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Add default operations to EC_METHOD
[thirdparty/openssl.git] / crypto / ec / ecp_nistz256.c
1 /******************************************************************************
2 * *
3 * Copyright 2014 Intel Corporation *
4 * *
5 * Licensed under the Apache License, Version 2.0 (the "License"); *
6 * you may not use this file except in compliance with the License. *
7 * You may obtain a copy of the License at *
8 * *
9 * http://www.apache.org/licenses/LICENSE-2.0 *
10 * *
11 * Unless required by applicable law or agreed to in writing, software *
12 * distributed under the License is distributed on an "AS IS" BASIS, *
13 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. *
14 * See the License for the specific language governing permissions and *
15 * limitations under the License. *
16 * *
17 ******************************************************************************
18 * *
19 * Developers and authors: *
20 * Shay Gueron (1, 2), and Vlad Krasnov (1) *
21 * (1) Intel Corporation, Israel Development Center *
22 * (2) University of Haifa *
23 * Reference: *
24 * S.Gueron and V.Krasnov, "Fast Prime Field Elliptic Curve Cryptography with *
25 * 256 Bit Primes" *
26 * *
27 ******************************************************************************/
28
29 #include <string.h>
30
31 #include "internal/cryptlib.h"
32 #include "internal/bn_int.h"
33 #include "ec_lcl.h"
34
35 #if BN_BITS2 != 64
36 # define TOBN(hi,lo) lo,hi
37 #else
38 # define TOBN(hi,lo) ((BN_ULONG)hi<<32|lo)
39 #endif
40
41 #if defined(__GNUC__)
42 # define ALIGN32 __attribute((aligned(32)))
43 #elif defined(_MSC_VER)
44 # define ALIGN32 __declspec(align(32))
45 #else
46 # define ALIGN32
47 #endif
48
49 #define ALIGNPTR(p,N) ((unsigned char *)p+N-(size_t)p%N)
50 #define P256_LIMBS (256/BN_BITS2)
51
52 typedef unsigned short u16;
53
54 typedef struct {
55 BN_ULONG X[P256_LIMBS];
56 BN_ULONG Y[P256_LIMBS];
57 BN_ULONG Z[P256_LIMBS];
58 } P256_POINT;
59
60 typedef struct {
61 BN_ULONG X[P256_LIMBS];
62 BN_ULONG Y[P256_LIMBS];
63 } P256_POINT_AFFINE;
64
65 typedef P256_POINT_AFFINE PRECOMP256_ROW[64];
66
67 /* structure for precomputed multiples of the generator */
68 struct nistz256_pre_comp_st {
69 const EC_GROUP *group; /* Parent EC_GROUP object */
70 size_t w; /* Window size */
71 /*
72 * Constant time access to the X and Y coordinates of the pre-computed,
73 * generator multiplies, in the Montgomery domain. Pre-calculated
74 * multiplies are stored in affine form.
75 */
76 PRECOMP256_ROW *precomp;
77 void *precomp_storage;
78 int references;
79 };
80
81 /* Functions implemented in assembly */
82 /* Modular mul by 2: res = 2*a mod P */
83 void ecp_nistz256_mul_by_2(BN_ULONG res[P256_LIMBS],
84 const BN_ULONG a[P256_LIMBS]);
85 /* Modular div by 2: res = a/2 mod P */
86 void ecp_nistz256_div_by_2(BN_ULONG res[P256_LIMBS],
87 const BN_ULONG a[P256_LIMBS]);
88 /* Modular mul by 3: res = 3*a mod P */
89 void ecp_nistz256_mul_by_3(BN_ULONG res[P256_LIMBS],
90 const BN_ULONG a[P256_LIMBS]);
91 /* Modular add: res = a+b mod P */
92 void ecp_nistz256_add(BN_ULONG res[P256_LIMBS],
93 const BN_ULONG a[P256_LIMBS],
94 const BN_ULONG b[P256_LIMBS]);
95 /* Modular sub: res = a-b mod P */
96 void ecp_nistz256_sub(BN_ULONG res[P256_LIMBS],
97 const BN_ULONG a[P256_LIMBS],
98 const BN_ULONG b[P256_LIMBS]);
99 /* Modular neg: res = -a mod P */
100 void ecp_nistz256_neg(BN_ULONG res[P256_LIMBS], const BN_ULONG a[P256_LIMBS]);
101 /* Montgomery mul: res = a*b*2^-256 mod P */
102 void ecp_nistz256_mul_mont(BN_ULONG res[P256_LIMBS],
103 const BN_ULONG a[P256_LIMBS],
104 const BN_ULONG b[P256_LIMBS]);
105 /* Montgomery sqr: res = a*a*2^-256 mod P */
106 void ecp_nistz256_sqr_mont(BN_ULONG res[P256_LIMBS],
107 const BN_ULONG a[P256_LIMBS]);
108 /* Convert a number from Montgomery domain, by multiplying with 1 */
109 void ecp_nistz256_from_mont(BN_ULONG res[P256_LIMBS],
110 const BN_ULONG in[P256_LIMBS]);
111 /* Convert a number to Montgomery domain, by multiplying with 2^512 mod P*/
112 void ecp_nistz256_to_mont(BN_ULONG res[P256_LIMBS],
113 const BN_ULONG in[P256_LIMBS]);
114 /* Functions that perform constant time access to the precomputed tables */
115 void ecp_nistz256_scatter_w5(P256_POINT *val,
116 const P256_POINT *in_t, int idx);
117 void ecp_nistz256_gather_w5(P256_POINT *val,
118 const P256_POINT *in_t, int idx);
119 void ecp_nistz256_scatter_w7(P256_POINT_AFFINE *val,
120 const P256_POINT_AFFINE *in_t, int idx);
121 void ecp_nistz256_gather_w7(P256_POINT_AFFINE *val,
122 const P256_POINT_AFFINE *in_t, int idx);
123
124 /* One converted into the Montgomery domain */
125 static const BN_ULONG ONE[P256_LIMBS] = {
126 TOBN(0x00000000, 0x00000001), TOBN(0xffffffff, 0x00000000),
127 TOBN(0xffffffff, 0xffffffff), TOBN(0x00000000, 0xfffffffe)
128 };
129
130 static NISTZ256_PRE_COMP *ecp_nistz256_pre_comp_new(const EC_GROUP *group);
131
132 /* Precomputed tables for the default generator */
133 extern const PRECOMP256_ROW ecp_nistz256_precomputed[37];
134
135 /* Recode window to a signed digit, see ecp_nistputil.c for details */
136 static unsigned int _booth_recode_w5(unsigned int in)
137 {
138 unsigned int s, d;
139
140 s = ~((in >> 5) - 1);
141 d = (1 << 6) - in - 1;
142 d = (d & s) | (in & ~s);
143 d = (d >> 1) + (d & 1);
144
145 return (d << 1) + (s & 1);
146 }
147
148 static unsigned int _booth_recode_w7(unsigned int in)
149 {
150 unsigned int s, d;
151
152 s = ~((in >> 7) - 1);
153 d = (1 << 8) - in - 1;
154 d = (d & s) | (in & ~s);
155 d = (d >> 1) + (d & 1);
156
157 return (d << 1) + (s & 1);
158 }
159
160 static void copy_conditional(BN_ULONG dst[P256_LIMBS],
161 const BN_ULONG src[P256_LIMBS], BN_ULONG move)
