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Call single parent free_comp routine.
[thirdparty/openssl.git] / crypto / ec / ecp_nistz256.c
1 /******************************************************************************
2 * *
3 * Copyright 2014 Intel Corporation *
4 * *
5 * Licensed under the Apache License, Version 2.0 (the "License"); *
6 * you may not use this file except in compliance with the License. *
7 * You may obtain a copy of the License at *
8 * *
9 * http://www.apache.org/licenses/LICENSE-2.0 *
10 * *
11 * Unless required by applicable law or agreed to in writing, software *
12 * distributed under the License is distributed on an "AS IS" BASIS, *
13 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. *
14 * See the License for the specific language governing permissions and *
15 * limitations under the License. *
16 * *
17 ******************************************************************************
18 * *
19 * Developers and authors: *
20 * Shay Gueron (1, 2), and Vlad Krasnov (1) *
21 * (1) Intel Corporation, Israel Development Center *
22 * (2) University of Haifa *
23 * Reference: *
24 * S.Gueron and V.Krasnov, "Fast Prime Field Elliptic Curve Cryptography with *
25 * 256 Bit Primes" *
26 * *
27 ******************************************************************************/
28
29 #include <string.h>
30
31 #include "internal/cryptlib.h"
32 #include "internal/bn_int.h"
33 #include "ec_lcl.h"
34
35 #if BN_BITS2 != 64
36 # define TOBN(hi,lo) lo,hi
37 #else
38 # define TOBN(hi,lo) ((BN_ULONG)hi<<32|lo)
39 #endif
40
41 #if defined(__GNUC__)
42 # define ALIGN32 __attribute((aligned(32)))
43 #elif defined(_MSC_VER)
44 # define ALIGN32 __declspec(align(32))
45 #else
46 # define ALIGN32
47 #endif
48
49 #define ALIGNPTR(p,N) ((unsigned char *)p+N-(size_t)p%N)
50 #define P256_LIMBS (256/BN_BITS2)
51
52 typedef unsigned short u16;
53
54 typedef struct {
55 BN_ULONG X[P256_LIMBS];
56 BN_ULONG Y[P256_LIMBS];
57 BN_ULONG Z[P256_LIMBS];
58 } P256_POINT;
59
60 typedef struct {
61 BN_ULONG X[P256_LIMBS];
62 BN_ULONG Y[P256_LIMBS];
63 } P256_POINT_AFFINE;
64
65 typedef P256_POINT_AFFINE PRECOMP256_ROW[64];
66
67 /* structure for precomputed multiples of the generator */
68 struct nistz256_pre_comp_st {
69 const EC_GROUP *group; /* Parent EC_GROUP object */
70 size_t w; /* Window size */
71 /*
72 * Constant time access to the X and Y coordinates of the pre-computed,
73 * generator multiplies, in the Montgomery domain. Pre-calculated
74 * multiplies are stored in affine form.
75 */
76 PRECOMP256_ROW *precomp;
77 void *precomp_storage;
78 int references;
79 };
80
81 /* Functions implemented in assembly */
82 /* Modular mul by 2: res = 2*a mod P */
83 void ecp_nistz256_mul_by_2(BN_ULONG res[P256_LIMBS],
84 const BN_ULONG a[P256_LIMBS]);
85 /* Modular div by 2: res = a/2 mod P */
86 void ecp_nistz256_div_by_2(BN_ULONG res[P256_LIMBS],
87 const BN_ULONG a[P256_LIMBS]);
88 /* Modular mul by 3: res = 3*a mod P */
89 void ecp_nistz256_mul_by_3(BN_ULONG res[P256_LIMBS],
90 const BN_ULONG a[P256_LIMBS]);
91 /* Modular add: res = a+b mod P */
92 void ecp_nistz256_add(BN_ULONG res[P256_LIMBS],
93 const BN_ULONG a[P256_LIMBS],
94 const BN_ULONG b[P256_LIMBS]);
95 /* Modular sub: res = a-b mod P */
96 void ecp_nistz256_sub(BN_ULONG res[P256_LIMBS],
97 const BN_ULONG a[P256_LIMBS],
98 const BN_ULONG b[P256_LIMBS]);
99 /* Modular neg: res = -a mod P */
100 void ecp_nistz256_neg(BN_ULONG res[P256_LIMBS], const BN_ULONG a[P256_LIMBS]);
101 /* Montgomery mul: res = a*b*2^-256 mod P */
102 void ecp_nistz256_mul_mont(BN_ULONG res[P256_LIMBS],
103 const BN_ULONG a[P256_LIMBS],
104 const BN_ULONG b[P256_LIMBS]);
105 /* Montgomery sqr: res = a*a*2^-256 mod P */
106 void ecp_nistz256_sqr_mont(BN_ULONG res[P256_LIMBS],
107 const BN_ULONG a[P256_LIMBS]);
108 /* Convert a number from Montgomery domain, by multiplying with 1 */
109 void ecp_nistz256_from_mont(BN_ULONG res[P256_LIMBS],
110 const BN_ULONG in[P256_LIMBS]);
111 /* Convert a number to Montgomery domain, by multiplying with 2^512 mod P*/
112 void ecp_nistz256_to_mont(BN_ULONG res[P256_LIMBS],
113 const BN_ULONG in[P256_LIMBS]);
114 /* Functions that perform constant time access to the precomputed tables */
115 void ecp_nistz256_scatter_w5(P256_POINT *val,
116 const P256_POINT *in_t, int idx);
117 void ecp_nistz256_gather_w5(P256_POINT *val,
118 const P256_POINT *in_t, int idx);
119 void ecp_nistz256_scatter_w7(P256_POINT_AFFINE *val,
120 const P256_POINT_AFFINE *in_t, int idx);
121 void ecp_nistz256_gather_w7(P256_POINT_AFFINE *val,
122 const P256_POINT_AFFINE *in_t, int idx);
123
124 /* One converted into the Montgomery domain */
125 static const BN_ULONG ONE[P256_LIMBS] = {
126 TOBN(0x00000000, 0x00000001), TOBN(0xffffffff, 0x00000000),
127 TOBN(0xffffffff, 0xffffffff), TOBN(0x00000000, 0xfffffffe)
128 };
129
130 static NISTZ256_PRE_COMP *ecp_nistz256_pre_comp_new(const EC_GROUP *group);
131
132 /* Precomputed tables for the default generator */
133 extern const PRECOMP256_ROW ecp_nistz256_precomputed[37];
134
135 /* Recode window to a signed digit, see ecp_nistputil.c for details */
136 static unsigned int _booth_recode_w5(unsigned int in)
137 {
138 unsigned int s, d;
139
140 s = ~((in >> 5) - 1);
141 d = (1 << 6) - in - 1;
142 d = (d & s) | (in & ~s);
143 d = (d >> 1) + (d & 1);
144
145 return (d << 1) + (s & 1);
146 }
147
148 static unsigned int _booth_recode_w7(unsigned int in)
149 {
150 unsigned int s, d;
151
152 s = ~((in >> 7) - 1);
153 d = (1 << 8) - in - 1;
154 d = (d & s) | (in & ~s);
155 d = (d >> 1) + (d & 1);
156
157 return (d << 1) + (s & 1);
158 }
159
160 static void copy_conditional(BN_ULONG dst[P256_LIMBS],
161 const BN_ULONG src[P256_LIMBS], BN_ULONG move)
162 {
