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1/* $OpenBSD: ecp_nistp224.c,v 1.30 2022/12/26 07:18:51 jmc Exp $ */
2/*
3 * Written by Emilia Kasper (Google) for the OpenSSL project.
4 */
5/*
6 * Copyright (c) 2011 Google Inc.
7 *
8 * Permission to use, copy, modify, and distribute this software for any
9 * purpose with or without fee is hereby granted, provided that the above
10 * copyright notice and this permission notice appear in all copies.
11 *
12 * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
13 * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
14 * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
15 * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
16 * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
17 * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
18 * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
19 */
20
21/*
22 * A 64-bit implementation of the NIST P-224 elliptic curve point multiplication
23 *
24 * Inspired by Daniel J. Bernstein's public domain nistp224 implementation
25 * and Adam Langley's public domain 64-bit C implementation of curve25519
26 */
27
28#include <stdint.h>
29#include <string.h>
30
31#include <openssl/opensslconf.h>
32
33#ifndef OPENSSL_NO_EC_NISTP_64_GCC_128
34
35#include <openssl/err.h>
36#include "ec_local.h"
37
38#if defined(__GNUC__) && (__GNUC__ > 3 || (__GNUC__ == 3 && __GNUC_MINOR__ >= 1))
39 /* even with gcc, the typedef won't work for 32-bit platforms */
40 typedef __uint128_t uint128_t; /* nonstandard; implemented by gcc on 64-bit platforms */
41#else
42 #error "Need GCC 3.1 or later to define type uint128_t"
43#endif
44
45typedef uint8_t u8;
46typedef uint64_t u64;
47typedef int64_t s64;
48
49
50/******************************************************************************/
51/* INTERNAL REPRESENTATION OF FIELD ELEMENTS
52 *
53 * Field elements are represented as a_0 + 2^56*a_1 + 2^112*a_2 + 2^168*a_3
54 * using 64-bit coefficients called 'limbs',
55 * and sometimes (for multiplication results) as
56 * b_0 + 2^56*b_1 + 2^112*b_2 + 2^168*b_3 + 2^224*b_4 + 2^280*b_5 + 2^336*b_6
57 * using 128-bit coefficients called 'widelimbs'.
58 * A 4-limb representation is an 'felem';
59 * a 7-widelimb representation is a 'widefelem'.
60 * Even within felems, bits of adjacent limbs overlap, and we don't always
61 * reduce the representations: we ensure that inputs to each felem
62 * multiplication satisfy a_i < 2^60, so outputs satisfy b_i < 4*2^60*2^60,
63 * and fit into a 128-bit word without overflow. The coefficients are then
64 * again partially reduced to obtain an felem satisfying a_i < 2^57.
65 * We only reduce to the unique minimal representation at the end of the
66 * computation.
67 */
68
69typedef uint64_t limb;
70typedef uint128_t widelimb;
71
72typedef limb felem[4];
73typedef widelimb widefelem[7];
74
75/* Field element represented as a byte array.
76 * 28*8 = 224 bits is also the group order size for the elliptic curve,
77 * and we also use this type for scalars for point multiplication.
78 */
79typedef u8 felem_bytearray[28];
80
81static const felem_bytearray nistp224_curve_params[5] = {
82 {0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* p */
83 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0x00,0x00,0x00,0x00,
84 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x01},
85 {0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* a */
86 0xFF,0xFF,0xFF,0xFF,0xFF,0xFE,0xFF,0xFF,0xFF,0xFF,
87 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFE},
88 {0xB4,0x05,0x0A,0x85,0x0C,0x04,0xB3,0xAB,0xF5,0x41, /* b */
89 0x32,0x56,0x50,0x44,0xB0,0xB7,0xD7,0xBF,0xD8,0xBA,
90 0x27,0x0B,0x39,0x43,0x23,0x55,0xFF,0xB4},
91 {0xB7,0x0E,0x0C,0xBD,0x6B,0xB4,0xBF,0x7F,0x32,0x13, /* x */
92 0x90,0xB9,0x4A,0x03,0xC1,0xD3,0x56,0xC2,0x11,0x22,
93 0x34,0x32,0x80,0xD6,0x11,0x5C,0x1D,0x21},
94 {0xbd,0x37,0x63,0x88,0xb5,0xf7,0x23,0xfb,0x4c,0x22, /* y */
95 0xdf,0xe6,0xcd,0x43,0x75,0xa0,0x5a,0x07,0x47,0x64,
96 0x44,0xd5,0x81,0x99,0x85,0x00,0x7e,0x34}
97};
98
99/* Precomputed multiples of the standard generator
100 * Points are given in coordinates (X, Y, Z) where Z normally is 1
101 * (0 for the point at infinity).
102 * For each field element, slice a_0 is word 0, etc.
103 *
104 * The table has 2 * 16 elements, starting with the following:
105 * index | bits | point
106 * ------+---------+------------------------------
107 * 0 | 0 0 0 0 | 0G
108 * 1 | 0 0 0 1 | 1G
109 * 2 | 0 0 1 0 | 2^56G
110 * 3 | 0 0 1 1 | (2^56 + 1)G
111 * 4 | 0 1 0 0 | 2^112G
112 * 5 | 0 1 0 1 | (2^112 + 1)G
113 * 6 | 0 1 1 0 | (2^112 + 2^56)G
114 * 7 | 0 1 1 1 | (2^112 + 2^56 + 1)G
115 * 8 | 1 0 0 0 | 2^168G
116 * 9 | 1 0 0 1 | (2^168 + 1)G
117 * 10 | 1 0 1 0 | (2^168 + 2^56)G
118 * 11 | 1 0 1 1 | (2^168 + 2^56 + 1)G
119 * 12 | 1 1 0 0 | (2^168 + 2^112)G
120 * 13 | 1 1 0 1 | (2^168 + 2^112 + 1)G
121 * 14 | 1 1 1 0 | (2^168 + 2^112 + 2^56)G
122 * 15 | 1 1 1 1 | (2^168 + 2^112 + 2^56 + 1)G
123 * followed by a copy of this with each element multiplied by 2^28.
124 *
125 * The reason for this is so that we can clock bits into four different
126 * locations when doing simple scalar multiplies against the base point,
127 * and then another four locations using the second 16 elements.
128 */
129static const felem gmul[2][16][3] =
130{{{{0, 0, 0, 0},
131 {0, 0, 0, 0},
132 {0, 0, 0, 0}},
133 {{0x3280d6115c1d21, 0xc1d356c2112234, 0x7f321390b94a03, 0xb70e0cbd6bb4bf},
134 {0xd5819985007e34, 0x75a05a07476444, 0xfb4c22dfe6cd43, 0xbd376388b5f723},
135 {1, 0, 0, 0}},
136 {{0xfd9675666ebbe9, 0xbca7664d40ce5e, 0x2242df8d8a2a43, 0x1f49bbb0f99bc5},
137 {0x29e0b892dc9c43, 0xece8608436e662, 0xdc858f185310d0, 0x9812dd4eb8d321},
138 {1, 0, 0, 0}},
139 {{0x6d3e678d5d8eb8, 0x559eed1cb362f1, 0x16e9a3bbce8a3f, 0xeedcccd8c2a748},
140 {0xf19f90ed50266d, 0xabf2b4bf65f9df, 0x313865468fafec, 0x5cb379ba910a17},
141 {1, 0, 0, 0}},
142 {{0x0641966cab26e3, 0x91fb2991fab0a0, 0xefec27a4e13a0b, 0x0499aa8a5f8ebe},
143 {0x7510407766af5d, 0x84d929610d5450, 0x81d77aae82f706, 0x6916f6d4338c5b},
144 {1, 0, 0, 0}},
145 {{0xea95ac3b1f15c6, 0x086000905e82d4, 0xdd323ae4d1c8b1, 0x932b56be7685a3},
146 {0x9ef93dea25dbbf, 0x41665960f390f0, 0xfdec76dbe2a8a7, 0x523e80f019062a},
147 {1, 0, 0, 0}},
148 {{0x822fdd26732c73, 0xa01c83531b5d0f, 0x363f37347c1ba4, 0xc391b45c84725c},
149 {0xbbd5e1b2d6ad24, 0xddfbcde19dfaec, 0xc393da7e222a7f, 0x1efb7890ede244},
150 {1, 0, 0, 0}},
151 {{0x4c9e90ca217da1, 0xd11beca79159bb, 0xff8d33c2c98b7c, 0x2610b39409f849},
152 {0x44d1352ac64da0, 0xcdbb7b2c46b4fb, 0x966c079b753c89, 0xfe67e4e820b112},
153 {1, 0, 0, 0}},
154 {{0xe28cae2df5312d, 0xc71b61d16f5c6e, 0x79b7619a3e7c4c, 0x05c73240899b47},
155 {0x9f7f6382c73e3a, 0x18615165c56bda, 0x641fab2116fd56, 0x72855882b08394},
156 {1, 0, 0, 0}},
157 {{0x0469182f161c09, 0x74a98ca8d00fb5, 0xb89da93489a3e0, 0x41c98768fb0c1d},
158 {0xe5ea05fb32da81, 0x3dce9ffbca6855, 0x1cfe2d3fbf59e6, 0x0e5e03408738a7},
159 {1, 0, 0, 0}},
160 {{0xdab22b2333e87f, 0x4430137a5dd2f6, 0xe03ab9f738beb8, 0xcb0c5d0dc34f24},
161 {0x764a7df0c8fda5, 0x185ba5c3fa2044, 0x9281d688bcbe50, 0xc40331df893881},
162 {1, 0, 0, 0}},
163 {{0xb89530796f0f60, 0xade92bd26909a3, 0x1a0c83fb4884da, 0x1765bf22a5a984},
164 {0x772a9ee75db09e, 0x23bc6c67cec16f, 0x4c1edba8b14e2f, 0xe2a215d9611369},
165 {1, 0, 0, 0}},
166 {{0x571e509fb5efb3, 0xade88696410552, 0xc8ae85fada74fe, 0x6c7e4be83bbde3},
