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[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 "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 typedef struct ec_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 } EC_PRE_COMP;
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 void *ecp_nistz256_pre_comp_dup(void *);
131 static void ecp_nistz256_pre_comp_free(void *);
132 static void ecp_nistz256_pre_comp_clear_free(void *);
133 static EC_PRE_COMP *ecp_nistz256_pre_comp_new(const EC_GROUP *group);
134
135 /* Precomputed tables for the default generator */
136 extern const PRECOMP256_ROW ecp_nistz256_precomputed[37];
137
138 /* Recode window to a signed digit, see ecp_nistputil.c for details */
139 static unsigned int _booth_recode_w5(unsigned int in)
140 {
141 unsigned int s, d;
142
143 s = ~((in >> 5) - 1);
144 d = (1 << 6) - in - 1;
145 d = (d & s) | (in & ~s);
146 d = (d >> 1) + (d & 1);
147
148 return (d << 1) + (s & 1);
149 }
150
151 static unsigned int _booth_recode_w7(unsigned int in)
152 {
153 unsigned int s, d;
154
155 s = ~((in >> 7) - 1);
156 d = (1 << 8) - in - 1;
157 d = (d & s) | (in & ~s);
158 d = (d >> 1) + (d & 1);
159
160 return (d << 1) + (s & 1);
161 }
162
163 static void copy_conditional(BN_ULONG dst[P256_LIMBS],
164 const BN_ULONG src[P256_LIMBS], BN_ULONG move)
165 {
166 BN_ULONG mask1 = 0-move;
167 BN_ULONG mask2 = ~mask1;
168
169 dst[0] = (src[0] & mask1) ^ (dst[0] & mask2);
170 dst[1] = (src[1] & mask1) ^ (dst[1] & mask2);
171 dst[2] = (src[2] & mask1) ^ (dst[2] & mask2);
172 dst[3] = (src[3] & mask1) ^ (dst[3] & mask2);
173 if (P256_LIMBS == 8) {
174 dst[4] = (src[4] & mask1) ^ (dst[4] & mask2);
175 dst[5] = (src[5] & mask1) ^ (dst[5] & mask2);
176 dst[6] = (src[6] & mask1) ^ (dst[6] & mask2);
177 dst[7] = (src[7] & mask1) ^ (dst[7] & mask2);
178 }
179 }
180
181 static BN_ULONG is_zero(BN_ULONG in)
182 {
183 in |= (0 - in);
184 in = ~in;
185 in &= BN_MASK2;
186 in >>= BN_BITS2 - 1;
187 return in;
188 }
189
190 static BN_ULONG is_equal(const BN_ULONG a[P256_LIMBS],
191 const BN_ULONG b[P256_LIMBS])
192 {
193 BN_ULONG res;
194
195 res = a[0] ^ b[0];
196 res |= a[1] ^ b[1];
197 res |= a[2] ^ b[2];
198 res |= a[3] ^ b[3];
199 if (P256_LIMBS == 8) {
200 res |= a[4] ^ b[4];
201 res |= a[5] ^ b[5];
202 res |= a[6] ^ b[6];
203 res |= a[7] ^ b[7];
204 }
205
206 return is_zero(res);
207 }
208
209 static BN_ULONG is_one(const BN_ULONG a[P256_LIMBS])
210 {
211 BN_ULONG res;
212
213 res = a[0] ^ ONE[0];
214 res |= a[1] ^ ONE[1];
215 res |= a[2] ^ ONE[2];
216 res |= a[3] ^ ONE[3];
217 if (P256_LIMBS == 8) {
218 res |= a[4] ^ ONE[4];
219 res |= a[5] ^ ONE[5];
220 res |= a[6] ^ ONE[6];
221 }
222
223 return is_zero(res);
224 }
225
226 #ifndef ECP_NISTZ256_REFERENCE_IMPLEMENTATION
227 void ecp_nistz256_point_double(P256_POINT *r, const P256_POINT *a);
228 void ecp_nistz256_point_add(P256_POINT *r,
229 const P256_POINT *a, const P256_POINT *b);
230 void ecp_nistz256_point_add_affine(P256_POINT *r,
231 const P256_POINT *a,
232 const P256_POINT_AFFINE *b);
233 #else
234 /* Point double: r = 2*a */
235 static void ecp_nistz256_point_double(P256_POINT *r, const P256_POINT *a)
236 {
237 BN_ULONG S[P256_LIMBS];
238 BN_ULONG M[P256_LIMBS];
239 BN_ULONG Zsqr[P256_LIMBS];
240 BN_ULONG tmp0[P256_LIMBS];
241
242 const BN_ULONG *in_x = a->X;
243 const BN_ULONG *in_y = a->Y;
244 const BN_ULONG *in_z = a->Z;
245
246 BN_ULONG *res_x = r->X;
247 BN_ULONG *res_y = r->Y;
248 BN_ULONG *res_z = r->Z;
249
250 ecp_nistz256_mul_by_2(S, in_y);
251
252 ecp_nistz256_sqr_mont(Zsqr, in_z);
253
254 ecp_nistz256_sqr_mont(S, S);
255
256 ecp_nistz256_mul_mont(res_z, in_z, in_y);
257 ecp_nistz256_mul_by_2(res_z, res_z);
258
259 ecp_nistz256_add(M, in_x, Zsqr);
260 ecp_nistz256_sub(Zsqr, in_x, Zsqr);
261
262 ecp_nistz256_sqr_mont(res_y, S);
263 ecp_nistz256_div_by_2(res_y, res_y);
264
265 ecp_nistz256_mul_mont(M, M, Zsqr);
266 ecp_nistz256_mul_by_3(M, M);
267
268 ecp_nistz256_mul_mont(S, S, in_x);
269 ecp_nistz256_mul_by_2(tmp0, S);
270
271 ecp_nistz256_sqr_mont(res_x, M);
272
273 ecp_nistz256_sub(res_x, res_x, tmp0);
274 ecp_nistz256_sub(S, S, res_x);
275
276 ecp_nistz256_mul_mont(S, S, M);
277 ecp_nistz256_sub(res_y, S, res_y);
278 }
279
280 /* Point addition: r = a+b */
281 static void ecp_nistz256_point_add(P256_POINT *r,
282 const P256_POINT *a, const P256_POINT *b)
283 {
284 BN_ULONG U2[P256_LIMBS], S2[P256_LIMBS];
285 BN_ULONG U1[P256_LIMBS], S1[P256_LIMBS];
286 BN_ULONG Z1sqr[P256_LIMBS];
287 BN_ULONG Z2sqr[P256_LIMBS];
288 BN_ULONG H[P256_LIMBS], R[P256_LIMBS];
289 BN_ULONG Hsqr[P256_LIMBS];
290 BN_ULONG Rsqr[P256_LIMBS];
291 BN_ULONG Hcub[P256_LIMBS];
292
293 BN_ULONG res_x[P256_LIMBS];
294 BN_ULONG res_y[P256_LIMBS];
295 BN_ULONG res_z[P256_LIMBS];
296
297 BN_ULONG in1infty, in2infty;
298
299 const BN_ULONG *in1_x = a->X;
300 const BN_ULONG *in1_y = a->Y;
301 const BN_ULONG *in1_z = a->Z;
302
303 const BN_ULONG *in2_x = b->X;
304 const BN_ULONG *in2_y = b->Y;
305 const BN_ULONG *in2_z = b->Z;
306
307 /* We encode infinity as (0,0), which is not on the curve,
308 * so it is OK. */
309 in1infty = (in1_x[0] | in1_x[1] | in1_x[2] | in1_x[3] |
310 in1_y[0] | in1_y[1] | in1_y[2] | in1_y[3]);