163 BN_ULONG mask1 = 0-move;
164 BN_ULONG mask2 = ~mask1;
165
166 dst[0] = (src[0] & mask1) ^ (dst[0] & mask2);
167 dst[1] = (src[1] & mask1) ^ (dst[1] & mask2);
168 dst[2] = (src[2] & mask1) ^ (dst[2] & mask2);
169 dst[3] = (src[3] & mask1) ^ (dst[3] & mask2);
170 if (P256_LIMBS == 8) {
171 dst[4] = (src[4] & mask1) ^ (dst[4] & mask2);
172 dst[5] = (src[5] & mask1) ^ (dst[5] & mask2);
173 dst[6] = (src[6] & mask1) ^ (dst[6] & mask2);
174 dst[7] = (src[7] & mask1) ^ (dst[7] & mask2);
175 }
176 }
177
178 static BN_ULONG is_zero(BN_ULONG in)
179 {
180 in |= (0 - in);
181 in = ~in;
182 in &= BN_MASK2;
183 in >>= BN_BITS2 - 1;
184 return in;
185 }
186
187 static BN_ULONG is_equal(const BN_ULONG a[P256_LIMBS],
188 const BN_ULONG b[P256_LIMBS])
189 {
190 BN_ULONG res;
191
192 res = a[0] ^ b[0];
193 res |= a[1] ^ b[1];
194 res |= a[2] ^ b[2];
195 res |= a[3] ^ b[3];
196 if (P256_LIMBS == 8) {
197 res |= a[4] ^ b[4];
198 res |= a[5] ^ b[5];
199 res |= a[6] ^ b[6];
200 res |= a[7] ^ b[7];
201 }
202
203 return is_zero(res);
204 }
205
206 static BN_ULONG is_one(const BN_ULONG a[P256_LIMBS])
207 {
208 BN_ULONG res;
209
210 res = a[0] ^ ONE[0];
211 res |= a[1] ^ ONE[1];
212 res |= a[2] ^ ONE[2];
213 res |= a[3] ^ ONE[3];
214 if (P256_LIMBS == 8) {
215 res |= a[4] ^ ONE[4];
216 res |= a[5] ^ ONE[5];
217 res |= a[6] ^ ONE[6];
218 }
219
220 return is_zero(res);
221 }
222
223 #ifndef ECP_NISTZ256_REFERENCE_IMPLEMENTATION
224 void ecp_nistz256_point_double(P256_POINT *r, const P256_POINT *a);
225 void ecp_nistz256_point_add(P256_POINT *r,
226 const P256_POINT *a, const P256_POINT *b);
227 void ecp_nistz256_point_add_affine(P256_POINT *r,
228 const P256_POINT *a,
229 const P256_POINT_AFFINE *b);
230 #else
231 /* Point double: r = 2*a */
232 static void ecp_nistz256_point_double(P256_POINT *r, const P256_POINT *a)
233 {
234 BN_ULONG S[P256_LIMBS];
235 BN_ULONG M[P256_LIMBS];
236 BN_ULONG Zsqr[P256_LIMBS];
237 BN_ULONG tmp0[P256_LIMBS];
238
239 const BN_ULONG *in_x = a->X;
240 const BN_ULONG *in_y = a->Y;
241 const BN_ULONG *in_z = a->Z;
242
243 BN_ULONG *res_x = r->X;
244 BN_ULONG *res_y = r->Y;
245 BN_ULONG *res_z = r->Z;
246
247 ecp_nistz256_mul_by_2(S, in_y);
248
249 ecp_nistz256_sqr_mont(Zsqr, in_z);
250
251 ecp_nistz256_sqr_mont(S, S);
252
253 ecp_nistz256_mul_mont(res_z, in_z, in_y);
254 ecp_nistz256_mul_by_2(res_z, res_z);
255
256 ecp_nistz256_add(M, in_x, Zsqr);
257 ecp_nistz256_sub(Zsqr, in_x, Zsqr);
258
259 ecp_nistz256_sqr_mont(res_y, S);
260 ecp_nistz256_div_by_2(res_y, res_y);
261
262 ecp_nistz256_mul_mont(M, M, Zsqr);
263 ecp_nistz256_mul_by_3(M, M);
264
265 ecp_nistz256_mul_mont(S, S, in_x);
266 ecp_nistz256_mul_by_2(tmp0, S);
267
268 ecp_nistz256_sqr_mont(res_x, M);
269
270 ecp_nistz256_sub(res_x, res_x, tmp0);
271 ecp_nistz256_sub(S, S, res_x);
272
273 ecp_nistz256_mul_mont(S, S, M);
274 ecp_nistz256_sub(res_y, S, res_y);
275 }
276
277 /* Point addition: r = a+b */
278 static void ecp_nistz256_point_add(P256_POINT *r,
279 const P256_POINT *a, const P256_POINT *b)
280 {
281 BN_ULONG U2[P256_LIMBS], S2[P256_LIMBS];
282 BN_ULONG U1[P256_LIMBS], S1[P256_LIMBS];
283 BN_ULONG Z1sqr[P256_LIMBS];
284 BN_ULONG Z2sqr[P256_LIMBS];
285 BN_ULONG H[P256_LIMBS], R[P256_LIMBS];
286 BN_ULONG Hsqr[P256_LIMBS];
287 BN_ULONG Rsqr[P256_LIMBS];
288 BN_ULONG Hcub[P256_LIMBS];
289
290 BN_ULONG res_x[P256_LIMBS];
291 BN_ULONG res_y[P256_LIMBS];
292 BN_ULONG res_z[P256_LIMBS];
293
294 BN_ULONG in1infty, in2infty;
295
296 const BN_ULONG *in1_x = a->X;
297 const BN_ULONG *in1_y = a->Y;
298 const BN_ULONG *in1_z = a->Z;
299
300 const BN_ULONG *in2_x = b->X;
301 const BN_ULONG *in2_y = b->Y;
302 const BN_ULONG *in2_z = b->Z;
303
304 /* We encode infinity as (0,0), which is not on the curve,
305 * so it is OK. */
306 in1infty = (in1_x[0] | in1_x[1] | in1_x[2] | in1_x[3] |
307 in1_y[0] | in1_y[1] | in1_y[2] | in1_y[3]);
308 if (P256_LIMBS == 8)
309 in1infty |= (in1_x[4] | in1_x[5] | in1_x[6] | in1_x[7] |
310 in1_y[4] | in1_y[5] | in1_y[6] | in1_y[7]);
311
312 in2infty = (in2_x[0] | in2_x[1] | in2_x[2] | in2_x[3] |
313 in2_y[0] | in2_y[1] | in2_y[2] | in2_y[3]);
314 if (P256_LIMBS == 8)
315 in2infty |= (in2_x[4] | in2_x[5] | in2_x[6] | in2_x[7] |
316 in2_y[4] | in2_y[5] | in2_y[6] | in2_y[7]);
317
318 in1infty = is_zero(in1infty);
319 in2infty = is_zero(in2infty);
320
321 ecp_nistz256_sqr_mont(Z2sqr, in2_z); /* Z2^2 */
322 ecp_nistz256_sqr_mont(Z1sqr, in1_z); /* Z1^2 */
323
324 ecp_nistz256_mul_mont(S1, Z2sqr, in2_z); /* S1 = Z2^3 */
325 ecp_nistz256_mul_mont(S2, Z1sqr, in1_z); /* S2 = Z1^3 */
326
327 ecp_nistz256_mul_mont(S1, S1, in1_y); /* S1 = Y1*Z2^3 */
328 ecp_nistz256_mul_mont(S2, S2, in2_y); /* S2 = Y2*Z1^3 */
329 ecp_nistz256_sub(R, S2, S1); /* R = S2 - S1 */
330
331 ecp_nistz256_mul_mont(U1, in1_x, Z2sqr); /* U1 = X1*Z2^2 */
332 ecp_nistz256_mul_mont(U2, in2_x, Z1sqr); /* U2 = X2*Z1^2 */
333 ecp_nistz256_sub(H, U2, U1); /* H = U2 - U1 */
334
335 /*
336 * This should not happen during sign/ecdh, so no constant time violation
337 */
338 if (is_equal(U1, U2) && !in1infty && !in2infty) {
339 if (is_equal(S1, S2)) {
340 ecp_nistz256_point_double(r, a);
341 return;
342 } else {
343 memset(r, 0, sizeof(*r));
344 return;
345 }
346 }
347
348 ecp_nistz256_sqr_mont(Rsqr, R); /* R^2 */
349 ecp_nistz256_mul_mont(res_z, H, in1_z); /* Z3 = H*Z1*Z2 */
350 ecp_nistz256_sqr_mont(Hsqr, H); /* H^2 */
351 ecp_nistz256_mul_mont(res_z, res_z, in2_z); /* Z3 = H*Z1*Z2 */
352 ecp_nistz256_mul_mont(Hcub, Hsqr, H); /* H^3 */
353
354 ecp_nistz256_mul_mont(U2, U1, Hsqr); /* U1*H^2 */
355 ecp_nistz256_mul_by_2(Hsqr, U2); /* 2*U1*H^2 */
356
357 ecp_nistz256_sub(res_x, Rsqr, Hsqr);
358 ecp_nistz256_sub(res_x, res_x, Hcub);
359
360 ecp_nistz256_sub(res_y, U2, res_x);
361
