2 * Copyright 2014-2017 The OpenSSL Project Authors. All Rights Reserved.
3 * Copyright (c) 2014, Intel Corporation. All Rights Reserved.
5 * Licensed under the OpenSSL license (the "License"). You may not use
6 * this file except in compliance with the License. You can obtain a copy
7 * in the file LICENSE in the source distribution or at
8 * https://www.openssl.org/source/license.html
10 * Originally written by Shay Gueron (1, 2), and Vlad Krasnov (1)
11 * (1) Intel Corporation, Israel Development Center, Haifa, Israel
12 * (2) University of Haifa, Israel
15 * S.Gueron and V.Krasnov, "Fast Prime Field Elliptic Curve Cryptography with
21 #include "internal/cryptlib.h"
22 #include "internal/bn_int.h"
24 #include "internal/refcount.h"
27 # define TOBN(hi,lo) lo,hi
29 # define TOBN(hi,lo) ((BN_ULONG)hi<<32|lo)
33 # define ALIGN32 __attribute((aligned(32)))
34 #elif defined(_MSC_VER)
35 # define ALIGN32 __declspec(align(32))
40 #define ALIGNPTR(p,N) ((unsigned char *)p+N-(size_t)p%N)
41 #define P256_LIMBS (256/BN_BITS2)
43 typedef unsigned short u16;
46 BN_ULONG X[P256_LIMBS];
47 BN_ULONG Y[P256_LIMBS];
48 BN_ULONG Z[P256_LIMBS];
52 BN_ULONG X[P256_LIMBS];
53 BN_ULONG Y[P256_LIMBS];
56 typedef P256_POINT_AFFINE PRECOMP256_ROW[64];
58 /* structure for precomputed multiples of the generator */
59 struct nistz256_pre_comp_st {
60 const EC_GROUP *group; /* Parent EC_GROUP object */
61 size_t w; /* Window size */
63 * Constant time access to the X and Y coordinates of the pre-computed,
64 * generator multiplies, in the Montgomery domain. Pre-calculated
65 * multiplies are stored in affine form.
67 PRECOMP256_ROW *precomp;
68 void *precomp_storage;
69 CRYPTO_REF_COUNT references;
73 /* Functions implemented in assembly */
75 * Most of below mentioned functions *preserve* the property of inputs
76 * being fully reduced, i.e. being in [0, modulus) range. Simply put if
77 * inputs are fully reduced, then output is too. Note that reverse is
78 * not true, in sense that given partially reduced inputs output can be
79 * either, not unlikely reduced. And "most" in first sentence refers to
80 * the fact that given the calculations flow one can tolerate that
81 * addition, 1st function below, produces partially reduced result *if*
82 * multiplications by 2 and 3, which customarily use addition, fully
83 * reduce it. This effectively gives two options: a) addition produces
84 * fully reduced result [as long as inputs are, just like remaining
85 * functions]; b) addition is allowed to produce partially reduced
86 * result, but multiplications by 2 and 3 perform additional reduction
87 * step. Choice between the two can be platform-specific, but it was a)
88 * in all cases so far...
90 /* Modular add: res = a+b mod P */
91 void ecp_nistz256_add(BN_ULONG res[P256_LIMBS],
92 const BN_ULONG a[P256_LIMBS],
93 const BN_ULONG b[P256_LIMBS]);
94 /* Modular mul by 2: res = 2*a mod P */
95 void ecp_nistz256_mul_by_2(BN_ULONG res[P256_LIMBS],
96 const BN_ULONG a[P256_LIMBS]);
97 /* Modular mul by 3: res = 3*a mod P */
98 void ecp_nistz256_mul_by_3(BN_ULONG res[P256_LIMBS],
99 const BN_ULONG a[P256_LIMBS]);
101 /* Modular div by 2: res = a/2 mod P */
102 void ecp_nistz256_div_by_2(BN_ULONG res[P256_LIMBS],
103 const BN_ULONG a[P256_LIMBS]);
104 /* Modular sub: res = a-b mod P */
105 void ecp_nistz256_sub(BN_ULONG res[P256_LIMBS],
106 const BN_ULONG a[P256_LIMBS],
107 const BN_ULONG b[P256_LIMBS]);
108 /* Modular neg: res = -a mod P */
109 void ecp_nistz256_neg(BN_ULONG res[P256_LIMBS], const BN_ULONG a[P256_LIMBS]);
110 /* Montgomery mul: res = a*b*2^-256 mod P */
111 void ecp_nistz256_mul_mont(BN_ULONG res[P256_LIMBS],
112 const BN_ULONG a[P256_LIMBS],
113 const BN_ULONG b[P256_LIMBS]);
114 /* Montgomery sqr: res = a*a*2^-256 mod P */
115 void ecp_nistz256_sqr_mont(BN_ULONG res[P256_LIMBS],
116 const BN_ULONG a[P256_LIMBS]);
117 /* Convert a number from Montgomery domain, by multiplying with 1 */
118 void ecp_nistz256_from_mont(BN_ULONG res[P256_LIMBS],
119 const BN_ULONG in[P256_LIMBS]);
120 /* Convert a number to Montgomery domain, by multiplying with 2^512 mod P*/
121 void ecp_nistz256_to_mont(BN_ULONG res[P256_LIMBS],
122 const BN_ULONG in[P256_LIMBS]);
123 /* Functions that perform constant time access to the precomputed tables */
124 void ecp_nistz256_scatter_w5(P256_POINT *val,
125 const P256_POINT *in_t, int idx);
126 void ecp_nistz256_gather_w5(P256_POINT *val,
127 const P256_POINT *in_t, int idx);
128 void ecp_nistz256_scatter_w7(P256_POINT_AFFINE *val,
129 const P256_POINT_AFFINE *in_t, int idx);
130 void ecp_nistz256_gather_w7(P256_POINT_AFFINE *val,
131 const P256_POINT_AFFINE *in_t, int idx);
133 /* One converted into the Montgomery domain */
134 static const BN_ULONG ONE[P256_LIMBS] = {
135 TOBN(0x00000000, 0x00000001), TOBN(0xffffffff, 0x00000000),
136 TOBN(0xffffffff, 0xffffffff), TOBN(0x00000000, 0xfffffffe)
139 static NISTZ256_PRE_COMP *ecp_nistz256_pre_comp_new(const EC_GROUP *group);
141 /* Precomputed tables for the default generator */
142 extern const PRECOMP256_ROW ecp_nistz256_precomputed[37];
144 /* Recode window to a signed digit, see ecp_nistputil.c for details */
145 static unsigned int _booth_recode_w5(unsigned int in)
149 s = ~((in >> 5) - 1);
150 d = (1 << 6) - in - 1;
151 d = (d & s) | (in & ~s);
152 d = (d >> 1) + (d & 1);
154 return (d << 1) + (s & 1);
157 static unsigned int _booth_recode_w7(unsigned int in)
161 s = ~((in >> 7) - 1);
162 d = (1 << 8) - in - 1;
163 d = (d & s) | (in & ~s);
164 d = (d >> 1) + (d & 1);
166 return (d << 1) + (s & 1);
169 static void copy_conditional(BN_ULONG dst[P256_LIMBS],
170 const BN_ULONG src[P256_LIMBS], BN_ULONG move)
172 BN_ULONG mask1 = 0-move;
173 BN_ULONG mask2 = ~mask1;
175 dst[0] = (src[0] & mask1) ^ (dst[0] & mask2);
176 dst[1] = (src[1] & mask1) ^ (dst[1] & mask2);
177 dst[2] = (src[2] & mask1) ^ (dst[2] & mask2);
178 dst[3] = (src[3] & mask1) ^ (dst[3] & mask2);
179 if (P256_LIMBS == 8) {
180 dst[4] = (src[4] & mask1) ^ (dst[4] & mask2);
181 dst[5] = (src[5] & mask1) ^ (dst[5] & mask2);
182 dst[6] = (src[6] & mask1) ^ (dst[6] & mask2);
183 dst[7] = (src[7] & mask1) ^ (dst[7] & mask2);
187 static BN_ULONG is_zero(BN_ULONG in)
195 static BN_ULONG is_equal(const BN_ULONG a[P256_LIMBS],
196 const BN_ULONG b[P256_LIMBS])
204 if (P256_LIMBS == 8) {
214 static BN_ULONG is_one(const BIGNUM *z)
217 BN_ULONG *a = bn_get_words(z);
219 if (bn_get_top(z) == (P256_LIMBS - P256_LIMBS / 8)) {
221 res |= a[1] ^ ONE[1];
222 res |= a[2] ^ ONE[2];
223 res |= a[3] ^ ONE[3];
224 if (P256_LIMBS == 8) {
225 res |= a[4] ^ ONE[4];
226 res |= a[5] ^ ONE[5];
227 res |= a[6] ^ ONE[6];
229 * no check for a[7] (being zero) on 32-bit platforms,
230 * because value of "one" takes only 7 limbs.
