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free null cleanup finale
[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 OPENSSL_free(table_storage);
725 OPENSSL_free(p_str);
726 OPENSSL_free(scalars);
727 return ret;
728 }
729
730 /* Coordinates of G, for which we have precomputed tables */
731 const static BN_ULONG def_xG[P256_LIMBS] = {
732 TOBN(0x79e730d4, 0x18a9143c), TOBN(0x75ba95fc, 0x5fedb601),
733 TOBN(0x79fb732b, 0x77622510), TOBN(0x18905f76, 0xa53755c6)
734 };
735
736 const static BN_ULONG def_yG[P256_LIMBS] = {
737 TOBN(0xddf25357, 0xce95560a), TOBN(0x8b4ab8e4, 0xba19e45c),
738 TOBN(0xd2e88688, 0xdd21f325), TOBN(0x8571ff18, 0x25885d85)
739 };
740
741 /*
742 * ecp_nistz256_is_affine_G returns one if |generator| is the standard, P-256
743 * generator.
744 */
745 static int ecp_nistz256_is_affine_G(const EC_POINT *generator)
746 {
747 return (bn_get_top(generator->X) == P256_LIMBS) &&
748 (bn_get_top(generator->Y) == P256_LIMBS) &&
749 (bn_get_top(generator->Z) == (P256_LIMBS - P256_LIMBS / 8)) &&
750 is_equal(bn_get_words(generator->X), def_xG) &&
751 is_equal(bn_get_words(generator->Y), def_yG) &&
752 is_one(bn_get_words(generator->Z));
753 }
754
755 __owur static int ecp_nistz256_mult_precompute(EC_GROUP *group, BN_CTX *ctx)
756 {
757 /*
758 * We precompute a table for a Booth encoded exponent (wNAF) based
759 * computation. Each table holds 64 values for safe access, with an
760 * implicit value of infinity at index zero. We use window of size 7, and
761 * therefore require ceil(256/7) = 37 tables.
762 */
763 BIGNUM *order;
764 EC_POINT *P = NULL, *T = NULL;
765 const EC_POINT *generator;
766 EC_PRE_COMP *pre_comp;
767 BN_CTX *new_ctx = NULL;
768 int i, j, k, ret = 0;
769 size_t w;
770
771 PRECOMP256_ROW *preComputedTable = NULL;
772 unsigned char *precomp_storage = NULL;
773
774 /* if there is an old EC_PRE_COMP object, throw it away */
775 EC_EX_DATA_free_data(&group->extra_data, ecp_nistz256_pre_comp_dup,
776 ecp_nistz256_pre_comp_free,
777 ecp_nistz256_pre_comp_clear_free);
778
779 generator = EC_GROUP_get0_generator(group);
780 if (generator == NULL) {
781 ECerr(EC_F_ECP_NISTZ256_MULT_PRECOMPUTE, EC_R_UNDEFINED_GENERATOR);
782 return 0;
783 }
784
785 if (ecp_nistz256_is_affine_G(generator)) {
786 /*
787 * No need to calculate tables for the standard generator because we
788 * have them statically.
789 */
790 return 1;
791 }
792
793 if ((pre_comp = ecp_nistz256_pre_comp_new(group)) == NULL)
794 return 0;
795
796 if (ctx == NULL) {
797 ctx = new_ctx = BN_CTX_new();
798 if (ctx == NULL)
799 goto err;
800 }
801
802 BN_CTX_start(ctx);
803 order = BN_CTX_get(ctx);
804
805 if (order == NULL)
806 goto err;
807
808 if (!EC_GROUP_get_order(group, order, ctx))
809 goto err;
810
811 if (BN_is_zero(order)) {
812 ECerr(EC_F_ECP_NISTZ256_MULT_PRECOMPUTE, EC_R_UNKNOWN_ORDER);
813 goto err;
814 }
815
816 w = 7;
817
818 if ((precomp_storage =
819 OPENSSL_malloc(37 * 64 * sizeof(P256_POINT_AFFINE) + 64)) == NULL) {
820 ECerr(EC_F_ECP_NISTZ256_MULT_PRECOMPUTE, ERR_R_MALLOC_FAILURE);
821 goto err;
822 }
823
824 preComputedTable = (void *)ALIGNPTR(precomp_storage, 64);
825
826 P = EC_POINT_new(group);
827 T = EC_POINT_new(group);
828 if (P == NULL || T == NULL)
829 goto err;
830
831 /*
832 * The zero entry is implicitly infinity, and we skip it, storing other
833 * values with -1 offset.
