | int i; | |
543 | ||
544 | ecp_nistz256_sqr_mont(res, in); | |
545 | ecp_nistz256_mul_mont(p2, res, in); /* 3*p */ | |
546 | ||
547 | ecp_nistz256_sqr_mont(res, p2); | |
548 | ecp_nistz256_sqr_mont(res, res); | |
549 | ecp_nistz256_mul_mont(p4, res, p2); /* f*p */ | |
550 | ||
551 | ecp_nistz256_sqr_mont(res, p4); | |
552 | ecp_nistz256_sqr_mont(res, res); | |
553 | ecp_nistz256_sqr_mont(res, res); | |
554 | ecp_nistz256_sqr_mont(res, res); | |
555 | ecp_nistz256_mul_mont(p8, res, p4); /* ff*p */ | |
556 | ||
557 | ecp_nistz256_sqr_mont(res, p8); | |
558 | for (i = 0; i < 7; i++) | |
559 | ecp_nistz256_sqr_mont(res, res); | |
560 | ecp_nistz256_mul_mont(p16, res, p8); /* ffff*p */ | |
561 | ||
562 | ecp_nistz256_sqr_mont(res, p16); | |
563 | for (i = 0; i < 15; i++) | |
564 | ecp_nistz256_sqr_mont(res, res); | |
565 | ecp_nistz256_mul_mont(p32, res, p16); /* ffffffff*p */ | |
566 | ||
567 | ecp_nistz256_sqr_mont(res, p32); | |
568 | for (i = 0; i < 31; i++) | |
569 | ecp_nistz256_sqr_mont(res, res); | |
570 | ecp_nistz256_mul_mont(res, res, in); | |
571 | ||
572 | for (i = 0; i < 32 * 4; i++) | |
573 | ecp_nistz256_sqr_mont(res, res); | |
574 | ecp_nistz256_mul_mont(res, res, p32); | |
575 | ||
576 | for (i = 0; i < 32; i++) | |
577 | ecp_nistz256_sqr_mont(res, res); | |
578 | ecp_nistz256_mul_mont(res, res, p32); | |
579 | ||
580 | for (i = 0; i < 16; i++) | |
581 | ecp_nistz256_sqr_mont(res, res); | |
582 | ecp_nistz256_mul_mont(res, res, p16); | |
583 | ||
584 | for (i = 0; i < 8; i++) | |
585 | ecp_nistz256_sqr_mont(res, res); | |
586 | ecp_nistz256_mul_mont(res, res, p8); | |
587 | ||
588 | ecp_nistz256_sqr_mont(res, res); | |
589 | ecp_nistz256_sqr_mont(res, res); | |
590 | ecp_nistz256_sqr_mont(res, res); | |
591 | ecp_nistz256_sqr_mont(res, res); | |
592 | ecp_nistz256_mul_mont(res, res, p4); | |
593 | ||
594 | ecp_nistz256_sqr_mont(res, res); | |
595 | ecp_nistz256_sqr_mont(res, res); | |
596 | ecp_nistz256_mul_mont(res, res, p2); | |
597 | ||
598 | ecp_nistz256_sqr_mont(res, res); | |
599 | ecp_nistz256_sqr_mont(res, res); | |
600 | ecp_nistz256_mul_mont(res, res, in); | |
601 | ||
602 | memcpy(r, res, sizeof(res)); | |
603 | } | |
604 | ||
20728adc AP |
605 | /* |
606 | * ecp_nistz256_bignum_to_field_elem copies the contents of |in| to |out| and | |
607 | * returns one if it fits. Otherwise it returns zero. | |
608 | */ | |
5956b110 EK |
609 | __owur static int ecp_nistz256_bignum_to_field_elem(BN_ULONG out[P256_LIMBS], |
610 | const BIGNUM *in) | |
4d3fa06f | 611 | { |
5784a521 | 612 | return bn_copy_words(out, in, P256_LIMBS); |
4d3fa06f AP |
613 | } |
614 | ||
615 | /* r = sum(scalar[i]*point[i]) */ | |
5956b110 EK |
616 | __owur static int ecp_nistz256_windowed_mul(const EC_GROUP *group, |
617 | P256_POINT *r, | |
618 | const BIGNUM **scalar, | |
619 | const EC_POINT **point, | |
620 | size_t num, BN_CTX *ctx) | |
4d3fa06f | 621 | { |
5afc296a | 622 | size_t i; |
a4d5269e | 623 | int j, ret = 0; |
49b05c7d | 624 | unsigned int idx; |
4d3fa06f AP |
625 | unsigned char (*p_str)[33] = NULL; |
626 | const unsigned int window_size = 5; | |
627 | const unsigned int mask = (1 << (window_size + 1)) - 1; | |
628 | unsigned int wvalue; | |
20728adc | 629 | P256_POINT *temp; /* place for 5 temporary points */ |
4d3fa06f | 630 | const BIGNUM **scalars = NULL; |
20728adc | 631 | P256_POINT (*table)[16] = NULL; |
4d3fa06f AP |
632 | void *table_storage = NULL; |
633 | ||
5afc296a AP |
634 | if ((num * 16 + 6) > OPENSSL_MALLOC_MAX_NELEMS(P256_POINT) |
635 | || (table_storage = | |
636 | OPENSSL_malloc((num * 16 + 5) * sizeof(P256_POINT) + 64)) == NULL | |
4d3fa06f AP |
637 | || (p_str = |
638 | OPENSSL_malloc(num * 33 * sizeof(unsigned char))) == NULL | |
639 | || (scalars = OPENSSL_malloc(num * sizeof(BIGNUM *))) == NULL) { | |
9311d0c4 | 640 | ERR_raise(ERR_LIB_EC, ERR_R_MALLOC_FAILURE); |
4d3fa06f | 641 | goto err; |
4d3fa06f AP |
642 | } |
643 | ||
3ff08e1d | 644 | table = (void *)ALIGNPTR(table_storage, 64); |
20728adc | 645 | temp = (P256_POINT *)(table + num); |
3ff08e1d | 646 | |
4d3fa06f AP |
647 | for (i = 0; i < num; i++) { |
648 | P256_POINT *row = table[i]; | |
649 | ||
c028254b | 650 | /* This is an unusual input, we don't guarantee constant-timeness. */ |
4d3fa06f AP |
651 | if ((BN_num_bits(scalar[i]) > 256) || BN_is_negative(scalar[i])) { |
652 | BIGNUM *mod; | |
653 | ||
654 | if ((mod = BN_CTX_get(ctx)) == NULL) | |
655 | goto err; | |
5784a521 | 656 | if (!BN_nnmod(mod, scalar[i], group->order, ctx)) { |
9311d0c4 | 657 | ERR_raise(ERR_LIB_EC, ERR_R_BN_LIB); |
4d3fa06f AP |
658 | goto err; |
659 | } | |
660 | scalars[i] = mod; | |
661 | } else | |
662 | scalars[i] = scalar[i]; | |
663 | ||
5784a521 MC |
664 | for (j = 0; j < bn_get_top(scalars[i]) * BN_BYTES; j += BN_BYTES) { |
665 | BN_ULONG d = bn_get_words(scalars[i])[j / BN_BYTES]; | |
4d3fa06f | 666 | |
5afc296a AP |
667 | p_str[i][j + 0] = (unsigned char)d; |
668 | p_str[i][j + 1] = (unsigned char)(d >> 8); | |