240 * For reference, this macro is used only when new ecp_nistz256 assembly
241 * module is being developed. For example, configure with
242 * -DECP_NISTZ256_REFERENCE_IMPLEMENTATION and implement only functions
243 * performing simplest arithmetic operations on 256-bit vectors. Then
244 * work on implementation of higher-level functions performing point
245 * operations. Then remove ECP_NISTZ256_REFERENCE_IMPLEMENTATION
246 * and never define it again. (The correct macro denoting presence of
247 * ecp_nistz256 module is ECP_NISTZ256_ASM.)
249 #ifndef ECP_NISTZ256_REFERENCE_IMPLEMENTATION
250 void ecp_nistz256_point_double(P256_POINT *r, const P256_POINT *a);
251 void ecp_nistz256_point_add(P256_POINT *r,
252 const P256_POINT *a, const P256_POINT *b);
253 void ecp_nistz256_point_add_affine(P256_POINT *r,
255 const P256_POINT_AFFINE *b);
257 /* Point double: r = 2*a */
258 static void ecp_nistz256_point_double(P256_POINT *r, const P256_POINT *a)
260 BN_ULONG S[P256_LIMBS];
261 BN_ULONG M[P256_LIMBS];
262 BN_ULONG Zsqr[P256_LIMBS];
263 BN_ULONG tmp0[P256_LIMBS];
265 const BN_ULONG *in_x = a->X;
266 const BN_ULONG *in_y = a->Y;
267 const BN_ULONG *in_z = a->Z;
269 BN_ULONG *res_x = r->X;
270 BN_ULONG *res_y = r->Y;
271 BN_ULONG *res_z = r->Z;
273 ecp_nistz256_mul_by_2(S, in_y);
275 ecp_nistz256_sqr_mont(Zsqr, in_z);
277 ecp_nistz256_sqr_mont(S, S);
279 ecp_nistz256_mul_mont(res_z, in_z, in_y);
280 ecp_nistz256_mul_by_2(res_z, res_z);
282 ecp_nistz256_add(M, in_x, Zsqr);
283 ecp_nistz256_sub(Zsqr, in_x, Zsqr);
285 ecp_nistz256_sqr_mont(res_y, S);
286 ecp_nistz256_div_by_2(res_y, res_y);
288 ecp_nistz256_mul_mont(M, M, Zsqr);
289 ecp_nistz256_mul_by_3(M, M);
291 ecp_nistz256_mul_mont(S, S, in_x);
292 ecp_nistz256_mul_by_2(tmp0, S);
294 ecp_nistz256_sqr_mont(res_x, M);
296 ecp_nistz256_sub(res_x, res_x, tmp0);
297 ecp_nistz256_sub(S, S, res_x);
299 ecp_nistz256_mul_mont(S, S, M);
300 ecp_nistz256_sub(res_y, S, res_y);
303 /* Point addition: r = a+b */
304 static void ecp_nistz256_point_add(P256_POINT *r,
305 const P256_POINT *a, const P256_POINT *b)
307 BN_ULONG U2[P256_LIMBS], S2[P256_LIMBS];
308 BN_ULONG U1[P256_LIMBS], S1[P256_LIMBS];
309 BN_ULONG Z1sqr[P256_LIMBS];
310 BN_ULONG Z2sqr[P256_LIMBS];
311 BN_ULONG H[P256_LIMBS], R[P256_LIMBS];
312 BN_ULONG Hsqr[P256_LIMBS];
313 BN_ULONG Rsqr[P256_LIMBS];
314 BN_ULONG Hcub[P256_LIMBS];
316 BN_ULONG res_x[P256_LIMBS];
317 BN_ULONG res_y[P256_LIMBS];
318 BN_ULONG res_z[P256_LIMBS];
320 BN_ULONG in1infty, in2infty;
322 const BN_ULONG *in1_x = a->X;
323 const BN_ULONG *in1_y = a->Y;
324 const BN_ULONG *in1_z = a->Z;
326 const BN_ULONG *in2_x = b->X;
327 const BN_ULONG *in2_y = b->Y;
328 const BN_ULONG *in2_z = b->Z;
331 * Infinity in encoded as (,,0)
333 in1infty = (in1_z[0] | in1_z[1] | in1_z[2] | in1_z[3]);
335 in1infty |= (in1_z[4] | in1_z[5] | in1_z[6] | in1_z[7]);
337 in2infty = (in2_z[0] | in2_z[1] | in2_z[2] | in2_z[3]);
339 in2infty |= (in2_z[4] | in2_z[5] | in2_z[6] | in2_z[7]);
341 in1infty = is_zero(in1infty);
342 in2infty = is_zero(in2infty);
344 ecp_nistz256_sqr_mont(Z2sqr, in2_z); /* Z2^2 */
345 ecp_nistz256_sqr_mont(Z1sqr, in1_z); /* Z1^2 */
347 ecp_nistz256_mul_mont(S1, Z2sqr, in2_z); /* S1 = Z2^3 */
348 ecp_nistz256_mul_mont(S2, Z1sqr, in1_z); /* S2 = Z1^3 */
350 ecp_nistz256_mul_mont(S1, S1, in1_y); /* S1 = Y1*Z2^3 */
351 ecp_nistz256_mul_mont(S2, S2, in2_y); /* S2 = Y2*Z1^3 */
352 ecp_nistz256_sub(R, S2, S1); /* R = S2 - S1 */
354 ecp_nistz256_mul_mont(U1, in1_x, Z2sqr); /* U1 = X1*Z2^2 */
355 ecp_nistz256_mul_mont(U2, in2_x, Z1sqr); /* U2 = X2*Z1^2 */
356 ecp_nistz256_sub(H, U2, U1); /* H = U2 - U1 */
359 * This should not happen during sign/ecdh, so no constant time violation
361 if (is_equal(U1, U2) && !in1infty && !in2infty) {
362 if (is_equal(S1, S2)) {
363 ecp_nistz256_point_double(r, a);
366 memset(r, 0, sizeof(*r));
371 ecp_nistz256_sqr_mont(Rsqr, R); /* R^2 */
372 ecp_nistz256_mul_mont(res_z, H, in1_z); /* Z3 = H*Z1*Z2 */
373 ecp_nistz256_sqr_mont(Hsqr, H); /* H^2 */
374 ecp_nistz256_mul_mont(res_z, res_z, in2_z); /* Z3 = H*Z1*Z2 */
375 ecp_nistz256_mul_mont(Hcub, Hsqr, H); /* H^3 */
377 ecp_nistz256_mul_mont(U2, U1, Hsqr); /* U1*H^2 */
378 ecp_nistz256_mul_by_2(Hsqr, U2); /* 2*U1*H^2 */
380 ecp_nistz256_sub(res_x, Rsqr, Hsqr);
381 ecp_nistz256_sub(res_x, res_x, Hcub);
383 ecp_nistz256_sub(res_y, U2, res_x);
385 ecp_nistz256_mul_mont(S2, S1, Hcub);
386 ecp_nistz256_mul_mont(res_y, R, res_y);
387 ecp_nistz256_sub(res_y, res_y, S2);
389 copy_conditional(res_x, in2_x, in1infty);
390 copy_conditional(res_y, in2_y, in1infty);
391 copy_conditional(res_z, in2_z, in1infty);
393 copy_conditional(res_x, in1_x, in2infty);
394 copy_conditional(res_y, in1_y, in2infty);
395 copy_conditional(res_z, in1_z, in2infty);
397 memcpy(r->X, res_x, sizeof(res_x));
398 memcpy(r->Y, res_y, sizeof(res_y));
