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[thirdparty/openssl.git] / crypto / ec / ecp_nistz256.c
1 /******************************************************************************
2 * *
3 * Copyright 2014 Intel Corporation *
4 * *
5 * Licensed under the Apache License, Version 2.0 (the "License"); *
6 * you may not use this file except in compliance with the License. *
7 * You may obtain a copy of the License at *
8 * *
9 * http://www.apache.org/licenses/LICENSE-2.0 *
10 * *
11 * Unless required by applicable law or agreed to in writing, software *
12 * distributed under the License is distributed on an "AS IS" BASIS, *
13 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. *
14 * See the License for the specific language governing permissions and *
15 * limitations under the License. *
16 * *
17 ******************************************************************************
18 * *
19 * Developers and authors: *
20 * Shay Gueron (1, 2), and Vlad Krasnov (1) *
21 * (1) Intel Corporation, Israel Development Center *
22 * (2) University of Haifa *
23 * Reference: *
24 * S.Gueron and V.Krasnov, "Fast Prime Field Elliptic Curve Cryptography with *
25 * 256 Bit Primes" *
26 * *
27 ******************************************************************************/
28
29 #include <string.h>
30
31 #include "internal/bn_int.h"
32 #include <openssl/err.h>
33 #include <openssl/ec.h>
34 #include "cryptlib.h"
35
36 #include "ec_lcl.h"
37
38 #if BN_BITS2 != 64
39 # define TOBN(hi,lo) lo,hi
40 #else
41 # define TOBN(hi,lo) ((BN_ULONG)hi<<32|lo)
42 #endif
43
44 #if defined(__GNUC__)
45 # define ALIGN32 __attribute((aligned(32)))
46 #elif defined(_MSC_VER)
47 # define ALIGN32 __declspec(align(32))
48 #else
49 # define ALIGN32
50 #endif
51
52 #define ALIGNPTR(p,N) ((unsigned char *)p+N-(size_t)p%N)
53 #define P256_LIMBS (256/BN_BITS2)
54
55 typedef unsigned short u16;
56
57 typedef struct {
58 BN_ULONG X[P256_LIMBS];
59 BN_ULONG Y[P256_LIMBS];
60 BN_ULONG Z[P256_LIMBS];
61 } P256_POINT;
62
63 typedef struct {
64 BN_ULONG X[P256_LIMBS];
65 BN_ULONG Y[P256_LIMBS];
66 } P256_POINT_AFFINE;
67
68 typedef P256_POINT_AFFINE PRECOMP256_ROW[64];
69
70 /* structure for precomputed multiples of the generator */
71 typedef struct ec_pre_comp_st {
72 const EC_GROUP *group; /* Parent EC_GROUP object */
73 size_t w; /* Window size */
74 /*
75 * Constant time access to the X and Y coordinates of the pre-computed,
76 * generator multiplies, in the Montgomery domain. Pre-calculated
77 * multiplies are stored in affine form.
78 */
79 PRECOMP256_ROW *precomp;
80 void *precomp_storage;
81 int references;
82 } EC_PRE_COMP;
83
84 /* Functions implemented in assembly */
85 /* Modular mul by 2: res = 2*a mod P */
86 void ecp_nistz256_mul_by_2(BN_ULONG res[P256_LIMBS],
87 const BN_ULONG a[P256_LIMBS]);
88 /* Modular div by 2: res = a/2 mod P */
89 void ecp_nistz256_div_by_2(BN_ULONG res[P256_LIMBS],
90 const BN_ULONG a[P256_LIMBS]);
91 /* Modular mul by 3: res = 3*a mod P */
92 void ecp_nistz256_mul_by_3(BN_ULONG res[P256_LIMBS],
93 const BN_ULONG a[P256_LIMBS]);
94 /* Modular add: res = a+b mod P */
95 void ecp_nistz256_add(BN_ULONG res[P256_LIMBS],
96 const BN_ULONG a[P256_LIMBS],
97 const BN_ULONG b[P256_LIMBS]);
98 /* Modular sub: res = a-b mod P */
99 void ecp_nistz256_sub(BN_ULONG res[P256_LIMBS],
100 const BN_ULONG a[P256_LIMBS],
101 const BN_ULONG b[P256_LIMBS]);
102 /* Modular neg: res = -a mod P */
103 void ecp_nistz256_neg(BN_ULONG res[P256_LIMBS], const BN_ULONG a[P256_LIMBS]);
104 /* Montgomery mul: res = a*b*2^-256 mod P */
105 void ecp_nistz256_mul_mont(BN_ULONG res[P256_LIMBS],
106 const BN_ULONG a[P256_LIMBS],
107 const BN_ULONG b[P256_LIMBS]);
108 /* Montgomery sqr: res = a*a*2^-256 mod P */
109 void ecp_nistz256_sqr_mont(BN_ULONG res[P256_LIMBS],
110 const BN_ULONG a[P256_LIMBS]);
111 /* Convert a number from Montgomery domain, by multiplying with 1 */
112 void ecp_nistz256_from_mont(BN_ULONG res[P256_LIMBS],
113 const BN_ULONG in[P256_LIMBS]);
114 /* Convert a number to Montgomery domain, by multiplying with 2^512 mod P*/
115 void ecp_nistz256_to_mont(BN_ULONG res[P256_LIMBS],
116 const BN_ULONG in[P256_LIMBS]);
117 /* Functions that perform constant time access to the precomputed tables */
118 void ecp_nistz256_scatter_w5(P256_POINT *val,
119 const P256_POINT *in_t, int idx);
120 void ecp_nistz256_gather_w5(P256_POINT *val,
121 const P256_POINT *in_t, int idx);
122 void ecp_nistz256_scatter_w7(P256_POINT_AFFINE *val,
123 const P256_POINT_AFFINE *in_t, int idx);
124 void ecp_nistz256_gather_w7(P256_POINT_AFFINE *val,
125 const P256_POINT_AFFINE *in_t, int idx);
126
127 /* One converted into the Montgomery domain */
128 static const BN_ULONG ONE[P256_LIMBS] = {
129 TOBN(0x00000000, 0x00000001), TOBN(0xffffffff, 0x00000000),
130 TOBN(0xffffffff, 0xffffffff), TOBN(0x00000000, 0xfffffffe)
131 };
132
133 static void *ecp_nistz256_pre_comp_dup(void *);
134 static void ecp_nistz256_pre_comp_free(void *);
135 static void ecp_nistz256_pre_comp_clear_free(void *);
136 static EC_PRE_COMP *ecp_nistz256_pre_comp_new(const EC_GROUP *group);
137