669 | p_str[i][j + 2] = (unsigned char)(d >> 16); | |
670 | p_str[i][j + 3] = (unsigned char)(d >>= 24); | |
4d3fa06f AP |
671 | if (BN_BYTES == 8) { |
672 | d >>= 8; | |
5afc296a AP |
673 | p_str[i][j + 4] = (unsigned char)d; |
674 | p_str[i][j + 5] = (unsigned char)(d >> 8); | |
675 | p_str[i][j + 6] = (unsigned char)(d >> 16); | |
676 | p_str[i][j + 7] = (unsigned char)(d >> 24); | |
4d3fa06f AP |
677 | } |
678 | } | |
679 | for (; j < 33; j++) | |
680 | p_str[i][j] = 0; | |
681 | ||
5784a521 MC |
682 | if (!ecp_nistz256_bignum_to_field_elem(temp[0].X, point[i]->X) |
683 | || !ecp_nistz256_bignum_to_field_elem(temp[0].Y, point[i]->Y) | |
684 | || !ecp_nistz256_bignum_to_field_elem(temp[0].Z, point[i]->Z)) { | |
9311d0c4 | 685 | ERR_raise(ERR_LIB_EC, EC_R_COORDINATES_OUT_OF_RANGE); |
4d3fa06f AP |
686 | goto err; |
687 | } | |
688 | ||
20728adc | 689 | /* |
dccd20d1 F |
690 | * row[0] is implicitly (0,0,0) (the point at infinity), therefore it |
691 | * is not stored. All other values are actually stored with an offset | |
692 | * of -1 in table. | |
3ff08e1d AP |
693 | */ |
694 | ||
695 | ecp_nistz256_scatter_w5 (row, &temp[0], 1); | |
696 | ecp_nistz256_point_double(&temp[1], &temp[0]); /*1+1=2 */ | |
697 | ecp_nistz256_scatter_w5 (row, &temp[1], 2); | |
698 | ecp_nistz256_point_add (&temp[2], &temp[1], &temp[0]); /*2+1=3 */ | |
699 | ecp_nistz256_scatter_w5 (row, &temp[2], 3); | |
700 | ecp_nistz256_point_double(&temp[1], &temp[1]); /*2*2=4 */ | |
701 | ecp_nistz256_scatter_w5 (row, &temp[1], 4); | |
702 | ecp_nistz256_point_double(&temp[2], &temp[2]); /*2*3=6 */ | |
703 | ecp_nistz256_scatter_w5 (row, &temp[2], 6); | |
704 | ecp_nistz256_point_add (&temp[3], &temp[1], &temp[0]); /*4+1=5 */ | |
705 | ecp_nistz256_scatter_w5 (row, &temp[3], 5); | |
706 | ecp_nistz256_point_add (&temp[4], &temp[2], &temp[0]); /*6+1=7 */ | |
707 | ecp_nistz256_scatter_w5 (row, &temp[4], 7); | |
708 | ecp_nistz256_point_double(&temp[1], &temp[1]); /*2*4=8 */ | |
709 | ecp_nistz256_scatter_w5 (row, &temp[1], 8); | |
710 | ecp_nistz256_point_double(&temp[2], &temp[2]); /*2*6=12 */ | |
711 | ecp_nistz256_scatter_w5 (row, &temp[2], 12); | |
712 | ecp_nistz256_point_double(&temp[3], &temp[3]); /*2*5=10 */ | |
713 | ecp_nistz256_scatter_w5 (row, &temp[3], 10); | |
714 | ecp_nistz256_point_double(&temp[4], &temp[4]); /*2*7=14 */ | |
715 | ecp_nistz256_scatter_w5 (row, &temp[4], 14); | |
716 | ecp_nistz256_point_add (&temp[2], &temp[2], &temp[0]); /*12+1=13*/ | |
717 | ecp_nistz256_scatter_w5 (row, &temp[2], 13); | |
718 | ecp_nistz256_point_add (&temp[3], &temp[3], &temp[0]); /*10+1=11*/ | |
719 | ecp_nistz256_scatter_w5 (row, &temp[3], 11); | |
720 | ecp_nistz256_point_add (&temp[4], &temp[4], &temp[0]); /*14+1=15*/ | |
721 | ecp_nistz256_scatter_w5 (row, &temp[4], 15); | |
722 | ecp_nistz256_point_add (&temp[2], &temp[1], &temp[0]); /*8+1=9 */ | |
723 | ecp_nistz256_scatter_w5 (row, &temp[2], 9); | |
724 | ecp_nistz256_point_double(&temp[1], &temp[1]); /*2*8=16 */ | |
725 | ecp_nistz256_scatter_w5 (row, &temp[1], 16); | |
4d3fa06f AP |
726 | } |
727 | ||
49b05c7d | 728 | idx = 255; |
4d3fa06f | 729 | |
49b05c7d RS |
730 | wvalue = p_str[0][(idx - 1) / 8]; |
731 | wvalue = (wvalue >> ((idx - 1) % 8)) & mask; | |
4d3fa06f | 732 | |
3ff08e1d AP |
733 | /* |
734 | * We gather to temp[0], because we know it's position relative | |
735 | * to table | |
736 | */ | |
737 | ecp_nistz256_gather_w5(&temp[0], table[0], _booth_recode_w5(wvalue) >> 1); | |
738 | memcpy(r, &temp[0], sizeof(temp[0])); | |
4d3fa06f | 739 | |
49b05c7d RS |
740 | while (idx >= 5) { |
741 | for (i = (idx == 255 ? 1 : 0); i < num; i++) { | |
742 | unsigned int off = (idx - 1) / 8; | |
4d3fa06f AP |
743 | |
744 | wvalue = p_str[i][off] | p_str[i][off + 1] << 8; | |
49b05c7d | 745 | wvalue = (wvalue >> ((idx - 1) % 8)) & mask; |
4d3fa06f AP |
746 | |
747 | wvalue = _booth_recode_w5(wvalue); | |
748 | ||
3ff08e1d | 749 | ecp_nistz256_gather_w5(&temp[0], table[i], wvalue >> 1); |
4d3fa06f | 750 | |
3ff08e1d AP |
751 | ecp_nistz256_neg(temp[1].Y, temp[0].Y); |
752 | copy_conditional(temp[0].Y, temp[1].Y, (wvalue & 1)); | |
4d3fa06f | 753 | |
3ff08e1d | 754 | ecp_nistz256_point_add(r, r, &temp[0]); |
4d3fa06f AP |
755 | } |
756 | ||
49b05c7d | 757 | idx -= window_size; |
4d3fa06f AP |
758 | |
759 | ecp_nistz256_point_double(r, r); | |
760 | ecp_nistz256_point_double(r, r); | |
761 | ecp_nistz256_point_double(r, r); | |
762 | ecp_nistz256_point_double(r, r); | |
763 | ecp_nistz256_point_double(r, r); | |
764 | } | |
765 | ||
766 | /* Final window */ | |
767 | for (i = 0; i < num; i++) { | |
768 | wvalue = p_str[i][0]; | |
769 | wvalue = (wvalue << 1) & mask; | |
770 | ||
771 | wvalue = _booth_recode_w5(wvalue); | |
772 | ||
3ff08e1d | 773 | ecp_nistz256_gather_w5(&temp[0], table[i], wvalue >> 1); |
4d3fa06f | 774 | |
3ff08e1d AP |
775 | ecp_nistz256_neg(temp[1].Y, temp[0].Y); |
776 | copy_conditional(temp[0].Y, temp[1].Y, wvalue & 1); | |