162 {
163 BN_ULONG mask1 = 0-move;
164 BN_ULONG mask2 = ~mask1;
165
166 dst[0] = (src[0] & mask1) ^ (dst[0] & mask2);
167 dst[1] = (src[1] & mask1) ^ (dst[1] & mask2);
168 dst[2] = (src[2] & mask1) ^ (dst[2] & mask2);
169 dst[3] = (src[3] & mask1) ^ (dst[3] & mask2);
170 if (P256_LIMBS == 8) {
171 dst[4] = (src[4] & mask1) ^ (dst[4] & mask2);
172 dst[5] = (src[5] & mask1) ^ (dst[5] & mask2);
173 dst[6] = (src[6] & mask1) ^ (dst[6] & mask2);
174 dst[7] = (src[7] & mask1) ^ (dst[7] & mask2);
175 }
176 }
177
178 static BN_ULONG is_zero(BN_ULONG in)
179 {
180 in |= (0 - in);
181 in = ~in;
182 in >>= BN_BITS2 - 1;
183 return in;
184 }
185
186 static BN_ULONG is_equal(const BN_ULONG a[P256_LIMBS],
187 const BN_ULONG b[P256_LIMBS])
188 {
189 BN_ULONG res;
190
191 res = a[0] ^ b[0];
192 res |= a[1] ^ b[1];
193 res |= a[2] ^ b[2];
194 res |= a[3] ^ b[3];
195 if (P256_LIMBS == 8) {
196 res |= a[4] ^ b[4];
197 res |= a[5] ^ b[5];
198 res |= a[6] ^ b[6];
199 res |= a[7] ^ b[7];
200 }
201
202 return is_zero(res);
203 }
204
205 static BN_ULONG is_one(const BN_ULONG a[P256_LIMBS])
206 {
207 BN_ULONG res;
208
209 res = a[0] ^ ONE[0];
210 res |= a[1] ^ ONE[1];
211 res |= a[2] ^ ONE[2];
212 res |= a[3] ^ ONE[3];
213 if (P256_LIMBS == 8) {
214 res |= a[4] ^ ONE[4];
215 res |= a[5] ^ ONE[5];
216 res |= a[6] ^ ONE[6];
217 }
218
219 return is_zero(res);
220 }
221
222 #ifndef ECP_NISTZ256_REFERENCE_IMPLEMENTATION
223 void ecp_nistz256_point_double(P256_POINT *r, const P256_POINT *a);
224 void ecp_nistz256_point_add(P256_POINT *r,
225 const P256_POINT *a, const P256_POINT *b);
226 void ecp_nistz256_point_add_affine(P256_POINT *r,
227 const P256_POINT *a,
228 const P256_POINT_AFFINE *b);
229 #else
230 /* Point double: r = 2*a */
231 static void ecp_nistz256_point_double(P256_POINT *r, const P256_POINT *a)
232 {
233 BN_ULONG S[P256_LIMBS];
234 BN_ULONG M[P256_LIMBS];
235 BN_ULONG Zsqr[P256_LIMBS];
236 BN_ULONG tmp0[P256_LIMBS];
237
238 const BN_ULONG *in_x = a->X;
239 const BN_ULONG *in_y = a->Y;
240 const BN_ULONG *in_z = a->Z;
241
242 BN_ULONG *res_x = r->X;
243 BN_ULONG *res_y = r->Y;
244 BN_ULONG *res_z = r->Z;
245
246 ecp_nistz256_mul_by_2(S, in_y);
247
248 ecp_nistz256_sqr_mont(Zsqr, in_z);
249
250 ecp_nistz256_sqr_mont(S, S);
251
252 ecp_nistz256_mul_mont(res_z, in_z, in_y);
253 ecp_nistz256_mul_by_2(res_z, res_z);
254
255 ecp_nistz256_add(M, in_x, Zsqr);
256 ecp_nistz256_sub(Zsqr, in_x, Zsqr);
257
258 ecp_nistz256_sqr_mont(res_y, S);
259 ecp_nistz256_div_by_2(res_y, res_y);
260
261 ecp_nistz256_mul_mont(M, M, Zsqr);
262 ecp_nistz256_mul_by_3(M, M);
263
264 ecp_nistz256_mul_mont(S, S, in_x);
265 ecp_nistz256_mul_by_2(tmp0, S);
266
267 ecp_nistz256_sqr_mont(res_x, M);
268
269 ecp_nistz256_sub(res_x, res_x, tmp0);
270 ecp_nistz256_sub(S, S, res_x);
271
272 ecp_nistz256_mul_mont(S, S, M);
273 ecp_nistz256_sub(res_y, S, res_y);
274 }
275
276 /* Point addition: r = a+b */
277 static void ecp_nistz256_point_add(P256_POINT *r,
278 const P256_POINT *a, const P256_POINT *b)
279 {
280 BN_ULONG U2[P256_LIMBS], S2[P256_LIMBS];
281 BN_ULONG U1[P256_LIMBS], S1[P256_LIMBS];
282 BN_ULONG Z1sqr[P256_LIMBS];
283 BN_ULONG Z2sqr[P256_LIMBS];
284 BN_ULONG H[P256_LIMBS], R[P256_LIMBS];
285 BN_ULONG Hsqr[P256_LIMBS];
286 BN_ULONG Rsqr[P256_LIMBS];
287 BN_ULONG Hcub[P256_LIMBS];
288
289 BN_ULONG res_x[P256_LIMBS];
290 BN_ULONG res_y[P256_LIMBS];
291 BN_ULONG res_z[P256_LIMBS];
292
293 BN_ULONG in1infty, in2infty;
294
295 const BN_ULONG *in1_x = a->X;
296 const BN_ULONG *in1_y = a->Y;
297 const BN_ULONG *in1_z = a->Z;
298
299 const BN_ULONG *in2_x = b->X;
300 const BN_ULONG *in2_y = b->Y;
301 const BN_ULONG *in2_z = b->Z;
302
303 /* We encode infinity as (0,0), which is not on the curve,
304 * so it is OK. */
305 in1infty = (in1_x[0] | in1_x[1] | in1_x[2] | in1_x[3] |
306 in1_y[0] | in1_y[1] | in1_y[2] | in1_y[3]);
307 if (P256_LIMBS == 8)
308 in1infty |= (in1_x[4] | in1_x[5] | in1_x[6] | in1_x[7] |
309 in1_y[4] | in1_y[5] | in1_y[6] | in1_y[7]);
310
311 in2infty = (in2_x[0] | in2_x[1] | in2_x[2] | in2_x[3] |
312 in2_y[0] | in2_y[1] | in2_y[2] | in2_y[3]);
313 if (P256_LIMBS == 8)
314 in2infty |= (in2_x[4] | in2_x[5] | in2_x[6] | in2_x[7] |
315 in2_y[4] | in2_y[5] | in2_y[6] | in2_y[7]);
316
317 in1infty = is_zero(in1infty);
318 in2infty = is_zero(in2infty);
319
320 ecp_nistz256_sqr_mont(Z2sqr, in2_z); /* Z2^2 */
321 ecp_nistz256_sqr_mont(Z1sqr, in1_z); /* Z1^2 */
322
323 ecp_nistz256_mul_mont(S1, Z2sqr, in2_z); /* S1 = Z2^3 */
324 ecp_nistz256_mul_mont(S2, Z1sqr, in1_z); /* S2 = Z1^3 */
325
326 ecp_nistz256_mul_mont(S1, S1, in1_y); /* S1 = Y1*Z2^3 */
327 ecp_nistz256_mul_mont(S2, S2, in2_y); /* S2 = Y2*Z1^3 */
328 ecp_nistz256_sub(R, S2, S1); /* R = S2 - S1 */
329
330 ecp_nistz256_mul_mont(U1, in1_x, Z2sqr); /* U1 = X1*Z2^2 */
331 ecp_nistz256_mul_mont(U2, in2_x, Z1sqr); /* U2 = X2*Z1^2 */
332 ecp_nistz256_sub(H, U2, U1); /* H = U2 - U1 */
333
334 /*
335 * This should not happen during sign/ecdh, so no constant time violation
336 */
337 if (is_equal(U1, U2) && !in1infty && !in2infty) {
338 if (is_equal(S1, S2)) {
339 ecp_nistz256_point_double(r, a);
340 return;
341 } else {
342 memset(r, 0, sizeof(*r));
343 return;
344 }
345 }
346
347 ecp_nistz256_sqr_mont(Rsqr, R); /* R^2 */
348 ecp_nistz256_mul_mont(res_z, H, in1_z); /* Z3 = H*Z1*Z2 */
349 ecp_nistz256_sqr_mont(Hsqr, H); /* H^2 */
350 ecp_nistz256_mul_mont(res_z, res_z, in2_z); /* Z3 = H*Z1*Z2 */
351 ecp_nistz256_mul_mont(Hcub, Hsqr, H); /* H^3 */
352
353 ecp_nistz256_mul_mont(U2, U1, Hsqr); /* U1*H^2 */
354 ecp_nistz256_mul_by_2(Hsqr, U2); /* 2*U1*H^2 */
355
356 ecp_nistz256_sub(res_x, Rsqr, Hsqr);
357 ecp_nistz256_sub(res_x, res_x, Hcub);
358
359 ecp_nistz256_sub(res_y, U2, res_x);
360