167 {0xff9f51160f4652, 0xb47ce2495a6539, 0xa2946c53b582f4, 0x286d2db3ee9a60},
168 {1, 0, 0, 0}},
169 {{0x40bbd5081a44af, 0x0995183b13926c, 0xbcefba6f47f6d0, 0x215619e9cc0057},
170 {0x8bc94d3b0df45e, 0xf11c54a3694f6f, 0x8631b93cdfe8b5, 0xe7e3f4b0982db9},
171 {1, 0, 0, 0}},
172 {{0xb17048ab3e1c7b, 0xac38f36ff8a1d8, 0x1c29819435d2c6, 0xc813132f4c07e9},
173 {0x2891425503b11f, 0x08781030579fea, 0xf5426ba5cc9674, 0x1e28ebf18562bc},
174 {1, 0, 0, 0}},
175 {{0x9f31997cc864eb, 0x06cd91d28b5e4c, 0xff17036691a973, 0xf1aef351497c58},
176 {0xdd1f2d600564ff, 0xdead073b1402db, 0x74a684435bd693, 0xeea7471f962558},
177 {1, 0, 0, 0}}},
178 {{{0, 0, 0, 0},
179 {0, 0, 0, 0},
180 {0, 0, 0, 0}},
181 {{0x9665266dddf554, 0x9613d78b60ef2d, 0xce27a34cdba417, 0xd35ab74d6afc31},
182 {0x85ccdd22deb15e, 0x2137e5783a6aab, 0xa141cffd8c93c6, 0x355a1830e90f2d},
183 {1, 0, 0, 0}},
184 {{0x1a494eadaade65, 0xd6da4da77fe53c, 0xe7992996abec86, 0x65c3553c6090e3},
185 {0xfa610b1fb09346, 0xf1c6540b8a4aaf, 0xc51a13ccd3cbab, 0x02995b1b18c28a},
186 {1, 0, 0, 0}},
187 {{0x7874568e7295ef, 0x86b419fbe38d04, 0xdc0690a7550d9a, 0xd3966a44beac33},
188 {0x2b7280ec29132f, 0xbeaa3b6a032df3, 0xdc7dd88ae41200, 0xd25e2513e3a100},
189 {1, 0, 0, 0}},
190 {{0x924857eb2efafd, 0xac2bce41223190, 0x8edaa1445553fc, 0x825800fd3562d5},
191 {0x8d79148ea96621, 0x23a01c3dd9ed8d, 0xaf8b219f9416b5, 0xd8db0cc277daea},
192 {1, 0, 0, 0}},
193 {{0x76a9c3b1a700f0, 0xe9acd29bc7e691, 0x69212d1a6b0327, 0x6322e97fe154be},
194 {0x469fc5465d62aa, 0x8d41ed18883b05, 0x1f8eae66c52b88, 0xe4fcbe9325be51},
195 {1, 0, 0, 0}},
196 {{0x825fdf583cac16, 0x020b857c7b023a, 0x683c17744b0165, 0x14ffd0a2daf2f1},
197 {0x323b36184218f9, 0x4944ec4e3b47d4, 0xc15b3080841acf, 0x0bced4b01a28bb},
198 {1, 0, 0, 0}},
199 {{0x92ac22230df5c4, 0x52f33b4063eda8, 0xcb3f19870c0c93, 0x40064f2ba65233},
200 {0xfe16f0924f8992, 0x012da25af5b517, 0x1a57bb24f723a6, 0x06f8bc76760def},
201 {1, 0, 0, 0}},
202 {{0x4a7084f7817cb9, 0xbcab0738ee9a78, 0x3ec11e11d9c326, 0xdc0fe90e0f1aae},
203 {0xcf639ea5f98390, 0x5c350aa22ffb74, 0x9afae98a4047b7, 0x956ec2d617fc45},
204 {1, 0, 0, 0}},
205 {{0x4306d648c1be6a, 0x9247cd8bc9a462, 0xf5595e377d2f2e, 0xbd1c3caff1a52e},
206 {0x045e14472409d0, 0x29f3e17078f773, 0x745a602b2d4f7d, 0x191837685cdfbb},
207 {1, 0, 0, 0}},
208 {{0x5b6ee254a8cb79, 0x4953433f5e7026, 0xe21faeb1d1def4, 0xc4c225785c09de},
209 {0x307ce7bba1e518, 0x31b125b1036db8, 0x47e91868839e8f, 0xc765866e33b9f3},
210 {1, 0, 0, 0}},
211 {{0x3bfece24f96906, 0x4794da641e5093, 0xde5df64f95db26, 0x297ecd89714b05},
212 {0x701bd3ebb2c3aa, 0x7073b4f53cb1d5, 0x13c5665658af16, 0x9895089d66fe58},
213 {1, 0, 0, 0}},
214 {{0x0fef05f78c4790, 0x2d773633b05d2e, 0x94229c3a951c94, 0xbbbd70df4911bb},
215 {0xb2c6963d2c1168, 0x105f47a72b0d73, 0x9fdf6111614080, 0x7b7e94b39e67b0},
216 {1, 0, 0, 0}},
217 {{0xad1a7d6efbe2b3, 0xf012482c0da69d, 0x6b3bdf12438345, 0x40d7558d7aa4d9},
218 {0x8a09fffb5c6d3d, 0x9a356e5d9ffd38, 0x5973f15f4f9b1c, 0xdcd5f59f63c3ea},
219 {1, 0, 0, 0}},
220 {{0xacf39f4c5ca7ab, 0x4c8071cc5fd737, 0xc64e3602cd1184, 0x0acd4644c9abba},
221 {0x6c011a36d8bf6e, 0xfecd87ba24e32a, 0x19f6f56574fad8, 0x050b204ced9405},
222 {1, 0, 0, 0}},
223 {{0xed4f1cae7d9a96, 0x5ceef7ad94c40a, 0x778e4a3bf3ef9b, 0x7405783dc3b55e},
224 {0x32477c61b6e8c6, 0xb46a97570f018b, 0x91176d0a7e95d1, 0x3df90fbc4c7d0e},
225 {1, 0, 0, 0}}}};
226
227/* Precomputation for the group generator. */
228typedef struct {
229 felem g_pre_comp[2][16][3];
230 int references;
231} NISTP224_PRE_COMP;
232
233const EC_METHOD *
234EC_GFp_nistp224_method(void)
235{
236 static const EC_METHOD ret = {
237 .flags = EC_FLAGS_DEFAULT_OCT,
238 .field_type = NID_X9_62_prime_field,
239 .group_init = ec_GFp_nistp224_group_init,
240 .group_finish = ec_GFp_simple_group_finish,
241 .group_clear_finish = ec_GFp_simple_group_clear_finish,
242 .group_copy = ec_GFp_nist_group_copy,
243 .group_set_curve = ec_GFp_nistp224_group_set_curve,
244 .group_get_curve = ec_GFp_simple_group_get_curve,
245 .group_get_degree = ec_GFp_simple_group_get_degree,
246 .group_order_bits = ec_group_simple_order_bits,
247 .group_check_discriminant =
248 ec_GFp_simple_group_check_discriminant,
249 .point_init = ec_GFp_simple_point_init,
250 .point_finish = ec_GFp_simple_point_finish,
251 .point_clear_finish = ec_GFp_simple_point_clear_finish,
252 .point_copy = ec_GFp_simple_point_copy,
253 .point_set_to_infinity = ec_GFp_simple_point_set_to_infinity,
254 .point_set_Jprojective_coordinates =
255 ec_GFp_simple_set_Jprojective_coordinates,
256 .point_get_Jprojective_coordinates =
257 ec_GFp_simple_get_Jprojective_coordinates,
258 .point_set_affine_coordinates =
259 ec_GFp_simple_point_set_affine_coordinates,
260 .point_get_affine_coordinates =
261 ec_GFp_nistp224_point_get_affine_coordinates,
262 .add = ec_GFp_simple_add,
263 .dbl = ec_GFp_simple_dbl,
264 .invert = ec_GFp_simple_invert,
265 .is_at_infinity = ec_GFp_simple_is_at_infinity,
266 .is_on_curve = ec_GFp_simple_is_on_curve,
267 .point_cmp = ec_GFp_simple_cmp,
268 .make_affine = ec_GFp_simple_make_affine,
269 .points_make_affine = ec_GFp_simple_points_make_affine,
270 .mul = ec_GFp_nistp224_points_mul,
271 .precompute_mult = ec_GFp_nistp224_precompute_mult,
272 .have_precompute_mult = ec_GFp_nistp224_have_precompute_mult,
273 .field_mul = ec_GFp_nist_field_mul,
274 .field_sqr = ec_GFp_nist_field_sqr,
275 .blind_coordinates = NULL,
276 };
277
278 return &ret;
279}
280
281/* Helper functions to convert field elements to/from internal representation */
282static void
283bin28_to_felem(felem out, const u8 in[28])
284{
285 out[0] = *((const uint64_t *) (in)) & 0x00ffffffffffffff;
286 out[1] = (*((const uint64_t *) (in + 7))) & 0x00ffffffffffffff;
287 out[2] = (*((const uint64_t *) (in + 14))) & 0x00ffffffffffffff;
288 out[3] = (*((const uint64_t *) (in + 21))) & 0x00ffffffffffffff;
289}
290
291static void
292felem_to_bin28(u8 out[28], const felem in)
293{
294 unsigned i;
295 for (i = 0; i < 7; ++i) {
296 out[i] = in[0] >> (8 * i);
297 out[i + 7] = in[1] >> (8 * i);
298 out[i + 14] = in[2] >> (8 * i);
299 out[i + 21] = in[3] >> (8 * i);
300 }
301}
302
303/* To preserve endianness when using BN_bn2bin and BN_bin2bn */
304static void
305flip_endian(u8 *out, const u8 *in, unsigned len)
306{
307 unsigned i;
308 for (i = 0; i < len; ++i)
309 out[i] = in[len - 1 - i];
310}
311
312/* From OpenSSL BIGNUM to internal representation */
313static int
314BN_to_felem(felem out, const BIGNUM *bn)
315{
316 felem_bytearray b_in;
317 felem_bytearray b_out;
318 unsigned num_bytes;
319
320 /* BN_bn2bin eats leading zeroes */
321 memset(b_out, 0, sizeof b_out);
322 num_bytes = BN_num_bytes(bn);
323 if (num_bytes > sizeof b_out) {
324 ECerror(EC_R_BIGNUM_OUT_OF_RANGE);
325 return 0;
326 }
327 if (BN_is_negative(bn)) {
328 ECerror(EC_R_BIGNUM_OUT_OF_RANGE);
329 return 0;
330 }
331 num_bytes = BN_bn2bin(bn, b_in);
332 flip_endian(b_out, b_in, num_bytes);
333 bin28_to_felem(out, b_out);
334 return 1;
335}
336
337/* From internal representation to OpenSSL BIGNUM */
338static BIGNUM *
339felem_to_BN(BIGNUM *out, const felem in)
340{
341 felem_bytearray b_in, b_out;
342 felem_to_bin28(b_in, in);
343 flip_endian(b_out, b_in, sizeof b_out);
344 return BN_bin2bn(b_out, sizeof b_out, out);
345}
346
347/******************************************************************************/
348/* FIELD OPERATIONS
349 *
350 * Field operations, using the internal representation of field elements.