4d3fa06f | 777 | |
3ff08e1d | 778 | ecp_nistz256_point_add(r, r, &temp[0]); |
4d3fa06f AP |
779 | } |
780 | ||
a4d5269e | 781 | ret = 1; |
58d47cf0 | 782 | err: |
b548a1f1 RS |
783 | OPENSSL_free(table_storage); |
784 | OPENSSL_free(p_str); | |
785 | OPENSSL_free(scalars); | |
a4d5269e | 786 | return ret; |
4d3fa06f AP |
787 | } |
788 | ||
789 | /* Coordinates of G, for which we have precomputed tables */ | |
f44903a4 | 790 | static const BN_ULONG def_xG[P256_LIMBS] = { |
4d3fa06f AP |
791 | TOBN(0x79e730d4, 0x18a9143c), TOBN(0x75ba95fc, 0x5fedb601), |
792 | TOBN(0x79fb732b, 0x77622510), TOBN(0x18905f76, 0xa53755c6) | |
793 | }; | |
794 | ||
f44903a4 | 795 | static const BN_ULONG def_yG[P256_LIMBS] = { |
4d3fa06f AP |
796 | TOBN(0xddf25357, 0xce95560a), TOBN(0x8b4ab8e4, 0xba19e45c), |
797 | TOBN(0xd2e88688, 0xdd21f325), TOBN(0x8571ff18, 0x25885d85) | |
798 | }; | |
799 | ||
20728adc AP |
800 | /* |
801 | * ecp_nistz256_is_affine_G returns one if |generator| is the standard, P-256 | |
802 | * generator. | |
803 | */ | |
58d47cf0 | 804 | static int ecp_nistz256_is_affine_G(const EC_POINT *generator) |
4d3fa06f | 805 | { |
5784a521 MC |
806 | return (bn_get_top(generator->X) == P256_LIMBS) && |
807 | (bn_get_top(generator->Y) == P256_LIMBS) && | |
5784a521 MC |
808 | is_equal(bn_get_words(generator->X), def_xG) && |
809 | is_equal(bn_get_words(generator->Y), def_yG) && | |
2e929e53 | 810 | is_one(generator->Z); |
4d3fa06f AP |
811 | } |
812 | ||
5956b110 | 813 | __owur static int ecp_nistz256_mult_precompute(EC_GROUP *group, BN_CTX *ctx) |
4d3fa06f | 814 | { |
20728adc AP |
815 | /* |
816 | * We precompute a table for a Booth encoded exponent (wNAF) based | |
4d3fa06f | 817 | * computation. Each table holds 64 values for safe access, with an |
20728adc AP |
818 | * implicit value of infinity at index zero. We use window of size 7, and |
819 | * therefore require ceil(256/7) = 37 tables. | |
820 | */ | |
be2e334f | 821 | const BIGNUM *order; |
4d3fa06f AP |
822 | EC_POINT *P = NULL, *T = NULL; |
823 | const EC_POINT *generator; | |
3aef36ff | 824 | NISTZ256_PRE_COMP *pre_comp; |
53dd4ddf | 825 | BN_CTX *new_ctx = NULL; |
4d3fa06f AP |
826 | int i, j, k, ret = 0; |
827 | size_t w; | |
828 | ||
829 | PRECOMP256_ROW *preComputedTable = NULL; | |
830 | unsigned char *precomp_storage = NULL; | |
831 | ||
3aef36ff | 832 | /* if there is an old NISTZ256_PRE_COMP object, throw it away */ |
2c52ac9b | 833 | EC_pre_comp_free(group); |
4d3fa06f AP |
834 | generator = EC_GROUP_get0_generator(group); |
835 | if (generator == NULL) { | |
9311d0c4 | 836 | ERR_raise(ERR_LIB_EC, EC_R_UNDEFINED_GENERATOR); |
4d3fa06f AP |
837 | return 0; |
838 | } | |
839 | ||
840 | if (ecp_nistz256_is_affine_G(generator)) { | |
20728adc AP |
841 | /* |
842 | * No need to calculate tables for the standard generator because we | |
843 | * have them statically. | |
844 | */ | |
4d3fa06f AP |
845 | return 1; |
846 | } | |
847 | ||
be07ae9b | 848 | if ((pre_comp = ecp_nistz256_pre_comp_new(group)) == NULL) |
4d3fa06f AP |
849 | return 0; |
850 | ||
851 | if (ctx == NULL) { | |
a9612d6c | 852 | ctx = new_ctx = BN_CTX_new_ex(group->libctx); |
4d3fa06f AP |
853 | if (ctx == NULL) |
854 | goto err; | |
855 | } | |
856 | ||
857 | BN_CTX_start(ctx); | |
4d3fa06f | 858 | |
be2e334f | 859 | order = EC_GROUP_get0_order(group); |
4d3fa06f AP |
860 | if (order == NULL) |
861 | goto err; | |
862 | ||
4d3fa06f | 863 | if (BN_is_zero(order)) { |
9311d0c4 | 864 | ERR_raise(ERR_LIB_EC, EC_R_UNKNOWN_ORDER); |
4d3fa06f AP |
865 | goto err; |
866 | } | |
867 | ||
868 | w = 7; | |
869 | ||
870 | if ((precomp_storage = | |
871 | OPENSSL_malloc(37 * 64 * sizeof(P256_POINT_AFFINE) + 64)) == NULL) { | |
9311d0c4 | 872 | ERR_raise(ERR_LIB_EC, ERR_R_MALLOC_FAILURE); |
4d3fa06f | 873 | goto err; |
4d3fa06f AP |
874 | } |
875 | ||
3ff08e1d AP |
876 | preComputedTable = (void *)ALIGNPTR(precomp_storage, 64); |
877 | ||
4d3fa06f AP |
878 | P = EC_POINT_new(group); |
879 | T = EC_POINT_new(group); | |
53dd4ddf EK |
880 | if (P == NULL || T == NULL) |
881 | goto err; | |
4d3fa06f | 882 | |
20728adc AP |
883 | /* |
884 | * The zero entry is implicitly infinity, and we skip it, storing other | |
885 | * values with -1 offset. | |
886 | */ | |
53dd4ddf EK |
887 | if (!EC_POINT_copy(T, generator)) |
888 | goto err; | |
4d3fa06f AP |
889 | |
890 | for (k = 0; k < 64; k++) { | |
53dd4ddf EK |
891 | if (!EC_POINT_copy(P, T)) |
892 | goto err; | |
4d3fa06f | 893 | for (j = 0; j < 37; j++) { |
3ff08e1d | 894 | P256_POINT_AFFINE temp; |
20728adc | 895 | /* |
6038354c | 896 | * It would be faster to use EC_POINTs_make_affine and |
20728adc AP |
897 | * make multiple points affine at the same time. |
898 | */ | |
c2f2db9b BB |
899 | if (group->meth->make_affine == NULL |
900 | || !group->meth->make_affine(group, P, ctx)) | |
6038354c EK |
901 | goto err; |
902 | if (!ecp_nistz256_bignum_to_field_elem(temp.X, P->X) || | |
903 | !ecp_nistz256_bignum_to_field_elem(temp.Y, P->Y)) { | |