311 if (P256_LIMBS == 8)
312 in1infty |= (in1_x[4] | in1_x[5] | in1_x[6] | in1_x[7] |
313 in1_y[4] | in1_y[5] | in1_y[6] | in1_y[7]);
314
315 in2infty = (in2_x[0] | in2_x[1] | in2_x[2] | in2_x[3] |
316 in2_y[0] | in2_y[1] | in2_y[2] | in2_y[3]);
317 if (P256_LIMBS == 8)
318 in2infty |= (in2_x[4] | in2_x[5] | in2_x[6] | in2_x[7] |
319 in2_y[4] | in2_y[5] | in2_y[6] | in2_y[7]);
320
321 in1infty = is_zero(in1infty);
322 in2infty = is_zero(in2infty);
323
324 ecp_nistz256_sqr_mont(Z2sqr, in2_z); /* Z2^2 */
325 ecp_nistz256_sqr_mont(Z1sqr, in1_z); /* Z1^2 */
326
327 ecp_nistz256_mul_mont(S1, Z2sqr, in2_z); /* S1 = Z2^3 */
328 ecp_nistz256_mul_mont(S2, Z1sqr, in1_z); /* S2 = Z1^3 */
329
330 ecp_nistz256_mul_mont(S1, S1, in1_y); /* S1 = Y1*Z2^3 */
331 ecp_nistz256_mul_mont(S2, S2, in2_y); /* S2 = Y2*Z1^3 */
332 ecp_nistz256_sub(R, S2, S1); /* R = S2 - S1 */
333
334 ecp_nistz256_mul_mont(U1, in1_x, Z2sqr); /* U1 = X1*Z2^2 */
335 ecp_nistz256_mul_mont(U2, in2_x, Z1sqr); /* U2 = X2*Z1^2 */
336 ecp_nistz256_sub(H, U2, U1); /* H = U2 - U1 */
337
338 /*
339 * This should not happen during sign/ecdh, so no constant time violation
340 */
341 if (is_equal(U1, U2) && !in1infty && !in2infty) {
342 if (is_equal(S1, S2)) {
343 ecp_nistz256_point_double(r, a);
344 return;
345 } else {
346 memset(r, 0, sizeof(*r));
347 return;
348 }
349 }
350
351 ecp_nistz256_sqr_mont(Rsqr, R); /* R^2 */
352 ecp_nistz256_mul_mont(res_z, H, in1_z); /* Z3 = H*Z1*Z2 */
353 ecp_nistz256_sqr_mont(Hsqr, H); /* H^2 */
354 ecp_nistz256_mul_mont(res_z, res_z, in2_z); /* Z3 = H*Z1*Z2 */
355 ecp_nistz256_mul_mont(Hcub, Hsqr, H); /* H^3 */
356
357 ecp_nistz256_mul_mont(U2, U1, Hsqr); /* U1*H^2 */
358 ecp_nistz256_mul_by_2(Hsqr, U2); /* 2*U1*H^2 */
359
360 ecp_nistz256_sub(res_x, Rsqr, Hsqr);
361 ecp_nistz256_sub(res_x, res_x, Hcub);
362
363 ecp_nistz256_sub(res_y, U2, res_x);
364
365 ecp_nistz256_mul_mont(S2, S1, Hcub);
366 ecp_nistz256_mul_mont(res_y, R, res_y);
367 ecp_nistz256_sub(res_y, res_y, S2);
368
369 copy_conditional(res_x, in2_x, in1infty);
370 copy_conditional(res_y, in2_y, in1infty);
371 copy_conditional(res_z, in2_z, in1infty);
372
373 copy_conditional(res_x, in1_x, in2infty);
374 copy_conditional(res_y, in1_y, in2infty);
375 copy_conditional(res_z, in1_z, in2infty);
376
377 memcpy(r->X, res_x, sizeof(res_x));
378 memcpy(r->Y, res_y, sizeof(res_y));
379 memcpy(r->Z, res_z, sizeof(res_z));
380 }
381
382 /* Point addition when b is known to be affine: r = a+b */
383 static void ecp_nistz256_point_add_affine(P256_POINT *r,
384 const P256_POINT *a,
385 const P256_POINT_AFFINE *b)
386 {
387 BN_ULONG U2[P256_LIMBS], S2[P256_LIMBS];
388 BN_ULONG Z1sqr[P256_LIMBS];
389 BN_ULONG H[P256_LIMBS], R[P256_LIMBS];
390 BN_ULONG Hsqr[P256_LIMBS];
391 BN_ULONG Rsqr[P256_LIMBS];
392 BN_ULONG Hcub[P256_LIMBS];
393
394 BN_ULONG res_x[P256_LIMBS];
395 BN_ULONG res_y[P256_LIMBS];
396 BN_ULONG res_z[P256_LIMBS];
397
398 BN_ULONG in1infty, in2infty;
399
400 const BN_ULONG *in1_x = a->X;
401 const BN_ULONG *in1_y = a->Y;
402 const BN_ULONG *in1_z = a->Z;
403
404 const BN_ULONG *in2_x = b->X;
405 const BN_ULONG *in2_y = b->Y;
406
407 /*
408 * In affine representation we encode infty as (0,0), which is not on the
409 * curve, so it is OK
410 */
411 in1infty = (in1_x[0] | in1_x[1] | in1_x[2] | in1_x[3] |
412 in1_y[0] | in1_y[1] | in1_y[2] | in1_y[3]);
413 if (P256_LIMBS == 8)
414 in1infty |= (in1_x[4] | in1_x[5] | in1_x[6] | in1_x[7] |
415 in1_y[4] | in1_y[5] | in1_y[6] | in1_y[7]);
416
417 in2infty = (in2_x[0] | in2_x[1] | in2_x[2] | in2_x[3] |
418 in2_y[0] | in2_y[1] | in2_y[2] | in2_y[3]);
419 if (P256_LIMBS == 8)
420 in2infty |= (in2_x[4] | in2_x[5] | in2_x[6] | in2_x[7] |
421 in2_y[4] | in2_y[5] | in2_y[6] | in2_y[7]);
422
423 in1infty = is_zero(in1infty);
424 in2infty = is_zero(in2infty);
425
426 ecp_nistz256_sqr_mont(Z1sqr, in1_z); /* Z1^2 */
427
428 ecp_nistz256_mul_mont(U2, in2_x, Z1sqr); /* U2 = X2*Z1^2 */
429 ecp_nistz256_sub(H, U2, in1_x); /* H = U2 - U1 */
430
431 ecp_nistz256_mul_mont(S2, Z1sqr, in1_z); /* S2 = Z1^3 */
432
433 ecp_nistz256_mul_mont(res_z, H, in1_z); /* Z3 = H*Z1*Z2 */
434
435 ecp_nistz256_mul_mont(S2, S2, in2_y); /* S2 = Y2*Z1^3 */
436 ecp_nistz256_sub(R, S2, in1_y); /* R = S2 - S1 */
437
438 ecp_nistz256_sqr_mont(Hsqr, H); /* H^2 */
439 ecp_nistz256_sqr_mont(Rsqr, R); /* R^2 */
440 ecp_nistz256_mul_mont(Hcub, Hsqr, H); /* H^3 */
441
442 ecp_nistz256_mul_mont(U2, in1_x, Hsqr); /* U1*H^2 */
443 ecp_nistz256_mul_by_2(Hsqr, U2); /* 2*U1*H^2 */
444
445 ecp_nistz256_sub(res_x, Rsqr, Hsqr);
446 ecp_nistz256_sub(res_x, res_x, Hcub);
447 ecp_nistz256_sub(H, U2, res_x);
448
449 ecp_nistz256_mul_mont(S2, in1_y, Hcub);
450 ecp_nistz256_mul_mont(H, H, R);
451 ecp_nistz256_sub(res_y, H, S2);
452
453 copy_conditional(res_x, in2_x, in1infty);
454 copy_conditional(res_x, in1_x, in2infty);
455
456 copy_conditional(res_y, in2_y, in1infty);
457 copy_conditional(res_y, in1_y, in2infty);
458
459 copy_conditional(res_z, ONE, in1infty);
460 copy_conditional(res_z, in1_z, in2infty);
461
462 memcpy(r->X, res_x, sizeof(res_x));
463 memcpy(r->Y, res_y, sizeof(res_y));
464 memcpy(r->Z, res_z, sizeof(res_z));
465 }
466 #endif
467
468 /* r = in^-1 mod p */