362 ecp_nistz256_mul_mont(S2, S1, Hcub);
363 ecp_nistz256_mul_mont(res_y, R, res_y);
364 ecp_nistz256_sub(res_y, res_y, S2);
365
366 copy_conditional(res_x, in2_x, in1infty);
367 copy_conditional(res_y, in2_y, in1infty);
368 copy_conditional(res_z, in2_z, in1infty);
369
370 copy_conditional(res_x, in1_x, in2infty);
371 copy_conditional(res_y, in1_y, in2infty);
372 copy_conditional(res_z, in1_z, in2infty);
373
374 memcpy(r->X, res_x, sizeof(res_x));
375 memcpy(r->Y, res_y, sizeof(res_y));
376 memcpy(r->Z, res_z, sizeof(res_z));
377 }
378
379 /* Point addition when b is known to be affine: r = a+b */
380 static void ecp_nistz256_point_add_affine(P256_POINT *r,
381 const P256_POINT *a,
382 const P256_POINT_AFFINE *b)
383 {
384 BN_ULONG U2[P256_LIMBS], S2[P256_LIMBS];
385 BN_ULONG Z1sqr[P256_LIMBS];
386 BN_ULONG H[P256_LIMBS], R[P256_LIMBS];
387 BN_ULONG Hsqr[P256_LIMBS];
388 BN_ULONG Rsqr[P256_LIMBS];
389 BN_ULONG Hcub[P256_LIMBS];
390
391 BN_ULONG res_x[P256_LIMBS];
392 BN_ULONG res_y[P256_LIMBS];
393 BN_ULONG res_z[P256_LIMBS];
394
395 BN_ULONG in1infty, in2infty;
396
397 const BN_ULONG *in1_x = a->X;
398 const BN_ULONG *in1_y = a->Y;
399 const BN_ULONG *in1_z = a->Z;
400
401 const BN_ULONG *in2_x = b->X;
402 const BN_ULONG *in2_y = b->Y;
403
404 /*
405 * In affine representation we encode infty as (0,0), which is not on the
406 * curve, so it is OK
407 */
408 in1infty = (in1_x[0] | in1_x[1] | in1_x[2] | in1_x[3] |
409 in1_y[0] | in1_y[1] | in1_y[2] | in1_y[3]);
410 if (P256_LIMBS == 8)
411 in1infty |= (in1_x[4] | in1_x[5] | in1_x[6] | in1_x[7] |
412 in1_y[4] | in1_y[5] | in1_y[6] | in1_y[7]);
413
414 in2infty = (in2_x[0] | in2_x[1] | in2_x[2] | in2_x[3] |
415 in2_y[0] | in2_y[1] | in2_y[2] | in2_y[3]);
416 if (P256_LIMBS == 8)
417 in2infty |= (in2_x[4] | in2_x[5] | in2_x[6] | in2_x[7] |
418 in2_y[4] | in2_y[5] | in2_y[6] | in2_y[7]);
419
420 in1infty = is_zero(in1infty);
421 in2infty = is_zero(in2infty);
422
423 ecp_nistz256_sqr_mont(Z1sqr, in1_z); /* Z1^2 */
424
425 ecp_nistz256_mul_mont(U2, in2_x, Z1sqr); /* U2 = X2*Z1^2 */
426 ecp_nistz256_sub(H, U2, in1_x); /* H = U2 - U1 */
427
428 ecp_nistz256_mul_mont(S2, Z1sqr, in1_z); /* S2 = Z1^3 */
429
430 ecp_nistz256_mul_mont(res_z, H, in1_z); /* Z3 = H*Z1*Z2 */
431
432 ecp_nistz256_mul_mont(S2, S2, in2_y); /* S2 = Y2*Z1^3 */
433 ecp_nistz256_sub(R, S2, in1_y); /* R = S2 - S1 */
434
435 ecp_nistz256_sqr_mont(Hsqr, H); /* H^2 */
436 ecp_nistz256_sqr_mont(Rsqr, R); /* R^2 */
437 ecp_nistz256_mul_mont(Hcub, Hsqr, H); /* H^3 */
438
439 ecp_nistz256_mul_mont(U2, in1_x, Hsqr); /* U1*H^2 */
440 ecp_nistz256_mul_by_2(Hsqr, U2); /* 2*U1*H^2 */
441
442 ecp_nistz256_sub(res_x, Rsqr, Hsqr);
443 ecp_nistz256_sub(res_x, res_x, Hcub);
444 ecp_nistz256_sub(H, U2, res_x);
445
446 ecp_nistz256_mul_mont(S2, in1_y, Hcub);
447 ecp_nistz256_mul_mont(H, H, R);
448 ecp_nistz256_sub(res_y, H, S2);
449
450 copy_conditional(res_x, in2_x, in1infty);
451 copy_conditional(res_x, in1_x, in2infty);
452
453 copy_conditional(res_y, in2_y, in1infty);
454 copy_conditional(res_y, in1_y, in2infty);
455
456 copy_conditional(res_z, ONE, in1infty);
457 copy_conditional(res_z, in1_z, in2infty);
458
459 memcpy(r->X, res_x, sizeof(res_x));
460 memcpy(r->Y, res_y, sizeof(res_y));
461 memcpy(r->Z, res_z, sizeof(res_z));
462 }
463 #endif
464
465 /* r = in^-1 mod p */
466 static void ecp_nistz256_mod_inverse(BN_ULONG r[P256_LIMBS],
467 const BN_ULONG in[P256_LIMBS])
468 {
469 /*
470 * The poly is ffffffff 00000001 00000000 00000000 00000000 ffffffff
471 * ffffffff ffffffff We use FLT and used poly-2 as exponent
472 */
473 BN_ULONG p2[P256_LIMBS];
474 BN_ULONG p4[P256_LIMBS];
475 BN_ULONG p8[P256_LIMBS];
476 BN_ULONG p16[P256_LIMBS];
477 BN_ULONG p32[P256_LIMBS];
478 BN_ULONG res[P256_LIMBS];
479 int i;
480
481 ecp_nistz256_sqr_mont(res, in);
482 ecp_nistz256_mul_mont(p2, res, in); /* 3*p */
483
484 ecp_nistz256_sqr_mont(res, p2);
485 ecp_nistz256_sqr_mont(res, res);
486 ecp_nistz256_mul_mont(p4, res, p2); /* f*p */
487
488 ecp_nistz256_sqr_mont(res, p4);
489 ecp_nistz256_sqr_mont(res, res);
490 ecp_nistz256_sqr_mont(res, res);
491 ecp_nistz256_sqr_mont(res, res);
492 ecp_nistz256_mul_mont(p8, res, p4); /* ff*p */
493
494 ecp_nistz256_sqr_mont(res, p8);
495 for (i = 0; i < 7; i++)
496 ecp_nistz256_sqr_mont(res, res);
497 ecp_nistz256_mul_mont(p16, res, p8); /* ffff*p */
498
499 ecp_nistz256_sqr_mont(res, p16);
500 for (i = 0; i < 15; i++)
501 ecp_nistz256_sqr_mont(res, res);
502 ecp_nistz256_mul_mont(p32, res, p16); /* ffffffff*p */
503
504 ecp_nistz256_sqr_mont(res, p32);
505 for (i = 0; i < 31; i++)
506 ecp_nistz256_sqr_mont(res, res);
507 ecp_nistz256_mul_mont(res, res, in);
508
509 for (i = 0; i < 32 * 4; i++)
510 ecp_nistz256_sqr_mont(res, res);
511 ecp_nistz256_mul_mont(res, res, p32);
512
513 for (i = 0; i < 32; i++)
514 ecp_nistz256_sqr_mont(res, res);
515 ecp_nistz256_mul_mont(res, res, p32);
516
517 for (i = 0; i < 16; i++)
518 ecp_nistz256_sqr_mont(res, res);
519 ecp_nistz256_mul_mont(res, res, p16);
520
521 for (i = 0; i < 8; i++)
522 ecp_nistz256_sqr_mont(res, res);
523 ecp_nistz256_mul_mont(res, res, p8);
524
525 ecp_nistz256_sqr_mont(res, res);
526 ecp_nistz256_sqr_mont(res, res);
527 ecp_nistz256_sqr_mont(res, res);
528 ecp_nistz256_sqr_mont(res, res);
529 ecp_nistz256_mul_mont(res, res, p4);
530
531 ecp_nistz256_sqr_mont(res, res);
532 ecp_nistz256_sqr_mont(res, res);
533 ecp_nistz256_mul_mont(res, res, p2);
534
535 ecp_nistz256_sqr_mont(res, res);
536 ecp_nistz256_sqr_mont(res, res);
537 ecp_nistz256_mul_mont(res, res, in);
538
539 memcpy(r, res, sizeof(res));
540 }
541
542 /*
543 * ecp_nistz256_bignum_to_field_elem copies the contents of |in| to |out| and
544 * returns one if it fits. Otherwise it returns zero.