9311d0c4 | 904 | ERR_raise(ERR_LIB_EC, EC_R_COORDINATES_OUT_OF_RANGE); |
6038354c EK |
905 | goto err; |
906 | } | |
3ff08e1d | 907 | ecp_nistz256_scatter_w7(preComputedTable[j], &temp, k); |
6038354c EK |
908 | for (i = 0; i < 7; i++) { |
909 | if (!EC_POINT_dbl(group, P, P, ctx)) | |
910 | goto err; | |
911 | } | |
4d3fa06f | 912 | } |
6038354c EK |
913 | if (!EC_POINT_add(group, T, T, generator, ctx)) |
914 | goto err; | |
4d3fa06f AP |
915 | } |
916 | ||
917 | pre_comp->group = group; | |
918 | pre_comp->w = w; | |
919 | pre_comp->precomp = preComputedTable; | |
920 | pre_comp->precomp_storage = precomp_storage; | |
4d3fa06f | 921 | precomp_storage = NULL; |
3aef36ff | 922 | SETPRECOMP(group, nistz256, pre_comp); |
4d3fa06f | 923 | pre_comp = NULL; |
4d3fa06f AP |
924 | ret = 1; |
925 | ||
58d47cf0 | 926 | err: |
ce1415ed | 927 | BN_CTX_end(ctx); |
53dd4ddf EK |
928 | BN_CTX_free(new_ctx); |
929 | ||
3aef36ff | 930 | EC_nistz256_pre_comp_free(pre_comp); |
b548a1f1 | 931 | OPENSSL_free(precomp_storage); |
8fdc3734 RS |
932 | EC_POINT_free(P); |
933 | EC_POINT_free(T); | |
4d3fa06f AP |
934 | return ret; |
935 | } | |
936 | ||
5956b110 EK |
937 | __owur static int ecp_nistz256_set_from_affine(EC_POINT *out, const EC_GROUP *group, |
938 | const P256_POINT_AFFINE *in, | |
939 | BN_CTX *ctx) | |
4d3fa06f | 940 | { |
4d3fa06f AP |
941 | int ret = 0; |
942 | ||
8fc4aeb9 AP |
943 | if ((ret = bn_set_words(out->X, in->X, P256_LIMBS)) |
944 | && (ret = bn_set_words(out->Y, in->Y, P256_LIMBS)) | |
945 | && (ret = bn_set_words(out->Z, ONE, P256_LIMBS))) | |
946 | out->Z_is_one = 1; | |
4d3fa06f AP |
947 | |
948 | return ret; | |
949 | } | |
950 | ||
951 | /* r = scalar*G + sum(scalars[i]*points[i]) */ | |
5956b110 EK |
952 | __owur static int ecp_nistz256_points_mul(const EC_GROUP *group, |
953 | EC_POINT *r, | |
954 | const BIGNUM *scalar, | |
955 | size_t num, | |
956 | const EC_POINT *points[], | |
957 | const BIGNUM *scalars[], BN_CTX *ctx) | |
4d3fa06f AP |
958 | { |
959 | int i = 0, ret = 0, no_precomp_for_generator = 0, p_is_infinity = 0; | |
960 | unsigned char p_str[33] = { 0 }; | |
961 | const PRECOMP256_ROW *preComputedTable = NULL; | |
3aef36ff | 962 | const NISTZ256_PRE_COMP *pre_comp = NULL; |
4d3fa06f | 963 | const EC_POINT *generator = NULL; |
a4d5269e EK |
964 | const BIGNUM **new_scalars = NULL; |
965 | const EC_POINT **new_points = NULL; | |
49b05c7d | 966 | unsigned int idx = 0; |
4d3fa06f AP |
967 | const unsigned int window_size = 7; |
968 | const unsigned int mask = (1 << (window_size + 1)) - 1; | |
969 | unsigned int wvalue; | |
970 | ALIGN32 union { | |
971 | P256_POINT p; | |
972 | P256_POINT_AFFINE a; | |
973 | } t, p; | |
974 | BIGNUM *tmp_scalar; | |
975 | ||
58d47cf0 | 976 | if ((num + 1) == 0 || (num + 1) > OPENSSL_MALLOC_MAX_NELEMS(void *)) { |
9311d0c4 | 977 | ERR_raise(ERR_LIB_EC, ERR_R_MALLOC_FAILURE); |
3ff08e1d AP |
978 | return 0; |
979 | } | |
980 | ||
e22d2199 | 981 | BN_CTX_start(ctx); |
4d3fa06f AP |
982 | |
983 | if (scalar) { | |
984 | generator = EC_GROUP_get0_generator(group); | |
985 | if (generator == NULL) { | |
9311d0c4 | 986 | ERR_raise(ERR_LIB_EC, EC_R_UNDEFINED_GENERATOR); |
4d3fa06f AP |
987 | goto err; |
988 | } | |
989 | ||
990 | /* look if we can use precomputed multiples of generator */ | |
3aef36ff | 991 | pre_comp = group->pre_comp.nistz256; |
4d3fa06f AP |
992 | |
993 | if (pre_comp) { | |
20728adc AP |
994 | /* |
995 | * If there is a precomputed table for the generator, check that | |
996 | * it was generated with the same generator. | |
997 | */ | |
4d3fa06f AP |
998 | EC_POINT *pre_comp_generator = EC_POINT_new(group); |
999 | if (pre_comp_generator == NULL) | |
1000 | goto err; | |
1001 | ||
8fc4aeb9 | 1002 | ecp_nistz256_gather_w7(&p.a, pre_comp->precomp[0], 1); |
3ff08e1d | 1003 | if (!ecp_nistz256_set_from_affine(pre_comp_generator, |
8fc4aeb9 | 1004 | group, &p.a, ctx)) { |
e22d2199 | 1005 | EC_POINT_free(pre_comp_generator); |
4d3fa06f | 1006 | goto err; |
e22d2199 | 1007 | } |
4d3fa06f AP |
1008 | |
1009 | if (0 == EC_POINT_cmp(group, generator, pre_comp_generator, ctx)) | |
1010 | preComputedTable = (const PRECOMP256_ROW *)pre_comp->precomp; | |
1011 | ||
1012 | EC_POINT_free(pre_comp_generator); | |
1013 | } | |
1014 | ||
1015 | if (preComputedTable == NULL && ecp_nistz256_is_affine_G(generator)) { | |
20728adc AP |
1016 | /* |
1017 | * If there is no precomputed data, but the generator is the | |
1018 | * default, a hardcoded table of precomputed data is used. This | |
1019 | * is because applications, such as Apache, do not use | |
1020 | * EC_KEY_precompute_mult. | |
1021 | */ | |
3ff08e1d | 1022 | preComputedTable = ecp_nistz256_precomputed; |
4d3fa06f AP |
1023 | } |
1024 | ||
1025 | if (preComputedTable) { | |
00da0f69 NT |
1026 | BN_ULONG infty; |
1027 | ||
4d3fa06f AP |
1028 | if ((BN_num_bits(scalar) > 256) |
1029 | || BN_is_negative(scalar)) { | |
1030 | if ((tmp_scalar = BN_CTX_get(ctx)) == NULL) | |