834 */
835 if (!EC_POINT_copy(T, generator))
836 goto err;
837
838 for (k = 0; k < 64; k++) {
839 if (!EC_POINT_copy(P, T))
840 goto err;
841 for (j = 0; j < 37; j++) {
842 P256_POINT_AFFINE temp;
843 /*
844 * It would be faster to use EC_POINTs_make_affine and
845 * make multiple points affine at the same time.
846 */
847 if (!EC_POINT_make_affine(group, P, ctx))
848 goto err;
849 if (!ecp_nistz256_bignum_to_field_elem(temp.X, P->X) ||
850 !ecp_nistz256_bignum_to_field_elem(temp.Y, P->Y)) {
851 ECerr(EC_F_ECP_NISTZ256_MULT_PRECOMPUTE,
852 EC_R_COORDINATES_OUT_OF_RANGE);
853 goto err;
854 }
855 ecp_nistz256_scatter_w7(preComputedTable[j], &temp, k);
856 for (i = 0; i < 7; i++) {
857 if (!EC_POINT_dbl(group, P, P, ctx))
858 goto err;
859 }
860 }
861 if (!EC_POINT_add(group, T, T, generator, ctx))
862 goto err;
863 }
864
865 pre_comp->group = group;
866 pre_comp->w = w;
867 pre_comp->precomp = preComputedTable;
868 pre_comp->precomp_storage = precomp_storage;
869
870 precomp_storage = NULL;
871
872 if (!EC_EX_DATA_set_data(&group->extra_data, pre_comp,
873 ecp_nistz256_pre_comp_dup,
874 ecp_nistz256_pre_comp_free,
875 ecp_nistz256_pre_comp_clear_free)) {
876 goto err;
877 }
878
879 pre_comp = NULL;
880
881 ret = 1;
882
883 err:
884 if (ctx != NULL)
885 BN_CTX_end(ctx);
886 BN_CTX_free(new_ctx);
887
888 ecp_nistz256_pre_comp_free(pre_comp);
889 OPENSSL_free(precomp_storage);
890 EC_POINT_free(P);
891 EC_POINT_free(T);
892 return ret;
893 }
894
895 /*
896 * Note that by default ECP_NISTZ256_AVX2 is undefined. While it's great
897 * code processing 4 points in parallel, corresponding serial operation
898 * is several times slower, because it uses 29x29=58-bit multiplication
899 * as opposite to 64x64=128-bit in integer-only scalar case. As result
900 * it doesn't provide *significant* performance improvement. Note that
901 * just defining ECP_NISTZ256_AVX2 is not sufficient to make it work,
902 * you'd need to compile even asm/ecp_nistz256-avx.pl module.
903 */
904 #if defined(ECP_NISTZ256_AVX2)
905 # if !(defined(__x86_64) || defined(__x86_64__) || \
906 defined(_M_AMD64) || defined(_MX64)) || \
907 !(defined(__GNUC__) || defined(_MSC_VER)) /* this is for ALIGN32 */
908 # undef ECP_NISTZ256_AVX2
909 # else
910 /* Constant time access, loading four values, from four consecutive tables */
911 void ecp_nistz256_avx2_multi_gather_w7(void *result, const void *in,
912 int index0, int index1, int index2,
913 int index3);
914 void ecp_nistz256_avx2_transpose_convert(void *RESULTx4, const void *in);
915 void ecp_nistz256_avx2_convert_transpose_back(void *result, const void *Ax4);
916 void ecp_nistz256_avx2_point_add_affine_x4(void *RESULTx4, const void *Ax4,
917 const void *Bx4);
918 void ecp_nistz256_avx2_point_add_affines_x4(void *RESULTx4, const void *Ax4,
919 const void *Bx4);
920 void ecp_nistz256_avx2_to_mont(void *RESULTx4, const void *Ax4);
921 void ecp_nistz256_avx2_from_mont(void *RESULTx4, const void *Ax4);
922 void ecp_nistz256_avx2_set1(void *RESULTx4);
923 int ecp_nistz_avx2_eligible(void);
924
925 static void booth_recode_w7(unsigned char *sign,
926 unsigned char *digit, unsigned char in)
927 {
928 unsigned char s, d;
929
930 s = ~((in >> 7) - 1);
931 d = (1 << 8) - in - 1;
932 d = (d & s) | (in & ~s);
933 d = (d >> 1) + (d & 1);
934
935 *sign = s & 1;
936 *digit = d;
937 }
938
939 /*
940 * ecp_nistz256_avx2_mul_g performs multiplication by G, using only the
941 * precomputed table. It does 4 affine point additions in parallel,
942 * significantly speeding up point multiplication for a fixed value.