361 ecp_nistz256_mul_mont(S2, S1, Hcub);
362 ecp_nistz256_mul_mont(res_y, R, res_y);
363 ecp_nistz256_sub(res_y, res_y, S2);
364
365 copy_conditional(res_x, in2_x, in1infty);
366 copy_conditional(res_y, in2_y, in1infty);
367 copy_conditional(res_z, in2_z, in1infty);
368
369 copy_conditional(res_x, in1_x, in2infty);
370 copy_conditional(res_y, in1_y, in2infty);
371 copy_conditional(res_z, in1_z, in2infty);
372
373 memcpy(r->X, res_x, sizeof(res_x));
374 memcpy(r->Y, res_y, sizeof(res_y));
375 memcpy(r->Z, res_z, sizeof(res_z));
376 }
377
378 /* Point addition when b is known to be affine: r = a+b */
379 static void ecp_nistz256_point_add_affine(P256_POINT *r,
380 const P256_POINT *a,
381 const P256_POINT_AFFINE *b)
382 {
383 BN_ULONG U2[P256_LIMBS], S2[P256_LIMBS];
384 BN_ULONG Z1sqr[P256_LIMBS];
385 BN_ULONG H[P256_LIMBS], R[P256_LIMBS];
386 BN_ULONG Hsqr[P256_LIMBS];
387 BN_ULONG Rsqr[P256_LIMBS];
388 BN_ULONG Hcub[P256_LIMBS];
389
390 BN_ULONG res_x[P256_LIMBS];
391 BN_ULONG res_y[P256_LIMBS];
392 BN_ULONG res_z[P256_LIMBS];
393
394 BN_ULONG in1infty, in2infty;
395
396 const BN_ULONG *in1_x = a->X;
397 const BN_ULONG *in1_y = a->Y;
398 const BN_ULONG *in1_z = a->Z;
399
400 const BN_ULONG *in2_x = b->X;
401 const BN_ULONG *in2_y = b->Y;
402
403 /*
404 * In affine representation we encode infty as (0,0), which is not on the
405 * curve, so it is OK
406 */
407 in1infty = (in1_x[0] | in1_x[1] | in1_x[2] | in1_x[3] |
408 in1_y[0] | in1_y[1] | in1_y[2] | in1_y[3]);
409 if (P256_LIMBS == 8)
410 in1infty |= (in1_x[4] | in1_x[5] | in1_x[6] | in1_x[7] |
411 in1_y[4] | in1_y[5] | in1_y[6] | in1_y[7]);
412
413 in2infty = (in2_x[0] | in2_x[1] | in2_x[2] | in2_x[3] |
414 in2_y[0] | in2_y[1] | in2_y[2] | in2_y[3]);
415 if (P256_LIMBS == 8)
416 in2infty |= (in2_x[4] | in2_x[5] | in2_x[6] | in2_x[7] |
417 in2_y[4] | in2_y[5] | in2_y[6] | in2_y[7]);
418
419 in1infty = is_zero(in1infty);
420 in2infty = is_zero(in2infty);
421
422 ecp_nistz256_sqr_mont(Z1sqr, in1_z); /* Z1^2 */
423
424 ecp_nistz256_mul_mont(U2, in2_x, Z1sqr); /* U2 = X2*Z1^2 */
425 ecp_nistz256_sub(H, U2, in1_x); /* H = U2 - U1 */
426
427 ecp_nistz256_mul_mont(S2, Z1sqr, in1_z); /* S2 = Z1^3 */
428
429 ecp_nistz256_mul_mont(res_z, H, in1_z); /* Z3 = H*Z1*Z2 */
430
431 ecp_nistz256_mul_mont(S2, S2, in2_y); /* S2 = Y2*Z1^3 */
432 ecp_nistz256_sub(R, S2, in1_y); /* R = S2 - S1 */
433
434 ecp_nistz256_sqr_mont(Hsqr, H); /* H^2 */
435 ecp_nistz256_sqr_mont(Rsqr, R); /* R^2 */
436 ecp_nistz256_mul_mont(Hcub, Hsqr, H); /* H^3 */
437
438 ecp_nistz256_mul_mont(U2, in1_x, Hsqr); /* U1*H^2 */
439 ecp_nistz256_mul_by_2(Hsqr, U2); /* 2*U1*H^2 */
440
441 ecp_nistz256_sub(res_x, Rsqr, Hsqr);
442 ecp_nistz256_sub(res_x, res_x, Hcub);
443 ecp_nistz256_sub(H, U2, res_x);
444
445 ecp_nistz256_mul_mont(S2, in1_y, Hcub);
446 ecp_nistz256_mul_mont(H, H, R);
447 ecp_nistz256_sub(res_y, H, S2);
448
449 copy_conditional(res_x, in2_x, in1infty);
450 copy_conditional(res_x, in1_x, in2infty);
451
452 copy_conditional(res_y, in2_y, in1infty);
453 copy_conditional(res_y, in1_y, in2infty);
454
455 copy_conditional(res_z, ONE, in1infty);
456 copy_conditional(res_z, in1_z, in2infty);
457
458 memcpy(r->X, res_x, sizeof(res_x));
459 memcpy(r->Y, res_y, sizeof(res_y));
460 memcpy(r->Z, res_z, sizeof(res_z));
461 }
462 #endif
463
464 /* r = in^-1 mod p */
465 static void ecp_nistz256_mod_inverse(BN_ULONG r[P256_LIMBS],
466 const BN_ULONG in[P256_LIMBS])
467 {
468 /*
469 * The poly is ffffffff 00000001 00000000 00000000 00000000 ffffffff
470 * ffffffff ffffffff We use FLT and used poly-2 as exponent
471 */
472 BN_ULONG p2[P256_LIMBS];
473 BN_ULONG p4[P256_LIMBS];
474 BN_ULONG p8[P256_LIMBS];
475 BN_ULONG p16[P256_LIMBS];
476 BN_ULONG p32[P256_LIMBS];
477 BN_ULONG res[P256_LIMBS];
478 int i;
479
480 ecp_nistz256_sqr_mont(res, in);
481 ecp_nistz256_mul_mont(p2, res, in); /* 3*p */
482
483 ecp_nistz256_sqr_mont(res, p2);
484 ecp_nistz256_sqr_mont(res, res);
485 ecp_nistz256_mul_mont(p4, res, p2); /* f*p */
486
487 ecp_nistz256_sqr_mont(res, p4);
488 ecp_nistz256_sqr_mont(res, res);
489 ecp_nistz256_sqr_mont(res, res);
490 ecp_nistz256_sqr_mont(res, res);
491 ecp_nistz256_mul_mont(p8, res, p4); /* ff*p */
492
493 ecp_nistz256_sqr_mont(res, p8);
494 for (i = 0; i < 7; i++)
495 ecp_nistz256_sqr_mont(res, res);
496 ecp_nistz256_mul_mont(p16, res, p8); /* ffff*p */
497
498 ecp_nistz256_sqr_mont(res, p16);
499 for (i = 0; i < 15; i++)
500 ecp_nistz256_sqr_mont(res, res);
501 ecp_nistz256_mul_mont(p32, res, p16); /* ffffffff*p */
502
503 ecp_nistz256_sqr_mont(res, p32);
504 for (i = 0; i < 31; i++)
505 ecp_nistz256_sqr_mont(res, res);
506 ecp_nistz256_mul_mont(res, res, in);
507
508 for (i = 0; i < 32 * 4; i++)
509 ecp_nistz256_sqr_mont(res, res);
510 ecp_nistz256_mul_mont(res, res, p32);
511
512 for (i = 0; i < 32; i++)
513 ecp_nistz256_sqr_mont(res, res);
514 ecp_nistz256_mul_mont(res, res, p32);
515
516 for (i = 0; i < 16; i++)
517 ecp_nistz256_sqr_mont(res, res);
518 ecp_nistz256_mul_mont(res, res, p16);
519
520 for (i = 0; i < 8; i++)
521 ecp_nistz256_sqr_mont(res, res);
522 ecp_nistz256_mul_mont(res, res, p8);
523
524 ecp_nistz256_sqr_mont(res, res);
525 ecp_nistz256_sqr_mont(res, res);
526 ecp_nistz256_sqr_mont(res, res);
527 ecp_nistz256_sqr_mont(res, res);
528 ecp_nistz256_mul_mont(res, res, p4);
529
530 ecp_nistz256_sqr_mont(res, res);
531 ecp_nistz256_sqr_mont(res, res);
532 ecp_nistz256_mul_mont(res, res, p2);
533
534 ecp_nistz256_sqr_mont(res, res);
535 ecp_nistz256_sqr_mont(res, res);
536 ecp_nistz256_mul_mont(res, res, in);
537
538 memcpy(r, res, sizeof(res));
539 }
540
541 /*
542 * ecp_nistz256_bignum_to_field_elem copies the contents of |in| to |out| and
543 * returns one if it fits. Otherwise it returns zero.