1031 | goto err; | |
1032 | ||
5784a521 | 1033 | if (!BN_nnmod(tmp_scalar, scalar, group->order, ctx)) { |
9311d0c4 | 1034 | ERR_raise(ERR_LIB_EC, ERR_R_BN_LIB); |
4d3fa06f AP |
1035 | goto err; |
1036 | } | |
1037 | scalar = tmp_scalar; | |
1038 | } | |
1039 | ||
5784a521 MC |
1040 | for (i = 0; i < bn_get_top(scalar) * BN_BYTES; i += BN_BYTES) { |
1041 | BN_ULONG d = bn_get_words(scalar)[i / BN_BYTES]; | |
4d3fa06f | 1042 | |
5afc296a AP |
1043 | p_str[i + 0] = (unsigned char)d; |
1044 | p_str[i + 1] = (unsigned char)(d >> 8); | |
1045 | p_str[i + 2] = (unsigned char)(d >> 16); | |
1046 | p_str[i + 3] = (unsigned char)(d >>= 24); | |
4d3fa06f AP |
1047 | if (BN_BYTES == 8) { |
1048 | d >>= 8; | |
5afc296a AP |
1049 | p_str[i + 4] = (unsigned char)d; |
1050 | p_str[i + 5] = (unsigned char)(d >> 8); | |
1051 | p_str[i + 6] = (unsigned char)(d >> 16); | |
1052 | p_str[i + 7] = (unsigned char)(d >> 24); | |
4d3fa06f AP |
1053 | } |
1054 | } | |
1055 | ||
1056 | for (; i < 33; i++) | |
1057 | p_str[i] = 0; | |
1058 | ||
00da0f69 NT |
1059 | /* First window */ |
1060 | wvalue = (p_str[0] << 1) & mask; | |
1061 | idx += window_size; | |
e3057a57 | 1062 | |
00da0f69 | 1063 | wvalue = _booth_recode_w7(wvalue); |
4d3fa06f | 1064 | |
00da0f69 NT |
1065 | ecp_nistz256_gather_w7(&p.a, preComputedTable[0], |
1066 | wvalue >> 1); | |
4d3fa06f | 1067 | |
00da0f69 NT |
1068 | ecp_nistz256_neg(p.p.Z, p.p.Y); |
1069 | copy_conditional(p.p.Y, p.p.Z, wvalue & 1); | |
4d3fa06f | 1070 | |
00da0f69 NT |
1071 | /* |
1072 | * Since affine infinity is encoded as (0,0) and | |
1073 | * Jacobian is (,,0), we need to harmonize them | |
1074 | * by assigning "one" or zero to Z. | |
1075 | */ | |
1076 | infty = (p.p.X[0] | p.p.X[1] | p.p.X[2] | p.p.X[3] | | |
1077 | p.p.Y[0] | p.p.Y[1] | p.p.Y[2] | p.p.Y[3]); | |
1078 | if (P256_LIMBS == 8) | |
1079 | infty |= (p.p.X[4] | p.p.X[5] | p.p.X[6] | p.p.X[7] | | |
1080 | p.p.Y[4] | p.p.Y[5] | p.p.Y[6] | p.p.Y[7]); | |
1081 | ||
1082 | infty = 0 - is_zero(infty); | |
1083 | infty = ~infty; | |
1084 | ||
1085 | p.p.Z[0] = ONE[0] & infty; | |
1086 | p.p.Z[1] = ONE[1] & infty; | |
1087 | p.p.Z[2] = ONE[2] & infty; | |
1088 | p.p.Z[3] = ONE[3] & infty; | |
1089 | if (P256_LIMBS == 8) { | |
1090 | p.p.Z[4] = ONE[4] & infty; | |
1091 | p.p.Z[5] = ONE[5] & infty; | |
1092 | p.p.Z[6] = ONE[6] & infty; | |
1093 | p.p.Z[7] = ONE[7] & infty; | |
1094 | } | |
4d3fa06f | 1095 | |
00da0f69 NT |
1096 | for (i = 1; i < 37; i++) { |
1097 | unsigned int off = (idx - 1) / 8; | |
1098 | wvalue = p_str[off] | p_str[off + 1] << 8; | |
1099 | wvalue = (wvalue >> ((idx - 1) % 8)) & mask; | |
1100 | idx += window_size; | |
4d3fa06f | 1101 | |
00da0f69 | 1102 | wvalue = _booth_recode_w7(wvalue); |
4d3fa06f | 1103 | |
00da0f69 NT |
1104 | ecp_nistz256_gather_w7(&t.a, |
1105 | preComputedTable[i], wvalue >> 1); | |
4d3fa06f | 1106 | |
00da0f69 NT |
1107 | ecp_nistz256_neg(t.p.Z, t.a.Y); |
1108 | copy_conditional(t.a.Y, t.p.Z, wvalue & 1); | |
1109 | ||
1110 | ecp_nistz256_point_add_affine(&p.p, &p.p, &t.a); | |
4d3fa06f AP |
1111 | } |
1112 | } else { | |
1113 | p_is_infinity = 1; | |
1114 | no_precomp_for_generator = 1; | |
1115 | } | |
1116 | } else | |
1117 | p_is_infinity = 1; | |
1118 | ||
1119 | if (no_precomp_for_generator) { | |
20728adc AP |
1120 | /* |
1121 | * Without a precomputed table for the generator, it has to be | |
1122 | * handled like a normal point. | |
1123 | */ | |
4d3fa06f | 1124 | new_scalars = OPENSSL_malloc((num + 1) * sizeof(BIGNUM *)); |
90945fa3 | 1125 | if (new_scalars == NULL) { |
9311d0c4 | 1126 | ERR_raise(ERR_LIB_EC, ERR_R_MALLOC_FAILURE); |
e22d2199 | 1127 | goto err; |
4d3fa06f AP |
1128 | } |
1129 | ||
1130 | new_points = OPENSSL_malloc((num + 1) * sizeof(EC_POINT *)); | |
90945fa3 | 1131 | if (new_points == NULL) { |
9311d0c4 | 1132 | ERR_raise(ERR_LIB_EC, ERR_R_MALLOC_FAILURE); |
e22d2199 | 1133 | goto err; |
4d3fa06f AP |
1134 | } |
1135 | ||
1136 | memcpy(new_scalars, scalars, num * sizeof(BIGNUM *)); | |
1137 | new_scalars[num] = scalar; | |
1138 | memcpy(new_points, points, num * sizeof(EC_POINT *)); | |
1139 | new_points[num] = generator; | |
1140 | ||
1141 | scalars = new_scalars; | |
1142 | points = new_points; | |
1143 | num++; | |
1144 | } | |
1145 | ||
1146 | if (num) { | |
1147 | P256_POINT *out = &t.p; | |
1148 | if (p_is_infinity) | |
1149 | out = &p.p; | |
1150 | ||
a4d5269e EK |
1151 | if (!ecp_nistz256_windowed_mul(group, out, scalars, points, num, ctx)) |
1152 | goto err; | |
4d3fa06f AP |
1153 | |
1154 | if (!p_is_infinity) | |
1155 | ecp_nistz256_point_add(&p.p, &p.p, out); | |
1156 | } | |
1157 | ||
c028254b | 1158 | /* Not constant-time, but we're only operating on the public output. */ |
e22d2199 EK |
1159 | if (!bn_set_words(r->X, p.p.X, P256_LIMBS) || |
1160 | !bn_set_words(r->Y, p.p.Y, P256_LIMBS) || | |
1161 | !bn_set_words(r->Z, p.p.Z, P256_LIMBS)) { | |
1162 | goto err; | |
1163 | } | |