943 */
944 static void ecp_nistz256_avx2_mul_g(P256_POINT *r,
945 unsigned char p_str[33],
946 const P256_POINT_AFFINE(*preComputedTable)[64])
947 {
948 const unsigned int window_size = 7;
949 const unsigned int mask = (1 << (window_size + 1)) - 1;
950 unsigned int wvalue;
951 /* Using 4 windows at a time */
952 unsigned char sign0, digit0;
953 unsigned char sign1, digit1;
954 unsigned char sign2, digit2;
955 unsigned char sign3, digit3;
956 unsigned int idx = 0;
957 BN_ULONG tmp[P256_LIMBS];
958 int i;
959
960 ALIGN32 BN_ULONG aX4[4 * 9 * 3] = { 0 };
961 ALIGN32 BN_ULONG bX4[4 * 9 * 2] = { 0 };
962 ALIGN32 P256_POINT_AFFINE point_arr[4];
963 ALIGN32 P256_POINT res_point_arr[4];
964
965 /* Initial four windows */
966 wvalue = *((u16 *) & p_str[0]);
967 wvalue = (wvalue << 1) & mask;
968 idx += window_size;
969 booth_recode_w7(&sign0, &digit0, wvalue);
970 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
971 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
972 idx += window_size;
973 booth_recode_w7(&sign1, &digit1, wvalue);
974 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
975 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
976 idx += window_size;
977 booth_recode_w7(&sign2, &digit2, wvalue);
978 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
979 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
980 idx += window_size;
981 booth_recode_w7(&sign3, &digit3, wvalue);
982
983 ecp_nistz256_avx2_multi_gather_w7(point_arr, preComputedTable[0],
984 digit0, digit1, digit2, digit3);
985
986 ecp_nistz256_neg(tmp, point_arr[0].Y);
987 copy_conditional(point_arr[0].Y, tmp, sign0);
988 ecp_nistz256_neg(tmp, point_arr[1].Y);
989 copy_conditional(point_arr[1].Y, tmp, sign1);
990 ecp_nistz256_neg(tmp, point_arr[2].Y);
991 copy_conditional(point_arr[2].Y, tmp, sign2);
992 ecp_nistz256_neg(tmp, point_arr[3].Y);
993 copy_conditional(point_arr[3].Y, tmp, sign3);
994
995 ecp_nistz256_avx2_transpose_convert(aX4, point_arr);
996 ecp_nistz256_avx2_to_mont(aX4, aX4);
997 ecp_nistz256_avx2_to_mont(&aX4[4 * 9], &aX4[4 * 9]);
998 ecp_nistz256_avx2_set1(&aX4[4 * 9 * 2]);
999
1000 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
1001 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
1002 idx += window_size;
1003 booth_recode_w7(&sign0, &digit0, wvalue);
1004 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
1005 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
1006 idx += window_size;
1007 booth_recode_w7(&sign1, &digit1, wvalue);
1008 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
1009 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
1010 idx += window_size;
1011 booth_recode_w7(&sign2, &digit2, wvalue);
1012 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
1013 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
1014 idx += window_size;
1015 booth_recode_w7(&sign3, &digit3, wvalue);
1016
1017 ecp_nistz256_avx2_multi_gather_w7(point_arr, preComputedTable[4 * 1],
1018 digit0, digit1, digit2, digit3);
1019
1020 ecp_nistz256_neg(tmp, point_arr[0].Y);
1021 copy_conditional(point_arr[0].Y, tmp, sign0);
1022 ecp_nistz256_neg(tmp, point_arr[1].Y);
1023 copy_conditional(point_arr[1].Y, tmp, sign1);
1024 ecp_nistz256_neg(tmp, point_arr[2].Y);
1025 copy_conditional(point_arr[2].Y, tmp, sign2);