469 static void ecp_nistz256_mod_inverse(BN_ULONG r[P256_LIMBS],
470 const BN_ULONG in[P256_LIMBS])
471 {
472 /*
473 * The poly is ffffffff 00000001 00000000 00000000 00000000 ffffffff
474 * ffffffff ffffffff We use FLT and used poly-2 as exponent
475 */
476 BN_ULONG p2[P256_LIMBS];
477 BN_ULONG p4[P256_LIMBS];
478 BN_ULONG p8[P256_LIMBS];
479 BN_ULONG p16[P256_LIMBS];
480 BN_ULONG p32[P256_LIMBS];
481 BN_ULONG res[P256_LIMBS];
482 int i;
483
484 ecp_nistz256_sqr_mont(res, in);
485 ecp_nistz256_mul_mont(p2, res, in); /* 3*p */
486
487 ecp_nistz256_sqr_mont(res, p2);
488 ecp_nistz256_sqr_mont(res, res);
489 ecp_nistz256_mul_mont(p4, res, p2); /* f*p */
490
491 ecp_nistz256_sqr_mont(res, p4);
492 ecp_nistz256_sqr_mont(res, res);
493 ecp_nistz256_sqr_mont(res, res);
494 ecp_nistz256_sqr_mont(res, res);
495 ecp_nistz256_mul_mont(p8, res, p4); /* ff*p */
496
497 ecp_nistz256_sqr_mont(res, p8);
498 for (i = 0; i < 7; i++)
499 ecp_nistz256_sqr_mont(res, res);
500 ecp_nistz256_mul_mont(p16, res, p8); /* ffff*p */
501
502 ecp_nistz256_sqr_mont(res, p16);
503 for (i = 0; i < 15; i++)
504 ecp_nistz256_sqr_mont(res, res);
505 ecp_nistz256_mul_mont(p32, res, p16); /* ffffffff*p */
506
507 ecp_nistz256_sqr_mont(res, p32);
508 for (i = 0; i < 31; i++)
509 ecp_nistz256_sqr_mont(res, res);
510 ecp_nistz256_mul_mont(res, res, in);
511
512 for (i = 0; i < 32 * 4; i++)
513 ecp_nistz256_sqr_mont(res, res);
514 ecp_nistz256_mul_mont(res, res, p32);
515
516 for (i = 0; i < 32; i++)
517 ecp_nistz256_sqr_mont(res, res);
518 ecp_nistz256_mul_mont(res, res, p32);
519
520 for (i = 0; i < 16; i++)
521 ecp_nistz256_sqr_mont(res, res);
522 ecp_nistz256_mul_mont(res, res, p16);
523
524 for (i = 0; i < 8; i++)
525 ecp_nistz256_sqr_mont(res, res);
526 ecp_nistz256_mul_mont(res, res, p8);
527
528 ecp_nistz256_sqr_mont(res, res);
529 ecp_nistz256_sqr_mont(res, res);
530 ecp_nistz256_sqr_mont(res, res);
531 ecp_nistz256_sqr_mont(res, res);
532 ecp_nistz256_mul_mont(res, res, p4);
533
534 ecp_nistz256_sqr_mont(res, res);
535 ecp_nistz256_sqr_mont(res, res);
536 ecp_nistz256_mul_mont(res, res, p2);
537
538 ecp_nistz256_sqr_mont(res, res);
539 ecp_nistz256_sqr_mont(res, res);
540 ecp_nistz256_mul_mont(res, res, in);
541
542 memcpy(r, res, sizeof(res));
543 }
544
545 /*
546 * ecp_nistz256_bignum_to_field_elem copies the contents of |in| to |out| and
547 * returns one if it fits. Otherwise it returns zero.
548 */
549 __owur static int ecp_nistz256_bignum_to_field_elem(BN_ULONG out[P256_LIMBS],
550 const BIGNUM *in)
551 {
552 return bn_copy_words(out, in, P256_LIMBS);
553 }
554
555 /* r = sum(scalar[i]*point[i]) */
556 __owur static int ecp_nistz256_windowed_mul(const EC_GROUP *group,
557 P256_POINT *r,
558 const BIGNUM **scalar,
559 const EC_POINT **point,
560 size_t num, BN_CTX *ctx)
561 {
562 size_t i;
563 int j, ret = 0;
564 unsigned int idx;
565 unsigned char (*p_str)[33] = NULL;
566 const unsigned int window_size = 5;
567 const unsigned int mask = (1 << (window_size + 1)) - 1;
568 unsigned int wvalue;
569 P256_POINT *temp; /* place for 5 temporary points */
570 const BIGNUM **scalars = NULL;
571 P256_POINT (*table)[16] = NULL;
572 void *table_storage = NULL;
573
574 if ((num * 16 + 6) > OPENSSL_MALLOC_MAX_NELEMS(P256_POINT)
575 || (table_storage =
576 OPENSSL_malloc((num * 16 + 5) * sizeof(P256_POINT) + 64)) == NULL
577 || (p_str =
578 OPENSSL_malloc(num * 33 * sizeof(unsigned char))) == NULL
579 || (scalars = OPENSSL_malloc(num * sizeof(BIGNUM *))) == NULL) {
580 ECerr(EC_F_ECP_NISTZ256_WINDOWED_MUL, ERR_R_MALLOC_FAILURE);
581 goto err;
582 }
583
584 table = (void *)ALIGNPTR(table_storage, 64);
585 temp = (P256_POINT *)(table + num);
586
587 for (i = 0; i < num; i++) {
588 P256_POINT *row = table[i];
589
590 /* This is an unusual input, we don't guarantee constant-timeness. */
591 if ((BN_num_bits(scalar[i]) > 256) || BN_is_negative(scalar[i])) {
592 BIGNUM *mod;
593
594 if ((mod = BN_CTX_get(ctx)) == NULL)
595 goto err;
596 if (!BN_nnmod(mod, scalar[i], group->order, ctx)) {
597 ECerr(EC_F_ECP_NISTZ256_WINDOWED_MUL, ERR_R_BN_LIB);
598 goto err;
599 }
600 scalars[i] = mod;
601 } else
602 scalars[i] = scalar[i];
603
604 for (j = 0; j < bn_get_top(scalars[i]) * BN_BYTES; j += BN_BYTES) {
605 BN_ULONG d = bn_get_words(scalars[i])[j / BN_BYTES];
606
607 p_str[i][j + 0] = (unsigned char)d;
608 p_str[i][j + 1] = (unsigned char)(d >> 8);
609 p_str[i][j + 2] = (unsigned char)(d >> 16);
610 p_str[i][j + 3] = (unsigned char)(d >>= 24);
611 if (BN_BYTES == 8) {
612 d >>= 8;
613 p_str[i][j + 4] = (unsigned char)d;
614 p_str[i][j + 5] = (unsigned char)(d >> 8);
615 p_str[i][j + 6] = (unsigned char)(d >> 16);
616 p_str[i][j + 7] = (unsigned char)(d >> 24);
617 }
618 }
619 for (; j < 33; j++)
620 p_str[i][j] = 0;
621
622 if (!ecp_nistz256_bignum_to_field_elem(temp[0].X, point[i]->X)
623 || !ecp_nistz256_bignum_to_field_elem(temp[0].Y, point[i]->Y)
624 || !ecp_nistz256_bignum_to_field_elem(temp[0].Z, point[i]->Z)) {
625 ECerr(EC_F_ECP_NISTZ256_WINDOWED_MUL,
626 EC_R_COORDINATES_OUT_OF_RANGE);
627 goto err;
628 }
629
630 /*
631 * row[0] is implicitly (0,0,0) (the point at infinity), therefore it
632 * is not stored. All other values are actually stored with an offset
633 * of -1 in table.