351 * NB! These operations are specific to our point multiplication and cannot be
352 * expected to be correct in general - e.g., multiplication with a large scalar
353 * will cause an overflow.
354 *
355 */
356
357static void
358felem_one(felem out)
359{
360 out[0] = 1;
361 out[1] = 0;
362 out[2] = 0;
363 out[3] = 0;
364}
365
366static void
367felem_assign(felem out, const felem in)
368{
369 out[0] = in[0];
370 out[1] = in[1];
371 out[2] = in[2];
372 out[3] = in[3];
373}
374
375/* Sum two field elements: out += in */
376static void
377felem_sum(felem out, const felem in)
378{
379 out[0] += in[0];
380 out[1] += in[1];
381 out[2] += in[2];
382 out[3] += in[3];
383}
384
385/* Get negative value: out = -in */
386/* Assumes in[i] < 2^57 */
387static void
388felem_neg(felem out, const felem in)
389{
390 static const limb two58p2 = (((limb) 1) << 58) + (((limb) 1) << 2);
391 static const limb two58m2 = (((limb) 1) << 58) - (((limb) 1) << 2);
392 static const limb two58m42m2 = (((limb) 1) << 58) -
393 (((limb) 1) << 42) - (((limb) 1) << 2);
394
395 /* Set to 0 mod 2^224-2^96+1 to ensure out > in */
396 out[0] = two58p2 - in[0];
397 out[1] = two58m42m2 - in[1];
398 out[2] = two58m2 - in[2];
399 out[3] = two58m2 - in[3];
400}
401
402/* Subtract field elements: out -= in */
403/* Assumes in[i] < 2^57 */
404static void
405felem_diff(felem out, const felem in)
406{
407 static const limb two58p2 = (((limb) 1) << 58) + (((limb) 1) << 2);
408 static const limb two58m2 = (((limb) 1) << 58) - (((limb) 1) << 2);
409 static const limb two58m42m2 = (((limb) 1) << 58) -
410 (((limb) 1) << 42) - (((limb) 1) << 2);
411
412 /* Add 0 mod 2^224-2^96+1 to ensure out > in */
413 out[0] += two58p2;
414 out[1] += two58m42m2;
415 out[2] += two58m2;
416 out[3] += two58m2;
417
418 out[0] -= in[0];
419 out[1] -= in[1];
420 out[2] -= in[2];
421 out[3] -= in[3];
422}
423
424/* Subtract in unreduced 128-bit mode: out -= in */
425/* Assumes in[i] < 2^119 */
426static void
427widefelem_diff(widefelem out, const widefelem in)
428{
429 static const widelimb two120 = ((widelimb) 1) << 120;
430 static const widelimb two120m64 = (((widelimb) 1) << 120) -
431 (((widelimb) 1) << 64);
432 static const widelimb two120m104m64 = (((widelimb) 1) << 120) -
433 (((widelimb) 1) << 104) - (((widelimb) 1) << 64);
434
435 /* Add 0 mod 2^224-2^96+1 to ensure out > in */
436 out[0] += two120;
437 out[1] += two120m64;
438 out[2] += two120m64;
439 out[3] += two120;
440 out[4] += two120m104m64;
441 out[5] += two120m64;
442 out[6] += two120m64;
443
444 out[0] -= in[0];
445 out[1] -= in[1];
446 out[2] -= in[2];
447 out[3] -= in[3];
448 out[4] -= in[4];
449 out[5] -= in[5];
450 out[6] -= in[6];
451}
452
453/* Subtract in mixed mode: out128 -= in64 */
454/* in[i] < 2^63 */
455static void
456felem_diff_128_64(widefelem out, const felem in)
457{
458 static const widelimb two64p8 = (((widelimb) 1) << 64) +
459 (((widelimb) 1) << 8);
460 static const widelimb two64m8 = (((widelimb) 1) << 64) -
461 (((widelimb) 1) << 8);
462 static const widelimb two64m48m8 = (((widelimb) 1) << 64) -
463 (((widelimb) 1) << 48) - (((widelimb) 1) << 8);
464
465 /* Add 0 mod 2^224-2^96+1 to ensure out > in */
466 out[0] += two64p8;
467 out[1] += two64m48m8;
468 out[2] += two64m8;
469 out[3] += two64m8;
470
471 out[0] -= in[0];
472 out[1] -= in[1];
473 out[2] -= in[2];
474 out[3] -= in[3];
475}
476
477/* Multiply a field element by a scalar: out = out * scalar
478 * The scalars we actually use are small, so results fit without overflow */
479static void
480felem_scalar(felem out, const limb scalar)
481{
482 out[0] *= scalar;
483 out[1] *= scalar;
484 out[2] *= scalar;
485 out[3] *= scalar;
486}
487
488/* Multiply an unreduced field element by a scalar: out = out * scalar
489 * The scalars we actually use are small, so results fit without overflow */
490static void
491widefelem_scalar(widefelem out, const widelimb scalar)
492{
493 out[0] *= scalar;
494 out[1] *= scalar;
495 out[2] *= scalar;
496 out[3] *= scalar;
497 out[4] *= scalar;
498 out[5] *= scalar;
499 out[6] *= scalar;
500}
501
502/* Square a field element: out = in^2 */
503static void
504felem_square(widefelem out, const felem in)
505{
506 limb tmp0, tmp1, tmp2;
507 tmp0 = 2 * in[0];
508 tmp1 = 2 * in[1];
509 tmp2 = 2 * in[2];
510 out[0] = ((widelimb) in[0]) * in[0];
511 out[1] = ((widelimb) in[0]) * tmp1;
512 out[2] = ((widelimb) in[0]) * tmp2 + ((widelimb) in[1]) * in[1];
513 out[3] = ((widelimb) in[3]) * tmp0 +
514 ((widelimb) in[1]) * tmp2;
515 out[4] = ((widelimb) in[3]) * tmp1 + ((widelimb) in[2]) * in[2];
516 out[5] = ((widelimb) in[3]) * tmp2;
517 out[6] = ((widelimb) in[3]) * in[3];
518}
519
520/* Multiply two field elements: out = in1 * in2 */
521static void
522felem_mul(widefelem out, const felem in1, const felem in2)
523{
524 out[0] = ((widelimb) in1[0]) * in2[0];
525 out[1] = ((widelimb) in1[0]) * in2[1] + ((widelimb) in1[1]) * in2[0];
526 out[2] = ((widelimb) in1[0]) * in2[2] + ((widelimb) in1[1]) * in2[1] +
527 ((widelimb) in1[2]) * in2[0];
528 out[3] = ((widelimb) in1[0]) * in2[3] + ((widelimb) in1[1]) * in2[2] +
529 ((widelimb) in1[2]) * in2[1] + ((widelimb) in1[3]) * in2[0];
530 out[4] = ((widelimb) in1[1]) * in2[3] + ((widelimb) in1[2]) * in2[2] +
531 ((widelimb) in1[3]) * in2[1];
532 out[5] = ((widelimb) in1[2]) * in2[3] + ((widelimb) in1[3]) * in2[2];
533 out[6] = ((widelimb) in1[3]) * in2[3];
534}
535
536/* Reduce seven 128-bit coefficients to four 64-bit coefficients.
537 * Requires in[i] < 2^126,
538 * ensures out[0] < 2^56, out[1] < 2^56, out[2] < 2^56, out[3] <= 2^56 + 2^16 */
539static void
540felem_reduce(felem out, const widefelem in)
541{
542 static const widelimb two127p15 = (((widelimb) 1) << 127) +
543 (((widelimb) 1) << 15);
544 static const widelimb two127m71 = (((widelimb) 1) << 127) -
545 (((widelimb) 1) << 71);
546 static const widelimb two127m71m55 = (((widelimb) 1) << 127) -
547 (((widelimb) 1) << 71) - (((widelimb) 1) << 55);
548 widelimb output[5];
549
550 /* Add 0 mod 2^224-2^96+1 to ensure all differences are positive */
551 output[0] = in[0] + two127p15;
552 output[1] = in[1] + two127m71m55;
553 output[2] = in[2] + two127m71;
554 output[3] = in[3];
555 output[4] = in[4];
556
557 /* Eliminate in[4], in[5], in[6] */
558 output[4] += in[6] >> 16;
559 output[3] += (in[6] & 0xffff) << 40;
560 output[2] -= in[6];
561
562 output[3] += in[5] >> 16;
563 output[2] += (in[5] & 0xffff) << 40;
564 output[1] -= in[5];
565
566 output[2] += output[4] >> 16;
567 output[1] += (output[4] & 0xffff) << 40;
568 output[0] -= output[4];
569
570 /* Carry 2 -> 3 -> 4 */
571 output[3] += output[2] >> 56;
572 output[2] &= 0x00ffffffffffffff;
573
574 output[4] = output[3] >> 56;
575 output[3] &= 0x00ffffffffffffff;
576
577 /* Now output[2] < 2^56, output[3] < 2^56, output[4] < 2^72 */
578
579 /* Eliminate output[4] */
580 output[2] += output[4] >> 16;
581 /* output[2] < 2^56 + 2^56 = 2^57 */
582 output[1] += (output[4] & 0xffff) << 40;
583 output[0] -= output[4];
584
585 /* Carry 0 -> 1 -> 2 -> 3 */
586 output[1] += output[0] >> 56;
587 out[0] = output[0] & 0x00ffffffffffffff;
588
589 output[2] += output[1] >> 56;
590 /* output[2] < 2^57 + 2^72 */
591 out[1] = output[1] & 0x00ffffffffffffff;
592 output[3] += output[2] >> 56;
593 /* output[3] <= 2^56 + 2^16 */
594 out[2] = output[2] & 0x00ffffffffffffff;
595
596 /*
597 * out[0] < 2^56, out[1] < 2^56, out[2] < 2^56, out[3] <= 2^56 + 2^16
598 * (due to final carry), so out < 2*p
599 */
600 out[3] = output[3];
601}
602
603static void
604felem_square_reduce(felem out, const felem in)
605{
606 widefelem tmp;
607 felem_square(tmp, in);
608 felem_reduce(out, tmp);
609}
610
611static void
612felem_mul_reduce(felem out, const felem in1, const felem in2)
613{
614 widefelem tmp;
615 felem_mul(tmp, in1, in2);
616 felem_reduce(out, tmp);
617}
618
619/* Reduce to unique minimal representation.