138 /* Precomputed tables for the default generator */
139 extern const PRECOMP256_ROW ecp_nistz256_precomputed[37];
140
141 /* Recode window to a signed digit, see ecp_nistputil.c for details */
142 static unsigned int _booth_recode_w5(unsigned int in)
143 {
144 unsigned int s, d;
145
146 s = ~((in >> 5) - 1);
147 d = (1 << 6) - in - 1;
148 d = (d & s) | (in & ~s);
149 d = (d >> 1) + (d & 1);
150
151 return (d << 1) + (s & 1);
152 }
153
154 static unsigned int _booth_recode_w7(unsigned int in)
155 {
156 unsigned int s, d;
157
158 s = ~((in >> 7) - 1);
159 d = (1 << 8) - in - 1;
160 d = (d & s) | (in & ~s);
161 d = (d >> 1) + (d & 1);
162
163 return (d << 1) + (s & 1);
164 }
165
166 static void copy_conditional(BN_ULONG dst[P256_LIMBS],
167 const BN_ULONG src[P256_LIMBS], BN_ULONG move)
168 {
169 BN_ULONG mask1 = -move;
170 BN_ULONG mask2 = ~mask1;
171
172 dst[0] = (src[0] & mask1) ^ (dst[0] & mask2);
173 dst[1] = (src[1] & mask1) ^ (dst[1] & mask2);
174 dst[2] = (src[2] & mask1) ^ (dst[2] & mask2);
175 dst[3] = (src[3] & mask1) ^ (dst[3] & mask2);
176 if (P256_LIMBS == 8) {
177 dst[4] = (src[4] & mask1) ^ (dst[4] & mask2);
178 dst[5] = (src[5] & mask1) ^ (dst[5] & mask2);
179 dst[6] = (src[6] & mask1) ^ (dst[6] & mask2);
180 dst[7] = (src[7] & mask1) ^ (dst[7] & mask2);
181 }
182 }
183
184 static BN_ULONG is_zero(BN_ULONG in)
185 {
186 in |= (0 - in);
187 in = ~in;
188 in &= BN_MASK2;
189 in >>= BN_BITS2 - 1;
190 return in;
191 }
192
193 static BN_ULONG is_equal(const BN_ULONG a[P256_LIMBS],
194 const BN_ULONG b[P256_LIMBS])
195 {
196 BN_ULONG res;
197
198 res = a[0] ^ b[0];
199 res |= a[1] ^ b[1];
200 res |= a[2] ^ b[2];
201 res |= a[3] ^ b[3];
202 if (P256_LIMBS == 8) {
203 res |= a[4] ^ b[4];
204 res |= a[5] ^ b[5];
205 res |= a[6] ^ b[6];
206 res |= a[7] ^ b[7];
207 }
208
209 return is_zero(res);
210 }
211
212 static BN_ULONG is_one(const BN_ULONG a[P256_LIMBS])
213 {
214 BN_ULONG res;
215
216 res = a[0] ^ ONE[0];
217 res |= a[1] ^ ONE[1];
218 res |= a[2] ^ ONE[2];
219 res |= a[3] ^ ONE[3];
220 if (P256_LIMBS == 8) {
221 res |= a[4] ^ ONE[4];
222 res |= a[5] ^ ONE[5];
223 res |= a[6] ^ ONE[6];
224 }
225
226 return is_zero(res);
227 }
228
229 #ifndef ECP_NISTZ256_REFERENCE_IMPLEMENTATION
230 void ecp_nistz256_point_double(P256_POINT *r, const P256_POINT *a);
231 void ecp_nistz256_point_add(P256_POINT *r,
232 const P256_POINT *a, const P256_POINT *b);
233 void ecp_nistz256_point_add_affine(P256_POINT *r,
234 const P256_POINT *a,
235 const P256_POINT_AFFINE *b);
236 #else
237 /* Point double: r = 2*a */
238 static void ecp_nistz256_point_double(P256_POINT *r, const P256_POINT *a)
239 {
240 BN_ULONG S[P256_LIMBS];
241 BN_ULONG M[P256_LIMBS];
242 BN_ULONG Zsqr[P256_LIMBS];
243 BN_ULONG tmp0[P256_LIMBS];
244
245 const BN_ULONG *in_x = a->X;
246 const BN_ULONG *in_y = a->Y;
247 const BN_ULONG *in_z = a->Z;
248
249 BN_ULONG *res_x = r->X;
250 BN_ULONG *res_y = r->Y;
251 BN_ULONG *res_z = r->Z;
252
253 ecp_nistz256_mul_by_2(S, in_y);
254
255 ecp_nistz256_sqr_mont(Zsqr, in_z);
256
257 ecp_nistz256_sqr_mont(S, S);
258
259 ecp_nistz256_mul_mont(res_z, in_z, in_y);
260 ecp_nistz256_mul_by_2(res_z, res_z);
261
262 ecp_nistz256_add(M, in_x, Zsqr);
263 ecp_nistz256_sub(Zsqr, in_x, Zsqr);
264
265 ecp_nistz256_sqr_mont(res_y, S);
266 ecp_nistz256_div_by_2(res_y, res_y);
267
268 ecp_nistz256_mul_mont(M, M, Zsqr);
269 ecp_nistz256_mul_by_3(M, M);
270
271 ecp_nistz256_mul_mont(S, S, in_x);
272 ecp_nistz256_mul_by_2(tmp0, S);
273
274 ecp_nistz256_sqr_mont(res_x, M);
275
276 ecp_nistz256_sub(res_x, res_x, tmp0);
277 ecp_nistz256_sub(S, S, res_x);
278
279 ecp_nistz256_mul_mont(S, S, M);
280 ecp_nistz256_sub(res_y, S, res_y);
281 }
282
283 /* Point addition: r = a+b */
284 static void ecp_nistz256_point_add(P256_POINT *r,
285 const P256_POINT *a, const P256_POINT *b)
286 {
287 BN_ULONG U2[P256_LIMBS], S2[P256_LIMBS];
288 BN_ULONG U1[P256_LIMBS], S1[P256_LIMBS];
289 BN_ULONG Z1sqr[P256_LIMBS];
290 BN_ULONG Z2sqr[P256_LIMBS];
291 BN_ULONG H[P256_LIMBS], R[P256_LIMBS];
292 BN_ULONG Hsqr[P256_LIMBS];
293 BN_ULONG Rsqr[P256_LIMBS];
294 BN_ULONG Hcub[P256_LIMBS];
295
296 BN_ULONG res_x[P256_LIMBS];
297 BN_ULONG res_y[P256_LIMBS];
298 BN_ULONG res_z[P256_LIMBS];
299
300 BN_ULONG in1infty, in2infty;
301
302 const BN_ULONG *in1_x = a->X;
303 const BN_ULONG *in1_y = a->Y;
304 const BN_ULONG *in1_z = a->Z;
305
306 const BN_ULONG *in2_x = b->X;
307 const BN_ULONG *in2_y = b->Y;
308 const BN_ULONG *in2_z = b->Z;
309
310 /* We encode infinity as (0,0), which is not on the curve,
311 * so it is OK. */
312 in1infty = (in1_x[0] | in1_x[1] | in1_x[2] | in1_x[3] |
313 in1_y[0] | in1_y[1] | in1_y[2] | in1_y[3]);
314 if (P256_LIMBS == 8)
315 in1infty |= (in1_x[4] | in1_x[5] | in1_x[6] | in1_x[7] |
316 in1_y[4] | in1_y[5] | in1_y[6] | in1_y[7]);
317
318 in2infty = (in2_x[0] | in2_x[1] | in2_x[2] | in2_x[3] |
319 in2_y[0] | in2_y[1] | in2_y[2] | in2_y[3]);
320 if (P256_LIMBS == 8)
321 in2infty |= (in2_x[4] | in2_x[5] | in2_x[6] | in2_x[7] |
322 in2_y[4] | in2_y[5] | in2_y[6] | in2_y[7]);
323
324 in1infty = is_zero(in1infty);
325 in2infty = is_zero(in2infty);
326