634 */
635
636 ecp_nistz256_scatter_w5 (row, &temp[0], 1);
637 ecp_nistz256_point_double(&temp[1], &temp[0]); /*1+1=2 */
638 ecp_nistz256_scatter_w5 (row, &temp[1], 2);
639 ecp_nistz256_point_add (&temp[2], &temp[1], &temp[0]); /*2+1=3 */
640 ecp_nistz256_scatter_w5 (row, &temp[2], 3);
641 ecp_nistz256_point_double(&temp[1], &temp[1]); /*2*2=4 */
642 ecp_nistz256_scatter_w5 (row, &temp[1], 4);
643 ecp_nistz256_point_double(&temp[2], &temp[2]); /*2*3=6 */
644 ecp_nistz256_scatter_w5 (row, &temp[2], 6);
645 ecp_nistz256_point_add (&temp[3], &temp[1], &temp[0]); /*4+1=5 */
646 ecp_nistz256_scatter_w5 (row, &temp[3], 5);
647 ecp_nistz256_point_add (&temp[4], &temp[2], &temp[0]); /*6+1=7 */
648 ecp_nistz256_scatter_w5 (row, &temp[4], 7);
649 ecp_nistz256_point_double(&temp[1], &temp[1]); /*2*4=8 */
650 ecp_nistz256_scatter_w5 (row, &temp[1], 8);
651 ecp_nistz256_point_double(&temp[2], &temp[2]); /*2*6=12 */
652 ecp_nistz256_scatter_w5 (row, &temp[2], 12);
653 ecp_nistz256_point_double(&temp[3], &temp[3]); /*2*5=10 */
654 ecp_nistz256_scatter_w5 (row, &temp[3], 10);
655 ecp_nistz256_point_double(&temp[4], &temp[4]); /*2*7=14 */
656 ecp_nistz256_scatter_w5 (row, &temp[4], 14);
657 ecp_nistz256_point_add (&temp[2], &temp[2], &temp[0]); /*12+1=13*/
658 ecp_nistz256_scatter_w5 (row, &temp[2], 13);
659 ecp_nistz256_point_add (&temp[3], &temp[3], &temp[0]); /*10+1=11*/
660 ecp_nistz256_scatter_w5 (row, &temp[3], 11);
661 ecp_nistz256_point_add (&temp[4], &temp[4], &temp[0]); /*14+1=15*/
662 ecp_nistz256_scatter_w5 (row, &temp[4], 15);
663 ecp_nistz256_point_add (&temp[2], &temp[1], &temp[0]); /*8+1=9 */
664 ecp_nistz256_scatter_w5 (row, &temp[2], 9);
665 ecp_nistz256_point_double(&temp[1], &temp[1]); /*2*8=16 */
666 ecp_nistz256_scatter_w5 (row, &temp[1], 16);
667 }
668
669 idx = 255;
670
671 wvalue = p_str[0][(idx - 1) / 8];
672 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
673
674 /*
675 * We gather to temp[0], because we know it's position relative
676 * to table
677 */
678 ecp_nistz256_gather_w5(&temp[0], table[0], _booth_recode_w5(wvalue) >> 1);
679 memcpy(r, &temp[0], sizeof(temp[0]));
680
681 while (idx >= 5) {
682 for (i = (idx == 255 ? 1 : 0); i < num; i++) {
683 unsigned int off = (idx - 1) / 8;
684
685 wvalue = p_str[i][off] | p_str[i][off + 1] << 8;
686 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
687
688 wvalue = _booth_recode_w5(wvalue);
689
690 ecp_nistz256_gather_w5(&temp[0], table[i], wvalue >> 1);
691
692 ecp_nistz256_neg(temp[1].Y, temp[0].Y);
693 copy_conditional(temp[0].Y, temp[1].Y, (wvalue & 1));
694
695 ecp_nistz256_point_add(r, r, &temp[0]);
696 }
697
698 idx -= window_size;
699
700 ecp_nistz256_point_double(r, r);
701 ecp_nistz256_point_double(r, r);
702 ecp_nistz256_point_double(r, r);
703 ecp_nistz256_point_double(r, r);
704 ecp_nistz256_point_double(r, r);
705 }
706
707 /* Final window */
708 for (i = 0; i < num; i++) {
709 wvalue = p_str[i][0];
710 wvalue = (wvalue << 1) & mask;
711
712 wvalue = _booth_recode_w5(wvalue);
713
714 ecp_nistz256_gather_w5(&temp[0], table[i], wvalue >> 1);
715
716 ecp_nistz256_neg(temp[1].Y, temp[0].Y);
717 copy_conditional(temp[0].Y, temp[1].Y, wvalue & 1);
718
719 ecp_nistz256_point_add(r, r, &temp[0]);
720 }
721
722 ret = 1;
723 err:
724 if (table_storage)
725 OPENSSL_free(table_storage);
726 if (p_str)
727 OPENSSL_free(p_str);
728 if (scalars)
729 OPENSSL_free(scalars);
730 return ret;
731 }
732
733 /* Coordinates of G, for which we have precomputed tables */
734 const static BN_ULONG def_xG[P256_LIMBS] = {
735 TOBN(0x79e730d4, 0x18a9143c), TOBN(0x75ba95fc, 0x5fedb601),
736 TOBN(0x79fb732b, 0x77622510), TOBN(0x18905f76, 0xa53755c6)
737 };
738
739 const static BN_ULONG def_yG[P256_LIMBS] = {
740 TOBN(0xddf25357, 0xce95560a), TOBN(0x8b4ab8e4, 0xba19e45c),
741 TOBN(0xd2e88688, 0xdd21f325), TOBN(0x8571ff18, 0x25885d85)
742 };
743
744 /*
745 * ecp_nistz256_is_affine_G returns one if |generator| is the standard, P-256
746 * generator.
747 */
748 static int ecp_nistz256_is_affine_G(const EC_POINT *generator)
749 {
750 return (bn_get_top(generator->X) == P256_LIMBS) &&
751 (bn_get_top(generator->Y) == P256_LIMBS) &&
752 (bn_get_top(generator->Z) == (P256_LIMBS - P256_LIMBS / 8)) &&
753 is_equal(bn_get_words(generator->X), def_xG) &&
754 is_equal(bn_get_words(generator->Y), def_yG) &&
755 is_one(bn_get_words(generator->Z));
756 }
757
758 __owur static int ecp_nistz256_mult_precompute(EC_GROUP *group, BN_CTX *ctx)
759 {
760 /*
761 * We precompute a table for a Booth encoded exponent (wNAF) based
762 * computation. Each table holds 64 values for safe access, with an
763 * implicit value of infinity at index zero. We use window of size 7, and
764 * therefore require ceil(256/7) = 37 tables.
765 */
766 BIGNUM *order;
767 EC_POINT *P = NULL, *T = NULL;
768 const EC_POINT *generator;
769 EC_PRE_COMP *pre_comp;
770 BN_CTX *new_ctx = NULL;
771 int i, j, k, ret = 0;
772 size_t w;
773
774 PRECOMP256_ROW *preComputedTable = NULL;
775 unsigned char *precomp_storage = NULL;
776
777 /* if there is an old EC_PRE_COMP object, throw it away */
778 EC_EX_DATA_free_data(&group->extra_data, ecp_nistz256_pre_comp_dup,
779 ecp_nistz256_pre_comp_free,
780 ecp_nistz256_pre_comp_clear_free);
781
782 generator = EC_GROUP_get0_generator(group);
783 if (generator == NULL) {
784 ECerr(EC_F_ECP_NISTZ256_MULT_PRECOMPUTE, EC_R_UNDEFINED_GENERATOR);
785 return 0;
786 }
787
788 if (ecp_nistz256_is_affine_G(generator)) {
789 /*
790 * No need to calculate tables for the standard generator because we
791 * have them statically.