620 * Requires 0 <= in < 2*p (always call felem_reduce first) */
621static void
622felem_contract(felem out, const felem in)
623{
624 static const int64_t two56 = ((limb) 1) << 56;
625 /* 0 <= in < 2*p, p = 2^224 - 2^96 + 1 */
626 /* if in > p , reduce in = in - 2^224 + 2^96 - 1 */
627 int64_t tmp[4], a;
628 tmp[0] = in[0];
629 tmp[1] = in[1];
630 tmp[2] = in[2];
631 tmp[3] = in[3];
632 /* Case 1: a = 1 iff in >= 2^224 */
633 a = (in[3] >> 56);
634 tmp[0] -= a;
635 tmp[1] += a << 40;
636 tmp[3] &= 0x00ffffffffffffff;
637 /*
638 * Case 2: a = 0 iff p <= in < 2^224, i.e., the high 128 bits are all
639 * 1 and the lower part is non-zero
640 */
641 a = ((in[3] & in[2] & (in[1] | 0x000000ffffffffff)) + 1) |
642 (((int64_t) (in[0] + (in[1] & 0x000000ffffffffff)) - 1) >> 63);
643 a &= 0x00ffffffffffffff;
644 /* turn a into an all-one mask (if a = 0) or an all-zero mask */
645 a = (a - 1) >> 63;
646 /* subtract 2^224 - 2^96 + 1 if a is all-one */
647 tmp[3] &= a ^ 0xffffffffffffffff;
648 tmp[2] &= a ^ 0xffffffffffffffff;
649 tmp[1] &= (a ^ 0xffffffffffffffff) | 0x000000ffffffffff;
650 tmp[0] -= 1 & a;
651
652 /*
653 * eliminate negative coefficients: if tmp[0] is negative, tmp[1]
654 * must be non-zero, so we only need one step
655 */
656 a = tmp[0] >> 63;
657 tmp[0] += two56 & a;
658 tmp[1] -= 1 & a;
659
660 /* carry 1 -> 2 -> 3 */
661 tmp[2] += tmp[1] >> 56;
662 tmp[1] &= 0x00ffffffffffffff;
663
664 tmp[3] += tmp[2] >> 56;
665 tmp[2] &= 0x00ffffffffffffff;
666
667 /* Now 0 <= out < p */
668 out[0] = tmp[0];
669 out[1] = tmp[1];
670 out[2] = tmp[2];
671 out[3] = tmp[3];
672}
673
674/* Zero-check: returns 1 if input is 0, and 0 otherwise.
675 * We know that field elements are reduced to in < 2^225,
676 * so we only need to check three cases: 0, 2^224 - 2^96 + 1,
677 * and 2^225 - 2^97 + 2 */
678static limb
679felem_is_zero(const felem in)
680{
681 limb zero, two224m96p1, two225m97p2;
682
683 zero = in[0] | in[1] | in[2] | in[3];
684 zero = (((int64_t) (zero) - 1) >> 63) & 1;
685 two224m96p1 = (in[0] ^ 1) | (in[1] ^ 0x00ffff0000000000)
686 | (in[2] ^ 0x00ffffffffffffff) | (in[3] ^ 0x00ffffffffffffff);
687 two224m96p1 = (((int64_t) (two224m96p1) - 1) >> 63) & 1;
688 two225m97p2 = (in[0] ^ 2) | (in[1] ^ 0x00fffe0000000000)
689 | (in[2] ^ 0x00ffffffffffffff) | (in[3] ^ 0x01ffffffffffffff);
690 two225m97p2 = (((int64_t) (two225m97p2) - 1) >> 63) & 1;
691 return (zero | two224m96p1 | two225m97p2);
692}
693
694static limb
695felem_is_zero_int(const felem in)
696{
697 return (int) (felem_is_zero(in) & ((limb) 1));
698}
699
700/* Invert a field element */
701/* Computation chain copied from djb's code */
702static void
703felem_inv(felem out, const felem in)
704{
705 felem ftmp, ftmp2, ftmp3, ftmp4;
706 widefelem tmp;
707 unsigned i;
708
709 felem_square(tmp, in);
710 felem_reduce(ftmp, tmp);/* 2 */
711 felem_mul(tmp, in, ftmp);
712 felem_reduce(ftmp, tmp);/* 2^2 - 1 */
713 felem_square(tmp, ftmp);
714 felem_reduce(ftmp, tmp);/* 2^3 - 2 */
715 felem_mul(tmp, in, ftmp);
716 felem_reduce(ftmp, tmp);/* 2^3 - 1 */
717 felem_square(tmp, ftmp);
718 felem_reduce(ftmp2, tmp); /* 2^4 - 2 */
719 felem_square(tmp, ftmp2);
720 felem_reduce(ftmp2, tmp); /* 2^5 - 4 */
721 felem_square(tmp, ftmp2);
722 felem_reduce(ftmp2, tmp); /* 2^6 - 8 */
723 felem_mul(tmp, ftmp2, ftmp);
724 felem_reduce(ftmp, tmp);/* 2^6 - 1 */
725 felem_square(tmp, ftmp);
726 felem_reduce(ftmp2, tmp); /* 2^7 - 2 */
727 for (i = 0; i < 5; ++i) { /* 2^12 - 2^6 */
728 felem_square(tmp, ftmp2);
729 felem_reduce(ftmp2, tmp);
730 }
731 felem_mul(tmp, ftmp2, ftmp);
732 felem_reduce(ftmp2, tmp); /* 2^12 - 1 */
733 felem_square(tmp, ftmp2);
734 felem_reduce(ftmp3, tmp); /* 2^13 - 2 */
735 for (i = 0; i < 11; ++i) { /* 2^24 - 2^12 */
736 felem_square(tmp, ftmp3);
737 felem_reduce(ftmp3, tmp);
738 }
739 felem_mul(tmp, ftmp3, ftmp2);
740 felem_reduce(ftmp2, tmp); /* 2^24 - 1 */
741 felem_square(tmp, ftmp2);
742 felem_reduce(ftmp3, tmp); /* 2^25 - 2 */
743 for (i = 0; i < 23; ++i) { /* 2^48 - 2^24 */
744 felem_square(tmp, ftmp3);
745 felem_reduce(ftmp3, tmp);
746 }
747 felem_mul(tmp, ftmp3, ftmp2);
748 felem_reduce(ftmp3, tmp); /* 2^48 - 1 */
749 felem_square(tmp, ftmp3);
750 felem_reduce(ftmp4, tmp); /* 2^49 - 2 */
751 for (i = 0; i < 47; ++i) { /* 2^96 - 2^48 */
752 felem_square(tmp, ftmp4);
753 felem_reduce(ftmp4, tmp);
754 }
755 felem_mul(tmp, ftmp3, ftmp4);
756 felem_reduce(ftmp3, tmp); /* 2^96 - 1 */
757 felem_square(tmp, ftmp3);
758 felem_reduce(ftmp4, tmp); /* 2^97 - 2 */
759 for (i = 0; i < 23; ++i) { /* 2^120 - 2^24 */
760 felem_square(tmp, ftmp4);
761 felem_reduce(ftmp4, tmp);
762 }
763 felem_mul(tmp, ftmp2, ftmp4);
764 felem_reduce(ftmp2, tmp); /* 2^120 - 1 */
765 for (i = 0; i < 6; ++i) { /* 2^126 - 2^6 */
766 felem_square(tmp, ftmp2);
767 felem_reduce(ftmp2, tmp);
768 }
769 felem_mul(tmp, ftmp2, ftmp);
770 felem_reduce(ftmp, tmp);/* 2^126 - 1 */
771 felem_square(tmp, ftmp);
772 felem_reduce(ftmp, tmp);/* 2^127 - 2 */
773 felem_mul(tmp, ftmp, in);
774 felem_reduce(ftmp, tmp);/* 2^127 - 1 */
775 for (i = 0; i < 97; ++i) { /* 2^224 - 2^97 */
776 felem_square(tmp, ftmp);
777 felem_reduce(ftmp, tmp);
778 }
779 felem_mul(tmp, ftmp, ftmp3);
780 felem_reduce(out, tmp); /* 2^224 - 2^96 - 1 */
781}
782
783/* Copy in constant time:
784 * if icopy == 1, copy in to out,
785 * if icopy == 0, copy out to itself. */
786static void
787copy_conditional(felem out, const felem in, limb icopy)
788{
789 unsigned i;
790 /* icopy is a (64-bit) 0 or 1, so copy is either all-zero or all-one */
791 const limb copy = -icopy;
792 for (i = 0; i < 4; ++i) {
793 const limb tmp = copy & (in[i] ^ out[i]);
794 out[i] ^= tmp;
795 }
796}
797
798/******************************************************************************/
799/* ELLIPTIC CURVE POINT OPERATIONS
800 *
801 * Points are represented in Jacobian projective coordinates:
802 * (X, Y, Z) corresponds to the affine point (X/Z^2, Y/Z^3),
803 * or to the point at infinity if Z == 0.