327 ecp_nistz256_sqr_mont(Z2sqr, in2_z); /* Z2^2 */
328 ecp_nistz256_sqr_mont(Z1sqr, in1_z); /* Z1^2 */
329
330 ecp_nistz256_mul_mont(S1, Z2sqr, in2_z); /* S1 = Z2^3 */
331 ecp_nistz256_mul_mont(S2, Z1sqr, in1_z); /* S2 = Z1^3 */
332
333 ecp_nistz256_mul_mont(S1, S1, in1_y); /* S1 = Y1*Z2^3 */
334 ecp_nistz256_mul_mont(S2, S2, in2_y); /* S2 = Y2*Z1^3 */
335 ecp_nistz256_sub(R, S2, S1); /* R = S2 - S1 */
336
337 ecp_nistz256_mul_mont(U1, in1_x, Z2sqr); /* U1 = X1*Z2^2 */
338 ecp_nistz256_mul_mont(U2, in2_x, Z1sqr); /* U2 = X2*Z1^2 */
339 ecp_nistz256_sub(H, U2, U1); /* H = U2 - U1 */
340
341 /*
342 * This should not happen during sign/ecdh, so no constant time violation
343 */
344 if (is_equal(U1, U2) && !in1infty && !in2infty) {
345 if (is_equal(S1, S2)) {
346 ecp_nistz256_point_double(r, a);
347 return;
348 } else {
349 memset(r, 0, sizeof(*r));
350 return;
351 }
352 }
353
354 ecp_nistz256_sqr_mont(Rsqr, R); /* R^2 */
355 ecp_nistz256_mul_mont(res_z, H, in1_z); /* Z3 = H*Z1*Z2 */
356 ecp_nistz256_sqr_mont(Hsqr, H); /* H^2 */
357 ecp_nistz256_mul_mont(res_z, res_z, in2_z); /* Z3 = H*Z1*Z2 */
358 ecp_nistz256_mul_mont(Hcub, Hsqr, H); /* H^3 */
359
360 ecp_nistz256_mul_mont(U2, U1, Hsqr); /* U1*H^2 */
361 ecp_nistz256_mul_by_2(Hsqr, U2); /* 2*U1*H^2 */
362
363 ecp_nistz256_sub(res_x, Rsqr, Hsqr);
364 ecp_nistz256_sub(res_x, res_x, Hcub);
365
366 ecp_nistz256_sub(res_y, U2, res_x);
367
368 ecp_nistz256_mul_mont(S2, S1, Hcub);
369 ecp_nistz256_mul_mont(res_y, R, res_y);
370 ecp_nistz256_sub(res_y, res_y, S2);
371
372 copy_conditional(res_x, in2_x, in1infty);
373 copy_conditional(res_y, in2_y, in1infty);
374 copy_conditional(res_z, in2_z, in1infty);
375
376 copy_conditional(res_x, in1_x, in2infty);
377 copy_conditional(res_y, in1_y, in2infty);
378 copy_conditional(res_z, in1_z, in2infty);
379
380 memcpy(r->X, res_x, sizeof(res_x));
381 memcpy(r->Y, res_y, sizeof(res_y));
382 memcpy(r->Z, res_z, sizeof(res_z));
383 }
384
385 /* Point addition when b is known to be affine: r = a+b */
386 static void ecp_nistz256_point_add_affine(P256_POINT *r,
387 const P256_POINT *a,
388 const P256_POINT_AFFINE *b)
389 {
390 BN_ULONG U2[P256_LIMBS], S2[P256_LIMBS];
391 BN_ULONG Z1sqr[P256_LIMBS];
392 BN_ULONG H[P256_LIMBS], R[P256_LIMBS];
393 BN_ULONG Hsqr[P256_LIMBS];
394 BN_ULONG Rsqr[P256_LIMBS];
395 BN_ULONG Hcub[P256_LIMBS];
396
397 BN_ULONG res_x[P256_LIMBS];
398 BN_ULONG res_y[P256_LIMBS];
399 BN_ULONG res_z[P256_LIMBS];
400
401 BN_ULONG in1infty, in2infty;
402
403 const BN_ULONG *in1_x = a->X;
404 const BN_ULONG *in1_y = a->Y;
405 const BN_ULONG *in1_z = a->Z;
406
407 const BN_ULONG *in2_x = b->X;
408 const BN_ULONG *in2_y = b->Y;
409
410 /*
411 * In affine representation we encode infty as (0,0), which is not on the
412 * curve, so it is OK
413 */
414 in1infty = (in1_x[0] | in1_x[1] | in1_x[2] | in1_x[3] |
415 in1_y[0] | in1_y[1] | in1_y[2] | in1_y[3]);
416 if (P256_LIMBS == 8)
417 in1infty |= (in1_x[4] | in1_x[5] | in1_x[6] | in1_x[7] |
418 in1_y[4] | in1_y[5] | in1_y[6] | in1_y[7]);
419
420 in2infty = (in2_x[0] | in2_x[1] | in2_x[2] | in2_x[3] |
421 in2_y[0] | in2_y[1] | in2_y[2] | in2_y[3]);
422 if (P256_LIMBS == 8)
423 in2infty |= (in2_x[4] | in2_x[5] | in2_x[6] | in2_x[7] |
424 in2_y[4] | in2_y[5] | in2_y[6] | in2_y[7]);
425
426 in1infty = is_zero(in1infty);
427 in2infty = is_zero(in2infty);
428
429 ecp_nistz256_sqr_mont(Z1sqr, in1_z); /* Z1^2 */
430
431 ecp_nistz256_mul_mont(U2, in2_x, Z1sqr); /* U2 = X2*Z1^2 */
432 ecp_nistz256_sub(H, U2, in1_x); /* H = U2 - U1 */
433
434 ecp_nistz256_mul_mont(S2, Z1sqr, in1_z); /* S2 = Z1^3 */
435
436 ecp_nistz256_mul_mont(res_z, H, in1_z); /* Z3 = H*Z1*Z2 */
437
438 ecp_nistz256_mul_mont(S2, S2, in2_y); /* S2 = Y2*Z1^3 */
439 ecp_nistz256_sub(R, S2, in1_y); /* R = S2 - S1 */
440
441 ecp_nistz256_sqr_mont(Hsqr, H); /* H^2 */
442 ecp_nistz256_sqr_mont(Rsqr, R); /* R^2 */
443 ecp_nistz256_mul_mont(Hcub, Hsqr, H); /* H^3 */
444
445 ecp_nistz256_mul_mont(U2, in1_x, Hsqr); /* U1*H^2 */
446 ecp_nistz256_mul_by_2(Hsqr, U2); /* 2*U1*H^2 */
447
448 ecp_nistz256_sub(res_x, Rsqr, Hsqr);
449 ecp_nistz256_sub(res_x, res_x, Hcub);
450 ecp_nistz256_sub(H, U2, res_x);
451
452 ecp_nistz256_mul_mont(S2, in1_y, Hcub);
453 ecp_nistz256_mul_mont(H, H, R);
454 ecp_nistz256_sub(res_y, H, S2);
455
456 copy_conditional(res_x, in2_x, in1infty);
457 copy_conditional(res_x, in1_x, in2infty);
458
459 copy_conditional(res_y, in2_y, in1infty);
460 copy_conditional(res_y, in1_y, in2infty);
461
462 copy_conditional(res_z, ONE, in1infty);
463 copy_conditional(res_z, in1_z, in2infty);
464
465 memcpy(r->X, res_x, sizeof(res_x));
466 memcpy(r->Y, res_y, sizeof(res_y));
467 memcpy(r->Z, res_z, sizeof(res_z));
468 }
469 #endif
470
471 /* r = in^-1 mod p */
472 static void ecp_nistz256_mod_inverse(BN_ULONG r[P256_LIMBS],
473 const BN_ULONG in[P256_LIMBS])
474 {
475 /*
476 * The poly is ffffffff 00000001 00000000 00000000 00000000 ffffffff
477 * ffffffff ffffffff We use FLT and used poly-2 as exponent
478 */
479 BN_ULONG p2[P256_LIMBS];
480 BN_ULONG p4[P256_LIMBS];
481 BN_ULONG p8[P256_LIMBS];
482 BN_ULONG p16[P256_LIMBS];
483 BN_ULONG p32[P256_LIMBS];