1026 ecp_nistz256_neg(tmp, point_arr[3].Y);
1027 copy_conditional(point_arr[3].Y, tmp, sign3);
1028
1029 ecp_nistz256_avx2_transpose_convert(bX4, point_arr);
1030 ecp_nistz256_avx2_to_mont(bX4, bX4);
1031 ecp_nistz256_avx2_to_mont(&bX4[4 * 9], &bX4[4 * 9]);
1032 /* Optimized when both inputs are affine */
1033 ecp_nistz256_avx2_point_add_affines_x4(aX4, aX4, bX4);
1034
1035 for (i = 2; i < 9; i++) {
1036 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
1037 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
1038 idx += window_size;
1039 booth_recode_w7(&sign0, &digit0, wvalue);
1040 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
1041 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
1042 idx += window_size;
1043 booth_recode_w7(&sign1, &digit1, wvalue);
1044 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
1045 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
1046 idx += window_size;
1047 booth_recode_w7(&sign2, &digit2, wvalue);
1048 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
1049 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
1050 idx += window_size;
1051 booth_recode_w7(&sign3, &digit3, wvalue);
1052
1053 ecp_nistz256_avx2_multi_gather_w7(point_arr,
1054 preComputedTable[4 * i],
1055 digit0, digit1, digit2, digit3);
1056
1057 ecp_nistz256_neg(tmp, point_arr[0].Y);
1058 copy_conditional(point_arr[0].Y, tmp, sign0);
1059 ecp_nistz256_neg(tmp, point_arr[1].Y);
1060 copy_conditional(point_arr[1].Y, tmp, sign1);
1061 ecp_nistz256_neg(tmp, point_arr[2].Y);
1062 copy_conditional(point_arr[2].Y, tmp, sign2);
1063 ecp_nistz256_neg(tmp, point_arr[3].Y);
1064 copy_conditional(point_arr[3].Y, tmp, sign3);
1065
1066 ecp_nistz256_avx2_transpose_convert(bX4, point_arr);
1067 ecp_nistz256_avx2_to_mont(bX4, bX4);
1068 ecp_nistz256_avx2_to_mont(&bX4[4 * 9], &bX4[4 * 9]);
1069
1070 ecp_nistz256_avx2_point_add_affine_x4(aX4, aX4, bX4);
1071 }
1072
1073 ecp_nistz256_avx2_from_mont(&aX4[4 * 9 * 0], &aX4[4 * 9 * 0]);
1074 ecp_nistz256_avx2_from_mont(&aX4[4 * 9 * 1], &aX4[4 * 9 * 1]);
1075 ecp_nistz256_avx2_from_mont(&aX4[4 * 9 * 2], &aX4[4 * 9 * 2]);
1076
1077 ecp_nistz256_avx2_convert_transpose_back(res_point_arr, aX4);
1078 /* Last window is performed serially */
1079 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
1080 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
1081 booth_recode_w7(&sign0, &digit0, wvalue);
1082 ecp_nistz256_gather_w7((P256_POINT_AFFINE *)r,
1083 preComputedTable[36], digit0);
1084 ecp_nistz256_neg(tmp, r->Y);
1085 copy_conditional(r->Y, tmp, sign0);
1086 memcpy(r->Z, ONE, sizeof(ONE));
1087 /* Sum the four windows */
1088 ecp_nistz256_point_add(r, r, &res_point_arr[0]);
1089 ecp_nistz256_point_add(r, r, &res_point_arr[1]);
1090 ecp_nistz256_point_add(r, r, &res_point_arr[2]);
1091 ecp_nistz256_point_add(r, r, &res_point_arr[3]);
1092 }
1093 # endif
1094 #endif
1095
1096 __owur static int ecp_nistz256_set_from_affine(EC_POINT *out, const EC_GROUP *group,
1097 const P256_POINT_AFFINE *in,
1098 BN_CTX *ctx)
1099 {
1100 BIGNUM *x, *y;
1101 BN_ULONG d_x[P256_LIMBS], d_y[P256_LIMBS];
1102 int ret = 0;
1103
1104 x = BN_new();
1105 if (!x)
1106 return 0;
1107 y = BN_new();
1108 if (!y) {
1109 BN_free(x);
1110 return 0;
1111 }
1112 memcpy(d_x, in->X, sizeof(d_x));
1113 bn_set_static_words(x, d_x, P256_LIMBS);