399 memcpy(r->Z, res_z, sizeof(res_z));
402 /* Point addition when b is known to be affine: r = a+b */
403 static void ecp_nistz256_point_add_affine(P256_POINT *r,
405 const P256_POINT_AFFINE *b)
407 BN_ULONG U2[P256_LIMBS], S2[P256_LIMBS];
408 BN_ULONG Z1sqr[P256_LIMBS];
409 BN_ULONG H[P256_LIMBS], R[P256_LIMBS];
410 BN_ULONG Hsqr[P256_LIMBS];
411 BN_ULONG Rsqr[P256_LIMBS];
412 BN_ULONG Hcub[P256_LIMBS];
414 BN_ULONG res_x[P256_LIMBS];
415 BN_ULONG res_y[P256_LIMBS];
416 BN_ULONG res_z[P256_LIMBS];
418 BN_ULONG in1infty, in2infty;
420 const BN_ULONG *in1_x = a->X;
421 const BN_ULONG *in1_y = a->Y;
422 const BN_ULONG *in1_z = a->Z;
424 const BN_ULONG *in2_x = b->X;
425 const BN_ULONG *in2_y = b->Y;
428 * Infinity in encoded as (,,0)
430 in1infty = (in1_z[0] | in1_z[1] | in1_z[2] | in1_z[3]);
432 in1infty |= (in1_z[4] | in1_z[5] | in1_z[6] | in1_z[7]);
435 * In affine representation we encode infinity as (0,0), which is
436 * not on the curve, so it is OK
438 in2infty = (in2_x[0] | in2_x[1] | in2_x[2] | in2_x[3] |
439 in2_y[0] | in2_y[1] | in2_y[2] | in2_y[3]);
441 in2infty |= (in2_x[4] | in2_x[5] | in2_x[6] | in2_x[7] |
442 in2_y[4] | in2_y[5] | in2_y[6] | in2_y[7]);
444 in1infty = is_zero(in1infty);
445 in2infty = is_zero(in2infty);
447 ecp_nistz256_sqr_mont(Z1sqr, in1_z); /* Z1^2 */
449 ecp_nistz256_mul_mont(U2, in2_x, Z1sqr); /* U2 = X2*Z1^2 */
450 ecp_nistz256_sub(H, U2, in1_x); /* H = U2 - U1 */
452 ecp_nistz256_mul_mont(S2, Z1sqr, in1_z); /* S2 = Z1^3 */
454 ecp_nistz256_mul_mont(res_z, H, in1_z); /* Z3 = H*Z1*Z2 */
456 ecp_nistz256_mul_mont(S2, S2, in2_y); /* S2 = Y2*Z1^3 */
457 ecp_nistz256_sub(R, S2, in1_y); /* R = S2 - S1 */
459 ecp_nistz256_sqr_mont(Hsqr, H); /* H^2 */
460 ecp_nistz256_sqr_mont(Rsqr, R); /* R^2 */
461 ecp_nistz256_mul_mont(Hcub, Hsqr, H); /* H^3 */
463 ecp_nistz256_mul_mont(U2, in1_x, Hsqr); /* U1*H^2 */
464 ecp_nistz256_mul_by_2(Hsqr, U2); /* 2*U1*H^2 */
466 ecp_nistz256_sub(res_x, Rsqr, Hsqr);
467 ecp_nistz256_sub(res_x, res_x, Hcub);
468 ecp_nistz256_sub(H, U2, res_x);
470 ecp_nistz256_mul_mont(S2, in1_y, Hcub);
471 ecp_nistz256_mul_mont(H, H, R);
472 ecp_nistz256_sub(res_y, H, S2);
474 copy_conditional(res_x, in2_x, in1infty);
475 copy_conditional(res_x, in1_x, in2infty);
477 copy_conditional(res_y, in2_y, in1infty);
478 copy_conditional(res_y, in1_y, in2infty);
480 copy_conditional(res_z, ONE, in1infty);
481 copy_conditional(res_z, in1_z, in2infty);
483 memcpy(r->X, res_x, sizeof(res_x));
484 memcpy(r->Y, res_y, sizeof(res_y));
485 memcpy(r->Z, res_z, sizeof(res_z));
489 /* r = in^-1 mod p */
490 static void ecp_nistz256_mod_inverse(BN_ULONG r[P256_LIMBS],
491 const BN_ULONG in[P256_LIMBS])
494 * The poly is ffffffff 00000001 00000000 00000000 00000000 ffffffff
495 * ffffffff ffffffff We use FLT and used poly-2 as exponent
497 BN_ULONG p2[P256_LIMBS];
498 BN_ULONG p4[P256_LIMBS];
499 BN_ULONG p8[P256_LIMBS];
500 BN_ULONG p16[P256_LIMBS];
501 BN_ULONG p32[P256_LIMBS];
502 BN_ULONG res[P256_LIMBS];
505 ecp_nistz256_sqr_mont(res, in);
506 ecp_nistz256_mul_mont(p2, res, in); /* 3*p */
508 ecp_nistz256_sqr_mont(res, p2);
509 ecp_nistz256_sqr_mont(res, res);
510 ecp_nistz256_mul_mont(p4, res, p2); /* f*p */
512 ecp_nistz256_sqr_mont(res, p4);
513 ecp_nistz256_sqr_mont(res, res);
514 ecp_nistz256_sqr_mont(res, res);
515 ecp_nistz256_sqr_mont(res, res);
516 ecp_nistz256_mul_mont(p8, res, p4); /* ff*p */
518 ecp_nistz256_sqr_mont(res, p8);
519 for (i = 0; i < 7; i++)
520 ecp_nistz256_sqr_mont(res, res);
521 ecp_nistz256_mul_mont(p16, res, p8); /* ffff*p */
523 ecp_nistz256_sqr_mont(res, p16);
524 for (i = 0; i < 15; i++)
525 ecp_nistz256_sqr_mont(res, res);
526 ecp_nistz256_mul_mont(p32, res, p16); /* ffffffff*p */
528 ecp_nistz256_sqr_mont(res, p32);
529 for (i = 0; i < 31; i++)
530 ecp_nistz256_sqr_mont(res, res);
531 ecp_nistz256_mul_mont(res, res, in);
533 for (i = 0; i < 32 * 4; i++)
534 ecp_nistz256_sqr_mont(res, res);
535 ecp_nistz256_mul_mont(res, res, p32);
537 for (i = 0; i < 32; i++)
538 ecp_nistz256_sqr_mont(res, res);
539 ecp_nistz256_mul_mont(res, res, p32);
541 for (i = 0; i < 16; i++)
542 ecp_nistz256_sqr_mont(res, res);
543 ecp_nistz256_mul_mont(res, res, p16);
545 for (i = 0; i < 8; i++)
546 ecp_nistz256_sqr_mont(res, res);
547 ecp_nistz256_mul_mont(res, res, p8);
549 ecp_nistz256_sqr_mont(res, res);
550 ecp_nistz256_sqr_mont(res, res);
551 ecp_nistz256_sqr_mont(res, res);
552 ecp_nistz256_sqr_mont(res, res);
553 ecp_nistz256_mul_mont(res, res, p4);
555 ecp_nistz256_sqr_mont(res, res);
556 ecp_nistz256_sqr_mont(res, res);
557 ecp_nistz256_mul_mont(res, res, p2);
559 ecp_nistz256_sqr_mont(res, res);
560 ecp_nistz256_sqr_mont(res, res);
561 ecp_nistz256_mul_mont(res, res, in);
563 memcpy(r, res, sizeof(res));
567 * ecp_nistz256_bignum_to_field_elem copies the contents of |in| to |out| and
568 * returns one if it fits. Otherwise it returns zero.