545 */
546 __owur static int ecp_nistz256_bignum_to_field_elem(BN_ULONG out[P256_LIMBS],
547 const BIGNUM *in)
548 {
549 return bn_copy_words(out, in, P256_LIMBS);
550 }
551
552 /* r = sum(scalar[i]*point[i]) */
553 __owur static int ecp_nistz256_windowed_mul(const EC_GROUP *group,
554 P256_POINT *r,
555 const BIGNUM **scalar,
556 const EC_POINT **point,
557 size_t num, BN_CTX *ctx)
558 {
559 size_t i;
560 int j, ret = 0;
561 unsigned int idx;
562 unsigned char (*p_str)[33] = NULL;
563 const unsigned int window_size = 5;
564 const unsigned int mask = (1 << (window_size + 1)) - 1;
565 unsigned int wvalue;
566 P256_POINT *temp; /* place for 5 temporary points */
567 const BIGNUM **scalars = NULL;
568 P256_POINT (*table)[16] = NULL;
569 void *table_storage = NULL;
570
571 if ((num * 16 + 6) > OPENSSL_MALLOC_MAX_NELEMS(P256_POINT)
572 || (table_storage =
573 OPENSSL_malloc((num * 16 + 5) * sizeof(P256_POINT) + 64)) == NULL
574 || (p_str =
575 OPENSSL_malloc(num * 33 * sizeof(unsigned char))) == NULL
576 || (scalars = OPENSSL_malloc(num * sizeof(BIGNUM *))) == NULL) {
577 ECerr(EC_F_ECP_NISTZ256_WINDOWED_MUL, ERR_R_MALLOC_FAILURE);
578 goto err;
579 }
580
581 table = (void *)ALIGNPTR(table_storage, 64);
582 temp = (P256_POINT *)(table + num);
583
584 for (i = 0; i < num; i++) {
585 P256_POINT *row = table[i];
586
587 /* This is an unusual input, we don't guarantee constant-timeness. */
588 if ((BN_num_bits(scalar[i]) > 256) || BN_is_negative(scalar[i])) {
589 BIGNUM *mod;
590
591 if ((mod = BN_CTX_get(ctx)) == NULL)
592 goto err;
593 if (!BN_nnmod(mod, scalar[i], group->order, ctx)) {
594 ECerr(EC_F_ECP_NISTZ256_WINDOWED_MUL, ERR_R_BN_LIB);
595 goto err;
596 }
597 scalars[i] = mod;
598 } else
599 scalars[i] = scalar[i];
600
601 for (j = 0; j < bn_get_top(scalars[i]) * BN_BYTES; j += BN_BYTES) {
602 BN_ULONG d = bn_get_words(scalars[i])[j / BN_BYTES];
603
604 p_str[i][j + 0] = (unsigned char)d;
605 p_str[i][j + 1] = (unsigned char)(d >> 8);
606 p_str[i][j + 2] = (unsigned char)(d >> 16);
607 p_str[i][j + 3] = (unsigned char)(d >>= 24);
608 if (BN_BYTES == 8) {
609 d >>= 8;
610 p_str[i][j + 4] = (unsigned char)d;
611 p_str[i][j + 5] = (unsigned char)(d >> 8);
612 p_str[i][j + 6] = (unsigned char)(d >> 16);
613 p_str[i][j + 7] = (unsigned char)(d >> 24);
614 }
615 }
616 for (; j < 33; j++)
617 p_str[i][j] = 0;
618
619 if (!ecp_nistz256_bignum_to_field_elem(temp[0].X, point[i]->X)
620 || !ecp_nistz256_bignum_to_field_elem(temp[0].Y, point[i]->Y)
621 || !ecp_nistz256_bignum_to_field_elem(temp[0].Z, point[i]->Z)) {
622 ECerr(EC_F_ECP_NISTZ256_WINDOWED_MUL,
623 EC_R_COORDINATES_OUT_OF_RANGE);
624 goto err;
625 }
626
627 /*
628 * row[0] is implicitly (0,0,0) (the point at infinity), therefore it
629 * is not stored. All other values are actually stored with an offset
630 * of -1 in table.
631 */
632
633 ecp_nistz256_scatter_w5 (row, &temp[0], 1);
634 ecp_nistz256_point_double(&temp[1], &temp[0]); /*1+1=2 */
635 ecp_nistz256_scatter_w5 (row, &temp[1], 2);
636 ecp_nistz256_point_add (&temp[2], &temp[1], &temp[0]); /*2+1=3 */
637 ecp_nistz256_scatter_w5 (row, &temp[2], 3);
638 ecp_nistz256_point_double(&temp[1], &temp[1]); /*2*2=4 */
639 ecp_nistz256_scatter_w5 (row, &temp[1], 4);
640 ecp_nistz256_point_double(&temp[2], &temp[2]); /*2*3=6 */
641 ecp_nistz256_scatter_w5 (row, &temp[2], 6);
642 ecp_nistz256_point_add (&temp[3], &temp[1], &temp[0]); /*4+1=5 */
643 ecp_nistz256_scatter_w5 (row, &temp[3], 5);
644 ecp_nistz256_point_add (&temp[4], &temp[2], &temp[0]); /*6+1=7 */
645 ecp_nistz256_scatter_w5 (row, &temp[4], 7);
646 ecp_nistz256_point_double(&temp[1], &temp[1]); /*2*4=8 */
647 ecp_nistz256_scatter_w5 (row, &temp[1], 8);
648 ecp_nistz256_point_double(&temp[2], &temp[2]); /*2*6=12 */
649 ecp_nistz256_scatter_w5 (row, &temp[2], 12);
650 ecp_nistz256_point_double(&temp[3], &temp[3]); /*2*5=10 */
651 ecp_nistz256_scatter_w5 (row, &temp[3], 10);
652 ecp_nistz256_point_double(&temp[4], &temp[4]); /*2*7=14 */
653 ecp_nistz256_scatter_w5 (row, &temp[4], 14);
654 ecp_nistz256_point_add (&temp[2], &temp[2], &temp[0]); /*12+1=13*/
655 ecp_nistz256_scatter_w5 (row, &temp[2], 13);
656 ecp_nistz256_point_add (&temp[3], &temp[3], &temp[0]); /*10+1=11*/
657 ecp_nistz256_scatter_w5 (row, &temp[3], 11);
658 ecp_nistz256_point_add (&temp[4], &temp[4], &temp[0]); /*14+1=15*/
659 ecp_nistz256_scatter_w5 (row, &temp[4], 15);
660 ecp_nistz256_point_add (&temp[2], &temp[1], &temp[0]); /*8+1=9 */
661 ecp_nistz256_scatter_w5 (row, &temp[2], 9);
662 ecp_nistz256_point_double(&temp[1], &temp[1]); /*2*8=16 */
663 ecp_nistz256_scatter_w5 (row, &temp[1], 16);
664 }
665
666 idx = 255;
667
668 wvalue = p_str[0][(idx - 1) / 8];
669 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
670
671 /*
672 * We gather to temp[0], because we know it's position relative
673 * to table
674 */
675 ecp_nistz256_gather_w5(&temp[0], table[0], _booth_recode_w5(wvalue) >> 1);
676 memcpy(r, &temp[0], sizeof(temp[0]));
677
678 while (idx >= 5) {
679 for (i = (idx == 255 ? 1 : 0); i < num; i++) {
680 unsigned int off = (idx - 1) / 8;
681
682 wvalue = p_str[i][off] | p_str[i][off + 1] << 8;
683 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
684
685 wvalue = _booth_recode_w5(wvalue);
686
687 ecp_nistz256_gather_w5(&temp[0], table[i], wvalue >> 1);
688
689 ecp_nistz256_neg(temp[1].Y, temp[0].Y);
690 copy_conditional(temp[0].Y, temp[1].Y, (wvalue & 1));
691
692 ecp_nistz256_point_add(r, r, &temp[0]);
693 }
694
695 idx -= window_size;
696
697 ecp_nistz256_point_double(r, r);
698 ecp_nistz256_point_double(r, r);
699 ecp_nistz256_point_double(r, r);
700 ecp_nistz256_point_double(r, r);
701 ecp_nistz256_point_double(r, r);
702 }
703
704 /* Final window */
705 for (i = 0; i < num; i++) {
706 wvalue = p_str[i][0];
707 wvalue = (wvalue << 1) & mask;
708
709 wvalue = _booth_recode_w5(wvalue);
710
711 ecp_nistz256_gather_w5(&temp[0], table[i], wvalue >> 1);
712
713 ecp_nistz256_neg(temp[1].Y, temp[0].Y);
714 copy_conditional(temp[0].Y, temp[1].Y, wvalue & 1);
715
716 ecp_nistz256_point_add(r, r, &temp[0]);
717 }
718
719 ret = 1;
720 err:
721 OPENSSL_free(table_storage);
722 OPENSSL_free(p_str);
723 OPENSSL_free(scalars);
724 return ret;
725 }
726
727 /* Coordinates of G, for which we have precomputed tables */
728 const static BN_ULONG def_xG[P256_LIMBS] = {
729 TOBN(0x79e730d4, 0x18a9143c), TOBN(0x75ba95fc, 0x5fedb601),
730 TOBN(0x79fb732b, 0x77622510), TOBN(0x18905f76, 0xa53755c6)
731 };
732
733 const static BN_ULONG def_yG[P256_LIMBS] = {
734 TOBN(0xddf25357, 0xce95560a), TOBN(0x8b4ab8e4, 0xba19e45c),
735 TOBN(0xd2e88688, 0xdd21f325), TOBN(0x8571ff18, 0x25885d85)
736 };
737
738 /*
739 * ecp_nistz256_is_affine_G returns one if |generator| is the standard, P-256
740 * generator.