804 *
805 */
806
807/* Double an elliptic curve point:
808 * (X', Y', Z') = 2 * (X, Y, Z), where
809 * X' = (3 * (X - Z^2) * (X + Z^2))^2 - 8 * X * Y^2
810 * Y' = 3 * (X - Z^2) * (X + Z^2) * (4 * X * Y^2 - X') - 8 * Y^2
811 * Z' = (Y + Z)^2 - Y^2 - Z^2 = 2 * Y * Z
812 * Outputs can equal corresponding inputs, i.e., x_out == x_in is allowed,
813 * while x_out == y_in is not (maybe this works, but it's not tested). */
814static void
815point_double(felem x_out, felem y_out, felem z_out,
816 const felem x_in, const felem y_in, const felem z_in)
817{
818 widefelem tmp, tmp2;
819 felem delta, gamma, beta, alpha, ftmp, ftmp2;
820
821 felem_assign(ftmp, x_in);
822 felem_assign(ftmp2, x_in);
823
824 /* delta = z^2 */
825 felem_square(tmp, z_in);
826 felem_reduce(delta, tmp);
827
828 /* gamma = y^2 */
829 felem_square(tmp, y_in);
830 felem_reduce(gamma, tmp);
831
832 /* beta = x*gamma */
833 felem_mul(tmp, x_in, gamma);
834 felem_reduce(beta, tmp);
835
836 /* alpha = 3*(x-delta)*(x+delta) */
837 felem_diff(ftmp, delta);
838 /* ftmp[i] < 2^57 + 2^58 + 2 < 2^59 */
839 felem_sum(ftmp2, delta);
840 /* ftmp2[i] < 2^57 + 2^57 = 2^58 */
841 felem_scalar(ftmp2, 3);
842 /* ftmp2[i] < 3 * 2^58 < 2^60 */
843 felem_mul(tmp, ftmp, ftmp2);
844 /* tmp[i] < 2^60 * 2^59 * 4 = 2^121 */
845 felem_reduce(alpha, tmp);
846
847 /* x' = alpha^2 - 8*beta */
848 felem_square(tmp, alpha);
849 /* tmp[i] < 4 * 2^57 * 2^57 = 2^116 */
850 felem_assign(ftmp, beta);
851 felem_scalar(ftmp, 8);
852 /* ftmp[i] < 8 * 2^57 = 2^60 */
853 felem_diff_128_64(tmp, ftmp);
854 /* tmp[i] < 2^116 + 2^64 + 8 < 2^117 */
855 felem_reduce(x_out, tmp);
856
857 /* z' = (y + z)^2 - gamma - delta */
858 felem_sum(delta, gamma);
859 /* delta[i] < 2^57 + 2^57 = 2^58 */
860 felem_assign(ftmp, y_in);
861 felem_sum(ftmp, z_in);
862 /* ftmp[i] < 2^57 + 2^57 = 2^58 */
863 felem_square(tmp, ftmp);
864 /* tmp[i] < 4 * 2^58 * 2^58 = 2^118 */
865 felem_diff_128_64(tmp, delta);
866 /* tmp[i] < 2^118 + 2^64 + 8 < 2^119 */
867 felem_reduce(z_out, tmp);
868
869 /* y' = alpha*(4*beta - x') - 8*gamma^2 */
870 felem_scalar(beta, 4);
871 /* beta[i] < 4 * 2^57 = 2^59 */
872 felem_diff(beta, x_out);
873 /* beta[i] < 2^59 + 2^58 + 2 < 2^60 */
874 felem_mul(tmp, alpha, beta);
875 /* tmp[i] < 4 * 2^57 * 2^60 = 2^119 */
876 felem_square(tmp2, gamma);
877 /* tmp2[i] < 4 * 2^57 * 2^57 = 2^116 */
878 widefelem_scalar(tmp2, 8);
879 /* tmp2[i] < 8 * 2^116 = 2^119 */
880 widefelem_diff(tmp, tmp2);
881 /* tmp[i] < 2^119 + 2^120 < 2^121 */
882 felem_reduce(y_out, tmp);
883}
884
885/* Add two elliptic curve points:
886 * (X_1, Y_1, Z_1) + (X_2, Y_2, Z_2) = (X_3, Y_3, Z_3), where
887 * X_3 = (Z_1^3 * Y_2 - Z_2^3 * Y_1)^2 - (Z_1^2 * X_2 - Z_2^2 * X_1)^3 -
888 * 2 * Z_2^2 * X_1 * (Z_1^2 * X_2 - Z_2^2 * X_1)^2
889 * Y_3 = (Z_1^3 * Y_2 - Z_2^3 * Y_1) * (Z_2^2 * X_1 * (Z_1^2 * X_2 - Z_2^2 * X_1)^2 - X_3) -
890 * Z_2^3 * Y_1 * (Z_1^2 * X_2 - Z_2^2 * X_1)^3
891 * Z_3 = (Z_1^2 * X_2 - Z_2^2 * X_1) * (Z_1 * Z_2)
892 *
893 * This runs faster if 'mixed' is set, which requires Z_2 = 1 or Z_2 = 0.
894 */
895
896/* This function is not entirely constant-time:
897 * it includes a branch for checking whether the two input points are equal,
898 * (while not equal to the point at infinity).
899 * This case never happens during single point multiplication,
900 * so there is no timing leak for ECDH or ECDSA signing. */
901static void
902point_add(felem x3, felem y3, felem z3,
903 const felem x1, const felem y1, const felem z1,
904 const int mixed, const felem x2, const felem y2, const felem z2)
905{
906 felem ftmp, ftmp2, ftmp3, ftmp4, ftmp5, x_out, y_out, z_out;
907 widefelem tmp, tmp2;
908 limb z1_is_zero, z2_is_zero, x_equal, y_equal;
909
910 if (!mixed) {
911 /* ftmp2 = z2^2 */
912 felem_square(tmp, z2);
913 felem_reduce(ftmp2, tmp);
914
915 /* ftmp4 = z2^3 */
916 felem_mul(tmp, ftmp2, z2);
917 felem_reduce(ftmp4, tmp);
918
919 /* ftmp4 = z2^3*y1 */
920 felem_mul(tmp2, ftmp4, y1);
921 felem_reduce(ftmp4, tmp2);
922
923 /* ftmp2 = z2^2*x1 */
924 felem_mul(tmp2, ftmp2, x1);
925 felem_reduce(ftmp2, tmp2);
926 } else {
927 /* We'll assume z2 = 1 (special case z2 = 0 is handled later) */
928
929 /* ftmp4 = z2^3*y1 */
930 felem_assign(ftmp4, y1);
931
932 /* ftmp2 = z2^2*x1 */
933 felem_assign(ftmp2, x1);
934 }
935
936 /* ftmp = z1^2 */
937 felem_square(tmp, z1);
938 felem_reduce(ftmp, tmp);
939
940 /* ftmp3 = z1^3 */
941 felem_mul(tmp, ftmp, z1);
942 felem_reduce(ftmp3, tmp);
943
944 /* tmp = z1^3*y2 */
945 felem_mul(tmp, ftmp3, y2);
946 /* tmp[i] < 4 * 2^57 * 2^57 = 2^116 */
947
948 /* ftmp3 = z1^3*y2 - z2^3*y1 */
949 felem_diff_128_64(tmp, ftmp4);
950 /* tmp[i] < 2^116 + 2^64 + 8 < 2^117 */
951 felem_reduce(ftmp3, tmp);
952
953 /* tmp = z1^2*x2 */
954 felem_mul(tmp, ftmp, x2);
955 /* tmp[i] < 4 * 2^57 * 2^57 = 2^116 */
956
957 /* ftmp = z1^2*x2 - z2^2*x1 */
958 felem_diff_128_64(tmp, ftmp2);
959 /* tmp[i] < 2^116 + 2^64 + 8 < 2^117 */
960 felem_reduce(ftmp, tmp);
961
962 /*
963 * the formulae are incorrect if the points are equal so we check for
964 * this and do doubling if this happens
965 */
966 x_equal = felem_is_zero(ftmp);
967 y_equal = felem_is_zero(ftmp3);
968 z1_is_zero = felem_is_zero(z1);
969 z2_is_zero = felem_is_zero(z2);
970 /* In affine coordinates, (X_1, Y_1) == (X_2, Y_2) */
971 if (x_equal && y_equal && !z1_is_zero && !z2_is_zero) {
972 point_double(x3, y3, z3, x1, y1, z1);
973 return;
974 }
975 /* ftmp5 = z1*z2 */
976 if (!mixed) {
977 felem_mul(tmp, z1, z2);
978 felem_reduce(ftmp5, tmp);
979 } else {
980 /* special case z2 = 0 is handled later */
981 felem_assign(ftmp5, z1);
982 }
983
984 /* z_out = (z1^2*x2 - z2^2*x1)*(z1*z2) */
985 felem_mul(tmp, ftmp, ftmp5);
986 felem_reduce(z_out, tmp);
987
988 /* ftmp = (z1^2*x2 - z2^2*x1)^2 */
989 felem_assign(ftmp5, ftmp);
990 felem_square(tmp, ftmp);
991 felem_reduce(ftmp, tmp);
992
993 /* ftmp5 = (z1^2*x2 - z2^2*x1)^3 */
994 felem_mul(tmp, ftmp, ftmp5);
995 felem_reduce(ftmp5, tmp);
996
997 /* ftmp2 = z2^2*x1*(z1^2*x2 - z2^2*x1)^2 */
998 felem_mul(tmp, ftmp2, ftmp);
999 felem_reduce(ftmp2, tmp);
1000
1001 /* tmp = z2^3*y1*(z1^2*x2 - z2^2*x1)^3 */
1002 felem_mul(tmp, ftmp4, ftmp5);
1003 /* tmp[i] < 4 * 2^57 * 2^57 = 2^116 */
1004
1005 /* tmp2 = (z1^3*y2 - z2^3*y1)^2 */
1006 felem_square(tmp2, ftmp3);
1007 /* tmp2[i] < 4 * 2^57 * 2^57 < 2^116 */
1008
1009 /* tmp2 = (z1^3*y2 - z2^3*y1)^2 - (z1^2*x2 - z2^2*x1)^3 */
1010 felem_diff_128_64(tmp2, ftmp5);
1011 /* tmp2[i] < 2^116 + 2^64 + 8 < 2^117 */
1012
1013 /* ftmp5 = 2*z2^2*x1*(z1^2*x2 - z2^2*x1)^2 */
1014 felem_assign(ftmp5, ftmp2);
1015 felem_scalar(ftmp5, 2);
1016 /* ftmp5[i] < 2 * 2^57 = 2^58 */
1017
1018 /*
1019 * x_out = (z1^3*y2 - z2^3*y1)^2 - (z1^2*x2 - z2^2*x1)^3 -
1020 * 2*z2^2*x1*(z1^2*x2 - z2^2*x1)^2
1021 */
1022 felem_diff_128_64(tmp2, ftmp5);
1023 /* tmp2[i] < 2^117 + 2^64 + 8 < 2^118 */
1024 felem_reduce(x_out, tmp2);
1025
1026 /* ftmp2 = z2^2*x1*(z1^2*x2 - z2^2*x1)^2 - x_out */
1027 felem_diff(ftmp2, x_out);
1028 /* ftmp2[i] < 2^57 + 2^58 + 2 < 2^59 */
1029
1030 /* tmp2 = (z1^3*y2 - z2^3*y1)*(z2^2*x1*(z1^2*x2 - z2^2*x1)^2 - x_out) */
1031 felem_mul(tmp2, ftmp3, ftmp2);
1032 /* tmp2[i] < 4 * 2^57 * 2^59 = 2^118 */