2e929e53 | 1164 | r->Z_is_one = is_one(r->Z) & 1; |
4d3fa06f AP |
1165 | |
1166 | ret = 1; | |
1167 | ||
e22d2199 | 1168 | err: |
7b953da4 | 1169 | BN_CTX_end(ctx); |
b548a1f1 RS |
1170 | OPENSSL_free(new_points); |
1171 | OPENSSL_free(new_scalars); | |
4d3fa06f AP |
1172 | return ret; |
1173 | } | |
1174 | ||
5956b110 EK |
1175 | __owur static int ecp_nistz256_get_affine(const EC_GROUP *group, |
1176 | const EC_POINT *point, | |
1177 | BIGNUM *x, BIGNUM *y, BN_CTX *ctx) | |
4d3fa06f AP |
1178 | { |
1179 | BN_ULONG z_inv2[P256_LIMBS]; | |
1180 | BN_ULONG z_inv3[P256_LIMBS]; | |
1181 | BN_ULONG x_aff[P256_LIMBS]; | |
1182 | BN_ULONG y_aff[P256_LIMBS]; | |
1183 | BN_ULONG point_x[P256_LIMBS], point_y[P256_LIMBS], point_z[P256_LIMBS]; | |
e22d2199 | 1184 | BN_ULONG x_ret[P256_LIMBS], y_ret[P256_LIMBS]; |
4d3fa06f AP |
1185 | |
1186 | if (EC_POINT_is_at_infinity(group, point)) { | |
9311d0c4 | 1187 | ERR_raise(ERR_LIB_EC, EC_R_POINT_AT_INFINITY); |
4d3fa06f AP |
1188 | return 0; |
1189 | } | |
1190 | ||
5784a521 MC |
1191 | if (!ecp_nistz256_bignum_to_field_elem(point_x, point->X) || |
1192 | !ecp_nistz256_bignum_to_field_elem(point_y, point->Y) || | |
1193 | !ecp_nistz256_bignum_to_field_elem(point_z, point->Z)) { | |
9311d0c4 | 1194 | ERR_raise(ERR_LIB_EC, EC_R_COORDINATES_OUT_OF_RANGE); |
4d3fa06f AP |
1195 | return 0; |
1196 | } | |
1197 | ||
1198 | ecp_nistz256_mod_inverse(z_inv3, point_z); | |
1199 | ecp_nistz256_sqr_mont(z_inv2, z_inv3); | |
1200 | ecp_nistz256_mul_mont(x_aff, z_inv2, point_x); | |
1201 | ||
1202 | if (x != NULL) { | |
e22d2199 EK |
1203 | ecp_nistz256_from_mont(x_ret, x_aff); |
1204 | if (!bn_set_words(x, x_ret, P256_LIMBS)) | |
1205 | return 0; | |
4d3fa06f AP |
1206 | } |
1207 | ||
1208 | if (y != NULL) { | |
1209 | ecp_nistz256_mul_mont(z_inv3, z_inv3, z_inv2); | |
1210 | ecp_nistz256_mul_mont(y_aff, z_inv3, point_y); | |
e22d2199 EK |
1211 | ecp_nistz256_from_mont(y_ret, y_aff); |
1212 | if (!bn_set_words(y, y_ret, P256_LIMBS)) | |
1213 | return 0; | |
4d3fa06f AP |
1214 | } |
1215 | ||
1216 | return 1; | |
1217 | } | |
1218 | ||
3aef36ff | 1219 | static NISTZ256_PRE_COMP *ecp_nistz256_pre_comp_new(const EC_GROUP *group) |
4d3fa06f | 1220 | { |
3aef36ff | 1221 | NISTZ256_PRE_COMP *ret = NULL; |
4d3fa06f AP |
1222 | |
1223 | if (!group) | |
1224 | return NULL; | |
1225 | ||
3aef36ff | 1226 | ret = OPENSSL_zalloc(sizeof(*ret)); |
4d3fa06f | 1227 | |
90945fa3 | 1228 | if (ret == NULL) { |
9311d0c4 | 1229 | ERR_raise(ERR_LIB_EC, ERR_R_MALLOC_FAILURE); |
4d3fa06f AP |
1230 | return ret; |
1231 | } | |
1232 | ||
1233 | ret->group = group; | |
1234 | ret->w = 6; /* default */ | |
4d3fa06f | 1235 | ret->references = 1; |
9b398ef2 AG |
1236 | |
1237 | ret->lock = CRYPTO_THREAD_lock_new(); | |
1238 | if (ret->lock == NULL) { | |
9311d0c4 | 1239 | ERR_raise(ERR_LIB_EC, ERR_R_MALLOC_FAILURE); |
9b398ef2 AG |
1240 | OPENSSL_free(ret); |
1241 | return NULL; | |
1242 | } | |
4d3fa06f AP |
1243 | return ret; |
1244 | } | |
1245 | ||
3aef36ff | 1246 | NISTZ256_PRE_COMP *EC_nistz256_pre_comp_dup(NISTZ256_PRE_COMP *p) |
4d3fa06f | 1247 | { |
9b398ef2 | 1248 | int i; |
3aef36ff | 1249 | if (p != NULL) |
2f545ae4 | 1250 | CRYPTO_UP_REF(&p->references, &i, p->lock); |
3aef36ff | 1251 | return p; |
4d3fa06f AP |
1252 | } |
1253 | ||
3aef36ff | 1254 | void EC_nistz256_pre_comp_free(NISTZ256_PRE_COMP *pre) |
4d3fa06f | 1255 | { |
9b398ef2 AG |
1256 | int i; |
1257 | ||
1258 | if (pre == NULL) | |
4d3fa06f | 1259 | return; |
9b398ef2 | 1260 | |
2f545ae4 | 1261 | CRYPTO_DOWN_REF(&pre->references, &i, pre->lock); |
e26f653d | 1262 | REF_PRINT_COUNT("EC_nistz256", pre); |
9b398ef2 AG |
1263 | if (i > 0) |
1264 | return; | |
1265 | REF_ASSERT_ISNT(i < 0); | |
1266 | ||
b548a1f1 | 1267 | OPENSSL_free(pre->precomp_storage); |
9b398ef2 | 1268 | CRYPTO_THREAD_lock_free(pre->lock); |
4d3fa06f AP |
1269 | OPENSSL_free(pre); |
1270 | } | |
1271 | ||
4d3fa06f | 1272 | |
58d47cf0 | 1273 | static int ecp_nistz256_window_have_precompute_mult(const EC_GROUP *group) |
4d3fa06f AP |
1274 | { |
1275 | /* There is a hard-coded table for the default generator. */ | |
1276 | const EC_POINT *generator = EC_GROUP_get0_generator(group); | |
3aef36ff | 1277 | |
4d3fa06f AP |
1278 | if (generator != NULL && ecp_nistz256_is_affine_G(generator)) { |
1279 | /* There is a hard-coded table for the default generator. */ | |
1280 | return 1; | |
1281 | } | |
1282 | ||
3aef36ff | 1283 | return HAVEPRECOMP(group, nistz256); |
4d3fa06f AP |
1284 | } |
1285 | ||
eb791696 AP |
1286 | #if defined(__x86_64) || defined(__x86_64__) || \ |
1287 | defined(_M_AMD64) || defined(_M_X64) || \ | |
ab4f2026 AP |
1288 | defined(__powerpc64__) || defined(_ARCH_PP64) || \ |
1289 | defined(__aarch64__) | |
eb791696 AP |
1290 | /* |
1291 | * Montgomery mul modulo Order(P): res = a*b*2^-256 mod Order(P) | |
1292 | */ | |
1293 | void ecp_nistz256_ord_mul_mont(BN_ULONG res[P256_LIMBS], | |
1294 | const BN_ULONG a[P256_LIMBS], | |
1295 | const BN_ULONG b[P256_LIMBS]); | |