741 */
742 static int ecp_nistz256_is_affine_G(const EC_POINT *generator)
743 {
744 return (bn_get_top(generator->X) == P256_LIMBS) &&
745 (bn_get_top(generator->Y) == P256_LIMBS) &&
746 (bn_get_top(generator->Z) == (P256_LIMBS - P256_LIMBS / 8)) &&
747 is_equal(bn_get_words(generator->X), def_xG) &&
748 is_equal(bn_get_words(generator->Y), def_yG) &&
749 is_one(bn_get_words(generator->Z));
750 }
751
752 __owur static int ecp_nistz256_mult_precompute(EC_GROUP *group, BN_CTX *ctx)
753 {
754 /*
755 * We precompute a table for a Booth encoded exponent (wNAF) based
756 * computation. Each table holds 64 values for safe access, with an
757 * implicit value of infinity at index zero. We use window of size 7, and
758 * therefore require ceil(256/7) = 37 tables.
759 */
760 BIGNUM *order;
761 EC_POINT *P = NULL, *T = NULL;
762 const EC_POINT *generator;
763 NISTZ256_PRE_COMP *pre_comp;
764 BN_CTX *new_ctx = NULL;
765 int i, j, k, ret = 0;
766 size_t w;
767
768 PRECOMP256_ROW *preComputedTable = NULL;
769 unsigned char *precomp_storage = NULL;
770
771 /* if there is an old NISTZ256_PRE_COMP object, throw it away */
772 EC_pre_comp_free(group);
773 generator = EC_GROUP_get0_generator(group);
774 if (generator == NULL) {
775 ECerr(EC_F_ECP_NISTZ256_MULT_PRECOMPUTE, EC_R_UNDEFINED_GENERATOR);
776 return 0;
777 }
778
779 if (ecp_nistz256_is_affine_G(generator)) {
780 /*
781 * No need to calculate tables for the standard generator because we
782 * have them statically.
783 */
784 return 1;
785 }
786
787 if ((pre_comp = ecp_nistz256_pre_comp_new(group)) == NULL)
788 return 0;
789
790 if (ctx == NULL) {
791 ctx = new_ctx = BN_CTX_new();
792 if (ctx == NULL)
793 goto err;
794 }
795
796 BN_CTX_start(ctx);
797 order = BN_CTX_get(ctx);
798
799 if (order == NULL)
800 goto err;
801
802 if (!EC_GROUP_get_order(group, order, ctx))
803 goto err;
804
805 if (BN_is_zero(order)) {
806 ECerr(EC_F_ECP_NISTZ256_MULT_PRECOMPUTE, EC_R_UNKNOWN_ORDER);
807 goto err;
808 }
809
810 w = 7;
811
812 if ((precomp_storage =
813 OPENSSL_malloc(37 * 64 * sizeof(P256_POINT_AFFINE) + 64)) == NULL) {
814 ECerr(EC_F_ECP_NISTZ256_MULT_PRECOMPUTE, ERR_R_MALLOC_FAILURE);
815 goto err;
816 }
817
818 preComputedTable = (void *)ALIGNPTR(precomp_storage, 64);
819
820 P = EC_POINT_new(group);
821 T = EC_POINT_new(group);
822 if (P == NULL || T == NULL)
823 goto err;
824
825 /*
826 * The zero entry is implicitly infinity, and we skip it, storing other
827 * values with -1 offset.
828 */
829 if (!EC_POINT_copy(T, generator))
830 goto err;
831
832 for (k = 0; k < 64; k++) {
833 if (!EC_POINT_copy(P, T))
834 goto err;
835 for (j = 0; j < 37; j++) {
836 P256_POINT_AFFINE temp;
837 /*
838 * It would be faster to use EC_POINTs_make_affine and
839 * make multiple points affine at the same time.
840 */
841 if (!EC_POINT_make_affine(group, P, ctx))
842 goto err;
843 if (!ecp_nistz256_bignum_to_field_elem(temp.X, P->X) ||
844 !ecp_nistz256_bignum_to_field_elem(temp.Y, P->Y)) {
845 ECerr(EC_F_ECP_NISTZ256_MULT_PRECOMPUTE,
846 EC_R_COORDINATES_OUT_OF_RANGE);
847 goto err;
848 }
849 ecp_nistz256_scatter_w7(preComputedTable[j], &temp, k);
850 for (i = 0; i < 7; i++) {
851 if (!EC_POINT_dbl(group, P, P, ctx))
852 goto err;
853 }
854 }
855 if (!EC_POINT_add(group, T, T, generator, ctx))
856 goto err;
857 }
858
859 pre_comp->group = group;
860 pre_comp->w = w;
861 pre_comp->precomp = preComputedTable;
862 pre_comp->precomp_storage = precomp_storage;
863 precomp_storage = NULL;
864 SETPRECOMP(group, nistz256, pre_comp);
865 pre_comp = NULL;
866 ret = 1;
867
868 err:
869 if (ctx != NULL)
870 BN_CTX_end(ctx);
871 BN_CTX_free(new_ctx);
872
873 EC_nistz256_pre_comp_free(pre_comp);
874 OPENSSL_free(precomp_storage);
875 EC_POINT_free(P);
876 EC_POINT_free(T);
877 return ret;
878 }
879
880 /*
881 * Note that by default ECP_NISTZ256_AVX2 is undefined. While it's great
882 * code processing 4 points in parallel, corresponding serial operation
883 * is several times slower, because it uses 29x29=58-bit multiplication
884 * as opposite to 64x64=128-bit in integer-only scalar case. As result
885 * it doesn't provide *significant* performance improvement. Note that
886 * just defining ECP_NISTZ256_AVX2 is not sufficient to make it work,
887 * you'd need to compile even asm/ecp_nistz256-avx.pl module.