792 */
793 return 1;
794 }
795
796 if ((pre_comp = ecp_nistz256_pre_comp_new(group)) == NULL)
797 return 0;
798
799 if (ctx == NULL) {
800 ctx = new_ctx = BN_CTX_new();
801 if (ctx == NULL)
802 goto err;
803 }
804
805 BN_CTX_start(ctx);
806 order = BN_CTX_get(ctx);
807
808 if (order == NULL)
809 goto err;
810
811 if (!EC_GROUP_get_order(group, order, ctx))
812 goto err;
813
814 if (BN_is_zero(order)) {
815 ECerr(EC_F_ECP_NISTZ256_MULT_PRECOMPUTE, EC_R_UNKNOWN_ORDER);
816 goto err;
817 }
818
819 w = 7;
820
821 if ((precomp_storage =
822 OPENSSL_malloc(37 * 64 * sizeof(P256_POINT_AFFINE) + 64)) == NULL) {
823 ECerr(EC_F_ECP_NISTZ256_MULT_PRECOMPUTE, ERR_R_MALLOC_FAILURE);
824 goto err;
825 }
826
827 preComputedTable = (void *)ALIGNPTR(precomp_storage, 64);
828
829 P = EC_POINT_new(group);
830 T = EC_POINT_new(group);
831 if (P == NULL || T == NULL)
832 goto err;
833
834 /*
835 * The zero entry is implicitly infinity, and we skip it, storing other
836 * values with -1 offset.
837 */
838 if (!EC_POINT_copy(T, generator))
839 goto err;
840
841 for (k = 0; k < 64; k++) {
842 if (!EC_POINT_copy(P, T))
843 goto err;
844 for (j = 0; j < 37; j++) {
845 P256_POINT_AFFINE temp;
846 /*
847 * It would be faster to use EC_POINTs_make_affine and
848 * make multiple points affine at the same time.
849 */
850 if (!EC_POINT_make_affine(group, P, ctx))
851 goto err;
852 if (!ecp_nistz256_bignum_to_field_elem(temp.X, P->X) ||
853 !ecp_nistz256_bignum_to_field_elem(temp.Y, P->Y)) {
854 ECerr(EC_F_ECP_NISTZ256_MULT_PRECOMPUTE,
855 EC_R_COORDINATES_OUT_OF_RANGE);
856 goto err;
857 }
858 ecp_nistz256_scatter_w7(preComputedTable[j], &temp, k);
859 for (i = 0; i < 7; i++) {
860 if (!EC_POINT_dbl(group, P, P, ctx))
861 goto err;
862 }
863 }
864 if (!EC_POINT_add(group, T, T, generator, ctx))
865 goto err;
866 }
867
868 pre_comp->group = group;
869 pre_comp->w = w;
870 pre_comp->precomp = preComputedTable;
871 pre_comp->precomp_storage = precomp_storage;
872
873 precomp_storage = NULL;
874
875 if (!EC_EX_DATA_set_data(&group->extra_data, pre_comp,
876 ecp_nistz256_pre_comp_dup,
877 ecp_nistz256_pre_comp_free,
878 ecp_nistz256_pre_comp_clear_free)) {
879 goto err;
880 }
881
882 pre_comp = NULL;
883
884 ret = 1;
885
886 err:
887 if (ctx != NULL)
888 BN_CTX_end(ctx);
889 BN_CTX_free(new_ctx);
890
891 ecp_nistz256_pre_comp_free(pre_comp);
892 if (precomp_storage)
893 OPENSSL_free(precomp_storage);
894 EC_POINT_free(P);
895 EC_POINT_free(T);
896 return ret;
897 }
898
899 /*
900 * Note that by default ECP_NISTZ256_AVX2 is undefined. While it's great
901 * code processing 4 points in parallel, corresponding serial operation
902 * is several times slower, because it uses 29x29=58-bit multiplication
903 * as opposite to 64x64=128-bit in integer-only scalar case. As result
904 * it doesn't provide *significant* performance improvement. Note that
905 * just defining ECP_NISTZ256_AVX2 is not sufficient to make it work,
906 * you'd need to compile even asm/ecp_nistz256-avx.pl module.
907 */
908 #if defined(ECP_NISTZ256_AVX2)
909 # if !(defined(__x86_64) || defined(__x86_64__) || \
910 defined(_M_AMD64) || defined(_MX64)) || \
911 !(defined(__GNUC__) || defined(_MSC_VER)) /* this is for ALIGN32 */
912 # undef ECP_NISTZ256_AVX2
913 # else
914 /* Constant time access, loading four values, from four consecutive tables */
915 void ecp_nistz256_avx2_multi_gather_w7(void *result, const void *in,
916 int index0, int index1, int index2,
917 int index3);
918 void ecp_nistz256_avx2_transpose_convert(void *RESULTx4, const void *in);
919 void ecp_nistz256_avx2_convert_transpose_back(void *result, const void *Ax4);
920 void ecp_nistz256_avx2_point_add_affine_x4(void *RESULTx4, const void *Ax4,
921 const void *Bx4);
922 void ecp_nistz256_avx2_point_add_affines_x4(void *RESULTx4, const void *Ax4,
923 const void *Bx4);
924 void ecp_nistz256_avx2_to_mont(void *RESULTx4, const void *Ax4);
925 void ecp_nistz256_avx2_from_mont(void *RESULTx4, const void *Ax4);
926 void ecp_nistz256_avx2_set1(void *RESULTx4);
927 int ecp_nistz_avx2_eligible(void);
928
929 static void booth_recode_w7(unsigned char *sign,
930 unsigned char *digit, unsigned char in)
931 {
932 unsigned char s, d;
933
934 s = ~((in >> 7) - 1);
935 d = (1 << 8) - in - 1;
936 d = (d & s) | (in & ~s);
937 d = (d >> 1) + (d & 1);
938
939 *sign = s & 1;
940 *digit = d;
941 }
942
943 /*
944 * ecp_nistz256_avx2_mul_g performs multiplication by G, using only the
945 * precomputed table. It does 4 affine point additions in parallel,
946 * significantly speeding up point multiplication for a fixed value.