484 BN_ULONG res[P256_LIMBS];
485 int i;
486
487 ecp_nistz256_sqr_mont(res, in);
488 ecp_nistz256_mul_mont(p2, res, in); /* 3*p */
489
490 ecp_nistz256_sqr_mont(res, p2);
491 ecp_nistz256_sqr_mont(res, res);
492 ecp_nistz256_mul_mont(p4, res, p2); /* f*p */
493
494 ecp_nistz256_sqr_mont(res, p4);
495 ecp_nistz256_sqr_mont(res, res);
496 ecp_nistz256_sqr_mont(res, res);
497 ecp_nistz256_sqr_mont(res, res);
498 ecp_nistz256_mul_mont(p8, res, p4); /* ff*p */
499
500 ecp_nistz256_sqr_mont(res, p8);
501 for (i = 0; i < 7; i++)
502 ecp_nistz256_sqr_mont(res, res);
503 ecp_nistz256_mul_mont(p16, res, p8); /* ffff*p */
504
505 ecp_nistz256_sqr_mont(res, p16);
506 for (i = 0; i < 15; i++)
507 ecp_nistz256_sqr_mont(res, res);
508 ecp_nistz256_mul_mont(p32, res, p16); /* ffffffff*p */
509
510 ecp_nistz256_sqr_mont(res, p32);
511 for (i = 0; i < 31; i++)
512 ecp_nistz256_sqr_mont(res, res);
513 ecp_nistz256_mul_mont(res, res, in);
514
515 for (i = 0; i < 32 * 4; i++)
516 ecp_nistz256_sqr_mont(res, res);
517 ecp_nistz256_mul_mont(res, res, p32);
518
519 for (i = 0; i < 32; i++)
520 ecp_nistz256_sqr_mont(res, res);
521 ecp_nistz256_mul_mont(res, res, p32);
522
523 for (i = 0; i < 16; i++)
524 ecp_nistz256_sqr_mont(res, res);
525 ecp_nistz256_mul_mont(res, res, p16);
526
527 for (i = 0; i < 8; i++)
528 ecp_nistz256_sqr_mont(res, res);
529 ecp_nistz256_mul_mont(res, res, p8);
530
531 ecp_nistz256_sqr_mont(res, res);
532 ecp_nistz256_sqr_mont(res, res);
533 ecp_nistz256_sqr_mont(res, res);
534 ecp_nistz256_sqr_mont(res, res);
535 ecp_nistz256_mul_mont(res, res, p4);
536
537 ecp_nistz256_sqr_mont(res, res);
538 ecp_nistz256_sqr_mont(res, res);
539 ecp_nistz256_mul_mont(res, res, p2);
540
541 ecp_nistz256_sqr_mont(res, res);
542 ecp_nistz256_sqr_mont(res, res);
543 ecp_nistz256_mul_mont(res, res, in);
544
545 memcpy(r, res, sizeof(res));
546 }
547
548 /*
549 * ecp_nistz256_bignum_to_field_elem copies the contents of |in| to |out| and
550 * returns one if it fits. Otherwise it returns zero.
551 */
552 static int ecp_nistz256_bignum_to_field_elem(BN_ULONG out[P256_LIMBS],
553 const BIGNUM *in)
554 {
555 return bn_copy_words(out, in, P256_LIMBS);
556 }
557
558 /* r = sum(scalar[i]*point[i]) */
559 static void ecp_nistz256_windowed_mul(const EC_GROUP *group,
560 P256_POINT *r,
561 const BIGNUM **scalar,
562 const EC_POINT **point,
563 int num, BN_CTX *ctx)
564 {
565 int i, j;
566 unsigned int idx;
567 unsigned char (*p_str)[33] = NULL;
568 const unsigned int window_size = 5;
569 const unsigned int mask = (1 << (window_size + 1)) - 1;
570 unsigned int wvalue;
571 P256_POINT *temp; /* place for 5 temporary points */
572 const BIGNUM **scalars = NULL;
573 P256_POINT (*table)[16] = NULL;
574 void *table_storage = NULL;
575
576 if ((table_storage =
577 OPENSSL_malloc((num * 16 + 5) * sizeof(P256_POINT) + 64)) == NULL
578 || (p_str =
579 OPENSSL_malloc(num * 33 * sizeof(unsigned char))) == NULL
580 || (scalars = OPENSSL_malloc(num * sizeof(BIGNUM *))) == NULL) {
581 ECerr(EC_F_ECP_NISTZ256_WINDOWED_MUL, ERR_R_MALLOC_FAILURE);
582 goto err;
583 }
584
585 table = (void *)ALIGNPTR(table_storage, 64);
586 temp = (P256_POINT *)(table + num);
587
588 for (i = 0; i < num; i++) {
589 P256_POINT *row = table[i];
590
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] = d & 0xff;
608 p_str[i][j + 1] = (d >> 8) & 0xff;
609 p_str[i][j + 2] = (d >> 16) & 0xff;
610 p_str[i][j + 3] = (d >>= 24) & 0xff;
611 if (BN_BYTES == 8) {
612 d >>= 8;
613 p_str[i][j + 4] = d & 0xff;
614 p_str[i][j + 5] = (d >> 8) & 0xff;
615 p_str[i][j + 6] = (d >> 16) & 0xff;
616 p_str[i][j + 7] = (d >> 24) & 0xff;
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 err:
723 if (table_storage)
724 OPENSSL_free(table_storage);
725 if (p_str)
726 OPENSSL_free(p_str);
727 if (scalars)
728 OPENSSL_free(scalars);
729 }
730
731 /* Coordinates of G, for which we have precomputed tables */
732 const static BN_ULONG def_xG[P256_LIMBS] = {
733 TOBN(0x79e730d4, 0x18a9143c), TOBN(0x75ba95fc, 0x5fedb601),
734 TOBN(0x79fb732b, 0x77622510), TOBN(0x18905f76, 0xa53755c6)
735 };
736
737 const static BN_ULONG def_yG[P256_LIMBS] = {
738 TOBN(0xddf25357, 0xce95560a), TOBN(0x8b4ab8e4, 0xba19e45c),
739 TOBN(0xd2e88688, 0xdd21f325), TOBN(0x8571ff18, 0x25885d85)
740 };
741
742 /*
743 * ecp_nistz256_is_affine_G returns one if |generator| is the standard, P-256
744 * generator.
745 */
746 static int ecp_nistz256_is_affine_G(const EC_POINT *generator)
747 {
748 return (bn_get_top(generator->X) == P256_LIMBS) &&
749 (bn_get_top(generator->Y) == P256_LIMBS) &&
750 (bn_get_top(generator->Z) == (P256_LIMBS - P256_LIMBS / 8)) &&
751 is_equal(bn_get_words(generator->X), def_xG) &&
752 is_equal(bn_get_words(generator->Y), def_yG) &&
753 is_one(bn_get_words(generator->Z));
754 }
755
756 static int ecp_nistz256_mult_precompute(EC_GROUP *group, BN_CTX *ctx)
757 {
758 /*
759 * We precompute a table for a Booth encoded exponent (wNAF) based
760 * computation. Each table holds 64 values for safe access, with an
761 * implicit value of infinity at index zero. We use window of size 7, and
762 * therefore require ceil(256/7) = 37 tables.