1296 | void ecp_nistz256_ord_sqr_mont(BN_ULONG res[P256_LIMBS], | |
1297 | const BN_ULONG a[P256_LIMBS], | |
15972296 | 1298 | BN_ULONG rep); |
eb791696 AP |
1299 | |
1300 | static int ecp_nistz256_inv_mod_ord(const EC_GROUP *group, BIGNUM *r, | |
792546eb | 1301 | const BIGNUM *x, BN_CTX *ctx) |
eb791696 AP |
1302 | { |
1303 | /* RR = 2^512 mod ord(p256) */ | |
10bc3409 AP |
1304 | static const BN_ULONG RR[P256_LIMBS] = { |
1305 | TOBN(0x83244c95,0xbe79eea2), TOBN(0x4699799c,0x49bd6fa6), | |
1306 | TOBN(0x2845b239,0x2b6bec59), TOBN(0x66e12d94,0xf3d95620) | |
1307 | }; | |
eb791696 | 1308 | /* The constant 1 (unlike ONE that is one in Montgomery representation) */ |
10bc3409 AP |
1309 | static const BN_ULONG one[P256_LIMBS] = { |
1310 | TOBN(0,1), TOBN(0,0), TOBN(0,0), TOBN(0,0) | |
1311 | }; | |
eb791696 AP |
1312 | /* |
1313 | * We don't use entry 0 in the table, so we omit it and address | |
1314 | * with -1 offset. | |
1315 | */ | |
1316 | BN_ULONG table[15][P256_LIMBS]; | |
1317 | BN_ULONG out[P256_LIMBS], t[P256_LIMBS]; | |
1318 | int i, ret = 0; | |
8e403a79 TS |
1319 | enum { |
1320 | i_1 = 0, i_10, i_11, i_101, i_111, i_1010, i_1111, | |
1321 | i_10101, i_101010, i_101111, i_x6, i_x8, i_x16, i_x32 | |
1322 | }; | |
eb791696 AP |
1323 | |
1324 | /* | |
1325 | * Catch allocation failure early. | |
1326 | */ | |
1327 | if (bn_wexpand(r, P256_LIMBS) == NULL) { | |
9311d0c4 | 1328 | ERR_raise(ERR_LIB_EC, ERR_R_BN_LIB); |
eb791696 AP |
1329 | goto err; |
1330 | } | |
1331 | ||
1332 | if ((BN_num_bits(x) > 256) || BN_is_negative(x)) { | |
1333 | BIGNUM *tmp; | |
1334 | ||
1335 | if ((tmp = BN_CTX_get(ctx)) == NULL | |
1336 | || !BN_nnmod(tmp, x, group->order, ctx)) { | |
9311d0c4 | 1337 | ERR_raise(ERR_LIB_EC, ERR_R_BN_LIB); |
eb791696 AP |
1338 | goto err; |
1339 | } | |
1340 | x = tmp; | |
1341 | } | |
1342 | ||
1343 | if (!ecp_nistz256_bignum_to_field_elem(t, x)) { | |
9311d0c4 | 1344 | ERR_raise(ERR_LIB_EC, EC_R_COORDINATES_OUT_OF_RANGE); |
eb791696 AP |
1345 | goto err; |
1346 | } | |
1347 | ||
1348 | ecp_nistz256_ord_mul_mont(table[0], t, RR); | |
10bc3409 AP |
1349 | #if 0 |
1350 | /* | |
1351 | * Original sparse-then-fixed-window algorithm, retained for reference. | |
1352 | */ | |
eb791696 AP |
1353 | for (i = 2; i < 16; i += 2) { |
1354 | ecp_nistz256_ord_sqr_mont(table[i-1], table[i/2-1], 1); | |
1355 | ecp_nistz256_ord_mul_mont(table[i], table[i-1], table[0]); | |
1356 | } | |
1357 | ||
1358 | /* | |
1359 | * The top 128bit of the exponent are highly redudndant, so we | |
1360 | * perform an optimized flow | |
1361 | */ | |
1362 | ecp_nistz256_ord_sqr_mont(t, table[15-1], 4); /* f0 */ | |
1363 | ecp_nistz256_ord_mul_mont(t, t, table[15-1]); /* ff */ | |
1364 | ||
1365 | ecp_nistz256_ord_sqr_mont(out, t, 8); /* ff00 */ | |
1366 | ecp_nistz256_ord_mul_mont(out, out, t); /* ffff */ | |
1367 | ||
1368 | ecp_nistz256_ord_sqr_mont(t, out, 16); /* ffff0000 */ | |
1369 | ecp_nistz256_ord_mul_mont(t, t, out); /* ffffffff */ | |
1370 | ||
1371 | ecp_nistz256_ord_sqr_mont(out, t, 64); /* ffffffff0000000000000000 */ | |
1372 | ecp_nistz256_ord_mul_mont(out, out, t); /* ffffffff00000000ffffffff */ | |
1373 | ||
1374 | ecp_nistz256_ord_sqr_mont(out, out, 32); /* ffffffff00000000ffffffff00000000 */ | |
1375 | ecp_nistz256_ord_mul_mont(out, out, t); /* ffffffff00000000ffffffffffffffff */ | |
1376 | ||
1377 | /* | |
10bc3409 | 1378 | * The bottom 128 bit of the exponent are processed with fixed 4-bit window |
eb791696 AP |
1379 | */ |
1380 | for(i = 0; i < 32; i++) { | |
10bc3409 AP |
1381 | /* expLo - the low 128 bits of the exponent we use (ord(p256) - 2), |
1382 | * split into nibbles */ | |
1383 | static const unsigned char expLo[32] = { | |
1384 | 0xb,0xc,0xe,0x6,0xf,0xa,0xa,0xd,0xa,0x7,0x1,0x7,0x9,0xe,0x8,0x4, | |
1385 | 0xf,0x3,0xb,0x9,0xc,0xa,0xc,0x2,0xf,0xc,0x6,0x3,0x2,0x5,0x4,0xf | |
1386 | }; | |
1387 | ||
eb791696 AP |
1388 | ecp_nistz256_ord_sqr_mont(out, out, 4); |
1389 | /* The exponent is public, no need in constant-time access */ | |
1390 | ecp_nistz256_ord_mul_mont(out, out, table[expLo[i]-1]); | |
1391 | } | |
10bc3409 AP |
1392 | #else |
1393 | /* | |
1394 | * https://briansmith.org/ecc-inversion-addition-chains-01#p256_scalar_inversion | |
1395 | * | |
1396 | * Even though this code path spares 12 squarings, 4.5%, and 13 | |
1397 | * multiplications, 25%, on grand scale sign operation is not that | |
1398 | * much faster, not more that 2%... | |
1399 | */ | |
10bc3409 AP |
1400 | |
1401 | /* pre-calculate powers */ | |
1402 | ecp_nistz256_ord_sqr_mont(table[i_10], table[i_1], 1); | |
1403 | ||
1404 | ecp_nistz256_ord_mul_mont(table[i_11], table[i_1], table[i_10]); | |
1405 | ||
1406 | ecp_nistz256_ord_mul_mont(table[i_101], table[i_11], table[i_10]); | |
1407 | ||
1408 | ecp_nistz256_ord_mul_mont(table[i_111], table[i_101], table[i_10]); | |
1409 | ||
1410 | ecp_nistz256_ord_sqr_mont(table[i_1010], table[i_101], 1); | |
1411 | ||