570 __owur static int ecp_nistz256_bignum_to_field_elem(BN_ULONG out[P256_LIMBS],
573 return bn_copy_words(out, in, P256_LIMBS);
576 /* r = sum(scalar[i]*point[i]) */
577 __owur static int ecp_nistz256_windowed_mul(const EC_GROUP *group,
579 const BIGNUM **scalar,
580 const EC_POINT **point,
581 size_t num, BN_CTX *ctx)
586 unsigned char (*p_str)[33] = NULL;
587 const unsigned int window_size = 5;
588 const unsigned int mask = (1 << (window_size + 1)) - 1;
590 P256_POINT *temp; /* place for 5 temporary points */
591 const BIGNUM **scalars = NULL;
592 P256_POINT (*table)[16] = NULL;
593 void *table_storage = NULL;
595 if ((num * 16 + 6) > OPENSSL_MALLOC_MAX_NELEMS(P256_POINT)
597 OPENSSL_malloc((num * 16 + 5) * sizeof(P256_POINT) + 64)) == NULL
599 OPENSSL_malloc(num * 33 * sizeof(unsigned char))) == NULL
600 || (scalars = OPENSSL_malloc(num * sizeof(BIGNUM *))) == NULL) {
601 ECerr(EC_F_ECP_NISTZ256_WINDOWED_MUL, ERR_R_MALLOC_FAILURE);
605 table = (void *)ALIGNPTR(table_storage, 64);
606 temp = (P256_POINT *)(table + num);
608 for (i = 0; i < num; i++) {
609 P256_POINT *row = table[i];
611 /* This is an unusual input, we don't guarantee constant-timeness. */
612 if ((BN_num_bits(scalar[i]) > 256) || BN_is_negative(scalar[i])) {
615 if ((mod = BN_CTX_get(ctx)) == NULL)
617 if (!BN_nnmod(mod, scalar[i], group->order, ctx)) {
618 ECerr(EC_F_ECP_NISTZ256_WINDOWED_MUL, ERR_R_BN_LIB);
623 scalars[i] = scalar[i];
625 for (j = 0; j < bn_get_top(scalars[i]) * BN_BYTES; j += BN_BYTES) {
626 BN_ULONG d = bn_get_words(scalars[i])[j / BN_BYTES];
628 p_str[i][j + 0] = (unsigned char)d;
629 p_str[i][j + 1] = (unsigned char)(d >> 8);
630 p_str[i][j + 2] = (unsigned char)(d >> 16);
631 p_str[i][j + 3] = (unsigned char)(d >>= 24);
634 p_str[i][j + 4] = (unsigned char)d;
635 p_str[i][j + 5] = (unsigned char)(d >> 8);
636 p_str[i][j + 6] = (unsigned char)(d >> 16);
637 p_str[i][j + 7] = (unsigned char)(d >> 24);
643 if (!ecp_nistz256_bignum_to_field_elem(temp[0].X, point[i]->X)
644 || !ecp_nistz256_bignum_to_field_elem(temp[0].Y, point[i]->Y)
645 || !ecp_nistz256_bignum_to_field_elem(temp[0].Z, point[i]->Z)) {
646 ECerr(EC_F_ECP_NISTZ256_WINDOWED_MUL,
647 EC_R_COORDINATES_OUT_OF_RANGE);
652 * row[0] is implicitly (0,0,0) (the point at infinity), therefore it
653 * is not stored. All other values are actually stored with an offset
657 ecp_nistz256_scatter_w5 (row, &temp[0], 1);
658 ecp_nistz256_point_double(&temp[1], &temp[0]); /*1+1=2 */
659 ecp_nistz256_scatter_w5 (row, &temp[1], 2);
660 ecp_nistz256_point_add (&temp[2], &temp[1], &temp[0]); /*2+1=3 */
661 ecp_nistz256_scatter_w5 (row, &temp[2], 3);
662 ecp_nistz256_point_double(&temp[1], &temp[1]); /*2*2=4 */
663 ecp_nistz256_scatter_w5 (row, &temp[1], 4);
664 ecp_nistz256_point_double(&temp[2], &temp[2]); /*2*3=6 */
665 ecp_nistz256_scatter_w5 (row, &temp[2], 6);
666 ecp_nistz256_point_add (&temp[3], &temp[1], &temp[0]); /*4+1=5 */
667 ecp_nistz256_scatter_w5 (row, &temp[3], 5);
668 ecp_nistz256_point_add (&temp[4], &temp[2], &temp[0]); /*6+1=7 */
669 ecp_nistz256_scatter_w5 (row, &temp[4], 7);
670 ecp_nistz256_point_double(&temp[1], &temp[1]); /*2*4=8 */
671 ecp_nistz256_scatter_w5 (row, &temp[1], 8);
672 ecp_nistz256_point_double(&temp[2], &temp[2]); /*2*6=12 */
673 ecp_nistz256_scatter_w5 (row, &temp[2], 12);
674 ecp_nistz256_point_double(&temp[3], &temp[3]); /*2*5=10 */
675 ecp_nistz256_scatter_w5 (row, &temp[3], 10);
676 ecp_nistz256_point_double(&temp[4], &temp[4]); /*2*7=14 */
677 ecp_nistz256_scatter_w5 (row, &temp[4], 14);
678 ecp_nistz256_point_add (&temp[2], &temp[2], &temp[0]); /*12+1=13*/
679 ecp_nistz256_scatter_w5 (row, &temp[2], 13);
680 ecp_nistz256_point_add (&temp[3], &temp[3], &temp[0]); /*10+1=11*/
681 ecp_nistz256_scatter_w5 (row, &temp[3], 11);
682 ecp_nistz256_point_add (&temp[4], &temp[4], &temp[0]); /*14+1=15*/
683 ecp_nistz256_scatter_w5 (row, &temp[4], 15);
684 ecp_nistz256_point_add (&temp[2], &temp[1], &temp[0]); /*8+1=9 */
685 ecp_nistz256_scatter_w5 (row, &temp[2], 9);
686 ecp_nistz256_point_double(&temp[1], &temp[1]); /*2*8=16 */
687 ecp_nistz256_scatter_w5 (row, &temp[1], 16);
692 wvalue = p_str[0][(idx - 1) / 8];
693 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
696 * We gather to temp[0], because we know it's position relative
699 ecp_nistz256_gather_w5(&temp[0], table[0], _booth_recode_w5(wvalue) >> 1);
700 memcpy(r, &temp[0], sizeof(temp[0]));
703 for (i = (idx == 255 ? 1 : 0); i < num; i++) {
704 unsigned int off = (idx - 1) / 8;
706 wvalue = p_str[i][off] | p_str[i][off + 1] << 8;
707 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
709 wvalue = _booth_recode_w5(wvalue);
711 ecp_nistz256_gather_w5(&temp[0], table[i], wvalue >> 1);