763 */
764 BIGNUM *order;
765 EC_POINT *P = NULL, *T = NULL;
766 const EC_POINT *generator;
767 EC_PRE_COMP *pre_comp;
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 = 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
829 /*
830 * The zero entry is implicitly infinity, and we skip it, storing other
831 * values with -1 offset.
832 */
833 EC_POINT_copy(T, generator);
834
835 for (k = 0; k < 64; k++) {
836 EC_POINT_copy(P, T);
837 for (j = 0; j < 37; j++) {
838 P256_POINT_AFFINE temp;
839 /*
840 * It would be faster to use ec_GFp_simple_points_make_affine and
841 * make multiple points affine at the same time.
842 */
843 ec_GFp_simple_make_affine(group, P, ctx);
844 ecp_nistz256_bignum_to_field_elem(temp.X, P->X);
845 ecp_nistz256_bignum_to_field_elem(temp.Y, P->Y);
846 ecp_nistz256_scatter_w7(preComputedTable[j], &temp, k);
847 for (i = 0; i < 7; i++)
848 ec_GFp_simple_dbl(group, P, P, ctx);
849 }
850 ec_GFp_simple_add(group, T, T, generator, ctx);
851 }
852
853 pre_comp->group = group;
854 pre_comp->w = w;
855 pre_comp->precomp = preComputedTable;
856 pre_comp->precomp_storage = precomp_storage;
857
858 precomp_storage = NULL;
859
860 if (!EC_EX_DATA_set_data(&group->extra_data, pre_comp,
861 ecp_nistz256_pre_comp_dup,
862 ecp_nistz256_pre_comp_free,
863 ecp_nistz256_pre_comp_clear_free)) {
864 goto err;
865 }
866
867 pre_comp = NULL;
868
869 ret = 1;
870
871 err:
872 if (ctx != NULL)
873 BN_CTX_end(ctx);
874 if (pre_comp)
875 ecp_nistz256_pre_comp_free(pre_comp);
876 if (precomp_storage)
877 OPENSSL_free(precomp_storage);
878 if (P)
879 EC_POINT_free(P);
880 if (T)
881 EC_POINT_free(T);
882 return ret;
883 }
884
885 /*
886 * Note that by default ECP_NISTZ256_AVX2 is undefined. While it's great
887 * code processing 4 points in parallel, corresponding serial operation
888 * is several times slower, because it uses 29x29=58-bit multiplication
889 * as opposite to 64x64=128-bit in integer-only scalar case. As result
890 * it doesn't provide *significant* performance improvement. Note that
891 * just defining ECP_NISTZ256_AVX2 is not sufficient to make it work,
892 * you'd need to compile even asm/ecp_nistz256-avx.pl module.
893 */
894 #if defined(ECP_NISTZ256_AVX2)
895 # if !(defined(__x86_64) || defined(__x86_64__) || \
896 defined(_M_AMD64) || defined(_MX64)) || \
897 !(defined(__GNUC__) || defined(_MSC_VER)) /* this is for ALIGN32 */
898 # undef ECP_NISTZ256_AVX2
899 # else
900 /* Constant time access, loading four values, from four consecutive tables */
901 void ecp_nistz256_avx2_multi_gather_w7(void *result, const void *in,
902 int index0, int index1, int index2,
903 int index3);
904 void ecp_nistz256_avx2_transpose_convert(void *RESULTx4, const void *in);
905 void ecp_nistz256_avx2_convert_transpose_back(void *result, const void *Ax4);
906 void ecp_nistz256_avx2_point_add_affine_x4(void *RESULTx4, const void *Ax4,
907 const void *Bx4);
908 void ecp_nistz256_avx2_point_add_affines_x4(void *RESULTx4, const void *Ax4,
909 const void *Bx4);
910 void ecp_nistz256_avx2_to_mont(void *RESULTx4, const void *Ax4);
911 void ecp_nistz256_avx2_from_mont(void *RESULTx4, const void *Ax4);
912 void ecp_nistz256_avx2_set1(void *RESULTx4);
913 int ecp_nistz_avx2_eligible(void);
914
915 static void booth_recode_w7(unsigned char *sign,
916 unsigned char *digit, unsigned char in)
917 {
918 unsigned char s, d;
919
920 s = ~((in >> 7) - 1);
921 d = (1 << 8) - in - 1;
922 d = (d & s) | (in & ~s);
923 d = (d >> 1) + (d & 1);
924
925 *sign = s & 1;
926 *digit = d;
927 }
928
929 /*
930 * ecp_nistz256_avx2_mul_g performs multiplication by G, using only the
931 * precomputed table. It does 4 affine point additions in parallel,
932 * significantly speeding up point multiplication for a fixed value.
933 */
934 static void ecp_nistz256_avx2_mul_g(P256_POINT *r,
935 unsigned char p_str[33],
936 const P256_POINT_AFFINE(*preComputedTable)[64])
937 {
938 const unsigned int window_size = 7;
939 const unsigned int mask = (1 << (window_size + 1)) - 1;
940 unsigned int wvalue;
941 /* Using 4 windows at a time */
942 unsigned char sign0, digit0;
943 unsigned char sign1, digit1;
944 unsigned char sign2, digit2;
945 unsigned char sign3, digit3;
946 unsigned int idx = 0;
947 BN_ULONG tmp[P256_LIMBS];
948 int i;
949
950 ALIGN32 BN_ULONG aX4[4 * 9 * 3] = { 0 };
951 ALIGN32 BN_ULONG bX4[4 * 9 * 2] = { 0 };
952 ALIGN32 P256_POINT_AFFINE point_arr[4];
953 ALIGN32 P256_POINT res_point_arr[4];
954
955 /* Initial four windows */
956 wvalue = *((u16 *) & p_str[0]);
957 wvalue = (wvalue << 1) & mask;
958 idx += window_size;
959 booth_recode_w7(&sign0, &digit0, wvalue);
960 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
961 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
962 idx += window_size;
963 booth_recode_w7(&sign1, &digit1, wvalue);
964 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
965 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
966 idx += window_size;
967 booth_recode_w7(&sign2, &digit2, wvalue);
968 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
969 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
970 idx += window_size;
971 booth_recode_w7(&sign3, &digit3, wvalue);
972
973 ecp_nistz256_avx2_multi_gather_w7(point_arr, preComputedTable[0],
974 digit0, digit1, digit2, digit3);
975
976 ecp_nistz256_neg(tmp, point_arr[0].Y);
977 copy_conditional(point_arr[0].Y, tmp, sign0);
978 ecp_nistz256_neg(tmp, point_arr[1].Y);
979 copy_conditional(point_arr[1].Y, tmp, sign1);
980 ecp_nistz256_neg(tmp, point_arr[2].Y);
981 copy_conditional(point_arr[2].Y, tmp, sign2);
982 ecp_nistz256_neg(tmp, point_arr[3].Y);
983 copy_conditional(point_arr[3].Y, tmp, sign3);
984
985 ecp_nistz256_avx2_transpose_convert(aX4, point_arr);
986 ecp_nistz256_avx2_to_mont(aX4, aX4);
987 ecp_nistz256_avx2_to_mont(&aX4[4 * 9], &aX4[4 * 9]);
988 ecp_nistz256_avx2_set1(&aX4[4 * 9 * 2]);
989
990 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
991 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
992 idx += window_size;
993 booth_recode_w7(&sign0, &digit0, wvalue);
994 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
995 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
996 idx += window_size;
997 booth_recode_w7(&sign1, &digit1, wvalue);
998 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
999 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
1000 idx += window_size;
1001 booth_recode_w7(&sign2, &digit2, wvalue);