544 */
545 __owur static int ecp_nistz256_bignum_to_field_elem(BN_ULONG out[P256_LIMBS],
546 const BIGNUM *in)
547 {
548 return bn_copy_words(out, in, P256_LIMBS);
549 }
550
551 /* r = sum(scalar[i]*point[i]) */
552 __owur static int ecp_nistz256_windowed_mul(const EC_GROUP *group,
553 P256_POINT *r,
554 const BIGNUM **scalar,
555 const EC_POINT **point,
556 size_t num, BN_CTX *ctx)
557 {
558 size_t i;
559 int j, ret = 0;
560 unsigned int idx;
561 unsigned char (*p_str)[33] = NULL;
562 const unsigned int window_size = 5;
563 const unsigned int mask = (1 << (window_size + 1)) - 1;
564 unsigned int wvalue;
565 P256_POINT *temp; /* place for 5 temporary points */
566 const BIGNUM **scalars = NULL;
567 P256_POINT (*table)[16] = NULL;
568 void *table_storage = NULL;
569
570 if ((num * 16 + 6) > OPENSSL_MALLOC_MAX_NELEMS(P256_POINT)
571 || (table_storage =
572 OPENSSL_malloc((num * 16 + 5) * sizeof(P256_POINT) + 64)) == NULL
573 || (p_str =
574 OPENSSL_malloc(num * 33 * sizeof(unsigned char))) == NULL
575 || (scalars = OPENSSL_malloc(num * sizeof(BIGNUM *))) == NULL) {
576 ECerr(EC_F_ECP_NISTZ256_WINDOWED_MUL, ERR_R_MALLOC_FAILURE);
577 goto err;
578 }
579
580 table = (void *)ALIGNPTR(table_storage, 64);
581 temp = (P256_POINT *)(table + num);
582
583 for (i = 0; i < num; i++) {
584 P256_POINT *row = table[i];
585
586 /* This is an unusual input, we don't guarantee constant-timeness. */
587 if ((BN_num_bits(scalar[i]) > 256) || BN_is_negative(scalar[i])) {
588 BIGNUM *mod;
589
590 if ((mod = BN_CTX_get(ctx)) == NULL)
591 goto err;
592 if (!BN_nnmod(mod, scalar[i], group->order, ctx)) {
593 ECerr(EC_F_ECP_NISTZ256_WINDOWED_MUL, ERR_R_BN_LIB);
594 goto err;
595 }
596 scalars[i] = mod;
597 } else
598 scalars[i] = scalar[i];
599
600 for (j = 0; j < bn_get_top(scalars[i]) * BN_BYTES; j += BN_BYTES) {
601 BN_ULONG d = bn_get_words(scalars[i])[j / BN_BYTES];
602
603 p_str[i][j + 0] = (unsigned char)d;
604 p_str[i][j + 1] = (unsigned char)(d >> 8);
605 p_str[i][j + 2] = (unsigned char)(d >> 16);
606 p_str[i][j + 3] = (unsigned char)(d >>= 24);
607 if (BN_BYTES == 8) {
608 d >>= 8;
609 p_str[i][j + 4] = (unsigned char)d;
610 p_str[i][j + 5] = (unsigned char)(d >> 8);
611 p_str[i][j + 6] = (unsigned char)(d >> 16);
612 p_str[i][j + 7] = (unsigned char)(d >> 24);
613 }
614 }
615 for (; j < 33; j++)
616 p_str[i][j] = 0;
617
618 if (!ecp_nistz256_bignum_to_field_elem(temp[0].X, point[i]->X)
619 || !ecp_nistz256_bignum_to_field_elem(temp[0].Y, point[i]->Y)
620 || !ecp_nistz256_bignum_to_field_elem(temp[0].Z, point[i]->Z)) {
621 ECerr(EC_F_ECP_NISTZ256_WINDOWED_MUL,
622 EC_R_COORDINATES_OUT_OF_RANGE);
623 goto err;
624 }
625
626 /*
627 * row[0] is implicitly (0,0,0) (the point at infinity), therefore it
628 * is not stored. All other values are actually stored with an offset
629 * of -1 in table.
630 */
631
632 ecp_nistz256_scatter_w5 (row, &temp[0], 1);
633 ecp_nistz256_point_double(&temp[1], &temp[0]); /*1+1=2 */
634 ecp_nistz256_scatter_w5 (row, &temp[1], 2);
635 ecp_nistz256_point_add (&temp[2], &temp[1], &temp[0]); /*2+1=3 */
636 ecp_nistz256_scatter_w5 (row, &temp[2], 3);
637 ecp_nistz256_point_double(&temp[1], &temp[1]); /*2*2=4 */
638 ecp_nistz256_scatter_w5 (row, &temp[1], 4);
639 ecp_nistz256_point_double(&temp[2], &temp[2]); /*2*3=6 */
640 ecp_nistz256_scatter_w5 (row, &temp[2], 6);
641 ecp_nistz256_point_add (&temp[3], &temp[1], &temp[0]); /*4+1=5 */
642 ecp_nistz256_scatter_w5 (row, &temp[3], 5);
643 ecp_nistz256_point_add (&temp[4], &temp[2], &temp[0]); /*6+1=7 */
644 ecp_nistz256_scatter_w5 (row, &temp[4], 7);
645 ecp_nistz256_point_double(&temp[1], &temp[1]); /*2*4=8 */
646 ecp_nistz256_scatter_w5 (row, &temp[1], 8);
647 ecp_nistz256_point_double(&temp[2], &temp[2]); /*2*6=12 */
648 ecp_nistz256_scatter_w5 (row, &temp[2], 12);
649 ecp_nistz256_point_double(&temp[3], &temp[3]); /*2*5=10 */
650 ecp_nistz256_scatter_w5 (row, &temp[3], 10);
651 ecp_nistz256_point_double(&temp[4], &temp[4]); /*2*7=14 */
652 ecp_nistz256_scatter_w5 (row, &temp[4], 14);
653 ecp_nistz256_point_add (&temp[2], &temp[2], &temp[0]); /*12+1=13*/
654 ecp_nistz256_scatter_w5 (row, &temp[2], 13);
655 ecp_nistz256_point_add (&temp[3], &temp[3], &temp[0]); /*10+1=11*/
656 ecp_nistz256_scatter_w5 (row, &temp[3], 11);
657 ecp_nistz256_point_add (&temp[4], &temp[4], &temp[0]); /*14+1=15*/
658 ecp_nistz256_scatter_w5 (row, &temp[4], 15);
659 ecp_nistz256_point_add (&temp[2], &temp[1], &temp[0]); /*8+1=9 */
660 ecp_nistz256_scatter_w5 (row, &temp[2], 9);
661 ecp_nistz256_point_double(&temp[1], &temp[1]); /*2*8=16 */
662 ecp_nistz256_scatter_w5 (row, &temp[1], 16);
663 }
664
665 idx = 255;
666
667 wvalue = p_str[0][(idx - 1) / 8];
668 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
669
670 /*
671 * We gather to temp[0], because we know it's position relative
672 * to table
673 */
674 ecp_nistz256_gather_w5(&temp[0], table[0], _booth_recode_w5(wvalue) >> 1);
675 memcpy(r, &temp[0], sizeof(temp[0]));
676
677 while (idx >= 5) {
678 for (i = (idx == 255 ? 1 : 0); i < num; i++) {
679 unsigned int off = (idx - 1) / 8;
680
681 wvalue = p_str[i][off] | p_str[i][off + 1] << 8;
682 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
683
684 wvalue = _booth_recode_w5(wvalue);
685
686 ecp_nistz256_gather_w5(&temp[0], table[i], wvalue >> 1);
687
688 ecp_nistz256_neg(temp[1].Y, temp[0].Y);
689 copy_conditional(temp[0].Y, temp[1].Y, (wvalue & 1));
690
691 ecp_nistz256_point_add(r, r, &temp[0]);
692 }
693
694 idx -= window_size;
695
696 ecp_nistz256_point_double(r, r);
697 ecp_nistz256_point_double(r, r);
698 ecp_nistz256_point_double(r, r);
699 ecp_nistz256_point_double(r, r);
700 ecp_nistz256_point_double(r, r);
701 }
702
703 /* Final window */
704 for (i = 0; i < num; i++) {
705 wvalue = p_str[i][0];
706 wvalue = (wvalue << 1) & mask;
707
708 wvalue = _booth_recode_w5(wvalue);
709
710 ecp_nistz256_gather_w5(&temp[0], table[i], wvalue >> 1);
711
712 ecp_nistz256_neg(temp[1].Y, temp[0].Y);
713 copy_conditional(temp[0].Y, temp[1].Y, wvalue & 1);
714
715 ecp_nistz256_point_add(r, r, &temp[0]);
716 }
717
718 ret = 1;
719 err:
720 OPENSSL_free(table_storage);
721 OPENSSL_free(p_str);
722 OPENSSL_free(scalars);
723 return ret;
724 }
725
726 /* Coordinates of G, for which we have precomputed tables */
727 const static BN_ULONG def_xG[P256_LIMBS] = {
728 TOBN(0x79e730d4, 0x18a9143c), TOBN(0x75ba95fc, 0x5fedb601),
729 TOBN(0x79fb732b, 0x77622510), TOBN(0x18905f76, 0xa53755c6)
730 };
731
732 const static BN_ULONG def_yG[P256_LIMBS] = {
733 TOBN(0xddf25357, 0xce95560a), TOBN(0x8b4ab8e4, 0xba19e45c),
734 TOBN(0xd2e88688, 0xdd21f325), TOBN(0x8571ff18, 0x25885d85)
735 };
736
737 /*
738 * ecp_nistz256_is_affine_G returns one if |generator| is the standard, P-256
739 * generator.