1033
1034 /*
1035 * y_out = (z1^3*y2 - z2^3*y1)*(z2^2*x1*(z1^2*x2 - z2^2*x1)^2 -
1036 * x_out) - z2^3*y1*(z1^2*x2 - z2^2*x1)^3
1037 */
1038 widefelem_diff(tmp2, tmp);
1039 /* tmp2[i] < 2^118 + 2^120 < 2^121 */
1040 felem_reduce(y_out, tmp2);
1041
1042 /*
1043 * the result (x_out, y_out, z_out) is incorrect if one of the inputs
1044 * is the point at infinity, so we need to check for this separately
1045 */
1046
1047 /* if point 1 is at infinity, copy point 2 to output, and vice versa */
1048 copy_conditional(x_out, x2, z1_is_zero);
1049 copy_conditional(x_out, x1, z2_is_zero);
1050 copy_conditional(y_out, y2, z1_is_zero);
1051 copy_conditional(y_out, y1, z2_is_zero);
1052 copy_conditional(z_out, z2, z1_is_zero);
1053 copy_conditional(z_out, z1, z2_is_zero);
1054 felem_assign(x3, x_out);
1055 felem_assign(y3, y_out);
1056 felem_assign(z3, z_out);
1057}
1058
1059/* select_point selects the |idx|th point from a precomputation table and
1060 * copies it to out. */
1061static void
1062select_point(const u64 idx, unsigned int size, const felem pre_comp[ /* size */ ][3], felem out[3])
1063{
1064 unsigned i, j;
1065 limb *outlimbs = &out[0][0];
1066 memset(outlimbs, 0, 3 * sizeof(felem));
1067
1068 for (i = 0; i < size; i++) {
1069 const limb *inlimbs = &pre_comp[i][0][0];
1070 u64 mask = i ^ idx;
1071 mask |= mask >> 4;
1072 mask |= mask >> 2;
1073 mask |= mask >> 1;
1074 mask &= 1;
1075 mask--;
1076 for (j = 0; j < 4 * 3; j++)
1077 outlimbs[j] |= inlimbs[j] & mask;
1078 }
1079}
1080
1081/* get_bit returns the |i|th bit in |in| */
1082static char
1083get_bit(const felem_bytearray in, unsigned i)
1084{
1085 if (i >= 224)
1086 return 0;
1087 return (in[i >> 3] >> (i & 7)) & 1;
1088}
1089
1090/* Interleaved point multiplication using precomputed point multiples:
1091 * The small point multiples 0*P, 1*P, ..., 16*P are in pre_comp[],
1092 * the scalars in scalars[]. If g_scalar is non-NULL, we also add this multiple
1093 * of the generator, using certain (large) precomputed multiples in g_pre_comp.
1094 * Output point (X, Y, Z) is stored in x_out, y_out, z_out */
1095static void
1096batch_mul(felem x_out, felem y_out, felem z_out,
1097 const felem_bytearray scalars[], const unsigned num_points, const u8 * g_scalar,
1098 const int mixed, const felem pre_comp[][17][3], const felem g_pre_comp[2][16][3])
1099{
1100 int i, skip;
1101 unsigned num;
1102 unsigned gen_mul = (g_scalar != NULL);
1103 felem nq[3], tmp[4];
1104 u64 bits;
1105 u8 sign, digit;
1106
1107 /* set nq to the point at infinity */
1108 memset(nq, 0, 3 * sizeof(felem));
1109
1110 /*
1111 * Loop over all scalars msb-to-lsb, interleaving additions of
1112 * multiples of the generator (two in each of the last 28 rounds) and
1113 * additions of other points multiples (every 5th round).
1114 */
1115 skip = 1; /* save two point operations in the first
1116 * round */
1117 for (i = (num_points ? 220 : 27); i >= 0; --i) {
1118 /* double */
1119 if (!skip)
1120 point_double(nq[0], nq[1], nq[2], nq[0], nq[1], nq[2]);
1121
1122 /* add multiples of the generator */
1123 if (gen_mul && (i <= 27)) {
1124 /* first, look 28 bits upwards */
1125 bits = get_bit(g_scalar, i + 196) << 3;
1126 bits |= get_bit(g_scalar, i + 140) << 2;
1127 bits |= get_bit(g_scalar, i + 84) << 1;
1128 bits |= get_bit(g_scalar, i + 28);
1129 /* select the point to add, in constant time */
1130 select_point(bits, 16, g_pre_comp[1], tmp);
1131
1132 if (!skip) {
1133 point_add(nq[0], nq[1], nq[2],
1134 nq[0], nq[1], nq[2],
1135 1 /* mixed */ , tmp[0], tmp[1], tmp[2]);
1136 } else {
1137 memcpy(nq, tmp, 3 * sizeof(felem));
1138 skip = 0;
1139 }
1140
1141 /* second, look at the current position */
1142 bits = get_bit(g_scalar, i + 168) << 3;
1143 bits |= get_bit(g_scalar, i + 112) << 2;
1144 bits |= get_bit(g_scalar, i + 56) << 1;
1145 bits |= get_bit(g_scalar, i);
1146 /* select the point to add, in constant time */
1147 select_point(bits, 16, g_pre_comp[0], tmp);
1148 point_add(nq[0], nq[1], nq[2],
1149 nq[0], nq[1], nq[2],
1150 1 /* mixed */ , tmp[0], tmp[1], tmp[2]);
1151 }
1152 /* do other additions every 5 doublings */
1153 if (num_points && (i % 5 == 0)) {
1154 /* loop over all scalars */
1155 for (num = 0; num < num_points; ++num) {
1156 bits = get_bit(scalars[num], i + 4) << 5;
1157 bits |= get_bit(scalars[num], i + 3) << 4;
1158 bits |= get_bit(scalars[num], i + 2) << 3;
1159 bits |= get_bit(scalars[num], i + 1) << 2;
1160 bits |= get_bit(scalars[num], i) << 1;
1161 bits |= get_bit(scalars[num], i - 1);
1162 ec_GFp_nistp_recode_scalar_bits(&sign, &digit, bits);
1163
1164 /* select the point to add or subtract */
1165 select_point(digit, 17, pre_comp[num], tmp);
1166 felem_neg(tmp[3], tmp[1]); /* (X, -Y, Z) is the
1167 * negative point */
1168 copy_conditional(tmp[1], tmp[3], sign);
1169
1170 if (!skip) {
1171 point_add(nq[0], nq[1], nq[2],
1172 nq[0], nq[1], nq[2],
1173 mixed, tmp[0], tmp[1], tmp[2]);
1174 } else {
1175 memcpy(nq, tmp, 3 * sizeof(felem));
1176 skip = 0;
1177 }
1178 }
1179 }
1180 }
1181 felem_assign(x_out, nq[0]);
1182 felem_assign(y_out, nq[1]);
1183 felem_assign(z_out, nq[2]);
1184}
1185
1186/******************************************************************************/
1187/* FUNCTIONS TO MANAGE PRECOMPUTATION
1188 */
1189
1190static NISTP224_PRE_COMP *
1191nistp224_pre_comp_new()
1192{
1193 NISTP224_PRE_COMP *ret = NULL;
1194 ret = malloc(sizeof *ret);
1195 if (!ret) {
1196 ECerror(ERR_R_MALLOC_FAILURE);
1197 return ret;
1198 }
1199 memset(ret->g_pre_comp, 0, sizeof(ret->g_pre_comp));
1200 ret->references = 1;
1201 return ret;
1202}
1203
1204static void *
1205nistp224_pre_comp_dup(void *src_)
1206{
1207 NISTP224_PRE_COMP *src = src_;
1208
1209 /* no need to actually copy, these objects never change! */
1210 CRYPTO_add(&src->references, 1, CRYPTO_LOCK_EC_PRE_COMP);
1211
1212 return src_;
1213}
1214
1215static void
1216nistp224_pre_comp_free(void *pre_)
1217{
1218 int i;
1219 NISTP224_PRE_COMP *pre = pre_;
1220
1221 if (!pre)
1222 return;
1223
1224 i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP);
1225 if (i > 0)
1226 return;
1227
1228 free(pre);
1229}
1230
1231static void
1232nistp224_pre_comp_clear_free(void *pre_)
1233{
1234 int i;
1235 NISTP224_PRE_COMP *pre = pre_;
1236
1237 if (!pre)
1238 return;
1239
1240 i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP);
1241 if (i > 0)
1242 return;
1243
1244 freezero(pre, sizeof *pre);
1245}
1246
1247/******************************************************************************/
1248/* OPENSSL EC_METHOD FUNCTIONS
1249 */
1250
1251int
1252ec_GFp_nistp224_group_init(EC_GROUP *group)
1253{
1254 int ret;
1255 ret = ec_GFp_simple_group_init(group);
1256 group->a_is_minus3 = 1;
1257 return ret;
1258}
1259
1260int
1261ec_GFp_nistp224_group_set_curve(EC_GROUP *group, const BIGNUM *p,
1262 const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
1263{
1264 int ret = 0;
1265 BN_CTX *new_ctx = NULL;
1266 BIGNUM *curve_p, *curve_a, *curve_b;
1267
1268 if (ctx == NULL)
1269 if ((ctx = new_ctx = BN_CTX_new()) == NULL)
1270 return 0;
1271 BN_CTX_start(ctx);
1272 if (((curve_p = BN_CTX_get(ctx)) == NULL) ||