1002 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
1003 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
1004 idx += window_size;
1005 booth_recode_w7(&sign3, &digit3, wvalue);
1006
1007 ecp_nistz256_avx2_multi_gather_w7(point_arr, preComputedTable[4 * 1],
1008 digit0, digit1, digit2, digit3);
1009
1010 ecp_nistz256_neg(tmp, point_arr[0].Y);
1011 copy_conditional(point_arr[0].Y, tmp, sign0);
1012 ecp_nistz256_neg(tmp, point_arr[1].Y);
1013 copy_conditional(point_arr[1].Y, tmp, sign1);
1014 ecp_nistz256_neg(tmp, point_arr[2].Y);
1015 copy_conditional(point_arr[2].Y, tmp, sign2);
1016 ecp_nistz256_neg(tmp, point_arr[3].Y);
1017 copy_conditional(point_arr[3].Y, tmp, sign3);
1018
1019 ecp_nistz256_avx2_transpose_convert(bX4, point_arr);
1020 ecp_nistz256_avx2_to_mont(bX4, bX4);
1021 ecp_nistz256_avx2_to_mont(&bX4[4 * 9], &bX4[4 * 9]);
1022 /* Optimized when both inputs are affine */
1023 ecp_nistz256_avx2_point_add_affines_x4(aX4, aX4, bX4);
1024
1025 for (i = 2; i < 9; i++) {
1026 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
1027 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
1028 idx += window_size;
1029 booth_recode_w7(&sign0, &digit0, wvalue);
1030 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
1031 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
1032 idx += window_size;
1033 booth_recode_w7(&sign1, &digit1, wvalue);
1034 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
1035 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
1036 idx += window_size;
1037 booth_recode_w7(&sign2, &digit2, wvalue);
1038 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
1039 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
1040 idx += window_size;
1041 booth_recode_w7(&sign3, &digit3, wvalue);
1042
1043 ecp_nistz256_avx2_multi_gather_w7(point_arr,
1044 preComputedTable[4 * i],
1045 digit0, digit1, digit2, digit3);
1046
1047 ecp_nistz256_neg(tmp, point_arr[0].Y);
1048 copy_conditional(point_arr[0].Y, tmp, sign0);
1049 ecp_nistz256_neg(tmp, point_arr[1].Y);
1050 copy_conditional(point_arr[1].Y, tmp, sign1);
1051 ecp_nistz256_neg(tmp, point_arr[2].Y);
1052 copy_conditional(point_arr[2].Y, tmp, sign2);
1053 ecp_nistz256_neg(tmp, point_arr[3].Y);
1054 copy_conditional(point_arr[3].Y, tmp, sign3);
1055
1056 ecp_nistz256_avx2_transpose_convert(bX4, point_arr);
1057 ecp_nistz256_avx2_to_mont(bX4, bX4);
1058 ecp_nistz256_avx2_to_mont(&bX4[4 * 9], &bX4[4 * 9]);
1059
1060 ecp_nistz256_avx2_point_add_affine_x4(aX4, aX4, bX4);
1061 }
1062
1063 ecp_nistz256_avx2_from_mont(&aX4[4 * 9 * 0], &aX4[4 * 9 * 0]);
1064 ecp_nistz256_avx2_from_mont(&aX4[4 * 9 * 1], &aX4[4 * 9 * 1]);
1065 ecp_nistz256_avx2_from_mont(&aX4[4 * 9 * 2], &aX4[4 * 9 * 2]);
1066
1067 ecp_nistz256_avx2_convert_transpose_back(res_point_arr, aX4);
1068 /* Last window is performed serially */
1069 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
1070 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
1071 booth_recode_w7(&sign0, &digit0, wvalue);
1072 ecp_nistz256_gather_w7((P256_POINT_AFFINE *)r,
1073 preComputedTable[36], digit0);
1074 ecp_nistz256_neg(tmp, r->Y);
1075 copy_conditional(r->Y, tmp, sign0);
1076 memcpy(r->Z, ONE, sizeof(ONE));
1077 /* Sum the four windows */
1078 ecp_nistz256_point_add(r, r, &res_point_arr[0]);
1079 ecp_nistz256_point_add(r, r, &res_point_arr[1]);
1080 ecp_nistz256_point_add(r, r, &res_point_arr[2]);
1081 ecp_nistz256_point_add(r, r, &res_point_arr[3]);
1082 }
1083 # endif
1084 #endif
1085
1086 static int ecp_nistz256_set_from_affine(EC_POINT *out, const EC_GROUP *group,
1087 const P256_POINT_AFFINE *in,
1088 BN_CTX *ctx)
1089 {
1090 BIGNUM *x, *y;
1091 BN_ULONG d_x[P256_LIMBS], d_y[P256_LIMBS];
1092 int ret = 0;
1093
1094 x = BN_new();
1095 if (!x)
1096 return 0;
1097 y = BN_new();
1098 if (!y) {
1099 BN_free(x);
1100 return 0;
1101 }
1102 memcpy(d_x, in->X, sizeof(d_x));
1103 bn_set_static_words(x, d_x, P256_LIMBS);
1104
1105 memcpy(d_y, in->Y, sizeof(d_y));
1106 bn_set_static_words(y, d_y, P256_LIMBS);
1107
1108 ret = EC_POINT_set_affine_coordinates_GFp(group, out, x, y, ctx);
1109
1110 if (x)
1111 BN_free(x);
1112 if (y)
1113 BN_free(y);
1114
1115 return ret;
1116 }
1117
1118 /* r = scalar*G + sum(scalars[i]*points[i]) */
1119 static int ecp_nistz256_points_mul(const EC_GROUP *group,
1120 EC_POINT *r,
1121 const BIGNUM *scalar,
1122 size_t num,
1123 const EC_POINT *points[],
1124 const BIGNUM *scalars[], BN_CTX *ctx)
1125 {
1126 int i = 0, ret = 0, no_precomp_for_generator = 0, p_is_infinity = 0;
1127 size_t j;
1128 unsigned char p_str[33] = { 0 };
1129 const PRECOMP256_ROW *preComputedTable = NULL;
1130 const EC_PRE_COMP *pre_comp = NULL;
1131 const EC_POINT *generator = NULL;
1132 unsigned int idx = 0;
1133 const unsigned int window_size = 7;
1134 const unsigned int mask = (1 << (window_size + 1)) - 1;
1135 unsigned int wvalue;
1136 ALIGN32 union {
1137 P256_POINT p;
1138 P256_POINT_AFFINE a;
1139 } t, p;
1140 BIGNUM *tmp_scalar;
1141
1142 if ((num + 1) == 0 || (num + 1) > OPENSSL_MALLOC_MAX_NELEMS(void *)) {
1143 ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, ERR_R_MALLOC_FAILURE);
1144 return 0;
1145 }
1146
1147 if (group->meth != r->meth) {
1148 ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, EC_R_INCOMPATIBLE_OBJECTS);
1149 return 0;
1150 }
1151 if ((scalar == NULL) && (num == 0))
1152 return EC_POINT_set_to_infinity(group, r);
1153
1154 for (j = 0; j < num; j++) {
1155 if (group->meth != points[j]->meth) {
1156 ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, EC_R_INCOMPATIBLE_OBJECTS);
1157 return 0;
1158 }
1159 }
1160
1161 /* Need 256 bits for space for all coordinates. */
1162 bn_wexpand(r->X, P256_LIMBS);
1163 bn_wexpand(r->Y, P256_LIMBS);
1164 bn_wexpand(r->Z, P256_LIMBS);
1165 bn_set_top(r->X, P256_LIMBS);
1166 bn_set_top(r->Y, P256_LIMBS);
1167 bn_set_top(r->Z, P256_LIMBS);
1168
1169 if (scalar) {
1170 generator = EC_GROUP_get0_generator(group);
1171 if (generator == NULL) {
1172 ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, EC_R_UNDEFINED_GENERATOR);
1173 goto err;
1174 }
1175
1176 /* look if we can use precomputed multiples of generator */
1177 pre_comp =
1178 EC_EX_DATA_get_data(group->extra_data, ecp_nistz256_pre_comp_dup,
1179 ecp_nistz256_pre_comp_free,
1180 ecp_nistz256_pre_comp_clear_free);
1181
1182 if (pre_comp) {
1183 /*
1184 * If there is a precomputed table for the generator, check that
1185 * it was generated with the same generator.