713 ecp_nistz256_neg(temp[1].Y, temp[0].Y);
714 copy_conditional(temp[0].Y, temp[1].Y, (wvalue & 1));
716 ecp_nistz256_point_add(r, r, &temp[0]);
721 ecp_nistz256_point_double(r, r);
722 ecp_nistz256_point_double(r, r);
723 ecp_nistz256_point_double(r, r);
724 ecp_nistz256_point_double(r, r);
725 ecp_nistz256_point_double(r, r);
729 for (i = 0; i < num; i++) {
730 wvalue = p_str[i][0];
731 wvalue = (wvalue << 1) & mask;
733 wvalue = _booth_recode_w5(wvalue);
735 ecp_nistz256_gather_w5(&temp[0], table[i], wvalue >> 1);
737 ecp_nistz256_neg(temp[1].Y, temp[0].Y);
738 copy_conditional(temp[0].Y, temp[1].Y, wvalue & 1);
740 ecp_nistz256_point_add(r, r, &temp[0]);
745 OPENSSL_free(table_storage);
747 OPENSSL_free(scalars);
751 /* Coordinates of G, for which we have precomputed tables */
752 static const BN_ULONG def_xG[P256_LIMBS] = {
753 TOBN(0x79e730d4, 0x18a9143c), TOBN(0x75ba95fc, 0x5fedb601),
754 TOBN(0x79fb732b, 0x77622510), TOBN(0x18905f76, 0xa53755c6)
757 static const BN_ULONG def_yG[P256_LIMBS] = {
758 TOBN(0xddf25357, 0xce95560a), TOBN(0x8b4ab8e4, 0xba19e45c),
759 TOBN(0xd2e88688, 0xdd21f325), TOBN(0x8571ff18, 0x25885d85)
763 * ecp_nistz256_is_affine_G returns one if |generator| is the standard, P-256
766 static int ecp_nistz256_is_affine_G(const EC_POINT *generator)
768 return (bn_get_top(generator->X) == P256_LIMBS) &&
769 (bn_get_top(generator->Y) == P256_LIMBS) &&
770 is_equal(bn_get_words(generator->X), def_xG) &&
771 is_equal(bn_get_words(generator->Y), def_yG) &&
772 is_one(generator->Z);
775 __owur static int ecp_nistz256_mult_precompute(EC_GROUP *group, BN_CTX *ctx)
778 * We precompute a table for a Booth encoded exponent (wNAF) based
779 * computation. Each table holds 64 values for safe access, with an
780 * implicit value of infinity at index zero. We use window of size 7, and
781 * therefore require ceil(256/7) = 37 tables.
784 EC_POINT *P = NULL, *T = NULL;
785 const EC_POINT *generator;
786 NISTZ256_PRE_COMP *pre_comp;
787 BN_CTX *new_ctx = NULL;
788 int i, j, k, ret = 0;
791 PRECOMP256_ROW *preComputedTable = NULL;
792 unsigned char *precomp_storage = NULL;
794 /* if there is an old NISTZ256_PRE_COMP object, throw it away */
795 EC_pre_comp_free(group);
796 generator = EC_GROUP_get0_generator(group);
797 if (generator == NULL) {
798 ECerr(EC_F_ECP_NISTZ256_MULT_PRECOMPUTE, EC_R_UNDEFINED_GENERATOR);
802 if (ecp_nistz256_is_affine_G(generator)) {
804 * No need to calculate tables for the standard generator because we
805 * have them statically.
810 if ((pre_comp = ecp_nistz256_pre_comp_new(group)) == NULL)
814 ctx = new_ctx = BN_CTX_new();
821 order = EC_GROUP_get0_order(group);
825 if (BN_is_zero(order)) {
826 ECerr(EC_F_ECP_NISTZ256_MULT_PRECOMPUTE, EC_R_UNKNOWN_ORDER);
832 if ((precomp_storage =
833 OPENSSL_malloc(37 * 64 * sizeof(P256_POINT_AFFINE) + 64)) == NULL) {
834 ECerr(EC_F_ECP_NISTZ256_MULT_PRECOMPUTE, ERR_R_MALLOC_FAILURE);
838 preComputedTable = (void *)ALIGNPTR(precomp_storage, 64);
840 P = EC_POINT_new(group);
841 T = EC_POINT_new(group);
842 if (P == NULL || T == NULL)
846 * The zero entry is implicitly infinity, and we skip it, storing other
847 * values with -1 offset.
849 if (!EC_POINT_copy(T, generator))
852 for (k = 0; k < 64; k++) {
853 if (!EC_POINT_copy(P, T))
855 for (j = 0; j < 37; j++) {
856 P256_POINT_AFFINE temp;
858 * It would be faster to use EC_POINTs_make_affine and
859 * make multiple points affine at the same time.
861 if (!EC_POINT_make_affine(group, P, ctx))
863 if (!ecp_nistz256_bignum_to_field_elem(temp.X, P->X) ||
864 !ecp_nistz256_bignum_to_field_elem(temp.Y, P->Y)) {
865 ECerr(EC_F_ECP_NISTZ256_MULT_PRECOMPUTE,
866 EC_R_COORDINATES_OUT_OF_RANGE);
869 ecp_nistz256_scatter_w7(preComputedTable[j], &temp, k);
870 for (i = 0; i < 7; i++) {
871 if (!EC_POINT_dbl(group, P, P, ctx))
875 if (!EC_POINT_add(group, T, T, generator, ctx))
879 pre_comp->group = group;
881 pre_comp->precomp = preComputedTable;
882 pre_comp->precomp_storage = precomp_storage;
883 precomp_storage = NULL;
884 SETPRECOMP(group, nistz256, pre_comp);
891 BN_CTX_free(new_ctx);
893 EC_nistz256_pre_comp_free(pre_comp);
894 OPENSSL_free(precomp_storage);
901 * Note that by default ECP_NISTZ256_AVX2 is undefined. While it's great
902 * code processing 4 points in parallel, corresponding serial operation
903 * is several times slower, because it uses 29x29=58-bit multiplication
904 * as opposite to 64x64=128-bit in integer-only scalar case. As result
905 * it doesn't provide *significant* performance improvement. Note that
906 * just defining ECP_NISTZ256_AVX2 is not sufficient to make it work,
907 * you'd need to compile even asm/ecp_nistz256-avx.pl module.