1114
1115 memcpy(d_y, in->Y, sizeof(d_y));
1116 bn_set_static_words(y, d_y, P256_LIMBS);
1117
1118 ret = EC_POINT_set_affine_coordinates_GFp(group, out, x, y, ctx);
1119
1120 BN_free(x);
1121 BN_free(y);
1122
1123 return ret;
1124 }
1125
1126 /* r = scalar*G + sum(scalars[i]*points[i]) */
1127 __owur static int ecp_nistz256_points_mul(const EC_GROUP *group,
1128 EC_POINT *r,
1129 const BIGNUM *scalar,
1130 size_t num,
1131 const EC_POINT *points[],
1132 const BIGNUM *scalars[], BN_CTX *ctx)
1133 {
1134 int i = 0, ret = 0, no_precomp_for_generator = 0, p_is_infinity = 0;
1135 size_t j;
1136 unsigned char p_str[33] = { 0 };
1137 const PRECOMP256_ROW *preComputedTable = NULL;
1138 const EC_PRE_COMP *pre_comp = NULL;
1139 const EC_POINT *generator = NULL;
1140 BN_CTX *new_ctx = NULL;
1141 const BIGNUM **new_scalars = NULL;
1142 const EC_POINT **new_points = NULL;
1143 unsigned int idx = 0;
1144 const unsigned int window_size = 7;
1145 const unsigned int mask = (1 << (window_size + 1)) - 1;
1146 unsigned int wvalue;
1147 ALIGN32 union {
1148 P256_POINT p;
1149 P256_POINT_AFFINE a;
1150 } t, p;
1151 BIGNUM *tmp_scalar;
1152
1153 if ((num + 1) == 0 || (num + 1) > OPENSSL_MALLOC_MAX_NELEMS(void *)) {
1154 ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, ERR_R_MALLOC_FAILURE);
1155 return 0;
1156 }
1157
1158 if (group->meth != r->meth) {
1159 ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, EC_R_INCOMPATIBLE_OBJECTS);
1160 return 0;
1161 }
1162
1163 if ((scalar == NULL) && (num == 0))
1164 return EC_POINT_set_to_infinity(group, r);
1165
1166 for (j = 0; j < num; j++) {
1167 if (group->meth != points[j]->meth) {
1168 ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, EC_R_INCOMPATIBLE_OBJECTS);
1169 return 0;
1170 }
1171 }
1172
1173 if (ctx == NULL) {
1174 ctx = new_ctx = BN_CTX_new();
1175 if (ctx == NULL)
1176 goto err;
1177 }
1178
1179 BN_CTX_start(ctx);
1180
1181 if (scalar) {
1182 generator = EC_GROUP_get0_generator(group);
1183 if (generator == NULL) {
1184 ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, EC_R_UNDEFINED_GENERATOR);
1185 goto err;
1186 }
1187
1188 /* look if we can use precomputed multiples of generator */
1189 pre_comp =
1190 EC_EX_DATA_get_data(group->extra_data, ecp_nistz256_pre_comp_dup,
1191 ecp_nistz256_pre_comp_free,
1192 ecp_nistz256_pre_comp_clear_free);
1193
1194 if (pre_comp) {
1195 /*
1196 * If there is a precomputed table for the generator, check that
1197 * it was generated with the same generator.
1198 */
1199 EC_POINT *pre_comp_generator = EC_POINT_new(group);
1200 if (pre_comp_generator == NULL)
1201 goto err;
1202
1203 if (!ecp_nistz256_set_from_affine(pre_comp_generator,
1204 group, pre_comp->precomp[0],
1205 ctx)) {
1206 EC_POINT_free(pre_comp_generator);
1207 goto err;
1208 }
1209
1210 if (0 == EC_POINT_cmp(group, generator, pre_comp_generator, ctx))
1211 preComputedTable = (const PRECOMP256_ROW *)pre_comp->precomp;
1212
1213 EC_POINT_free(pre_comp_generator);
1214 }
1215
1216 if (preComputedTable == NULL && ecp_nistz256_is_affine_G(generator)) {
1217 /*
1218 * If there is no precomputed data, but the generator is the
1219 * default, a hardcoded table of precomputed data is used. This
1220 * is because applications, such as Apache, do not use
1221 * EC_KEY_precompute_mult.