740 */
741 static int ecp_nistz256_is_affine_G(const EC_POINT *generator)
742 {
743 return (bn_get_top(generator->X) == P256_LIMBS) &&
744 (bn_get_top(generator->Y) == P256_LIMBS) &&
745 (bn_get_top(generator->Z) == (P256_LIMBS - P256_LIMBS / 8)) &&
746 is_equal(bn_get_words(generator->X), def_xG) &&
747 is_equal(bn_get_words(generator->Y), def_yG) &&
748 is_one(bn_get_words(generator->Z));
749 }
750
751 __owur static int ecp_nistz256_mult_precompute(EC_GROUP *group, BN_CTX *ctx)
752 {
753 /*
754 * We precompute a table for a Booth encoded exponent (wNAF) based
755 * computation. Each table holds 64 values for safe access, with an
756 * implicit value of infinity at index zero. We use window of size 7, and
757 * therefore require ceil(256/7) = 37 tables.
758 */
759 const BIGNUM *order;
760 EC_POINT *P = NULL, *T = NULL;
761 const EC_POINT *generator;
762 NISTZ256_PRE_COMP *pre_comp;
763 BN_CTX *new_ctx = NULL;
764 int i, j, k, ret = 0;
765 size_t w;
766
767 PRECOMP256_ROW *preComputedTable = NULL;
768 unsigned char *precomp_storage = NULL;
769
770 /* if there is an old NISTZ256_PRE_COMP object, throw it away */
771 EC_pre_comp_free(group);
772 generator = EC_GROUP_get0_generator(group);
773 if (generator == NULL) {
774 ECerr(EC_F_ECP_NISTZ256_MULT_PRECOMPUTE, EC_R_UNDEFINED_GENERATOR);
775 return 0;
776 }
777
778 if (ecp_nistz256_is_affine_G(generator)) {
779 /*
780 * No need to calculate tables for the standard generator because we
781 * have them statically.
782 */
783 return 1;
784 }
785
786 if ((pre_comp = ecp_nistz256_pre_comp_new(group)) == NULL)
787 return 0;
788
789 if (ctx == NULL) {
790 ctx = new_ctx = BN_CTX_new();
791 if (ctx == NULL)
792 goto err;
793 }
794
795 BN_CTX_start(ctx);
796
797 order = EC_GROUP_get0_order(group);
798 if (order == NULL)
799 goto err;
800
801 if (BN_is_zero(order)) {
802 ECerr(EC_F_ECP_NISTZ256_MULT_PRECOMPUTE, EC_R_UNKNOWN_ORDER);
803 goto err;
804 }
805
806 w = 7;
807
808 if ((precomp_storage =
809 OPENSSL_malloc(37 * 64 * sizeof(P256_POINT_AFFINE) + 64)) == NULL) {
810 ECerr(EC_F_ECP_NISTZ256_MULT_PRECOMPUTE, ERR_R_MALLOC_FAILURE);
811 goto err;
812 }
813
814 preComputedTable = (void *)ALIGNPTR(precomp_storage, 64);
815
816 P = EC_POINT_new(group);
817 T = EC_POINT_new(group);
818 if (P == NULL || T == NULL)
819 goto err;
820
821 /*
822 * The zero entry is implicitly infinity, and we skip it, storing other
823 * values with -1 offset.
824 */
825 if (!EC_POINT_copy(T, generator))
826 goto err;
827
828 for (k = 0; k < 64; k++) {
829 if (!EC_POINT_copy(P, T))
830 goto err;
831 for (j = 0; j < 37; j++) {
832 P256_POINT_AFFINE temp;
833 /*
834 * It would be faster to use EC_POINTs_make_affine and
835 * make multiple points affine at the same time.
836 */
837 if (!EC_POINT_make_affine(group, P, ctx))
838 goto err;
839 if (!ecp_nistz256_bignum_to_field_elem(temp.X, P->X) ||
840 !ecp_nistz256_bignum_to_field_elem(temp.Y, P->Y)) {
841 ECerr(EC_F_ECP_NISTZ256_MULT_PRECOMPUTE,
842 EC_R_COORDINATES_OUT_OF_RANGE);
843 goto err;
844 }
845 ecp_nistz256_scatter_w7(preComputedTable[j], &temp, k);
846 for (i = 0; i < 7; i++) {
847 if (!EC_POINT_dbl(group, P, P, ctx))
848 goto err;
849 }
850 }
851 if (!EC_POINT_add(group, T, T, generator, ctx))
852 goto err;
853 }
854
855 pre_comp->group = group;
856 pre_comp->w = w;
857 pre_comp->precomp = preComputedTable;
858 pre_comp->precomp_storage = precomp_storage;
859 precomp_storage = NULL;
860 SETPRECOMP(group, nistz256, pre_comp);
861 pre_comp = NULL;
862 ret = 1;
863
864 err:
865 if (ctx != NULL)
866 BN_CTX_end(ctx);
867 BN_CTX_free(new_ctx);
868
869 EC_nistz256_pre_comp_free(pre_comp);
870 OPENSSL_free(precomp_storage);
871 EC_POINT_free(P);
872 EC_POINT_free(T);
873 return ret;
874 }
875
876 /*
877 * Note that by default ECP_NISTZ256_AVX2 is undefined. While it's great
878 * code processing 4 points in parallel, corresponding serial operation
879 * is several times slower, because it uses 29x29=58-bit multiplication
880 * as opposite to 64x64=128-bit in integer-only scalar case. As result
881 * it doesn't provide *significant* performance improvement. Note that
882 * just defining ECP_NISTZ256_AVX2 is not sufficient to make it work,
883 * you'd need to compile even asm/ecp_nistz256-avx.pl module.