947 */
948 static void ecp_nistz256_avx2_mul_g(P256_POINT *r,
949 unsigned char p_str[33],
950 const P256_POINT_AFFINE(*preComputedTable)[64])
951 {
952 const unsigned int window_size = 7;
953 const unsigned int mask = (1 << (window_size + 1)) - 1;
954 unsigned int wvalue;
955 /* Using 4 windows at a time */
956 unsigned char sign0, digit0;
957 unsigned char sign1, digit1;
958 unsigned char sign2, digit2;
959 unsigned char sign3, digit3;
960 unsigned int idx = 0;
961 BN_ULONG tmp[P256_LIMBS];
962 int i;
963
964 ALIGN32 BN_ULONG aX4[4 * 9 * 3] = { 0 };
965 ALIGN32 BN_ULONG bX4[4 * 9 * 2] = { 0 };
966 ALIGN32 P256_POINT_AFFINE point_arr[4];
967 ALIGN32 P256_POINT res_point_arr[4];
968
969 /* Initial four windows */
970 wvalue = *((u16 *) & p_str[0]);
971 wvalue = (wvalue << 1) & mask;
972 idx += window_size;
973 booth_recode_w7(&sign0, &digit0, wvalue);
974 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
975 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
976 idx += window_size;
977 booth_recode_w7(&sign1, &digit1, wvalue);
978 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
979 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
980 idx += window_size;
981 booth_recode_w7(&sign2, &digit2, wvalue);
982 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
983 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
984 idx += window_size;
985 booth_recode_w7(&sign3, &digit3, wvalue);
986
987 ecp_nistz256_avx2_multi_gather_w7(point_arr, preComputedTable[0],
988 digit0, digit1, digit2, digit3);
989
990 ecp_nistz256_neg(tmp, point_arr[0].Y);
991 copy_conditional(point_arr[0].Y, tmp, sign0);
992 ecp_nistz256_neg(tmp, point_arr[1].Y);
993 copy_conditional(point_arr[1].Y, tmp, sign1);
994 ecp_nistz256_neg(tmp, point_arr[2].Y);
995 copy_conditional(point_arr[2].Y, tmp, sign2);
996 ecp_nistz256_neg(tmp, point_arr[3].Y);
997 copy_conditional(point_arr[3].Y, tmp, sign3);
998
999 ecp_nistz256_avx2_transpose_convert(aX4, point_arr);
1000 ecp_nistz256_avx2_to_mont(aX4, aX4);
1001 ecp_nistz256_avx2_to_mont(&aX4[4 * 9], &aX4[4 * 9]);
1002 ecp_nistz256_avx2_set1(&aX4[4 * 9 * 2]);
1003
1004 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
1005 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
1006 idx += window_size;
1007 booth_recode_w7(&sign0, &digit0, wvalue);
1008 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
1009 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
1010 idx += window_size;
1011 booth_recode_w7(&sign1, &digit1, wvalue);
1012 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
1013 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
1014 idx += window_size;
1015 booth_recode_w7(&sign2, &digit2, wvalue);
1016 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
1017 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
1018 idx += window_size;
1019 booth_recode_w7(&sign3, &digit3, wvalue);
1020
1021 ecp_nistz256_avx2_multi_gather_w7(point_arr, preComputedTable[4 * 1],
1022 digit0, digit1, digit2, digit3);
1023
1024 ecp_nistz256_neg(tmp, point_arr[0].Y);
1025 copy_conditional(point_arr[0].Y, tmp, sign0);
1026 ecp_nistz256_neg(tmp, point_arr[1].Y);
1027 copy_conditional(point_arr[1].Y, tmp, sign1);
1028 ecp_nistz256_neg(tmp, point_arr[2].Y);
1029 copy_conditional(point_arr[2].Y, tmp, sign2);
1030 ecp_nistz256_neg(tmp, point_arr[3].Y);
1031 copy_conditional(point_arr[3].Y, tmp, sign3);
1032
1033 ecp_nistz256_avx2_transpose_convert(bX4, point_arr);
1034 ecp_nistz256_avx2_to_mont(bX4, bX4);
1035 ecp_nistz256_avx2_to_mont(&bX4[4 * 9], &bX4[4 * 9]);
1036 /* Optimized when both inputs are affine */
1037 ecp_nistz256_avx2_point_add_affines_x4(aX4, aX4, bX4);
1038
1039 for (i = 2; i < 9; i++) {
1040 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
1041 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
1042 idx += window_size;
1043 booth_recode_w7(&sign0, &digit0, wvalue);
1044 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
1045 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
1046 idx += window_size;
1047 booth_recode_w7(&sign1, &digit1, wvalue);
1048 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
1049 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
1050 idx += window_size;
1051 booth_recode_w7(&sign2, &digit2, wvalue);
1052 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
1053 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
1054 idx += window_size;
1055 booth_recode_w7(&sign3, &digit3, wvalue);
1056
1057 ecp_nistz256_avx2_multi_gather_w7(point_arr,
1058 preComputedTable[4 * i],
1059 digit0, digit1, digit2, digit3);
1060
1061 ecp_nistz256_neg(tmp, point_arr[0].Y);
1062 copy_conditional(point_arr[0].Y, tmp, sign0);
1063 ecp_nistz256_neg(tmp, point_arr[1].Y);
1064 copy_conditional(point_arr[1].Y, tmp, sign1);
1065 ecp_nistz256_neg(tmp, point_arr[2].Y);
1066 copy_conditional(point_arr[2].Y, tmp, sign2);
1067 ecp_nistz256_neg(tmp, point_arr[3].Y);
1068 copy_conditional(point_arr[3].Y, tmp, sign3);
1069
1070 ecp_nistz256_avx2_transpose_convert(bX4, point_arr);
1071 ecp_nistz256_avx2_to_mont(bX4, bX4);
1072 ecp_nistz256_avx2_to_mont(&bX4[4 * 9], &bX4[4 * 9]);
1073
1074 ecp_nistz256_avx2_point_add_affine_x4(aX4, aX4, bX4);
1075 }
1076
1077 ecp_nistz256_avx2_from_mont(&aX4[4 * 9 * 0], &aX4[4 * 9 * 0]);
1078 ecp_nistz256_avx2_from_mont(&aX4[4 * 9 * 1], &aX4[4 * 9 * 1]);
1079 ecp_nistz256_avx2_from_mont(&aX4[4 * 9 * 2], &aX4[4 * 9 * 2]);
1080
1081 ecp_nistz256_avx2_convert_transpose_back(res_point_arr, aX4);
1082 /* Last window is performed serially */
1083 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
1084 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
1085 booth_recode_w7(&sign0, &digit0, wvalue);
1086 ecp_nistz256_gather_w7((P256_POINT_AFFINE *)r,
1087 preComputedTable[36], digit0);
1088 ecp_nistz256_neg(tmp, r->Y);
1089 copy_conditional(r->Y, tmp, sign0);
1090 memcpy(r->Z, ONE, sizeof(ONE));
1091 /* Sum the four windows */
1092 ecp_nistz256_point_add(r, r, &res_point_arr[0]);
1093 ecp_nistz256_point_add(r, r, &res_point_arr[1]);
1094 ecp_nistz256_point_add(r, r, &res_point_arr[2]);
1095 ecp_nistz256_point_add(r, r, &res_point_arr[3]);
1096 }
1097 # endif
1098 #endif
1099
1100 __owur static int ecp_nistz256_set_from_affine(EC_POINT *out, const EC_GROUP *group,
1101 const P256_POINT_AFFINE *in,
1102 BN_CTX *ctx)
1103 {
1104 BIGNUM *x, *y;
1105 BN_ULONG d_x[P256_LIMBS], d_y[P256_LIMBS];
1106 int ret = 0;
1107
1108 x = BN_new();
1109 if (!x)
1110 return 0;
1111 y = BN_new();
1112 if (!y) {
1113 BN_free(x);
1114 return 0;
1115 }
1116 memcpy(d_x, in->X, sizeof(d_x));
1117 bn_set_static_words(x, d_x, P256_LIMBS);
1118
1119 memcpy(d_y, in->Y, sizeof(d_y));
1120 bn_set_static_words(y, d_y, P256_LIMBS);
1121
1122 ret = EC_POINT_set_affine_coordinates_GFp(group, out, x, y, ctx);
1123
1124 BN_free(x);
1125 BN_free(y);
1126
1127 return ret;
1128 }
1129
1130 /* r = scalar*G + sum(scalars[i]*points[i]) */
1131 __owur static int ecp_nistz256_points_mul(const EC_GROUP *group,
1132 EC_POINT *r,
1133 const BIGNUM *scalar,
1134 size_t num,
1135 const EC_POINT *points[],
1136 const BIGNUM *scalars[], BN_CTX *ctx)
1137 {
1138 int i = 0, ret = 0, no_precomp_for_generator = 0, p_is_infinity = 0;
1139 size_t j;
1140 unsigned char p_str[33] = { 0 };
1141 const PRECOMP256_ROW *preComputedTable = NULL;
1142 const EC_PRE_COMP *pre_comp = NULL;
1143 const EC_POINT *generator = NULL;
1144 BN_CTX *new_ctx = NULL;
1145 const BIGNUM **new_scalars = NULL;
1146 const EC_POINT **new_points = NULL;
1147 unsigned int idx = 0;
1148 const unsigned int window_size = 7;
1149 const unsigned int mask = (1 << (window_size + 1)) - 1;
1150 unsigned int wvalue;
1151 ALIGN32 union {
1152 P256_POINT p;
1153 P256_POINT_AFFINE a;
1154 } t, p;
1155 BIGNUM *tmp_scalar;
1156
1157 if ((num + 1) == 0 || (num + 1) > OPENSSL_MALLOC_MAX_NELEMS(void *)) {
1158 ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, ERR_R_MALLOC_FAILURE);
1159 return 0;
1160 }
1161
1162 if (group->meth != r->meth) {
1163 ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, EC_R_INCOMPATIBLE_OBJECTS);
1164 return 0;
1165 }
1166
1167 if ((scalar == NULL) && (num == 0))
1168 return EC_POINT_set_to_infinity(group, r);
1169
1170 for (j = 0; j < num; j++) {
1171 if (group->meth != points[j]->meth) {
1172 ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, EC_R_INCOMPATIBLE_OBJECTS);
1173 return 0;
1174 }
1175 }
1176
1177 if (ctx == NULL) {
1178 ctx = new_ctx = BN_CTX_new();
1179 if (ctx == NULL)
1180 goto err;
1181 }
1182
1183 BN_CTX_start(ctx);
1184
1185 if (scalar) {
1186 generator = EC_GROUP_get0_generator(group);
1187 if (generator == NULL) {
1188 ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, EC_R_UNDEFINED_GENERATOR);
1189 goto err;
1190 }
1191
1192 /* look if we can use precomputed multiples of generator */
1193 pre_comp =
1194 EC_EX_DATA_get_data(group->extra_data, ecp_nistz256_pre_comp_dup,
1195 ecp_nistz256_pre_comp_free,
1196 ecp_nistz256_pre_comp_clear_free);
1197
1198 if (pre_comp) {
1199 /*
1200 * If there is a precomputed table for the generator, check that
1201 * it was generated with the same generator.