1222 */
1223 preComputedTable = ecp_nistz256_precomputed;
1224 }
1225
1226 if (preComputedTable) {
1227 if ((BN_num_bits(scalar) > 256)
1228 || BN_is_negative(scalar)) {
1229 if ((tmp_scalar = BN_CTX_get(ctx)) == NULL)
1230 goto err;
1231
1232 if (!BN_nnmod(tmp_scalar, scalar, group->order, ctx)) {
1233 ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, ERR_R_BN_LIB);
1234 goto err;
1235 }
1236 scalar = tmp_scalar;
1237 }
1238
1239 for (i = 0; i < bn_get_top(scalar) * BN_BYTES; i += BN_BYTES) {
1240 BN_ULONG d = bn_get_words(scalar)[i / BN_BYTES];
1241
1242 p_str[i + 0] = (unsigned char)d;
1243 p_str[i + 1] = (unsigned char)(d >> 8);
1244 p_str[i + 2] = (unsigned char)(d >> 16);
1245 p_str[i + 3] = (unsigned char)(d >>= 24);
1246 if (BN_BYTES == 8) {
1247 d >>= 8;
1248 p_str[i + 4] = (unsigned char)d;
1249 p_str[i + 5] = (unsigned char)(d >> 8);
1250 p_str[i + 6] = (unsigned char)(d >> 16);
1251 p_str[i + 7] = (unsigned char)(d >> 24);
1252 }
1253 }
1254
1255 for (; i < 33; i++)
1256 p_str[i] = 0;
1257
1258 #if defined(ECP_NISTZ256_AVX2)
1259 if (ecp_nistz_avx2_eligible()) {
1260 ecp_nistz256_avx2_mul_g(&p.p, p_str, preComputedTable);
1261 } else
1262 #endif
1263 {
1264 /* First window */
1265 wvalue = (p_str[0] << 1) & mask;
1266 idx += window_size;
1267
1268 wvalue = _booth_recode_w7(wvalue);
1269
1270 ecp_nistz256_gather_w7(&p.a, preComputedTable[0],
1271 wvalue >> 1);
1272
1273 ecp_nistz256_neg(p.p.Z, p.p.Y);
1274 copy_conditional(p.p.Y, p.p.Z, wvalue & 1);
1275
1276 memcpy(p.p.Z, ONE, sizeof(ONE));
1277
1278 for (i = 1; i < 37; i++) {
1279 unsigned int off = (idx - 1) / 8;
1280 wvalue = p_str[off] | p_str[off + 1] << 8;
1281 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
1282 idx += window_size;
1283
1284 wvalue = _booth_recode_w7(wvalue);
1285
1286 ecp_nistz256_gather_w7(&t.a,
1287 preComputedTable[i], wvalue >> 1);
1288
1289 ecp_nistz256_neg(t.p.Z, t.a.Y);
1290 copy_conditional(t.a.Y, t.p.Z, wvalue & 1);
1291
1292 ecp_nistz256_point_add_affine(&p.p, &p.p, &t.a);
1293 }
1294 }
1295 } else {
1296 p_is_infinity = 1;
1297 no_precomp_for_generator = 1;
1298 }
1299 } else
1300 p_is_infinity = 1;
1301
1302 if (no_precomp_for_generator) {
1303 /*
1304 * Without a precomputed table for the generator, it has to be
1305 * handled like a normal point.