1186 */
1187 EC_POINT *pre_comp_generator = EC_POINT_new(group);
1188 if (pre_comp_generator == NULL)
1189 goto err;
1190
1191 if (!ecp_nistz256_set_from_affine(pre_comp_generator,
1192 group, pre_comp->precomp[0],
1193 ctx))
1194 goto err;
1195
1196 if (0 == EC_POINT_cmp(group, generator, pre_comp_generator, ctx))
1197 preComputedTable = (const PRECOMP256_ROW *)pre_comp->precomp;
1198
1199 EC_POINT_free(pre_comp_generator);
1200 }
1201
1202 if (preComputedTable == NULL && ecp_nistz256_is_affine_G(generator)) {
1203 /*
1204 * If there is no precomputed data, but the generator is the
1205 * default, a hardcoded table of precomputed data is used. This
1206 * is because applications, such as Apache, do not use
1207 * EC_KEY_precompute_mult.
1208 */
1209 preComputedTable = ecp_nistz256_precomputed;
1210 }
1211
1212 if (preComputedTable) {
1213 if ((BN_num_bits(scalar) > 256)
1214 || BN_is_negative(scalar)) {
1215 if ((tmp_scalar = BN_CTX_get(ctx)) == NULL)
1216 goto err;
1217
1218 if (!BN_nnmod(tmp_scalar, scalar, group->order, ctx)) {
1219 ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, ERR_R_BN_LIB);
1220 goto err;
1221 }
1222 scalar = tmp_scalar;
1223 }
1224
1225 for (i = 0; i < bn_get_top(scalar) * BN_BYTES; i += BN_BYTES) {
1226 BN_ULONG d = bn_get_words(scalar)[i / BN_BYTES];
1227
1228 p_str[i + 0] = d & 0xff;
1229 p_str[i + 1] = (d >> 8) & 0xff;
1230 p_str[i + 2] = (d >> 16) & 0xff;
1231 p_str[i + 3] = (d >>= 24) & 0xff;
1232 if (BN_BYTES == 8) {
1233 d >>= 8;
1234 p_str[i + 4] = d & 0xff;
1235 p_str[i + 5] = (d >> 8) & 0xff;
1236 p_str[i + 6] = (d >> 16) & 0xff;
1237 p_str[i + 7] = (d >> 24) & 0xff;
1238 }
1239 }
1240
1241 for (; i < 33; i++)
1242 p_str[i] = 0;
1243
1244 #if defined(ECP_NISTZ256_AVX2)
1245 if (ecp_nistz_avx2_eligible()) {
1246 ecp_nistz256_avx2_mul_g(&p.p, p_str, preComputedTable);
1247 } else
1248 #endif
1249 {
1250 /* First window */
1251 wvalue = (p_str[0] << 1) & mask;
1252 idx += window_size;
1253
1254 wvalue = _booth_recode_w7(wvalue);
1255
1256 ecp_nistz256_gather_w7(&p.a, preComputedTable[0],
1257 wvalue >> 1);
1258
1259 ecp_nistz256_neg(p.p.Z, p.p.Y);
1260 copy_conditional(p.p.Y, p.p.Z, wvalue & 1);
1261
1262 memcpy(p.p.Z, ONE, sizeof(ONE));
1263
1264 for (i = 1; i < 37; i++) {
1265 unsigned int off = (idx - 1) / 8;
1266 wvalue = p_str[off] | p_str[off + 1] << 8;
1267 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
1268 idx += window_size;
1269
1270 wvalue = _booth_recode_w7(wvalue);
1271
1272 ecp_nistz256_gather_w7(&t.a,
1273 preComputedTable[i], wvalue >> 1);
1274
1275 ecp_nistz256_neg(t.p.Z, t.a.Y);
1276 copy_conditional(t.a.Y, t.p.Z, wvalue & 1);
1277
1278 ecp_nistz256_point_add_affine(&p.p, &p.p, &t.a);
1279 }
1280 }
1281 } else {
1282 p_is_infinity = 1;
1283 no_precomp_for_generator = 1;
1284 }
1285 } else
1286 p_is_infinity = 1;
1287
1288 if (no_precomp_for_generator) {
1289 /*
1290 * Without a precomputed table for the generator, it has to be
1291 * handled like a normal point.