884 */
885 #if defined(ECP_NISTZ256_AVX2)
886 # if !(defined(__x86_64) || defined(__x86_64__) || \
887 defined(_M_AMD64) || defined(_MX64)) || \
888 !(defined(__GNUC__) || defined(_MSC_VER)) /* this is for ALIGN32 */
889 # undef ECP_NISTZ256_AVX2
890 # else
891 /* Constant time access, loading four values, from four consecutive tables */
892 void ecp_nistz256_avx2_multi_gather_w7(void *result, const void *in,
893 int index0, int index1, int index2,
894 int index3);
895 void ecp_nistz256_avx2_transpose_convert(void *RESULTx4, const void *in);
896 void ecp_nistz256_avx2_convert_transpose_back(void *result, const void *Ax4);
897 void ecp_nistz256_avx2_point_add_affine_x4(void *RESULTx4, const void *Ax4,
898 const void *Bx4);
899 void ecp_nistz256_avx2_point_add_affines_x4(void *RESULTx4, const void *Ax4,
900 const void *Bx4);
901 void ecp_nistz256_avx2_to_mont(void *RESULTx4, const void *Ax4);
902 void ecp_nistz256_avx2_from_mont(void *RESULTx4, const void *Ax4);
903 void ecp_nistz256_avx2_set1(void *RESULTx4);
904 int ecp_nistz_avx2_eligible(void);
905
906 static void booth_recode_w7(unsigned char *sign,
907 unsigned char *digit, unsigned char in)
908 {
909 unsigned char s, d;
910
911 s = ~((in >> 7) - 1);
912 d = (1 << 8) - in - 1;
913 d = (d & s) | (in & ~s);
914 d = (d >> 1) + (d & 1);
915
916 *sign = s & 1;
917 *digit = d;
918 }
919
920 /*
921 * ecp_nistz256_avx2_mul_g performs multiplication by G, using only the
922 * precomputed table. It does 4 affine point additions in parallel,
923 * significantly speeding up point multiplication for a fixed value.
924 */
925 static void ecp_nistz256_avx2_mul_g(P256_POINT *r,
926 unsigned char p_str[33],
927 const P256_POINT_AFFINE(*preComputedTable)[64])
928 {
929 const unsigned int window_size = 7;
930 const unsigned int mask = (1 << (window_size + 1)) - 1;
931 unsigned int wvalue;
932 /* Using 4 windows at a time */
933 unsigned char sign0, digit0;
934 unsigned char sign1, digit1;
935 unsigned char sign2, digit2;
936 unsigned char sign3, digit3;
937 unsigned int idx = 0;
938 BN_ULONG tmp[P256_LIMBS];
939 int i;
940
941 ALIGN32 BN_ULONG aX4[4 * 9 * 3] = { 0 };
942 ALIGN32 BN_ULONG bX4[4 * 9 * 2] = { 0 };
943 ALIGN32 P256_POINT_AFFINE point_arr[4];
944 ALIGN32 P256_POINT res_point_arr[4];
945
946 /* Initial four windows */
947 wvalue = *((u16 *) & p_str[0]);
948 wvalue = (wvalue << 1) & mask;
949 idx += window_size;
950 booth_recode_w7(&sign0, &digit0, wvalue);
951 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
952 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
953 idx += window_size;
954 booth_recode_w7(&sign1, &digit1, wvalue);
955 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
956 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
957 idx += window_size;
958 booth_recode_w7(&sign2, &digit2, wvalue);
959 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
960 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
961 idx += window_size;
962 booth_recode_w7(&sign3, &digit3, wvalue);
963
964 ecp_nistz256_avx2_multi_gather_w7(point_arr, preComputedTable[0],
965 digit0, digit1, digit2, digit3);
966
967 ecp_nistz256_neg(tmp, point_arr[0].Y);
968 copy_conditional(point_arr[0].Y, tmp, sign0);
969 ecp_nistz256_neg(tmp, point_arr[1].Y);
970 copy_conditional(point_arr[1].Y, tmp, sign1);
971 ecp_nistz256_neg(tmp, point_arr[2].Y);
972 copy_conditional(point_arr[2].Y, tmp, sign2);
973 ecp_nistz256_neg(tmp, point_arr[3].Y);
974 copy_conditional(point_arr[3].Y, tmp, sign3);
975
976 ecp_nistz256_avx2_transpose_convert(aX4, point_arr);
977 ecp_nistz256_avx2_to_mont(aX4, aX4);
978 ecp_nistz256_avx2_to_mont(&aX4[4 * 9], &aX4[4 * 9]);
979 ecp_nistz256_avx2_set1(&aX4[4 * 9 * 2]);
980
981 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
982 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
983 idx += window_size;
984 booth_recode_w7(&sign0, &digit0, wvalue);
985 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
986 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
987 idx += window_size;
988 booth_recode_w7(&sign1, &digit1, wvalue);
989 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
990 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
991 idx += window_size;
992 booth_recode_w7(&sign2, &digit2, wvalue);
993 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
994 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
995 idx += window_size;
996 booth_recode_w7(&sign3, &digit3, wvalue);
997
998 ecp_nistz256_avx2_multi_gather_w7(point_arr, preComputedTable[4 * 1],
999 digit0, digit1, digit2, digit3);
1000
1001 ecp_nistz256_neg(tmp, point_arr[0].Y);
1002 copy_conditional(point_arr[0].Y, tmp, sign0);
1003 ecp_nistz256_neg(tmp, point_arr[1].Y);
1004 copy_conditional(point_arr[1].Y, tmp, sign1);
1005 ecp_nistz256_neg(tmp, point_arr[2].Y);
1006 copy_conditional(point_arr[2].Y, tmp, sign2);
1007 ecp_nistz256_neg(tmp, point_arr[3].Y);
1008 copy_conditional(point_arr[3].Y, tmp, sign3);
1009
1010 ecp_nistz256_avx2_transpose_convert(bX4, point_arr);
1011 ecp_nistz256_avx2_to_mont(bX4, bX4);
1012 ecp_nistz256_avx2_to_mont(&bX4[4 * 9], &bX4[4 * 9]);
1013 /* Optimized when both inputs are affine */
1014 ecp_nistz256_avx2_point_add_affines_x4(aX4, aX4, bX4);
1015
1016 for (i = 2; i < 9; i++) {
1017 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
1018 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
1019 idx += window_size;
1020 booth_recode_w7(&sign0, &digit0, wvalue);
1021 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
1022 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
1023 idx += window_size;
1024 booth_recode_w7(&sign1, &digit1, wvalue);
1025 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
1026 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
1027 idx += window_size;
1028 booth_recode_w7(&sign2, &digit2, wvalue);
1029 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
1030 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
1031 idx += window_size;
1032 booth_recode_w7(&sign3, &digit3, wvalue);
1033
1034 ecp_nistz256_avx2_multi_gather_w7(point_arr,
1035 preComputedTable[4 * i],
1036 digit0, digit1, digit2, digit3);
1037
1038 ecp_nistz256_neg(tmp, point_arr[0].Y);
1039 copy_conditional(point_arr[0].Y, tmp, sign0);
1040 ecp_nistz256_neg(tmp, point_arr[1].Y);
1041 copy_conditional(point_arr[1].Y, tmp, sign1);
1042 ecp_nistz256_neg(tmp, point_arr[2].Y);
1043 copy_conditional(point_arr[2].Y, tmp, sign2);
1044 ecp_nistz256_neg(tmp, point_arr[3].Y);
1045 copy_conditional(point_arr[3].Y, tmp, sign3);
1046
1047 ecp_nistz256_avx2_transpose_convert(bX4, point_arr);
1048 ecp_nistz256_avx2_to_mont(bX4, bX4);
1049 ecp_nistz256_avx2_to_mont(&bX4[4 * 9], &bX4[4 * 9]);
1050
1051 ecp_nistz256_avx2_point_add_affine_x4(aX4, aX4, bX4);
1052 }
1053
1054 ecp_nistz256_avx2_from_mont(&aX4[4 * 9 * 0], &aX4[4 * 9 * 0]);