1202 */
1203 EC_POINT *pre_comp_generator = EC_POINT_new(group);
1204 if (pre_comp_generator == NULL)
1205 goto err;
1206
1207 if (!ecp_nistz256_set_from_affine(pre_comp_generator,
1208 group, pre_comp->precomp[0],
1209 ctx)) {
1210 EC_POINT_free(pre_comp_generator);
1211 goto err;
1212 }
1213
1214 if (0 == EC_POINT_cmp(group, generator, pre_comp_generator, ctx))
1215 preComputedTable = (const PRECOMP256_ROW *)pre_comp->precomp;
1216
1217 EC_POINT_free(pre_comp_generator);
1218 }
1219
1220 if (preComputedTable == NULL && ecp_nistz256_is_affine_G(generator)) {
1221 /*
1222 * If there is no precomputed data, but the generator is the
1223 * default, a hardcoded table of precomputed data is used. This
1224 * is because applications, such as Apache, do not use
1225 * EC_KEY_precompute_mult.
1226 */
1227 preComputedTable = ecp_nistz256_precomputed;
1228 }
1229
1230 if (preComputedTable) {
1231 if ((BN_num_bits(scalar) > 256)
1232 || BN_is_negative(scalar)) {
1233 if ((tmp_scalar = BN_CTX_get(ctx)) == NULL)
1234 goto err;
1235
1236 if (!BN_nnmod(tmp_scalar, scalar, group->order, ctx)) {
1237 ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, ERR_R_BN_LIB);
1238 goto err;
1239 }
1240 scalar = tmp_scalar;
1241 }
1242
1243 for (i = 0; i < bn_get_top(scalar) * BN_BYTES; i += BN_BYTES) {
1244 BN_ULONG d = bn_get_words(scalar)[i / BN_BYTES];
1245
1246 p_str[i + 0] = (unsigned char)d;
1247 p_str[i + 1] = (unsigned char)(d >> 8);
1248 p_str[i + 2] = (unsigned char)(d >> 16);
1249 p_str[i + 3] = (unsigned char)(d >>= 24);
1250 if (BN_BYTES == 8) {
1251 d >>= 8;
1252 p_str[i + 4] = (unsigned char)d;
1253 p_str[i + 5] = (unsigned char)(d >> 8);
1254 p_str[i + 6] = (unsigned char)(d >> 16);
1255 p_str[i + 7] = (unsigned char)(d >> 24);
1256 }
1257 }
1258
1259 for (; i < 33; i++)
1260 p_str[i] = 0;
1261
1262 #if defined(ECP_NISTZ256_AVX2)
1263 if (ecp_nistz_avx2_eligible()) {
1264 ecp_nistz256_avx2_mul_g(&p.p, p_str, preComputedTable);
1265 } else
1266 #endif
1267 {
1268 /* First window */
1269 wvalue = (p_str[0] << 1) & mask;
1270 idx += window_size;
1271
1272 wvalue = _booth_recode_w7(wvalue);
1273
1274 ecp_nistz256_gather_w7(&p.a, preComputedTable[0],
1275 wvalue >> 1);
1276
1277 ecp_nistz256_neg(p.p.Z, p.p.Y);
1278 copy_conditional(p.p.Y, p.p.Z, wvalue & 1);
1279
1280 memcpy(p.p.Z, ONE, sizeof(ONE));
1281
1282 for (i = 1; i < 37; i++) {
1283 unsigned int off = (idx - 1) / 8;
1284 wvalue = p_str[off] | p_str[off + 1] << 8;
1285 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
1286 idx += window_size;
1287
1288 wvalue = _booth_recode_w7(wvalue);
1289
1290 ecp_nistz256_gather_w7(&t.a,
1291 preComputedTable[i], wvalue >> 1);
1292
1293 ecp_nistz256_neg(t.p.Z, t.a.Y);
1294 copy_conditional(t.a.Y, t.p.Z, wvalue & 1);
1295
1296 ecp_nistz256_point_add_affine(&p.p, &p.p, &t.a);
1297 }
1298 }
1299 } else {
1300 p_is_infinity = 1;
1301 no_precomp_for_generator = 1;
1302 }
1303 } else
1304 p_is_infinity = 1;
1305
1306 if (no_precomp_for_generator) {
1307 /*
1308 * Without a precomputed table for the generator, it has to be
1309 * handled like a normal point.