1273 ((curve_a = BN_CTX_get(ctx)) == NULL) ||
1274 ((curve_b = BN_CTX_get(ctx)) == NULL))
1275 goto err;
1276 BN_bin2bn(nistp224_curve_params[0], sizeof(felem_bytearray), curve_p);
1277 BN_bin2bn(nistp224_curve_params[1], sizeof(felem_bytearray), curve_a);
1278 BN_bin2bn(nistp224_curve_params[2], sizeof(felem_bytearray), curve_b);
1279 if ((BN_cmp(curve_p, p)) || (BN_cmp(curve_a, a)) ||
1280 (BN_cmp(curve_b, b))) {
1281 ECerror(EC_R_WRONG_CURVE_PARAMETERS);
1282 goto err;
1283 }
1284 group->field_mod_func = BN_nist_mod_224;
1285 ret = ec_GFp_simple_group_set_curve(group, p, a, b, ctx);
1286 err:
1287 BN_CTX_end(ctx);
1288 BN_CTX_free(new_ctx);
1289 return ret;
1290}
1291
1292/* Takes the Jacobian coordinates (X, Y, Z) of a point and returns
1293 * (X', Y') = (X/Z^2, Y/Z^3) */
1294int
1295ec_GFp_nistp224_point_get_affine_coordinates(const EC_GROUP *group,
1296 const EC_POINT *point, BIGNUM *x, BIGNUM *y, BN_CTX *ctx)
1297{
1298 felem z1, z2, x_in, y_in, x_out, y_out;
1299 widefelem tmp;
1300
1301 if (EC_POINT_is_at_infinity(group, point) > 0) {
1302 ECerror(EC_R_POINT_AT_INFINITY);
1303 return 0;
1304 }
1305 if ((!BN_to_felem(x_in, &point->X)) || (!BN_to_felem(y_in, &point->Y)) ||
1306 (!BN_to_felem(z1, &point->Z)))
1307 return 0;
1308 felem_inv(z2, z1);
1309 felem_square(tmp, z2);
1310 felem_reduce(z1, tmp);
1311 felem_mul(tmp, x_in, z1);
1312 felem_reduce(x_in, tmp);
1313 felem_contract(x_out, x_in);
1314 if (x != NULL) {
1315 if (!felem_to_BN(x, x_out)) {
1316 ECerror(ERR_R_BN_LIB);
1317 return 0;
1318 }
1319 }
1320 felem_mul(tmp, z1, z2);
1321 felem_reduce(z1, tmp);
1322 felem_mul(tmp, y_in, z1);
1323 felem_reduce(y_in, tmp);
1324 felem_contract(y_out, y_in);
1325 if (y != NULL) {
1326 if (!felem_to_BN(y, y_out)) {
1327 ECerror(ERR_R_BN_LIB);
1328 return 0;
1329 }
1330 }
1331 return 1;
1332}
1333
1334static void
1335make_points_affine(size_t num, felem points[ /* num */ ][3], felem tmp_felems[ /* num+1 */ ])
1336{
1337 /*
1338 * Runs in constant time, unless an input is the point at infinity
1339 * (which normally shouldn't happen).
1340 */
1341 ec_GFp_nistp_points_make_affine_internal(
1342 num,
1343 points,
1344 sizeof(felem),
1345 tmp_felems,
1346 (void (*) (void *)) felem_one,
1347 (int (*) (const void *)) felem_is_zero_int,
1348 (void (*) (void *, const void *)) felem_assign,
1349 (void (*) (void *, const void *)) felem_square_reduce,
1350 (void (*) (void *, const void *, const void *)) felem_mul_reduce,
1351 (void (*) (void *, const void *)) felem_inv,
1352 (void (*) (void *, const void *)) felem_contract);
1353}
1354
1355/* Computes scalar*generator + \sum scalars[i]*points[i], ignoring NULL values
1356 * Result is stored in r (r can equal one of the inputs). */
1357int
1358ec_GFp_nistp224_points_mul(const EC_GROUP *group, EC_POINT *r,
1359 const BIGNUM *scalar, size_t num, const EC_POINT *points[],
1360 const BIGNUM *scalars[], BN_CTX *ctx)
1361{
1362 int ret = 0;
1363 int j;
1364 unsigned i;
1365 int mixed = 0;
1366 BN_CTX *new_ctx = NULL;
1367 BIGNUM *x, *y, *z, *tmp_scalar;
1368 felem_bytearray g_secret;
1369 felem_bytearray *secrets = NULL;
1370 felem(*pre_comp)[17][3] = NULL;
1371 felem *tmp_felems = NULL;
1372 felem_bytearray tmp;
1373 unsigned num_bytes;
1374 int have_pre_comp = 0;
1375 size_t num_points = num;
1376 felem x_in, y_in, z_in, x_out, y_out, z_out;
1377 NISTP224_PRE_COMP *pre = NULL;
1378 const felem(*g_pre_comp)[16][3] = NULL;
1379 EC_POINT *generator = NULL;
1380 const EC_POINT *p = NULL;
1381 const BIGNUM *p_scalar = NULL;
1382
1383 if (ctx == NULL)
1384 if ((ctx = new_ctx = BN_CTX_new()) == NULL)
1385 return 0;
1386 BN_CTX_start(ctx);
1387 if (((x = BN_CTX_get(ctx)) == NULL) ||
1388 ((y = BN_CTX_get(ctx)) == NULL) ||
1389 ((z = BN_CTX_get(ctx)) == NULL) ||
1390 ((tmp_scalar = BN_CTX_get(ctx)) == NULL))
1391 goto err;
1392
1393 if (scalar != NULL) {
1394 pre = EC_EX_DATA_get_data(group->extra_data,
1395 nistp224_pre_comp_dup, nistp224_pre_comp_free,
1396 nistp224_pre_comp_clear_free);
1397 if (pre)
1398 /* we have precomputation, try to use it */
1399 g_pre_comp = (const felem(*)[16][3]) pre->g_pre_comp;
1400 else
1401 /* try to use the standard precomputation */
1402 g_pre_comp = &gmul[0];
1403 generator = EC_POINT_new(group);
1404 if (generator == NULL)
1405 goto err;
1406 /* get the generator from precomputation */
1407 if (!felem_to_BN(x, g_pre_comp[0][1][0]) ||
1408 !felem_to_BN(y, g_pre_comp[0][1][1]) ||
1409 !felem_to_BN(z, g_pre_comp[0][1][2])) {
1410 ECerror(ERR_R_BN_LIB);
1411 goto err;
1412 }
1413 if (!EC_POINT_set_Jprojective_coordinates(group, generator,
1414 x, y, z, ctx))
1415 goto err;
1416 if (0 == EC_POINT_cmp(group, generator, group->generator, ctx))
1417 /* precomputation matches generator */
1418 have_pre_comp = 1;
1419 else
1420 /*
1421 * we don't have valid precomputation: treat the
1422 * generator as a random point
1423 */
1424 num_points = num_points + 1;
1425 }
1426 if (num_points > 0) {
1427 if (num_points >= 3) {
1428 /*
1429 * unless we precompute multiples for just one or two
1430 * points, converting those into affine form is time
1431 * well spent
1432 */
1433 mixed = 1;
1434 }
1435 secrets = calloc(num_points, sizeof(felem_bytearray));
1436 pre_comp = calloc(num_points, 17 * 3 * sizeof(felem));
1437 if (mixed) {
1438 /* XXX should do more int overflow checking */
1439 tmp_felems = reallocarray(NULL,
1440 (num_points * 17 + 1), sizeof(felem));
1441 }
1442 if ((secrets == NULL) || (pre_comp == NULL) || (mixed && (tmp_felems == NULL))) {
1443 ECerror(ERR_R_MALLOC_FAILURE);
1444 goto err;
1445 }
1446 /*
1447 * we treat NULL scalars as 0, and NULL points as points at
1448 * infinity, i.e., they contribute nothing to the linear
1449 * combination
1450 */
1451 for (i = 0; i < num_points; ++i) {
1452 if (i == num)
1453 /* the generator */
1454 {
1455 p = EC_GROUP_get0_generator(group);
1456 p_scalar = scalar;
1457 } else
1458 /* the i^th point */
1459 {
1460 p = points[i];
1461 p_scalar = scalars[i];
1462 }
1463 if ((p_scalar != NULL) && (p != NULL)) {
1464 /* reduce scalar to 0 <= scalar < 2^224 */
1465 if ((BN_num_bits(p_scalar) > 224) || (BN_is_negative(p_scalar))) {
1466 /*
1467 * this is an unusual input, and we
1468 * don't guarantee constant-timeness
1469 */
1470 if (!BN_nnmod(tmp_scalar, p_scalar, &group->order, ctx)) {
1471 ECerror(ERR_R_BN_LIB);
1472 goto err;
1473 }
1474 num_bytes = BN_bn2bin(tmp_scalar, tmp);
1475 } else
1476 num_bytes = BN_bn2bin(p_scalar, tmp);
1477 flip_endian(secrets[i], tmp, num_bytes);
1478 /* precompute multiples */
1479 if ((!BN_to_felem(x_out, &p->X)) ||
1480 (!BN_to_felem(y_out, &p->Y)) ||
1481 (!BN_to_felem(z_out, &p->Z)))
1482 goto err;
1483 felem_assign(pre_comp[i][1][0], x_out);
1484 felem_assign(pre_comp[i][1][1], y_out);
1485 felem_assign(pre_comp[i][1][2], z_out);
1486 for (j = 2; j <= 16; ++j) {
1487 if (j & 1) {
1488 point_add(
1489 pre_comp[i][j][0], pre_comp[i][j][1], pre_comp[i][j][2],
1490 pre_comp[i][1][0], pre_comp[i][1][1], pre_comp[i][1][2],
1491 0, pre_comp[i][j - 1][0], pre_comp[i][j - 1][1], pre_comp[i][j - 1][2]);
1492 } else {
1493 point_double(
1494 pre_comp[i][j][0], pre_comp[i][j][1], pre_comp[i][j][2],