1055 ecp_nistz256_avx2_from_mont(&aX4[4 * 9 * 1], &aX4[4 * 9 * 1]);
1056 ecp_nistz256_avx2_from_mont(&aX4[4 * 9 * 2], &aX4[4 * 9 * 2]);
1057
1058 ecp_nistz256_avx2_convert_transpose_back(res_point_arr, aX4);
1059 /* Last window is performed serially */
1060 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
1061 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
1062 booth_recode_w7(&sign0, &digit0, wvalue);
1063 ecp_nistz256_gather_w7((P256_POINT_AFFINE *)r,
1064 preComputedTable[36], digit0);
1065 ecp_nistz256_neg(tmp, r->Y);
1066 copy_conditional(r->Y, tmp, sign0);
1067 memcpy(r->Z, ONE, sizeof(ONE));
1068 /* Sum the four windows */
1069 ecp_nistz256_point_add(r, r, &res_point_arr[0]);
1070 ecp_nistz256_point_add(r, r, &res_point_arr[1]);
1071 ecp_nistz256_point_add(r, r, &res_point_arr[2]);
1072 ecp_nistz256_point_add(r, r, &res_point_arr[3]);
1073 }
1074 # endif
1075 #endif
1076
1077 __owur static int ecp_nistz256_set_from_affine(EC_POINT *out, const EC_GROUP *group,
1078 const P256_POINT_AFFINE *in,
1079 BN_CTX *ctx)
1080 {
1081 BIGNUM *x, *y;
1082 BN_ULONG d_x[P256_LIMBS], d_y[P256_LIMBS];
1083 int ret = 0;
1084
1085 x = BN_new();
1086 if (x == NULL)
1087 return 0;
1088 y = BN_new();
1089 if (y == NULL) {
1090 BN_free(x);
1091 return 0;
1092 }
1093 memcpy(d_x, in->X, sizeof(d_x));
1094 bn_set_static_words(x, d_x, P256_LIMBS);
1095
1096 memcpy(d_y, in->Y, sizeof(d_y));
1097 bn_set_static_words(y, d_y, P256_LIMBS);
1098
1099 ret = EC_POINT_set_affine_coordinates_GFp(group, out, x, y, ctx);
1100
1101 BN_free(x);
1102 BN_free(y);
1103
1104 return ret;
1105 }
1106
1107 /* r = scalar*G + sum(scalars[i]*points[i]) */
1108 __owur static int ecp_nistz256_points_mul(const EC_GROUP *group,
1109 EC_POINT *r,
1110 const BIGNUM *scalar,
1111 size_t num,
1112 const EC_POINT *points[],
1113 const BIGNUM *scalars[], BN_CTX *ctx)
1114 {
1115 int i = 0, ret = 0, no_precomp_for_generator = 0, p_is_infinity = 0;
1116 size_t j;
1117 unsigned char p_str[33] = { 0 };
1118 const PRECOMP256_ROW *preComputedTable = NULL;
1119 const NISTZ256_PRE_COMP *pre_comp = NULL;
1120 const EC_POINT *generator = NULL;
1121 BN_CTX *new_ctx = NULL;
1122 const BIGNUM **new_scalars = NULL;
1123 const EC_POINT **new_points = NULL;
1124 unsigned int idx = 0;
1125 const unsigned int window_size = 7;
1126 const unsigned int mask = (1 << (window_size + 1)) - 1;
1127 unsigned int wvalue;
1128 ALIGN32 union {
1129 P256_POINT p;
1130 P256_POINT_AFFINE a;
1131 } t, p;
1132 BIGNUM *tmp_scalar;
1133
1134 if ((num + 1) == 0 || (num + 1) > OPENSSL_MALLOC_MAX_NELEMS(void *)) {
1135 ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, ERR_R_MALLOC_FAILURE);
1136 return 0;
1137 }
1138
1139 if (group->meth != r->meth) {
1140 ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, EC_R_INCOMPATIBLE_OBJECTS);
1141 return 0;
1142 }
1143
1144 if ((scalar == NULL) && (num == 0))
1145 return EC_POINT_set_to_infinity(group, r);
1146
1147 for (j = 0; j < num; j++) {
1148 if (group->meth != points[j]->meth) {
1149 ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, EC_R_INCOMPATIBLE_OBJECTS);
1150 return 0;
1151 }
1152 }
1153
1154 if (ctx == NULL) {
1155 ctx = new_ctx = BN_CTX_new();
1156 if (ctx == NULL)
1157 goto err;
1158 }
1159
1160 BN_CTX_start(ctx);
1161
1162 if (scalar) {
1163 generator = EC_GROUP_get0_generator(group);
1164 if (generator == NULL) {
1165 ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, EC_R_UNDEFINED_GENERATOR);
1166 goto err;
1167 }
1168
1169 /* look if we can use precomputed multiples of generator */
1170 pre_comp = group->pre_comp.nistz256;
1171
1172 if (pre_comp) {
1173 /*
1174 * If there is a precomputed table for the generator, check that
1175 * it was generated with the same generator.
1176 */
1177 EC_POINT *pre_comp_generator = EC_POINT_new(group);
1178 if (pre_comp_generator == NULL)
1179 goto err;
1180
1181 if (!ecp_nistz256_set_from_affine(pre_comp_generator,
1182 group, pre_comp->precomp[0],
1183 ctx)) {
1184 EC_POINT_free(pre_comp_generator);
1185 goto err;
1186 }
1187
1188 if (0 == EC_POINT_cmp(group, generator, pre_comp_generator, ctx))
1189 preComputedTable = (const PRECOMP256_ROW *)pre_comp->precomp;
1190
1191 EC_POINT_free(pre_comp_generator);
1192 }
1193
1194 if (preComputedTable == NULL && ecp_nistz256_is_affine_G(generator)) {
1195 /*
1196 * If there is no precomputed data, but the generator is the
1197 * default, a hardcoded table of precomputed data is used. This
1198 * is because applications, such as Apache, do not use
1199 * EC_KEY_precompute_mult.
1200 */
1201 preComputedTable = ecp_nistz256_precomputed;
1202 }
1203
1204 if (preComputedTable) {
1205 if ((BN_num_bits(scalar) > 256)
1206 || BN_is_negative(scalar)) {
1207 if ((tmp_scalar = BN_CTX_get(ctx)) == NULL)
1208 goto err;
1209
1210 if (!BN_nnmod(tmp_scalar, scalar, group->order, ctx)) {
1211 ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, ERR_R_BN_LIB);
1212 goto err;
1213 }
1214 scalar = tmp_scalar;
1215 }
1216
1217 for (i = 0; i < bn_get_top(scalar) * BN_BYTES; i += BN_BYTES) {
1218 BN_ULONG d = bn_get_words(scalar)[i / BN_BYTES];
1219
1220 p_str[i + 0] = (unsigned char)d;
1221 p_str[i + 1] = (unsigned char)(d >> 8);
1222 p_str[i + 2] = (unsigned char)(d >> 16);
1223 p_str[i + 3] = (unsigned char)(d >>= 24);
1224 if (BN_BYTES == 8) {
1225 d >>= 8;
1226 p_str[i + 4] = (unsigned char)d;
1227 p_str[i + 5] = (unsigned char)(d >> 8);
1228 p_str[i + 6] = (unsigned char)(d >> 16);
1229 p_str[i + 7] = (unsigned char)(d >> 24);
1230 }
1231 }
1232
1233 for (; i < 33; i++)
1234 p_str[i] = 0;
1235
1236 #if defined(ECP_NISTZ256_AVX2)
1237 if (ecp_nistz_avx2_eligible()) {
1238 ecp_nistz256_avx2_mul_g(&p.p, p_str, preComputedTable);
1239 } else
1240 #endif
1241 {
1242 /* First window */
1243 wvalue = (p_str[0] << 1) & mask;
1244 idx += window_size;
1245
1246 wvalue = _booth_recode_w7(wvalue);
1247
1248 ecp_nistz256_gather_w7(&p.a, preComputedTable[0],
1249 wvalue >> 1);
1250
1251 ecp_nistz256_neg(p.p.Z, p.p.Y);
1252 copy_conditional(p.p.Y, p.p.Z, wvalue & 1);
1253
1254 memcpy(p.p.Z, ONE, sizeof(ONE));
1255
1256 for (i = 1; i < 37; i++) {
1257 unsigned int off = (idx - 1) / 8;
1258 wvalue = p_str[off] | p_str[off + 1] << 8;
1259 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
1260 idx += window_size;
1261
1262 wvalue = _booth_recode_w7(wvalue);
1263
1264 ecp_nistz256_gather_w7(&t.a,
1265 preComputedTable[i], wvalue >> 1);
1266
1267 ecp_nistz256_neg(t.p.Z, t.a.Y);
1268 copy_conditional(t.a.Y, t.p.Z, wvalue & 1);
1269
1270 ecp_nistz256_point_add_affine(&p.p, &p.p, &t.a);
1271 }
1272 }
1273 } else {
1274 p_is_infinity = 1;
1275 no_precomp_for_generator = 1;
1276 }
1277 } else
1278 p_is_infinity = 1;
1279
1280 if (no_precomp_for_generator) {
1281 /*
1282 * Without a precomputed table for the generator, it has to be
1283 * handled like a normal point.