888 */
889 #if defined(ECP_NISTZ256_AVX2)
890 # if !(defined(__x86_64) || defined(__x86_64__) || \
891 defined(_M_AMD64) || defined(_MX64)) || \
892 !(defined(__GNUC__) || defined(_MSC_VER)) /* this is for ALIGN32 */
893 # undef ECP_NISTZ256_AVX2
894 # else
895 /* Constant time access, loading four values, from four consecutive tables */
896 void ecp_nistz256_avx2_multi_gather_w7(void *result, const void *in,
897 int index0, int index1, int index2,
898 int index3);
899 void ecp_nistz256_avx2_transpose_convert(void *RESULTx4, const void *in);
900 void ecp_nistz256_avx2_convert_transpose_back(void *result, const void *Ax4);
901 void ecp_nistz256_avx2_point_add_affine_x4(void *RESULTx4, const void *Ax4,
902 const void *Bx4);
903 void ecp_nistz256_avx2_point_add_affines_x4(void *RESULTx4, const void *Ax4,
904 const void *Bx4);
905 void ecp_nistz256_avx2_to_mont(void *RESULTx4, const void *Ax4);
906 void ecp_nistz256_avx2_from_mont(void *RESULTx4, const void *Ax4);
907 void ecp_nistz256_avx2_set1(void *RESULTx4);
908 int ecp_nistz_avx2_eligible(void);
909
910 static void booth_recode_w7(unsigned char *sign,
911 unsigned char *digit, unsigned char in)
912 {
913 unsigned char s, d;
914
915 s = ~((in >> 7) - 1);
916 d = (1 << 8) - in - 1;
917 d = (d & s) | (in & ~s);
918 d = (d >> 1) + (d & 1);
919
920 *sign = s & 1;
921 *digit = d;
922 }
923
924 /*
925 * ecp_nistz256_avx2_mul_g performs multiplication by G, using only the
926 * precomputed table. It does 4 affine point additions in parallel,
927 * significantly speeding up point multiplication for a fixed value.
928 */
929 static void ecp_nistz256_avx2_mul_g(P256_POINT *r,
930 unsigned char p_str[33],
931 const P256_POINT_AFFINE(*preComputedTable)[64])
932 {
933 const unsigned int window_size = 7;
934 const unsigned int mask = (1 << (window_size + 1)) - 1;
935 unsigned int wvalue;
936 /* Using 4 windows at a time */
937 unsigned char sign0, digit0;
938 unsigned char sign1, digit1;
939 unsigned char sign2, digit2;
940 unsigned char sign3, digit3;
941 unsigned int idx = 0;
942 BN_ULONG tmp[P256_LIMBS];
943 int i;
944
945 ALIGN32 BN_ULONG aX4[4 * 9 * 3] = { 0 };
946 ALIGN32 BN_ULONG bX4[4 * 9 * 2] = { 0 };
947 ALIGN32 P256_POINT_AFFINE point_arr[4];
948 ALIGN32 P256_POINT res_point_arr[4];
949
950 /* Initial four windows */
951 wvalue = *((u16 *) & p_str[0]);
952 wvalue = (wvalue << 1) & mask;
953 idx += window_size;
954 booth_recode_w7(&sign0, &digit0, wvalue);
955 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
956 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
957 idx += window_size;
958 booth_recode_w7(&sign1, &digit1, wvalue);
959 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
960 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
961 idx += window_size;
962 booth_recode_w7(&sign2, &digit2, wvalue);
963 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
964 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
965 idx += window_size;
966 booth_recode_w7(&sign3, &digit3, wvalue);
967
968 ecp_nistz256_avx2_multi_gather_w7(point_arr, preComputedTable[0],
969 digit0, digit1, digit2, digit3);
970
971 ecp_nistz256_neg(tmp, point_arr[0].Y);
972 copy_conditional(point_arr[0].Y, tmp, sign0);
973 ecp_nistz256_neg(tmp, point_arr[1].Y);
974 copy_conditional(point_arr[1].Y, tmp, sign1);
975 ecp_nistz256_neg(tmp, point_arr[2].Y);
976 copy_conditional(point_arr[2].Y, tmp, sign2);
977 ecp_nistz256_neg(tmp, point_arr[3].Y);
978 copy_conditional(point_arr[3].Y, tmp, sign3);
979
980 ecp_nistz256_avx2_transpose_convert(aX4, point_arr);
981 ecp_nistz256_avx2_to_mont(aX4, aX4);
982 ecp_nistz256_avx2_to_mont(&aX4[4 * 9], &aX4[4 * 9]);
983 ecp_nistz256_avx2_set1(&aX4[4 * 9 * 2]);
984
985 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
986 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
987 idx += window_size;
988 booth_recode_w7(&sign0, &digit0, wvalue);
989 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
990 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
991 idx += window_size;
992 booth_recode_w7(&sign1, &digit1, wvalue);
993 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
994 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
995 idx += window_size;
996 booth_recode_w7(&sign2, &digit2, wvalue);
997 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
998 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
999 idx += window_size;
1000 booth_recode_w7(&sign3, &digit3, wvalue);
1001
1002 ecp_nistz256_avx2_multi_gather_w7(point_arr, preComputedTable[4 * 1],
1003 digit0, digit1, digit2, digit3);
1004
1005 ecp_nistz256_neg(tmp, point_arr[0].Y);
1006 copy_conditional(point_arr[0].Y, tmp, sign0);
1007 ecp_nistz256_neg(tmp, point_arr[1].Y);
1008 copy_conditional(point_arr[1].Y, tmp, sign1);
1009 ecp_nistz256_neg(tmp, point_arr[2].Y);
1010 copy_conditional(point_arr[2].Y, tmp, sign2);
1011 ecp_nistz256_neg(tmp, point_arr[3].Y);
1012 copy_conditional(point_arr[3].Y, tmp, sign3);
1013
1014 ecp_nistz256_avx2_transpose_convert(bX4, point_arr);
1015 ecp_nistz256_avx2_to_mont(bX4, bX4);
1016 ecp_nistz256_avx2_to_mont(&bX4[4 * 9], &bX4[4 * 9]);
1017 /* Optimized when both inputs are affine */
1018 ecp_nistz256_avx2_point_add_affines_x4(aX4, aX4, bX4);
1019
1020 for (i = 2; i < 9; i++) {
1021 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
1022 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
1023 idx += window_size;
1024 booth_recode_w7(&sign0, &digit0, wvalue);
1025 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
1026 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
1027 idx += window_size;
1028 booth_recode_w7(&sign1, &digit1, wvalue);
1029 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
1030 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
1031 idx += window_size;
1032 booth_recode_w7(&sign2, &digit2, wvalue);
1033 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
1034 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
1035 idx += window_size;
1036 booth_recode_w7(&sign3, &digit3, wvalue);
1037
1038 ecp_nistz256_avx2_multi_gather_w7(point_arr,
1039 preComputedTable[4 * i],
1040 digit0, digit1, digit2, digit3);
1041
1042 ecp_nistz256_neg(tmp, point_arr[0].Y);
1043 copy_conditional(point_arr[0].Y, tmp, sign0);
1044 ecp_nistz256_neg(tmp, point_arr[1].Y);
1045 copy_conditional(point_arr[1].Y, tmp, sign1);
1046 ecp_nistz256_neg(tmp, point_arr[2].Y);
1047 copy_conditional(point_arr[2].Y, tmp, sign2);
1048 ecp_nistz256_neg(tmp, point_arr[3].Y);
1049 copy_conditional(point_arr[3].Y, tmp, sign3);
1050
1051 ecp_nistz256_avx2_transpose_convert(bX4, point_arr);
1052 ecp_nistz256_avx2_to_mont(bX4, bX4);
1053 ecp_nistz256_avx2_to_mont(&bX4[4 * 9], &bX4[4 * 9]);
1054
1055 ecp_nistz256_avx2_point_add_affine_x4(aX4, aX4, bX4);
1056 }
1057
1058 ecp_nistz256_avx2_from_mont(&aX4[4 * 9 * 0], &aX4[4 * 9 * 0]);