1412 | ecp_nistz256_ord_mul_mont(table[i_1111], table[i_1010], table[i_101]); | |
1413 | ||
1414 | ecp_nistz256_ord_sqr_mont(table[i_10101], table[i_1010], 1); | |
1415 | ecp_nistz256_ord_mul_mont(table[i_10101], table[i_10101], table[i_1]); | |
1416 | ||
1417 | ecp_nistz256_ord_sqr_mont(table[i_101010], table[i_10101], 1); | |
1418 | ||
1419 | ecp_nistz256_ord_mul_mont(table[i_101111], table[i_101010], table[i_101]); | |
1420 | ||
1421 | ecp_nistz256_ord_mul_mont(table[i_x6], table[i_101010], table[i_10101]); | |
1422 | ||
1423 | ecp_nistz256_ord_sqr_mont(table[i_x8], table[i_x6], 2); | |
1424 | ecp_nistz256_ord_mul_mont(table[i_x8], table[i_x8], table[i_11]); | |
1425 | ||
1426 | ecp_nistz256_ord_sqr_mont(table[i_x16], table[i_x8], 8); | |
1427 | ecp_nistz256_ord_mul_mont(table[i_x16], table[i_x16], table[i_x8]); | |
1428 | ||
1429 | ecp_nistz256_ord_sqr_mont(table[i_x32], table[i_x16], 16); | |
1430 | ecp_nistz256_ord_mul_mont(table[i_x32], table[i_x32], table[i_x16]); | |
1431 | ||
1432 | /* calculations */ | |
1433 | ecp_nistz256_ord_sqr_mont(out, table[i_x32], 64); | |
1434 | ecp_nistz256_ord_mul_mont(out, out, table[i_x32]); | |
1435 | ||
1436 | for (i = 0; i < 27; i++) { | |
1437 | static const struct { unsigned char p, i; } chain[27] = { | |
1438 | { 32, i_x32 }, { 6, i_101111 }, { 5, i_111 }, | |
1439 | { 4, i_11 }, { 5, i_1111 }, { 5, i_10101 }, | |
1440 | { 4, i_101 }, { 3, i_101 }, { 3, i_101 }, | |
1441 | { 5, i_111 }, { 9, i_101111 }, { 6, i_1111 }, | |
1442 | { 2, i_1 }, { 5, i_1 }, { 6, i_1111 }, | |
1443 | { 5, i_111 }, { 4, i_111 }, { 5, i_111 }, | |
1444 | { 5, i_101 }, { 3, i_11 }, { 10, i_101111 }, | |
1445 | { 2, i_11 }, { 5, i_11 }, { 5, i_11 }, | |
1446 | { 3, i_1 }, { 7, i_10101 }, { 6, i_1111 } | |
1447 | }; | |
1448 | ||
1449 | ecp_nistz256_ord_sqr_mont(out, out, chain[i].p); | |
1450 | ecp_nistz256_ord_mul_mont(out, out, table[chain[i].i]); | |
1451 | } | |
1452 | #endif | |
eb791696 AP |
1453 | ecp_nistz256_ord_mul_mont(out, out, one); |
1454 | ||
1455 | /* | |
1456 | * Can't fail, but check return code to be consistent anyway. | |
1457 | */ | |
1458 | if (!bn_set_words(r, out, P256_LIMBS)) | |
1459 | goto err; | |
1460 | ||
1461 | ret = 1; | |
1462 | err: | |
1463 | return ret; | |
1464 | } | |
1465 | #else | |
1466 | # define ecp_nistz256_inv_mod_ord NULL | |
1467 | #endif | |
1468 | ||
4d3fa06f AP |
1469 | const EC_METHOD *EC_GFp_nistz256_method(void) |
1470 | { | |
1471 | static const EC_METHOD ret = { | |
1472 | EC_FLAGS_DEFAULT_OCT, | |
1473 | NID_X9_62_prime_field, | |
32ab57cb SL |
1474 | ossl_ec_GFp_mont_group_init, |
1475 | ossl_ec_GFp_mont_group_finish, | |
1476 | ossl_ec_GFp_mont_group_clear_finish, | |
1477 | ossl_ec_GFp_mont_group_copy, | |
1478 | ossl_ec_GFp_mont_group_set_curve, | |
1479 | ossl_ec_GFp_simple_group_get_curve, | |
1480 | ossl_ec_GFp_simple_group_get_degree, | |
1481 | ossl_ec_group_simple_order_bits, | |
1482 | ossl_ec_GFp_simple_group_check_discriminant, | |
1483 | ossl_ec_GFp_simple_point_init, | |
1484 | ossl_ec_GFp_simple_point_finish, | |
1485 | ossl_ec_GFp_simple_point_clear_finish, | |
1486 | ossl_ec_GFp_simple_point_copy, | |
1487 | ossl_ec_GFp_simple_point_set_to_infinity, | |
1488 | ossl_ec_GFp_simple_point_set_affine_coordinates, | |
4d3fa06f AP |
1489 | ecp_nistz256_get_affine, |
1490 | 0, 0, 0, | |
32ab57cb SL |
1491 | ossl_ec_GFp_simple_add, |
1492 | ossl_ec_GFp_simple_dbl, | |
1493 | ossl_ec_GFp_simple_invert, | |
1494 | ossl_ec_GFp_simple_is_at_infinity, | |
1495 | ossl_ec_GFp_simple_is_on_curve, | |
1496 | ossl_ec_GFp_simple_cmp, | |
1497 | ossl_ec_GFp_simple_make_affine, | |
1498 | ossl_ec_GFp_simple_points_make_affine, | |
4d3fa06f AP |
1499 | ecp_nistz256_points_mul, /* mul */ |
1500 | ecp_nistz256_mult_precompute, /* precompute_mult */ | |
1501 | ecp_nistz256_window_have_precompute_mult, /* have_precompute_mult */ | |
32ab57cb SL |
1502 | ossl_ec_GFp_mont_field_mul, |
1503 | ossl_ec_GFp_mont_field_sqr, | |
4d3fa06f | 1504 | 0, /* field_div */ |
32ab57cb SL |
1505 | ossl_ec_GFp_mont_field_inv, |
1506 | ossl_ec_GFp_mont_field_encode, | |
1507 | ossl_ec_GFp_mont_field_decode, | |
1508 | ossl_ec_GFp_mont_field_set_to_one, | |
1509 | ossl_ec_key_simple_priv2oct, | |
1510 | ossl_ec_key_simple_oct2priv, | |
9ff9bccc | 1511 | 0, /* set private */ |
32ab57cb SL |
1512 | ossl_ec_key_simple_generate_key, |
1513 | ossl_ec_key_simple_check_key, | |
1514 | ossl_ec_key_simple_generate_public_key, | |
9ff9bccc DSH |
1515 | 0, /* keycopy */ |
1516 | 0, /* keyfinish */ | |
32ab57cb SL |
1517 | ossl_ecdh_simple_compute_key, |
1518 | ossl_ecdsa_simple_sign_setup, | |
1519 | ossl_ecdsa_simple_sign_sig, | |
1520 | ossl_ecdsa_simple_verify_sig, | |
f667820c | 1521 | ecp_nistz256_inv_mod_ord, /* can be #define-d NULL */ |
37124360 NT |
1522 | 0, /* blind_coordinates */ |
1523 | 0, /* ladder_pre */ | |
1524 | 0, /* ladder_step */ | |
1525 | 0 /* ladder_post */ | |
4d3fa06f AP |
1526 | }; |
1527 | ||
1528 | return &ret; | |
1529 | } |