1306 */
1307 new_scalars = OPENSSL_malloc((num + 1) * sizeof(BIGNUM *));
1308 if (!new_scalars) {
1309 ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, ERR_R_MALLOC_FAILURE);
1310 goto err;
1311 }
1312
1313 new_points = OPENSSL_malloc((num + 1) * sizeof(EC_POINT *));
1314 if (!new_points) {
1315 ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, ERR_R_MALLOC_FAILURE);
1316 goto err;
1317 }
1318
1319 memcpy(new_scalars, scalars, num * sizeof(BIGNUM *));
1320 new_scalars[num] = scalar;
1321 memcpy(new_points, points, num * sizeof(EC_POINT *));
1322 new_points[num] = generator;
1323
1324 scalars = new_scalars;
1325 points = new_points;
1326 num++;
1327 }
1328
1329 if (num) {
1330 P256_POINT *out = &t.p;
1331 if (p_is_infinity)
1332 out = &p.p;
1333
1334 if (!ecp_nistz256_windowed_mul(group, out, scalars, points, num, ctx))
1335 goto err;
1336
1337 if (!p_is_infinity)
1338 ecp_nistz256_point_add(&p.p, &p.p, out);
1339 }
1340
1341 /* Not constant-time, but we're only operating on the public output. */
1342 if (!bn_set_words(r->X, p.p.X, P256_LIMBS) ||
1343 !bn_set_words(r->Y, p.p.Y, P256_LIMBS) ||
1344 !bn_set_words(r->Z, p.p.Z, P256_LIMBS)) {
1345 goto err;
1346 }
1347 r->Z_is_one = is_one(p.p.Z) & 1;
1348
1349 ret = 1;
1350
1351 err:
1352 if (ctx)
1353 BN_CTX_end(ctx);
1354 BN_CTX_free(new_ctx);
1355 OPENSSL_free(new_points);
1356 OPENSSL_free(new_scalars);
1357 return ret;
1358 }
1359
1360 __owur static int ecp_nistz256_get_affine(const EC_GROUP *group,
1361 const EC_POINT *point,
1362 BIGNUM *x, BIGNUM *y, BN_CTX *ctx)
1363 {
1364 BN_ULONG z_inv2[P256_LIMBS];
1365 BN_ULONG z_inv3[P256_LIMBS];
1366 BN_ULONG x_aff[P256_LIMBS];
1367 BN_ULONG y_aff[P256_LIMBS];
1368 BN_ULONG point_x[P256_LIMBS], point_y[P256_LIMBS], point_z[P256_LIMBS];
1369 BN_ULONG x_ret[P256_LIMBS], y_ret[P256_LIMBS];
1370
1371 if (EC_POINT_is_at_infinity(group, point)) {
1372 ECerr(EC_F_ECP_NISTZ256_GET_AFFINE, EC_R_POINT_AT_INFINITY);
1373 return 0;
1374 }
1375
1376 if (!ecp_nistz256_bignum_to_field_elem(point_x, point->X) ||
1377 !ecp_nistz256_bignum_to_field_elem(point_y, point->Y) ||
1378 !ecp_nistz256_bignum_to_field_elem(point_z, point->Z)) {
1379 ECerr(EC_F_ECP_NISTZ256_GET_AFFINE, EC_R_COORDINATES_OUT_OF_RANGE);
1380 return 0;
1381 }
1382
1383 ecp_nistz256_mod_inverse(z_inv3, point_z);
1384 ecp_nistz256_sqr_mont(z_inv2, z_inv3);
1385 ecp_nistz256_mul_mont(x_aff, z_inv2, point_x);
1386
1387 if (x != NULL) {
1388 ecp_nistz256_from_mont(x_ret, x_aff);
1389 if (!bn_set_words(x, x_ret, P256_LIMBS))
1390 return 0;
1391 }
1392
1393 if (y != NULL) {
1394 ecp_nistz256_mul_mont(z_inv3, z_inv3, z_inv2);
1395 ecp_nistz256_mul_mont(y_aff, z_inv3, point_y);
1396 ecp_nistz256_from_mont(y_ret, y_aff);
1397 if (!bn_set_words(y, y_ret, P256_LIMBS))
1398 return 0;
1399 }
1400
1401 return 1;
1402 }
1403
1404 static EC_PRE_COMP *ecp_nistz256_pre_comp_new(const EC_GROUP *group)
1405 {
1406 EC_PRE_COMP *ret = NULL;
1407
1408 if (!group)
1409 return NULL;
1410
1411 ret = OPENSSL_malloc(sizeof(EC_PRE_COMP));
1412
1413 if (!ret) {
1414 ECerr(EC_F_ECP_NISTZ256_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE);
1415 return ret;
1416 }
1417