1495 pre_comp[i][j / 2][0], pre_comp[i][j / 2][1], pre_comp[i][j / 2][2]);
1496 }
1497 }
1498 }
1499 }
1500 if (mixed)
1501 make_points_affine(num_points * 17, pre_comp[0], tmp_felems);
1502 }
1503 /* the scalar for the generator */
1504 if ((scalar != NULL) && (have_pre_comp)) {
1505 memset(g_secret, 0, sizeof g_secret);
1506 /* reduce scalar to 0 <= scalar < 2^224 */
1507 if ((BN_num_bits(scalar) > 224) || (BN_is_negative(scalar))) {
1508 /*
1509 * this is an unusual input, and we don't guarantee
1510 * constant-timeness
1511 */
1512 if (!BN_nnmod(tmp_scalar, scalar, &group->order, ctx)) {
1513 ECerror(ERR_R_BN_LIB);
1514 goto err;
1515 }
1516 num_bytes = BN_bn2bin(tmp_scalar, tmp);
1517 } else
1518 num_bytes = BN_bn2bin(scalar, tmp);
1519 flip_endian(g_secret, tmp, num_bytes);
1520 /* do the multiplication with generator precomputation */
1521 batch_mul(x_out, y_out, z_out,
1522 (const felem_bytearray(*)) secrets, num_points,
1523 g_secret,
1524 mixed, (const felem(*)[17][3]) pre_comp,
1525 g_pre_comp);
1526 } else
1527 /* do the multiplication without generator precomputation */
1528 batch_mul(x_out, y_out, z_out,
1529 (const felem_bytearray(*)) secrets, num_points,
1530 NULL, mixed, (const felem(*)[17][3]) pre_comp, NULL);
1531 /* reduce the output to its unique minimal representation */
1532 felem_contract(x_in, x_out);
1533 felem_contract(y_in, y_out);
1534 felem_contract(z_in, z_out);
1535 if ((!felem_to_BN(x, x_in)) || (!felem_to_BN(y, y_in)) ||
1536 (!felem_to_BN(z, z_in))) {
1537 ECerror(ERR_R_BN_LIB);
1538 goto err;
1539 }
1540 ret = EC_POINT_set_Jprojective_coordinates(group, r, x, y, z, ctx);
1541
1542 err:
1543 BN_CTX_end(ctx);
1544 EC_POINT_free(generator);
1545 BN_CTX_free(new_ctx);
1546 free(secrets);
1547 free(pre_comp);
1548 free(tmp_felems);
1549 return ret;
1550}
1551
1552int
1553ec_GFp_nistp224_precompute_mult(EC_GROUP *group, BN_CTX *ctx)
1554{
1555 int ret = 0;
1556 NISTP224_PRE_COMP *pre = NULL;
1557 int i, j;
1558 BN_CTX *new_ctx = NULL;
1559 BIGNUM *x, *y;
1560 EC_POINT *generator = NULL;
1561 felem tmp_felems[32];
1562
1563 /* throw away old precomputation */
1564 EC_EX_DATA_free_data(&group->extra_data, nistp224_pre_comp_dup,
1565 nistp224_pre_comp_free, nistp224_pre_comp_clear_free);
1566 if (ctx == NULL)
1567 if ((ctx = new_ctx = BN_CTX_new()) == NULL)
1568 return 0;
1569 BN_CTX_start(ctx);
1570 if (((x = BN_CTX_get(ctx)) == NULL) ||
1571 ((y = BN_CTX_get(ctx)) == NULL))
1572 goto err;
1573 /* get the generator */
1574 if (group->generator == NULL)
1575 goto err;
1576 generator = EC_POINT_new(group);
1577 if (generator == NULL)
1578 goto err;
1579 BN_bin2bn(nistp224_curve_params[3], sizeof(felem_bytearray), x);
1580 BN_bin2bn(nistp224_curve_params[4], sizeof(felem_bytearray), y);
1581 if (!EC_POINT_set_affine_coordinates(group, generator, x, y, ctx))
1582 goto err;
1583 if ((pre = nistp224_pre_comp_new()) == NULL)
1584 goto err;
1585 /* if the generator is the standard one, use built-in precomputation */
1586 if (0 == EC_POINT_cmp(group, generator, group->generator, ctx)) {
1587 memcpy(pre->g_pre_comp, gmul, sizeof(pre->g_pre_comp));
1588 ret = 1;
1589 goto err;
1590 }
1591 if ((!BN_to_felem(pre->g_pre_comp[0][1][0], &group->generator->X)) ||
1592 (!BN_to_felem(pre->g_pre_comp[0][1][1], &group->generator->Y)) ||
1593 (!BN_to_felem(pre->g_pre_comp[0][1][2], &group->generator->Z)))
1594 goto err;
1595 /*
1596 * compute 2^56*G, 2^112*G, 2^168*G for the first table, 2^28*G,
1597 * 2^84*G, 2^140*G, 2^196*G for the second one
1598 */
1599 for (i = 1; i <= 8; i <<= 1) {
1600 point_double(
1601 pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2],
1602 pre->g_pre_comp[0][i][0], pre->g_pre_comp[0][i][1], pre->g_pre_comp[0][i][2]);
1603 for (j = 0; j < 27; ++j) {
1604 point_double(
1605 pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2],
1606 pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2]);
1607 }
1608 if (i == 8)
1609 break;
1610 point_double(
1611 pre->g_pre_comp[0][2 * i][0], pre->g_pre_comp[0][2 * i][1], pre->g_pre_comp[0][2 * i][2],
1612 pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2]);
1613 for (j = 0; j < 27; ++j) {
1614 point_double(
1615 pre->g_pre_comp[0][2 * i][0], pre->g_pre_comp[0][2 * i][1], pre->g_pre_comp[0][2 * i][2],
1616 pre->g_pre_comp[0][2 * i][0], pre->g_pre_comp[0][2 * i][1], pre->g_pre_comp[0][2 * i][2]);
1617 }
1618 }
1619 for (i = 0; i < 2; i++) {
1620 /* g_pre_comp[i][0] is the point at infinity */
1621 memset(pre->g_pre_comp[i][0], 0, sizeof(pre->g_pre_comp[i][0]));
1622 /* the remaining multiples */
1623 /* 2^56*G + 2^112*G resp. 2^84*G + 2^140*G */
1624 point_add(
1625 pre->g_pre_comp[i][6][0], pre->g_pre_comp[i][6][1],
1626 pre->g_pre_comp[i][6][2], pre->g_pre_comp[i][4][0],
1627 pre->g_pre_comp[i][4][1], pre->g_pre_comp[i][4][2],
1628 0, pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1],
1629 pre->g_pre_comp[i][2][2]);
1630 /* 2^56*G + 2^168*G resp. 2^84*G + 2^196*G */
1631 point_add(
1632 pre->g_pre_comp[i][10][0], pre->g_pre_comp[i][10][1],
1633 pre->g_pre_comp[i][10][2], pre->g_pre_comp[i][8][0],
1634 pre->g_pre_comp[i][8][1], pre->g_pre_comp[i][8][2],
1635 0, pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1],
1636 pre->g_pre_comp[i][2][2]);
1637 /* 2^112*G + 2^168*G resp. 2^140*G + 2^196*G */
1638 point_add(
1639 pre->g_pre_comp[i][12][0], pre->g_pre_comp[i][12][1],
1640 pre->g_pre_comp[i][12][2], pre->g_pre_comp[i][8][0],
1641 pre->g_pre_comp[i][8][1], pre->g_pre_comp[i][8][2],
1642 0, pre->g_pre_comp[i][4][0], pre->g_pre_comp[i][4][1],
1643 pre->g_pre_comp[i][4][2]);
1644 /*
1645 * 2^56*G + 2^112*G + 2^168*G resp. 2^84*G + 2^140*G +
1646 * 2^196*G
1647 */
1648 point_add(
1649 pre->g_pre_comp[i][14][0], pre->g_pre_comp[i][14][1],
1650 pre->g_pre_comp[i][14][2], pre->g_pre_comp[i][12][0],
1651 pre->g_pre_comp[i][12][1], pre->g_pre_comp[i][12][2],
1652 0, pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1],
1653 pre->g_pre_comp[i][2][2]);
1654 for (j = 1; j < 8; ++j) {
1655 /* odd multiples: add G resp. 2^28*G */
1656 point_add(
1657 pre->g_pre_comp[i][2 * j + 1][0], pre->g_pre_comp[i][2 * j + 1][1],
1658 pre->g_pre_comp[i][2 * j + 1][2], pre->g_pre_comp[i][2 * j][0],
1659 pre->g_pre_comp[i][2 * j][1], pre->g_pre_comp[i][2 * j][2],
1660 0, pre->g_pre_comp[i][1][0], pre->g_pre_comp[i][1][1],
1661 pre->g_pre_comp[i][1][2]);
1662 }
1663 }
1664 make_points_affine(31, &(pre->g_pre_comp[0][1]), tmp_felems);
1665
1666 if (!EC_EX_DATA_set_data(&group->extra_data, pre, nistp224_pre_comp_dup,
1667 nistp224_pre_comp_free, nistp224_pre_comp_clear_free))
1668 goto err;
1669 ret = 1;
1670 pre = NULL;
1671 err:
1672 BN_CTX_end(ctx);
1673 EC_POINT_free(generator);
1674 BN_CTX_free(new_ctx);
1675 nistp224_pre_comp_free(pre);
1676 return ret;
1677}
1678
1679int
1680ec_GFp_nistp224_have_precompute_mult(const EC_GROUP *group)
1681{
1682 if (EC_EX_DATA_get_data(group->extra_data, nistp224_pre_comp_dup,
1683 nistp224_pre_comp_free, nistp224_pre_comp_clear_free)
1684 != NULL)
1685 return 1;
1686 else
1687 return 0;
1688}
1689
1690#endif
generated by cgit v1.2.3-55-g6feb (git 2.39.1) at 2025-08-15 19:31:48 +0000