909 #if defined(ECP_NISTZ256_AVX2)
910 # if !(defined(__x86_64) || defined(__x86_64__) || \
911 defined(_M_AMD64) || defined(_MX64)) || \
912 !(defined(__GNUC__) || defined(_MSC_VER)) /* this is for ALIGN32 */
913 # undef ECP_NISTZ256_AVX2
915 /* Constant time access, loading four values, from four consecutive tables */
916 void ecp_nistz256_avx2_multi_gather_w7(void *result, const void *in,
917 int index0, int index1, int index2,
919 void ecp_nistz256_avx2_transpose_convert(void *RESULTx4, const void *in);
920 void ecp_nistz256_avx2_convert_transpose_back(void *result, const void *Ax4);
921 void ecp_nistz256_avx2_point_add_affine_x4(void *RESULTx4, const void *Ax4,
923 void ecp_nistz256_avx2_point_add_affines_x4(void *RESULTx4, const void *Ax4,
925 void ecp_nistz256_avx2_to_mont(void *RESULTx4, const void *Ax4);
926 void ecp_nistz256_avx2_from_mont(void *RESULTx4, const void *Ax4);
927 void ecp_nistz256_avx2_set1(void *RESULTx4);
928 int ecp_nistz_avx2_eligible(void);
930 static void booth_recode_w7(unsigned char *sign,
931 unsigned char *digit, unsigned char in)
935 s = ~((in >> 7) - 1);
936 d = (1 << 8) - in - 1;
937 d = (d & s) | (in & ~s);
938 d = (d >> 1) + (d & 1);
945 * ecp_nistz256_avx2_mul_g performs multiplication by G, using only the
946 * precomputed table. It does 4 affine point additions in parallel,
947 * significantly speeding up point multiplication for a fixed value.
949 static void ecp_nistz256_avx2_mul_g(P256_POINT *r,
950 unsigned char p_str[33],
951 const P256_POINT_AFFINE(*preComputedTable)[64])
953 const unsigned int window_size = 7;
954 const unsigned int mask = (1 << (window_size + 1)) - 1;
956 /* Using 4 windows at a time */
957 unsigned char sign0, digit0;
958 unsigned char sign1, digit1;
959 unsigned char sign2, digit2;
960 unsigned char sign3, digit3;
961 unsigned int idx = 0;
962 BN_ULONG tmp[P256_LIMBS];
965 ALIGN32 BN_ULONG aX4[4 * 9 * 3] = { 0 };
966 ALIGN32 BN_ULONG bX4[4 * 9 * 2] = { 0 };
967 ALIGN32 P256_POINT_AFFINE point_arr[4];
968 ALIGN32 P256_POINT res_point_arr[4];
970 /* Initial four windows */
971 wvalue = *((u16 *) & p_str[0]);
972 wvalue = (wvalue << 1) & mask;
974 booth_recode_w7(&sign0, &digit0, wvalue);
975 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
976 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
978 booth_recode_w7(&sign1, &digit1, wvalue);
979 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
980 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
982 booth_recode_w7(&sign2, &digit2, wvalue);
983 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
984 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
986 booth_recode_w7(&sign3, &digit3, wvalue);
988 ecp_nistz256_avx2_multi_gather_w7(point_arr, preComputedTable[0],
989 digit0, digit1, digit2, digit3);
991 ecp_nistz256_neg(tmp, point_arr[0].Y);
992 copy_conditional(point_arr[0].Y, tmp, sign0);
993 ecp_nistz256_neg(tmp, point_arr[1].Y);
994 copy_conditional(point_arr[1].Y, tmp, sign1);
995 ecp_nistz256_neg(tmp, point_arr[2].Y);
996 copy_conditional(point_arr[2].Y, tmp, sign2);
997 ecp_nistz256_neg(tmp, point_arr[3].Y);
998 copy_conditional(point_arr[3].Y, tmp, sign3);
1000 ecp_nistz256_avx2_transpose_convert(aX4, point_arr);
1001 ecp_nistz256_avx2_to_mont(aX4, aX4);
1002 ecp_nistz256_avx2_to_mont(&aX4[4 * 9], &aX4[4 * 9]);
1003 ecp_nistz256_avx2_set1(&aX4[4 * 9 * 2]);
1005 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
1006 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
1008 booth_recode_w7(&sign0, &digit0, wvalue);
1009 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
1010 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
1012 booth_recode_w7(&sign1, &digit1, wvalue);
1013 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
1014 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
1016 booth_recode_w7(&sign2, &digit2, wvalue);
1017 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
1018 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
1020 booth_recode_w7(&sign3, &digit3, wvalue);
1022 ecp_nistz256_avx2_multi_gather_w7(point_arr, preComputedTable[4 * 1],
1023 digit0, digit1, digit2, digit3);
1025 ecp_nistz256_neg(tmp, point_arr[0].Y);
1026 copy_conditional(point_arr[0].Y, tmp, sign0);
1027 ecp_nistz256_neg(tmp, point_arr[1].Y);
1028 copy_conditional(point_arr[1].Y, tmp, sign1);
1029 ecp_nistz256_neg(tmp, point_arr[2].Y);
1030 copy_conditional(point_arr[2].Y, tmp, sign2);
1031 ecp_nistz256_neg(tmp, point_arr[3].Y);
1032 copy_conditional(point_arr[3].Y, tmp, sign3);
1034 ecp_nistz256_avx2_transpose_convert(bX4, point_arr);
1035 ecp_nistz256_avx2_to_mont(bX4, bX4);
1036 ecp_nistz256_avx2_to_mont(&bX4[4 * 9], &bX4[4 * 9]);
1037 /* Optimized when both inputs are affine */
1038 ecp_nistz256_avx2_point_add_affines_x4(aX4, aX4, bX4);
1040 for (i = 2; i < 9; i++) {
1041 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
1042 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
1044 booth_recode_w7(&sign0, &digit0, wvalue);
1045 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
1046 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
1048 booth_recode_w7(&sign1, &digit1, wvalue);
1049 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
1050 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
1052 booth_recode_w7(&sign2, &digit2, wvalue);
1053 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
1054 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
1056 booth_recode_w7(&sign3, &digit3, wvalue);
1058 ecp_nistz256_avx2_multi_gather_w7(point_arr,
1059 preComputedTable[4 * i],
1060 digit0, digit1, digit2, digit3);
1062 ecp_nistz256_neg(tmp, point_arr[0].Y);
1063 copy_conditional(point_arr[0].Y, tmp, sign0);
1064 ecp_nistz256_neg(tmp, point_arr[1].Y);
1065 copy_conditional(point_arr[1].Y, tmp, sign1);
1066 ecp_nistz256_neg(tmp, point_arr[2].Y);
1067 copy_conditional(point_arr[2].Y, tmp, sign2);
1068 ecp_nistz256_neg(tmp, point_arr[3].Y);
1069 copy_conditional(point_arr[3].Y, tmp, sign3);
1071 ecp_nistz256_avx2_transpose_convert(bX4, point_arr);
1072 ecp_nistz256_avx2_to_mont(bX4, bX4);
1073 ecp_nistz256_avx2_to_mont(&bX4[4 * 9], &bX4[4 * 9]);
1075 ecp_nistz256_avx2_point_add_affine_x4(aX4, aX4, bX4);
1078 ecp_nistz256_avx2_from_mont(&aX4[4 * 9 * 0], &aX4[4 * 9 * 0]);