1310 */
1311 new_scalars = OPENSSL_malloc((num + 1) * sizeof(BIGNUM *));
1312 if (!new_scalars) {
1313 ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, ERR_R_MALLOC_FAILURE);
1314 goto err;
1315 }
1316
1317 new_points = OPENSSL_malloc((num + 1) * sizeof(EC_POINT *));
1318 if (!new_points) {
1319 ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, ERR_R_MALLOC_FAILURE);
1320 goto err;
1321 }
1322
1323 memcpy(new_scalars, scalars, num * sizeof(BIGNUM *));
1324 new_scalars[num] = scalar;
1325 memcpy(new_points, points, num * sizeof(EC_POINT *));
1326 new_points[num] = generator;
1327
1328 scalars = new_scalars;
1329 points = new_points;
1330 num++;
1331 }
1332
1333 if (num) {
1334 P256_POINT *out = &t.p;
1335 if (p_is_infinity)
1336 out = &p.p;
1337
1338 if (!ecp_nistz256_windowed_mul(group, out, scalars, points, num, ctx))
1339 goto err;
1340
1341 if (!p_is_infinity)
1342 ecp_nistz256_point_add(&p.p, &p.p, out);
1343 }
1344
1345 /* Not constant-time, but we're only operating on the public output. */
1346 if (!bn_set_words(r->X, p.p.X, P256_LIMBS) ||
1347 !bn_set_words(r->Y, p.p.Y, P256_LIMBS) ||
1348 !bn_set_words(r->Z, p.p.Z, P256_LIMBS)) {
1349 goto err;
1350 }
1351 r->Z_is_one = is_one(p.p.Z) & 1;
1352
1353 ret = 1;
1354
1355 err:
1356 if (ctx)
1357 BN_CTX_end(ctx);
1358 BN_CTX_free(new_ctx);
1359 if (new_points)
1360 OPENSSL_free(new_points);
1361 if (new_scalars)
1362 OPENSSL_free(new_scalars);
1363 return ret;
1364 }
1365
1366 __owur static int ecp_nistz256_get_affine(const EC_GROUP *group,
1367 const EC_POINT *point,
1368 BIGNUM *x, BIGNUM *y, BN_CTX *ctx)
1369 {
1370 BN_ULONG z_inv2[P256_LIMBS];
1371 BN_ULONG z_inv3[P256_LIMBS];
1372 BN_ULONG x_aff[P256_LIMBS];
1373 BN_ULONG y_aff[P256_LIMBS];
1374 BN_ULONG point_x[P256_LIMBS], point_y[P256_LIMBS], point_z[P256_LIMBS];
1375 BN_ULONG x_ret[P256_LIMBS], y_ret[P256_LIMBS];
1376
1377 if (EC_POINT_is_at_infinity(group, point)) {
1378 ECerr(EC_F_ECP_NISTZ256_GET_AFFINE, EC_R_POINT_AT_INFINITY);
1379 return 0;
1380 }
1381
1382 if (!ecp_nistz256_bignum_to_field_elem(point_x, point->X) ||
1383 !ecp_nistz256_bignum_to_field_elem(point_y, point->Y) ||
1384 !ecp_nistz256_bignum_to_field_elem(point_z, point->Z)) {
1385 ECerr(EC_F_ECP_NISTZ256_GET_AFFINE, EC_R_COORDINATES_OUT_OF_RANGE);
1386 return 0;
1387 }
1388
1389 ecp_nistz256_mod_inverse(z_inv3, point_z);
1390 ecp_nistz256_sqr_mont(z_inv2, z_inv3);
1391 ecp_nistz256_mul_mont(x_aff, z_inv2, point_x);
1392
1393 if (x != NULL) {
1394 ecp_nistz256_from_mont(x_ret, x_aff);
1395 if (!bn_set_words(x, x_ret, P256_LIMBS))
1396 return 0;
1397 }
1398
1399 if (y != NULL) {
1400 ecp_nistz256_mul_mont(z_inv3, z_inv3, z_inv2);
1401 ecp_nistz256_mul_mont(y_aff, z_inv3, point_y);
1402 ecp_nistz256_from_mont(y_ret, y_aff);
1403 if (!bn_set_words(y, y_ret, P256_LIMBS))
1404 return 0;
1405 }
1406
1407 return 1;
1408 }
1409
1410 static EC_PRE_COMP *ecp_nistz256_pre_comp_new(const EC_GROUP *group)
1411 {
1412 EC_PRE_COMP *ret = NULL;
1413
1414 if (!group)
1415 return NULL;
1416
1417 ret = OPENSSL_malloc(sizeof(EC_PRE_COMP));
1418
1419 if (!ret) {
1420 ECerr(EC_F_ECP_NISTZ256_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE);
1421 return ret;
1422 }
1423
1424 ret->group = group;
1425 ret->w = 6; /* default */
1426 ret->precomp = NULL;
1427 ret->precomp_storage = NULL;
1428 ret->references = 1;
1429 return ret;
1430 }
1431
1432 static void *ecp_nistz256_pre_comp_dup(void *src_)
1433 {
1434 EC_PRE_COMP *src = src_;
1435
1436 /* no need to actually copy, these objects never change! */
1437 CRYPTO_add(&src->references, 1, CRYPTO_LOCK_EC_PRE_COMP);
1438
1439 return src_;
1440 }
1441
1442 static void ecp_nistz256_pre_comp_free(void *pre_)
1443 {
1444 int i;
1445 EC_PRE_COMP *pre = pre_;
1446
1447 if (!pre)
1448 return;
1449
1450 i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP);
1451 if (i > 0)
1452 return;
1453
1454 if (pre->precomp_storage)
1455 OPENSSL_free(pre->precomp_storage);
1456
1457 OPENSSL_free(pre);
1458 }
1459
1460 static void ecp_nistz256_pre_comp_clear_free(void *pre_)
1461 {
1462 int i;
1463 EC_PRE_COMP *pre = pre_;
1464
1465 if (!pre)
1466 return;
1467
1468 i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP);
1469 if (i > 0)
1470 return;
1471
1472 OPENSSL_clear_free(pre->precomp,
1473 32 * sizeof(unsigned char) * (1 << pre->w) * 2 * 37);
1474 OPENSSL_clear_free(pre, sizeof *pre);
1475 }
1476
1477 static int ecp_nistz256_window_have_precompute_mult(const EC_GROUP *group)
1478 {
1479 /* There is a hard-coded table for the default generator. */
1480 const EC_POINT *generator = EC_GROUP_get0_generator(group);
1481 if (generator != NULL && ecp_nistz256_is_affine_G(generator)) {
1482 /* There is a hard-coded table for the default generator. */
1483 return 1;
1484 }
1485
1486 return EC_EX_DATA_get_data(group->extra_data, ecp_nistz256_pre_comp_dup,
1487 ecp_nistz256_pre_comp_free,
1488 ecp_nistz256_pre_comp_clear_free) != NULL;
1489 }
1490
1491 const EC_METHOD *EC_GFp_nistz256_method(void)
1492 {
1493 static const EC_METHOD ret = {
1494 EC_FLAGS_DEFAULT_OCT,
1495 NID_X9_62_prime_field,
1496 ec_GFp_mont_group_init,
1497 ec_GFp_mont_group_finish,
1498 ec_GFp_mont_group_clear_finish,
1499 ec_GFp_mont_group_copy,
1500 ec_GFp_mont_group_set_curve,
1501 ec_GFp_simple_group_get_curve,
1502 ec_GFp_simple_group_get_degree,
1503 ec_GFp_simple_group_check_discriminant,
1504 ec_GFp_simple_point_init,
1505 ec_GFp_simple_point_finish,
1506 ec_GFp_simple_point_clear_finish,
1507 ec_GFp_simple_point_copy,
1508 ec_GFp_simple_point_set_to_infinity,
1509 ec_GFp_simple_set_Jprojective_coordinates_GFp,
1510 ec_GFp_simple_get_Jprojective_coordinates_GFp,
1511 ec_GFp_simple_point_set_affine_coordinates,
1512 ecp_nistz256_get_affine,
1513 0, 0, 0,
1514 ec_GFp_simple_add,
1515 ec_GFp_simple_dbl,
1516 ec_GFp_simple_invert,
1517 ec_GFp_simple_is_at_infinity,
1518 ec_GFp_simple_is_on_curve,
1519 ec_GFp_simple_cmp,
1520 ec_GFp_simple_make_affine,
1521 ec_GFp_simple_points_make_affine,
1522 ecp_nistz256_points_mul, /* mul */
1523 ecp_nistz256_mult_precompute, /* precompute_mult */
1524 ecp_nistz256_window_have_precompute_mult, /* have_precompute_mult */
1525 ec_GFp_mont_field_mul,
1526 ec_GFp_mont_field_sqr,
1527 0, /* field_div */
1528 ec_GFp_mont_field_encode,
1529 ec_GFp_mont_field_decode,
1530 ec_GFp_mont_field_set_to_one
1531 };
1532
1533 return &ret;
1534 }
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