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