1059 ecp_nistz256_avx2_from_mont(&aX4[4 * 9 * 1], &aX4[4 * 9 * 1]);
1060 ecp_nistz256_avx2_from_mont(&aX4[4 * 9 * 2], &aX4[4 * 9 * 2]);
1061
1062 ecp_nistz256_avx2_convert_transpose_back(res_point_arr, aX4);
1063 /* Last window is performed serially */
1064 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
1065 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
1066 booth_recode_w7(&sign0, &digit0, wvalue);
1067 ecp_nistz256_gather_w7((P256_POINT_AFFINE *)r,
1068 preComputedTable[36], digit0);
1069 ecp_nistz256_neg(tmp, r->Y);
1070 copy_conditional(r->Y, tmp, sign0);
1071 memcpy(r->Z, ONE, sizeof(ONE));
1072 /* Sum the four windows */
1073 ecp_nistz256_point_add(r, r, &res_point_arr[0]);
1074 ecp_nistz256_point_add(r, r, &res_point_arr[1]);
1075 ecp_nistz256_point_add(r, r, &res_point_arr[2]);
1076 ecp_nistz256_point_add(r, r, &res_point_arr[3]);
1077 }
1078 # endif
1079 #endif
1080
1081 __owur static int ecp_nistz256_set_from_affine(EC_POINT *out, const EC_GROUP *group,
1082 const P256_POINT_AFFINE *in,
1083 BN_CTX *ctx)
1084 {
1085 BIGNUM *x, *y;
1086 BN_ULONG d_x[P256_LIMBS], d_y[P256_LIMBS];
1087 int ret = 0;
1088
1089 x = BN_new();
1090 if (x == NULL)
1091 return 0;
1092 y = BN_new();
1093 if (y == NULL) {
1094 BN_free(x);
1095 return 0;
1096 }
1097 memcpy(d_x, in->X, sizeof(d_x));
1098 bn_set_static_words(x, d_x, P256_LIMBS);
1099
1100 memcpy(d_y, in->Y, sizeof(d_y));
1101 bn_set_static_words(y, d_y, P256_LIMBS);
1102
1103 ret = EC_POINT_set_affine_coordinates_GFp(group, out, x, y, ctx);
1104
1105 BN_free(x);
1106 BN_free(y);
1107
1108 return ret;
1109 }
1110
1111 /* r = scalar*G + sum(scalars[i]*points[i]) */
1112 __owur static int ecp_nistz256_points_mul(const EC_GROUP *group,
1113 EC_POINT *r,
1114 const BIGNUM *scalar,
1115 size_t num,
1116 const EC_POINT *points[],
1117 const BIGNUM *scalars[], BN_CTX *ctx)
1118 {
1119 int i = 0, ret = 0, no_precomp_for_generator = 0, p_is_infinity = 0;
1120 size_t j;
1121 unsigned char p_str[33] = { 0 };
1122 const PRECOMP256_ROW *preComputedTable = NULL;
1123 const NISTZ256_PRE_COMP *pre_comp = NULL;
1124 const EC_POINT *generator = NULL;
1125 BN_CTX *new_ctx = NULL;
1126 const BIGNUM **new_scalars = NULL;
1127 const EC_POINT **new_points = NULL;
1128 unsigned int idx = 0;
1129 const unsigned int window_size = 7;
1130 const unsigned int mask = (1 << (window_size + 1)) - 1;
1131 unsigned int wvalue;
1132 ALIGN32 union {
1133 P256_POINT p;
1134 P256_POINT_AFFINE a;
1135 } t, p;
1136 BIGNUM *tmp_scalar;
1137
1138 if ((num + 1) == 0 || (num + 1) > OPENSSL_MALLOC_MAX_NELEMS(void *)) {
1139 ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, ERR_R_MALLOC_FAILURE);
1140 return 0;
1141 }
1142
1143 if (group->meth != r->meth) {
1144 ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, EC_R_INCOMPATIBLE_OBJECTS);
1145 return 0;
1146 }
1147
1148 if ((scalar == NULL) && (num == 0))
1149 return EC_POINT_set_to_infinity(group, r);
1150
1151 for (j = 0; j < num; j++) {
1152 if (group->meth != points[j]->meth) {
1153 ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, EC_R_INCOMPATIBLE_OBJECTS);
1154 return 0;
1155 }
1156 }
1157
1158 if (ctx == NULL) {
1159 ctx = new_ctx = BN_CTX_new();
1160 if (ctx == NULL)
1161 goto err;
1162 }
1163
1164 BN_CTX_start(ctx);
1165
1166 if (scalar) {
1167 generator = EC_GROUP_get0_generator(group);
1168 if (generator == NULL) {
1169 ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, EC_R_UNDEFINED_GENERATOR);
1170 goto err;
1171 }
1172
1173 /* look if we can use precomputed multiples of generator */
1174 pre_comp = group->pre_comp.nistz256;
1175
1176 if (pre_comp) {
1177 /*
1178 * If there is a precomputed table for the generator, check that
1179 * it was generated with the same generator.
1180 */
1181 EC_POINT *pre_comp_generator = EC_POINT_new(group);
1182 if (pre_comp_generator == NULL)
1183 goto err;
1184
1185 if (!ecp_nistz256_set_from_affine(pre_comp_generator,
1186 group, pre_comp->precomp[0],
1187 ctx)) {
1188 EC_POINT_free(pre_comp_generator);
1189 goto err;
1190 }
1191
1192 if (0 == EC_POINT_cmp(group, generator, pre_comp_generator, ctx))
1193 preComputedTable = (const PRECOMP256_ROW *)pre_comp->precomp;
1194
1195 EC_POINT_free(pre_comp_generator);
1196 }
1197
1198 if (preComputedTable == NULL && ecp_nistz256_is_affine_G(generator)) {
1199 /*
1200 * If there is no precomputed data, but the generator is the
1201 * default, a hardcoded table of precomputed data is used. This
1202 * is because applications, such as Apache, do not use
1203 * EC_KEY_precompute_mult.
1204 */
1205 preComputedTable = ecp_nistz256_precomputed;
1206 }
1207
1208 if (preComputedTable) {
1209 if ((BN_num_bits(scalar) > 256)
1210 || BN_is_negative(scalar)) {
1211 if ((tmp_scalar = BN_CTX_get(ctx)) == NULL)
1212 goto err;
1213
1214 if (!BN_nnmod(tmp_scalar, scalar, group->order, ctx)) {
1215 ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, ERR_R_BN_LIB);
1216 goto err;
1217 }
1218 scalar = tmp_scalar;
1219 }
1220
1221 for (i = 0; i < bn_get_top(scalar) * BN_BYTES; i += BN_BYTES) {
1222 BN_ULONG d = bn_get_words(scalar)[i / BN_BYTES];
1223
1224 p_str[i + 0] = (unsigned char)d;
1225 p_str[i + 1] = (unsigned char)(d >> 8);
1226 p_str[i + 2] = (unsigned char)(d >> 16);
1227 p_str[i + 3] = (unsigned char)(d >>= 24);
1228 if (BN_BYTES == 8) {
1229 d >>= 8;
1230 p_str[i + 4] = (unsigned char)d;
1231 p_str[i + 5] = (unsigned char)(d >> 8);
1232 p_str[i + 6] = (unsigned char)(d >> 16);
1233 p_str[i + 7] = (unsigned char)(d >> 24);
1234 }
1235 }
1236
1237 for (; i < 33; i++)
1238 p_str[i] = 0;
1239
1240 #if defined(ECP_NISTZ256_AVX2)
1241 if (ecp_nistz_avx2_eligible()) {
1242 ecp_nistz256_avx2_mul_g(&p.p, p_str, preComputedTable);
1243 } else
1244 #endif
1245 {
1246 /* First window */
1247 wvalue = (p_str[0] << 1) & mask;
1248 idx += window_size;
1249
1250 wvalue = _booth_recode_w7(wvalue);
1251
1252 ecp_nistz256_gather_w7(&p.a, preComputedTable[0],
1253 wvalue >> 1);
1254
1255 ecp_nistz256_neg(p.p.Z, p.p.Y);
1256 copy_conditional(p.p.Y, p.p.Z, wvalue & 1);
1257
1258 memcpy(p.p.Z, ONE, sizeof(ONE));
1259
1260 for (i = 1; i < 37; i++) {
1261 unsigned int off = (idx - 1) / 8;
1262 wvalue = p_str[off] | p_str[off + 1] << 8;
1263 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
1264 idx += window_size;
1265
1266 wvalue = _booth_recode_w7(wvalue);
1267
1268 ecp_nistz256_gather_w7(&t.a,
1269 preComputedTable[i], wvalue >> 1);
1270
1271 ecp_nistz256_neg(t.p.Z, t.a.Y);
1272 copy_conditional(t.a.Y, t.p.Z, wvalue & 1);
1273
1274 ecp_nistz256_point_add_affine(&p.p, &p.p, &t.a);
1275 }
1276 }
1277 } else {
1278 p_is_infinity = 1;
1279 no_precomp_for_generator = 1;
1280 }
1281 } else
1282 p_is_infinity = 1;
1283
1284 if (no_precomp_for_generator) {
1285 /*
1286 * Without a precomputed table for the generator, it has to be
1287 * handled like a normal point.