1418 ret->group = group;
1419 ret->w = 6; /* default */
1420 ret->precomp = NULL;
1421 ret->precomp_storage = NULL;
1422 ret->references = 1;
1423 return ret;
1424 }
1425
1426 static void *ecp_nistz256_pre_comp_dup(void *src_)
1427 {
1428 EC_PRE_COMP *src = src_;
1429
1430 /* no need to actually copy, these objects never change! */
1431 CRYPTO_add(&src->references, 1, CRYPTO_LOCK_EC_PRE_COMP);
1432
1433 return src_;
1434 }
1435
1436 static void ecp_nistz256_pre_comp_free(void *pre_)
1437 {
1438 int i;
1439 EC_PRE_COMP *pre = pre_;
1440
1441 if (!pre)
1442 return;
1443
1444 i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP);
1445 if (i > 0)
1446 return;
1447
1448 OPENSSL_free(pre->precomp_storage);
1449 OPENSSL_free(pre);
1450 }
1451
1452 static void ecp_nistz256_pre_comp_clear_free(void *pre_)
1453 {
1454 int i;
1455 EC_PRE_COMP *pre = pre_;
1456
1457 if (!pre)
1458 return;
1459
1460 i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP);
1461 if (i > 0)
1462 return;
1463
1464 OPENSSL_clear_free(pre->precomp,
1465 32 * sizeof(unsigned char) * (1 << pre->w) * 2 * 37);
1466 OPENSSL_clear_free(pre, sizeof *pre);
1467 }
1468
1469 static int ecp_nistz256_window_have_precompute_mult(const EC_GROUP *group)
1470 {
1471 /* There is a hard-coded table for the default generator. */
1472 const EC_POINT *generator = EC_GROUP_get0_generator(group);
1473 if (generator != NULL && ecp_nistz256_is_affine_G(generator)) {
1474 /* There is a hard-coded table for the default generator. */
1475 return 1;
1476 }
1477
1478 return EC_EX_DATA_get_data(group->extra_data, ecp_nistz256_pre_comp_dup,
1479 ecp_nistz256_pre_comp_free,
1480 ecp_nistz256_pre_comp_clear_free) != NULL;
1481 }
1482
1483 const EC_METHOD *EC_GFp_nistz256_method(void)
1484 {
1485 static const EC_METHOD ret = {
1486 EC_FLAGS_DEFAULT_OCT,
1487 NID_X9_62_prime_field,
1488 ec_GFp_mont_group_init,
1489 ec_GFp_mont_group_finish,
1490 ec_GFp_mont_group_clear_finish,
1491 ec_GFp_mont_group_copy,
1492 ec_GFp_mont_group_set_curve,
1493 ec_GFp_simple_group_get_curve,
1494 ec_GFp_simple_group_get_degree,
1495 ec_GFp_simple_group_check_discriminant,
1496 ec_GFp_simple_point_init,
1497 ec_GFp_simple_point_finish,
1498 ec_GFp_simple_point_clear_finish,
1499 ec_GFp_simple_point_copy,
1500 ec_GFp_simple_point_set_to_infinity,
1501 ec_GFp_simple_set_Jprojective_coordinates_GFp,
1502 ec_GFp_simple_get_Jprojective_coordinates_GFp,
1503 ec_GFp_simple_point_set_affine_coordinates,
1504 ecp_nistz256_get_affine,
1505 0, 0, 0,
1506 ec_GFp_simple_add,
1507 ec_GFp_simple_dbl,
1508 ec_GFp_simple_invert,
1509 ec_GFp_simple_is_at_infinity,
1510 ec_GFp_simple_is_on_curve,
1511 ec_GFp_simple_cmp,
1512 ec_GFp_simple_make_affine,
1513 ec_GFp_simple_points_make_affine,
1514 ecp_nistz256_points_mul, /* mul */
1515 ecp_nistz256_mult_precompute, /* precompute_mult */
1516 ecp_nistz256_window_have_precompute_mult, /* have_precompute_mult */
1517 ec_GFp_mont_field_mul,
1518 ec_GFp_mont_field_sqr,
1519 0, /* field_div */
1520 ec_GFp_mont_field_encode,
1521 ec_GFp_mont_field_decode,
1522 ec_GFp_mont_field_set_to_one
1523 };
1524
1525 return &ret;
1526 }
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