1079 ecp_nistz256_avx2_from_mont(&aX4[4 * 9 * 1], &aX4[4 * 9 * 1]);
1080 ecp_nistz256_avx2_from_mont(&aX4[4 * 9 * 2], &aX4[4 * 9 * 2]);
1082 ecp_nistz256_avx2_convert_transpose_back(res_point_arr, aX4);
1083 /* Last window is performed serially */
1084 wvalue = *((u16 *) & p_str[(idx - 1) / 8]);
1085 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
1086 booth_recode_w7(&sign0, &digit0, wvalue);
1087 ecp_nistz256_gather_w7((P256_POINT_AFFINE *)r,
1088 preComputedTable[36], digit0);
1089 ecp_nistz256_neg(tmp, r->Y);
1090 copy_conditional(r->Y, tmp, sign0);
1091 memcpy(r->Z, ONE, sizeof(ONE));
1092 /* Sum the four windows */
1093 ecp_nistz256_point_add(r, r, &res_point_arr[0]);
1094 ecp_nistz256_point_add(r, r, &res_point_arr[1]);
1095 ecp_nistz256_point_add(r, r, &res_point_arr[2]);
1096 ecp_nistz256_point_add(r, r, &res_point_arr[3]);
1101 __owur static int ecp_nistz256_set_from_affine(EC_POINT *out, const EC_GROUP *group,
1102 const P256_POINT_AFFINE *in,
1106 BN_ULONG d_x[P256_LIMBS], d_y[P256_LIMBS];
1117 memcpy(d_x, in->X, sizeof(d_x));
1118 bn_set_static_words(x, d_x, P256_LIMBS);
1120 memcpy(d_y, in->Y, sizeof(d_y));
1121 bn_set_static_words(y, d_y, P256_LIMBS);
1123 ret = EC_POINT_set_affine_coordinates_GFp(group, out, x, y, ctx);
1131 /* r = scalar*G + sum(scalars[i]*points[i]) */
1132 __owur static int ecp_nistz256_points_mul(const EC_GROUP *group,
1134 const BIGNUM *scalar,
1136 const EC_POINT *points[],
1137 const BIGNUM *scalars[], BN_CTX *ctx)
1139 int i = 0, ret = 0, no_precomp_for_generator = 0, p_is_infinity = 0;
1141 unsigned char p_str[33] = { 0 };
1142 const PRECOMP256_ROW *preComputedTable = NULL;
1143 const NISTZ256_PRE_COMP *pre_comp = NULL;
1144 const EC_POINT *generator = NULL;
1145 BN_CTX *new_ctx = NULL;
1146 const BIGNUM **new_scalars = NULL;
1147 const EC_POINT **new_points = NULL;
1148 unsigned int idx = 0;
1149 const unsigned int window_size = 7;
1150 const unsigned int mask = (1 << (window_size + 1)) - 1;
1151 unsigned int wvalue;
1154 P256_POINT_AFFINE a;
1158 if ((num + 1) == 0 || (num + 1) > OPENSSL_MALLOC_MAX_NELEMS(void *)) {
1159 ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, ERR_R_MALLOC_FAILURE);
1163 if (group->meth != r->meth) {
1164 ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, EC_R_INCOMPATIBLE_OBJECTS);
1168 if ((scalar == NULL) && (num == 0))
1169 return EC_POINT_set_to_infinity(group, r);
1171 for (j = 0; j < num; j++) {
1172 if (group->meth != points[j]->meth) {
1173 ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, EC_R_INCOMPATIBLE_OBJECTS);
1179 ctx = new_ctx = BN_CTX_new();
1187 generator = EC_GROUP_get0_generator(group);
1188 if (generator == NULL) {
1189 ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, EC_R_UNDEFINED_GENERATOR);
1193 /* look if we can use precomputed multiples of generator */
1194 pre_comp = group->pre_comp.nistz256;
1198 * If there is a precomputed table for the generator, check that
1199 * it was generated with the same generator.
1201 EC_POINT *pre_comp_generator = EC_POINT_new(group);
1202 if (pre_comp_generator == NULL)
1205 if (!ecp_nistz256_set_from_affine(pre_comp_generator,
1206 group, pre_comp->precomp[0],
1208 EC_POINT_free(pre_comp_generator);
1212 if (0 == EC_POINT_cmp(group, generator, pre_comp_generator, ctx))
1213 preComputedTable = (const PRECOMP256_ROW *)pre_comp->precomp;
1215 EC_POINT_free(pre_comp_generator);
1218 if (preComputedTable == NULL && ecp_nistz256_is_affine_G(generator)) {
1220 * If there is no precomputed data, but the generator is the
1221 * default, a hardcoded table of precomputed data is used. This
1222 * is because applications, such as Apache, do not use
1223 * EC_KEY_precompute_mult.
1225 preComputedTable = ecp_nistz256_precomputed;
1228 if (preComputedTable) {
1229 if ((BN_num_bits(scalar) > 256)
1230 || BN_is_negative(scalar)) {
1231 if ((tmp_scalar = BN_CTX_get(ctx)) == NULL)
1234 if (!BN_nnmod(tmp_scalar, scalar, group->order, ctx)) {
1235 ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, ERR_R_BN_LIB);
1238 scalar = tmp_scalar;
1241 for (i = 0; i < bn_get_top(scalar) * BN_BYTES; i += BN_BYTES) {
1242 BN_ULONG d = bn_get_words(scalar)[i / BN_BYTES];
1244 p_str[i + 0] = (unsigned char)d;
1245 p_str[i + 1] = (unsigned char)(d >> 8);
1246 p_str[i + 2] = (unsigned char)(d >> 16);
1247 p_str[i + 3] = (unsigned char)(d >>= 24);
1248 if (BN_BYTES == 8) {
1250 p_str[i + 4] = (unsigned char)d;
1251 p_str[i + 5] = (unsigned char)(d >> 8);
1252 p_str[i + 6] = (unsigned char)(d >> 16);
1253 p_str[i + 7] = (unsigned char)(d >> 24);
1260 #if defined(ECP_NISTZ256_AVX2)
1261 if (ecp_nistz_avx2_eligible()) {
1262 ecp_nistz256_avx2_mul_g(&p.p, p_str, preComputedTable);
1269 wvalue = (p_str[0] << 1) & mask;
1272 wvalue = _booth_recode_w7(wvalue);
1274 ecp_nistz256_gather_w7(&p.a, preComputedTable[0],
1277 ecp_nistz256_neg(p.p.Z, p.p.Y);
1278 copy_conditional(p.p.Y, p.p.Z, wvalue & 1);
1281 * Since affine infinity is encoded as (0,0) and
1282 * Jacobian ias (,,0), we need to harmonize them
1283 * by assigning "one" or zero to Z.
1285 infty = (p.p.X[0] | p.p.X[1] | p.p.X[2] | p.p.X[3] |
1286 p.p.Y[0] | p.p.Y[1] | p.p.Y[2] | p.p.Y[3]);
1287 if (P256_LIMBS == 8)
1288 infty |= (p.p.X[4] | p.p.X[5] | p.p.X[6] | p.p.X[7] |
1289 p.p.Y[4] | p.p.Y[5] | p.p.Y[6] | p.p.Y[7]);
1291 infty = 0 - is_zero(infty);
1294 p.p.Z[0] = ONE[0] & infty;
1295 p.p.Z[1] = ONE[1] & infty;
1296 p.p.Z[2] = ONE[2] & infty;
1297 p.p.Z[3] = ONE[3] & infty;
1298 if (P256_LIMBS == 8) {
1299 p.p.Z[4] = ONE[4] & infty;
1300 p.p.Z[5] = ONE[5] & infty;
1301 p.p.Z[6] = ONE[6] & infty;
1302 p.p.Z[7] = ONE[7] & infty;
1305 for (i = 1; i < 37; i++) {
1306 unsigned int off = (idx - 1) / 8;
1307 wvalue = p_str[off] | p_str[off + 1] << 8;
1308 wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
1311 wvalue = _booth_recode_w7(wvalue);
1313 ecp_nistz256_gather_w7(&t.a,
1314 preComputedTable[i], wvalue >> 1);
1316 ecp_nistz256_neg(t.p.Z, t.a.Y);
1317 copy_conditional(t.a.Y, t.p.Z, wvalue & 1);
1319 ecp_nistz256_point_add_affine(&p.p, &p.p, &t.a);
1324 no_precomp_for_generator = 1;
1329 if (no_precomp_for_generator) {
1331 * Without a precomputed table for the generator, it has to be
1332 * handled like a normal point.