1288 */
1289 new_scalars = OPENSSL_malloc((num + 1) * sizeof(BIGNUM *));
1290 if (new_scalars == NULL) {
1291 ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, ERR_R_MALLOC_FAILURE);
1292 goto err;
1293 }
1294
1295 new_points = OPENSSL_malloc((num + 1) * sizeof(EC_POINT *));
1296 if (new_points == NULL) {
1297 ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, ERR_R_MALLOC_FAILURE);
1298 goto err;
1299 }
1300
1301 memcpy(new_scalars, scalars, num * sizeof(BIGNUM *));
1302 new_scalars[num] = scalar;
1303 memcpy(new_points, points, num * sizeof(EC_POINT *));
1304 new_points[num] = generator;
1305
1306 scalars = new_scalars;
1307 points = new_points;
1308 num++;
1309 }
1310
1311 if (num) {
1312 P256_POINT *out = &t.p;
1313 if (p_is_infinity)
1314 out = &p.p;
1315
1316 if (!ecp_nistz256_windowed_mul(group, out, scalars, points, num, ctx))
1317 goto err;
1318
1319 if (!p_is_infinity)
1320 ecp_nistz256_point_add(&p.p, &p.p, out);
1321 }
1322
1323 /* Not constant-time, but we're only operating on the public output. */
1324 if (!bn_set_words(r->X, p.p.X, P256_LIMBS) ||
1325 !bn_set_words(r->Y, p.p.Y, P256_LIMBS) ||
1326 !bn_set_words(r->Z, p.p.Z, P256_LIMBS)) {
1327 goto err;
1328 }
1329 r->Z_is_one = is_one(p.p.Z) & 1;
1330
1331 ret = 1;
1332
1333 err:
1334 if (ctx)
1335 BN_CTX_end(ctx);
1336 BN_CTX_free(new_ctx);
1337 OPENSSL_free(new_points);
1338 OPENSSL_free(new_scalars);
1339 return ret;
1340 }
1341
1342 __owur static int ecp_nistz256_get_affine(const EC_GROUP *group,
1343 const EC_POINT *point,
1344 BIGNUM *x, BIGNUM *y, BN_CTX *ctx)
1345 {
1346 BN_ULONG z_inv2[P256_LIMBS];
1347 BN_ULONG z_inv3[P256_LIMBS];
1348 BN_ULONG x_aff[P256_LIMBS];
1349 BN_ULONG y_aff[P256_LIMBS];
1350 BN_ULONG point_x[P256_LIMBS], point_y[P256_LIMBS], point_z[P256_LIMBS];
1351 BN_ULONG x_ret[P256_LIMBS], y_ret[P256_LIMBS];
1352
1353 if (EC_POINT_is_at_infinity(group, point)) {
1354 ECerr(EC_F_ECP_NISTZ256_GET_AFFINE, EC_R_POINT_AT_INFINITY);
1355 return 0;
1356 }
1357
1358 if (!ecp_nistz256_bignum_to_field_elem(point_x, point->X) ||
1359 !ecp_nistz256_bignum_to_field_elem(point_y, point->Y) ||
1360 !ecp_nistz256_bignum_to_field_elem(point_z, point->Z)) {
1361 ECerr(EC_F_ECP_NISTZ256_GET_AFFINE, EC_R_COORDINATES_OUT_OF_RANGE);
1362 return 0;
1363 }
1364
1365 ecp_nistz256_mod_inverse(z_inv3, point_z);
1366 ecp_nistz256_sqr_mont(z_inv2, z_inv3);
1367 ecp_nistz256_mul_mont(x_aff, z_inv2, point_x);
1368
1369 if (x != NULL) {
1370 ecp_nistz256_from_mont(x_ret, x_aff);
1371 if (!bn_set_words(x, x_ret, P256_LIMBS))
1372 return 0;
1373 }
1374
1375 if (y != NULL) {
1376 ecp_nistz256_mul_mont(z_inv3, z_inv3, z_inv2);
1377 ecp_nistz256_mul_mont(y_aff, z_inv3, point_y);
1378 ecp_nistz256_from_mont(y_ret, y_aff);
1379 if (!bn_set_words(y, y_ret, P256_LIMBS))
1380 return 0;
1381 }
1382
1383 return 1;
1384 }
1385
1386 static NISTZ256_PRE_COMP *ecp_nistz256_pre_comp_new(const EC_GROUP *group)
1387 {
1388 NISTZ256_PRE_COMP *ret = NULL;
1389
1390 if (!group)
1391 return NULL;
1392
1393 ret = OPENSSL_zalloc(sizeof(*ret));
1394
1395 if (ret == NULL) {
1396 ECerr(EC_F_ECP_NISTZ256_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE);
1397 return ret;
1398 }
1399
1400 ret->group = group;
1401 ret->w = 6; /* default */
1402 ret->precomp = NULL;
1403 ret->precomp_storage = NULL;
1404 ret->references = 1;
1405 return ret;
1406 }
1407
1408 NISTZ256_PRE_COMP *EC_nistz256_pre_comp_dup(NISTZ256_PRE_COMP *p)
1409 {
1410 if (p != NULL)
1411 CRYPTO_add(&p->references, 1, CRYPTO_LOCK_EC_PRE_COMP);
1412 return p;
1413 }
1414
1415 void EC_nistz256_pre_comp_free(NISTZ256_PRE_COMP *pre)
1416 {
1417 if (pre == NULL
1418 || CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP) > 0)
1419 return;
1420 OPENSSL_free(pre->precomp_storage);
1421 OPENSSL_free(pre);
1422 }
1423
1424
1425 static int ecp_nistz256_window_have_precompute_mult(const EC_GROUP *group)
1426 {
1427 /* There is a hard-coded table for the default generator. */
1428 const EC_POINT *generator = EC_GROUP_get0_generator(group);
1429
1430 if (generator != NULL && ecp_nistz256_is_affine_G(generator)) {
1431 /* There is a hard-coded table for the default generator. */
1432 return 1;
1433 }
1434
1435 return HAVEPRECOMP(group, nistz256);
1436 }
1437
1438 const EC_METHOD *EC_GFp_nistz256_method(void)
1439 {
1440 static const EC_METHOD ret = {
1441 EC_FLAGS_DEFAULT_OCT,
1442 NID_X9_62_prime_field,
1443 ec_GFp_mont_group_init,
1444 ec_GFp_mont_group_finish,
1445 ec_GFp_mont_group_clear_finish,
1446 ec_GFp_mont_group_copy,
1447 ec_GFp_mont_group_set_curve,
1448 ec_GFp_simple_group_get_curve,
1449 ec_GFp_simple_group_get_degree,
1450 ec_GFp_simple_group_check_discriminant,
1451 ec_GFp_simple_point_init,
1452 ec_GFp_simple_point_finish,
1453 ec_GFp_simple_point_clear_finish,
1454 ec_GFp_simple_point_copy,
1455 ec_GFp_simple_point_set_to_infinity,
1456 ec_GFp_simple_set_Jprojective_coordinates_GFp,
1457 ec_GFp_simple_get_Jprojective_coordinates_GFp,
1458 ec_GFp_simple_point_set_affine_coordinates,
1459 ecp_nistz256_get_affine,
1460 0, 0, 0,
1461 ec_GFp_simple_add,
1462 ec_GFp_simple_dbl,
1463 ec_GFp_simple_invert,
1464 ec_GFp_simple_is_at_infinity,
1465 ec_GFp_simple_is_on_curve,
1466 ec_GFp_simple_cmp,
1467 ec_GFp_simple_make_affine,
1468 ec_GFp_simple_points_make_affine,
1469 ecp_nistz256_points_mul, /* mul */
1470 ecp_nistz256_mult_precompute, /* precompute_mult */
1471 ecp_nistz256_window_have_precompute_mult, /* have_precompute_mult */
1472 ec_GFp_mont_field_mul,
1473 ec_GFp_mont_field_sqr,
1474 0, /* field_div */
1475 ec_GFp_mont_field_encode,
1476 ec_GFp_mont_field_decode,
1477 ec_GFp_mont_field_set_to_one
1478 };
1479
1480 return &ret;
1481 }
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