1292 */
1293 const BIGNUM **new_scalars;
1294 const EC_POINT **new_points;
1295
1296 new_scalars = OPENSSL_malloc((num + 1) * sizeof(BIGNUM *));
1297 if (!new_scalars) {
1298 ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, ERR_R_MALLOC_FAILURE);
1299 return 0;
1300 }
1301
1302 new_points = OPENSSL_malloc((num + 1) * sizeof(EC_POINT *));
1303 if (!new_points) {
1304 OPENSSL_free(new_scalars);
1305 ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, ERR_R_MALLOC_FAILURE);
1306 return 0;
1307 }
1308
1309 memcpy(new_scalars, scalars, num * sizeof(BIGNUM *));
1310 new_scalars[num] = scalar;
1311 memcpy(new_points, points, num * sizeof(EC_POINT *));
1312 new_points[num] = generator;
1313
1314 scalars = new_scalars;
1315 points = new_points;
1316 num++;
1317 }
1318
1319 if (num) {
1320 P256_POINT *out = &t.p;
1321 if (p_is_infinity)
1322 out = &p.p;
1323
1324 ecp_nistz256_windowed_mul(group, out, scalars, points, num, ctx);
1325
1326 if (!p_is_infinity)
1327 ecp_nistz256_point_add(&p.p, &p.p, out);
1328 }
1329
1330 if (no_precomp_for_generator) {
1331 OPENSSL_free(points);
1332 OPENSSL_free(scalars);
1333 }
1334
1335 bn_set_data(r->X, p.p.X, sizeof(p.p.X));
1336 bn_set_data(r->Y, p.p.Y, sizeof(p.p.Y));
1337 bn_set_data(r->Z, p.p.Z, sizeof(p.p.Z));
1338 bn_correct_top(r->X);
1339 bn_correct_top(r->Y);
1340 bn_correct_top(r->Z);
1341
1342 ret = 1;
1343
1344 err:
1345 return ret;
1346 }
1347
1348 static int ecp_nistz256_get_affine(const EC_GROUP *group,
1349 const EC_POINT *point,
1350 BIGNUM *x, BIGNUM *y, BN_CTX *ctx)
1351 {
1352 BN_ULONG z_inv2[P256_LIMBS];
1353 BN_ULONG z_inv3[P256_LIMBS];
1354 BN_ULONG x_aff[P256_LIMBS];
1355 BN_ULONG y_aff[P256_LIMBS];
1356 BN_ULONG point_x[P256_LIMBS], point_y[P256_LIMBS], point_z[P256_LIMBS];
1357
1358 if (EC_POINT_is_at_infinity(group, point)) {
1359 ECerr(EC_F_ECP_NISTZ256_GET_AFFINE, EC_R_POINT_AT_INFINITY);
1360 return 0;
1361 }
1362
1363 if (!ecp_nistz256_bignum_to_field_elem(point_x, point->X) ||
1364 !ecp_nistz256_bignum_to_field_elem(point_y, point->Y) ||
1365 !ecp_nistz256_bignum_to_field_elem(point_z, point->Z)) {
1366 ECerr(EC_F_ECP_NISTZ256_GET_AFFINE, EC_R_COORDINATES_OUT_OF_RANGE);
1367 return 0;
1368 }
1369
1370 ecp_nistz256_mod_inverse(z_inv3, point_z);
1371 ecp_nistz256_sqr_mont(z_inv2, z_inv3);
1372 ecp_nistz256_mul_mont(x_aff, z_inv2, point_x);
1373
1374 if (x != NULL) {
1375 bn_wexpand(x, P256_LIMBS);
1376 bn_set_top(x, P256_LIMBS);
1377 ecp_nistz256_from_mont(bn_get_words(x), x_aff);
1378 bn_correct_top(x);
1379 }
1380
1381 if (y != NULL) {
1382 ecp_nistz256_mul_mont(z_inv3, z_inv3, z_inv2);
1383 ecp_nistz256_mul_mont(y_aff, z_inv3, point_y);
1384 bn_wexpand(y, P256_LIMBS);
1385 bn_set_top(y, P256_LIMBS);
1386 ecp_nistz256_from_mont(bn_get_words(y), y_aff);
1387 bn_correct_top(y);
1388 }
1389
1390 return 1;
1391 }
1392
1393 static EC_PRE_COMP *ecp_nistz256_pre_comp_new(const EC_GROUP *group)
1394 {
1395 EC_PRE_COMP *ret = NULL;
1396
1397 if (!group)
1398 return NULL;
1399
1400 ret = (EC_PRE_COMP *)OPENSSL_malloc(sizeof(EC_PRE_COMP));
1401
1402 if (!ret) {
1403 ECerr(EC_F_ECP_NISTZ256_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE);
1404 return ret;
1405 }
1406
1407 ret->group = group;
1408 ret->w = 6; /* default */
1409 ret->precomp = NULL;
1410 ret->precomp_storage = NULL;
1411 ret->references = 1;
1412 return ret;
1413 }
1414
1415 static void *ecp_nistz256_pre_comp_dup(void *src_)
1416 {
1417 EC_PRE_COMP *src = src_;
1418
1419 /* no need to actually copy, these objects never change! */
1420 CRYPTO_add(&src->references, 1, CRYPTO_LOCK_EC_PRE_COMP);
1421
1422 return src_;
1423 }
1424
1425 static void ecp_nistz256_pre_comp_free(void *pre_)
1426 {
1427 int i;
1428 EC_PRE_COMP *pre = pre_;
1429
1430 if (!pre)
1431 return;
1432
1433 i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP);
1434 if (i > 0)
1435 return;
1436
1437 if (pre->precomp_storage)
1438 OPENSSL_free(pre->precomp_storage);
1439
1440 OPENSSL_free(pre);
1441 }
1442
1443 static void ecp_nistz256_pre_comp_clear_free(void *pre_)
1444 {
1445 int i;
1446 EC_PRE_COMP *pre = pre_;
1447
1448 if (!pre)
1449 return;
1450
1451 i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP);
1452 if (i > 0)
1453 return;
1454
1455 if (pre->precomp_storage) {
1456 OPENSSL_cleanse(pre->precomp,
1457 32 * sizeof(unsigned char) * (1 << pre->w) * 2 * 37);
1458 OPENSSL_free(pre->precomp_storage);
1459 }
1460 OPENSSL_cleanse(pre, sizeof *pre);
1461 OPENSSL_free(pre);
1462 }
1463
1464 static int ecp_nistz256_window_have_precompute_mult(const EC_GROUP *group)
1465 {
1466 /* There is a hard-coded table for the default generator. */
1467 const EC_POINT *generator = EC_GROUP_get0_generator(group);
1468 if (generator != NULL && ecp_nistz256_is_affine_G(generator)) {
1469 /* There is a hard-coded table for the default generator. */
1470 return 1;
1471 }
1472
1473 return EC_EX_DATA_get_data(group->extra_data, ecp_nistz256_pre_comp_dup,
1474 ecp_nistz256_pre_comp_free,
1475 ecp_nistz256_pre_comp_clear_free) != NULL;
1476 }
1477
1478 const EC_METHOD *EC_GFp_nistz256_method(void)
1479 {
1480 static const EC_METHOD ret = {
1481 EC_FLAGS_DEFAULT_OCT,
1482 NID_X9_62_prime_field,
1483 ec_GFp_mont_group_init,
1484 ec_GFp_mont_group_finish,
1485 ec_GFp_mont_group_clear_finish,
1486 ec_GFp_mont_group_copy,
1487 ec_GFp_mont_group_set_curve,
1488 ec_GFp_simple_group_get_curve,
1489 ec_GFp_simple_group_get_degree,
1490 ec_GFp_simple_group_check_discriminant,
1491 ec_GFp_simple_point_init,
1492 ec_GFp_simple_point_finish,
1493 ec_GFp_simple_point_clear_finish,
1494 ec_GFp_simple_point_copy,
1495 ec_GFp_simple_point_set_to_infinity,
1496 ec_GFp_simple_set_Jprojective_coordinates_GFp,
1497 ec_GFp_simple_get_Jprojective_coordinates_GFp,
1498 ec_GFp_simple_point_set_affine_coordinates,
1499 ecp_nistz256_get_affine,
1500 0, 0, 0,
1501 ec_GFp_simple_add,
1502 ec_GFp_simple_dbl,
1503 ec_GFp_simple_invert,
1504 ec_GFp_simple_is_at_infinity,
1505 ec_GFp_simple_is_on_curve,
1506 ec_GFp_simple_cmp,
1507 ec_GFp_simple_make_affine,
1508 ec_GFp_simple_points_make_affine,
1509 ecp_nistz256_points_mul, /* mul */
1510 ecp_nistz256_mult_precompute, /* precompute_mult */
1511 ecp_nistz256_window_have_precompute_mult, /* have_precompute_mult */
1512 ec_GFp_mont_field_mul,
1513 ec_GFp_mont_field_sqr,
1514 0, /* field_div */
1515 ec_GFp_mont_field_encode,
1516 ec_GFp_mont_field_decode,
1517 ec_GFp_mont_field_set_to_one
1518 };
1519
1520 return &ret;
1521 }
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