1334 new_scalars = OPENSSL_malloc((num + 1) * sizeof(BIGNUM *));
1335 if (new_scalars == NULL) {
1336 ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, ERR_R_MALLOC_FAILURE);
1340 new_points = OPENSSL_malloc((num + 1) * sizeof(EC_POINT *));
1341 if (new_points == NULL) {
1342 ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, ERR_R_MALLOC_FAILURE);
1346 memcpy(new_scalars, scalars, num * sizeof(BIGNUM *));
1347 new_scalars[num] = scalar;
1348 memcpy(new_points, points, num * sizeof(EC_POINT *));
1349 new_points[num] = generator;
1351 scalars = new_scalars;
1352 points = new_points;
1357 P256_POINT *out = &t.p;
1361 if (!ecp_nistz256_windowed_mul(group, out, scalars, points, num, ctx))
1365 ecp_nistz256_point_add(&p.p, &p.p, out);
1368 /* Not constant-time, but we're only operating on the public output. */
1369 if (!bn_set_words(r->X, p.p.X, P256_LIMBS) ||
1370 !bn_set_words(r->Y, p.p.Y, P256_LIMBS) ||
1371 !bn_set_words(r->Z, p.p.Z, P256_LIMBS)) {
1374 r->Z_is_one = is_one(r->Z) & 1;
1381 BN_CTX_free(new_ctx);
1382 OPENSSL_free(new_points);
1383 OPENSSL_free(new_scalars);
1387 __owur static int ecp_nistz256_get_affine(const EC_GROUP *group,
1388 const EC_POINT *point,
1389 BIGNUM *x, BIGNUM *y, BN_CTX *ctx)
1391 BN_ULONG z_inv2[P256_LIMBS];
1392 BN_ULONG z_inv3[P256_LIMBS];
1393 BN_ULONG x_aff[P256_LIMBS];
1394 BN_ULONG y_aff[P256_LIMBS];
1395 BN_ULONG point_x[P256_LIMBS], point_y[P256_LIMBS], point_z[P256_LIMBS];
1396 BN_ULONG x_ret[P256_LIMBS], y_ret[P256_LIMBS];
1398 if (EC_POINT_is_at_infinity(group, point)) {
1399 ECerr(EC_F_ECP_NISTZ256_GET_AFFINE, EC_R_POINT_AT_INFINITY);
1403 if (!ecp_nistz256_bignum_to_field_elem(point_x, point->X) ||
1404 !ecp_nistz256_bignum_to_field_elem(point_y, point->Y) ||
1405 !ecp_nistz256_bignum_to_field_elem(point_z, point->Z)) {
1406 ECerr(EC_F_ECP_NISTZ256_GET_AFFINE, EC_R_COORDINATES_OUT_OF_RANGE);
1410 ecp_nistz256_mod_inverse(z_inv3, point_z);
1411 ecp_nistz256_sqr_mont(z_inv2, z_inv3);
1412 ecp_nistz256_mul_mont(x_aff, z_inv2, point_x);
1415 ecp_nistz256_from_mont(x_ret, x_aff);
1416 if (!bn_set_words(x, x_ret, P256_LIMBS))
1421 ecp_nistz256_mul_mont(z_inv3, z_inv3, z_inv2);
1422 ecp_nistz256_mul_mont(y_aff, z_inv3, point_y);
1423 ecp_nistz256_from_mont(y_ret, y_aff);
1424 if (!bn_set_words(y, y_ret, P256_LIMBS))
1431 static NISTZ256_PRE_COMP *ecp_nistz256_pre_comp_new(const EC_GROUP *group)
1433 NISTZ256_PRE_COMP *ret = NULL;
1438 ret = OPENSSL_zalloc(sizeof(*ret));
1441 ECerr(EC_F_ECP_NISTZ256_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE);
1446 ret->w = 6; /* default */
1447 ret->references = 1;
1449 ret->lock = CRYPTO_THREAD_lock_new();
1450 if (ret->lock == NULL) {
1451 ECerr(EC_F_ECP_NISTZ256_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE);
1458 NISTZ256_PRE_COMP *EC_nistz256_pre_comp_dup(NISTZ256_PRE_COMP *p)
1462 CRYPTO_UP_REF(&p->references, &i, p->lock);
1466 void EC_nistz256_pre_comp_free(NISTZ256_PRE_COMP *pre)
1473 CRYPTO_DOWN_REF(&pre->references, &i, pre->lock);
1474 REF_PRINT_COUNT("EC_nistz256", x);
1477 REF_ASSERT_ISNT(i < 0);
1479 OPENSSL_free(pre->precomp_storage);
1480 CRYPTO_THREAD_lock_free(pre->lock);
1485 static int ecp_nistz256_window_have_precompute_mult(const EC_GROUP *group)
1487 /* There is a hard-coded table for the default generator. */
1488 const EC_POINT *generator = EC_GROUP_get0_generator(group);
1490 if (generator != NULL && ecp_nistz256_is_affine_G(generator)) {
1491 /* There is a hard-coded table for the default generator. */
1495 return HAVEPRECOMP(group, nistz256);
1498 const EC_METHOD *EC_GFp_nistz256_method(void)
1500 static const EC_METHOD ret = {
1501 EC_FLAGS_DEFAULT_OCT,
1502 NID_X9_62_prime_field,
1503 ec_GFp_mont_group_init,
1504 ec_GFp_mont_group_finish,
1505 ec_GFp_mont_group_clear_finish,
1506 ec_GFp_mont_group_copy,
1507 ec_GFp_mont_group_set_curve,
1508 ec_GFp_simple_group_get_curve,
1509 ec_GFp_simple_group_get_degree,
1510 ec_group_simple_order_bits,
1511 ec_GFp_simple_group_check_discriminant,
1512 ec_GFp_simple_point_init,
1513 ec_GFp_simple_point_finish,
1514 ec_GFp_simple_point_clear_finish,
1515 ec_GFp_simple_point_copy,
1516 ec_GFp_simple_point_set_to_infinity,
1517 ec_GFp_simple_set_Jprojective_coordinates_GFp,
1518 ec_GFp_simple_get_Jprojective_coordinates_GFp,
1519 ec_GFp_simple_point_set_affine_coordinates,
1520 ecp_nistz256_get_affine,
1524 ec_GFp_simple_invert,
1525 ec_GFp_simple_is_at_infinity,
1526 ec_GFp_simple_is_on_curve,
1528 ec_GFp_simple_make_affine,
1529 ec_GFp_simple_points_make_affine,
1530 ecp_nistz256_points_mul, /* mul */
1531 ecp_nistz256_mult_precompute, /* precompute_mult */
1532 ecp_nistz256_window_have_precompute_mult, /* have_precompute_mult */
1533 ec_GFp_mont_field_mul,
1534 ec_GFp_mont_field_sqr,
1536 ec_GFp_mont_field_encode,
1537 ec_GFp_mont_field_decode,
1538 ec_GFp_mont_field_set_to_one,
1539 ec_key_simple_priv2oct,
1540 ec_key_simple_oct2priv,
1541 0, /* set private */
1542 ec_key_simple_generate_key,
1543 ec_key_simple_check_key,
1544 ec_key_simple_generate_public_key,
1547 ecdh_simple_compute_key