1284 */
1285 new_scalars = OPENSSL_malloc((num + 1) * sizeof(BIGNUM *));
1286 if (new_scalars == NULL) {
1287 ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, ERR_R_MALLOC_FAILURE);
1288 goto err;
1289 }
1290
1291 new_points = OPENSSL_malloc((num + 1) * sizeof(EC_POINT *));
1292 if (new_points == NULL) {
1293 ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, ERR_R_MALLOC_FAILURE);
1294 goto err;
1295 }
1296
1297 memcpy(new_scalars, scalars, num * sizeof(BIGNUM *));
1298 new_scalars[num] = scalar;
1299 memcpy(new_points, points, num * sizeof(EC_POINT *));
1300 new_points[num] = generator;
1301
1302 scalars = new_scalars;
1303 points = new_points;
1304 num++;
1305 }
1306
1307 if (num) {
1308 P256_POINT *out = &t.p;
1309 if (p_is_infinity)
1310 out = &p.p;
1311
1312 if (!ecp_nistz256_windowed_mul(group, out, scalars, points, num, ctx))
1313 goto err;
1314
1315 if (!p_is_infinity)
1316 ecp_nistz256_point_add(&p.p, &p.p, out);
1317 }
1318
1319 /* Not constant-time, but we're only operating on the public output. */
1320 if (!bn_set_words(r->X, p.p.X, P256_LIMBS) ||
1321 !bn_set_words(r->Y, p.p.Y, P256_LIMBS) ||
1322 !bn_set_words(r->Z, p.p.Z, P256_LIMBS)) {
1323 goto err;
1324 }
1325 r->Z_is_one = is_one(p.p.Z) & 1;
1326
1327 ret = 1;
1328
1329 err:
1330 if (ctx)
1331 BN_CTX_end(ctx);
1332 BN_CTX_free(new_ctx);
1333 OPENSSL_free(new_points);
1334 OPENSSL_free(new_scalars);
1335 return ret;
1336 }
1337
1338 __owur static int ecp_nistz256_get_affine(const EC_GROUP *group,
1339 const EC_POINT *point,
1340 BIGNUM *x, BIGNUM *y, BN_CTX *ctx)
1341 {
1342 BN_ULONG z_inv2[P256_LIMBS];
1343 BN_ULONG z_inv3[P256_LIMBS];
1344 BN_ULONG x_aff[P256_LIMBS];
1345 BN_ULONG y_aff[P256_LIMBS];
1346 BN_ULONG point_x[P256_LIMBS], point_y[P256_LIMBS], point_z[P256_LIMBS];
1347 BN_ULONG x_ret[P256_LIMBS], y_ret[P256_LIMBS];
1348
1349 if (EC_POINT_is_at_infinity(group, point)) {
1350 ECerr(EC_F_ECP_NISTZ256_GET_AFFINE, EC_R_POINT_AT_INFINITY);
1351 return 0;
1352 }
1353
1354 if (!ecp_nistz256_bignum_to_field_elem(point_x, point->X) ||
1355 !ecp_nistz256_bignum_to_field_elem(point_y, point->Y) ||
1356 !ecp_nistz256_bignum_to_field_elem(point_z, point->Z)) {
1357 ECerr(EC_F_ECP_NISTZ256_GET_AFFINE, EC_R_COORDINATES_OUT_OF_RANGE);
1358 return 0;
1359 }
1360
1361 ecp_nistz256_mod_inverse(z_inv3, point_z);
1362 ecp_nistz256_sqr_mont(z_inv2, z_inv3);
1363 ecp_nistz256_mul_mont(x_aff, z_inv2, point_x);
1364
1365 if (x != NULL) {
1366 ecp_nistz256_from_mont(x_ret, x_aff);
1367 if (!bn_set_words(x, x_ret, P256_LIMBS))
1368 return 0;
1369 }
1370
1371 if (y != NULL) {
1372 ecp_nistz256_mul_mont(z_inv3, z_inv3, z_inv2);
1373 ecp_nistz256_mul_mont(y_aff, z_inv3, point_y);
1374 ecp_nistz256_from_mont(y_ret, y_aff);
1375 if (!bn_set_words(y, y_ret, P256_LIMBS))
1376 return 0;
1377 }
1378
1379 return 1;
1380 }
1381
1382 static NISTZ256_PRE_COMP *ecp_nistz256_pre_comp_new(const EC_GROUP *group)
1383 {
1384 NISTZ256_PRE_COMP *ret = NULL;
1385
1386 if (!group)
1387 return NULL;
1388
1389 ret = OPENSSL_zalloc(sizeof(*ret));
1390
1391 if (ret == NULL) {
1392 ECerr(EC_F_ECP_NISTZ256_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE);
1393 return ret;
1394 }
1395
1396 ret->group = group;
1397 ret->w = 6; /* default */
1398 ret->references = 1;
1399 return ret;
1400 }
1401
1402 NISTZ256_PRE_COMP *EC_nistz256_pre_comp_dup(NISTZ256_PRE_COMP *p)
1403 {
1404 if (p != NULL)
1405 CRYPTO_add(&p->references, 1, CRYPTO_LOCK_EC_PRE_COMP);
1406 return p;
1407 }
1408
1409 void EC_nistz256_pre_comp_free(NISTZ256_PRE_COMP *pre)
1410 {
1411 if (pre == NULL
1412 || CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP) > 0)
1413 return;
1414 OPENSSL_free(pre->precomp_storage);
1415 OPENSSL_free(pre);
1416 }
1417
1418
1419 static int ecp_nistz256_window_have_precompute_mult(const EC_GROUP *group)
1420 {
1421 /* There is a hard-coded table for the default generator. */
1422 const EC_POINT *generator = EC_GROUP_get0_generator(group);
1423
1424 if (generator != NULL && ecp_nistz256_is_affine_G(generator)) {
1425 /* There is a hard-coded table for the default generator. */
1426 return 1;
1427 }
1428
1429 return HAVEPRECOMP(group, nistz256);
1430 }
1431
1432 const EC_METHOD *EC_GFp_nistz256_method(void)
1433 {
1434 static const EC_METHOD ret = {
1435 EC_FLAGS_DEFAULT_OCT,
1436 NID_X9_62_prime_field,
1437 ec_GFp_mont_group_init,
1438 ec_GFp_mont_group_finish,
1439 ec_GFp_mont_group_clear_finish,
1440 ec_GFp_mont_group_copy,
1441 ec_GFp_mont_group_set_curve,
1442 ec_GFp_simple_group_get_curve,
1443 ec_GFp_simple_group_get_degree,
1444 ec_group_simple_order_bits,
1445 ec_GFp_simple_group_check_discriminant,
1446 ec_GFp_simple_point_init,
1447 ec_GFp_simple_point_finish,
1448 ec_GFp_simple_point_clear_finish,
1449 ec_GFp_simple_point_copy,
1450 ec_GFp_simple_point_set_to_infinity,
1451 ec_GFp_simple_set_Jprojective_coordinates_GFp,
1452 ec_GFp_simple_get_Jprojective_coordinates_GFp,
1453 ec_GFp_simple_point_set_affine_coordinates,
1454 ecp_nistz256_get_affine,
1455 0, 0, 0,
1456 ec_GFp_simple_add,
1457 ec_GFp_simple_dbl,
1458 ec_GFp_simple_invert,
1459 ec_GFp_simple_is_at_infinity,
1460 ec_GFp_simple_is_on_curve,
1461 ec_GFp_simple_cmp,
1462 ec_GFp_simple_make_affine,
1463 ec_GFp_simple_points_make_affine,
1464 ecp_nistz256_points_mul, /* mul */
1465 ecp_nistz256_mult_precompute, /* precompute_mult */
1466 ecp_nistz256_window_have_precompute_mult, /* have_precompute_mult */
1467 ec_GFp_mont_field_mul,
1468 ec_GFp_mont_field_sqr,
1469 0, /* field_div */
1470 ec_GFp_mont_field_encode,
1471 ec_GFp_mont_field_decode,
1472 ec_GFp_mont_field_set_to_one,
1473 ec_key_simple_priv2oct,
1474 ec_key_simple_oct2priv,
1475 0, /* set private */
1476 ec_key_simple_generate_key,
1477 ec_key_simple_check_key,
1478 ec_key_simple_generate_public_key,
1479 0, /* keycopy */
1480 0, /* keyfinish */
1481 ecdh_simple_compute_key
1482 };
1483
1484 return &ret;
1485 }
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