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1/* $OpenBSD: ecp_nistp224.c,v 1.17 2015/09/10 15:56:25 jsing 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_lcl.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 arrary.
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_check_discriminant =
247 ec_GFp_simple_group_check_discriminant,
248 .point_init = ec_GFp_simple_point_init,
249 .point_finish = ec_GFp_simple_point_finish,
250 .point_clear_finish = ec_GFp_simple_point_clear_finish,
251 .point_copy = ec_GFp_simple_point_copy,
252 .point_set_to_infinity = ec_GFp_simple_point_set_to_infinity,
253 .point_set_Jprojective_coordinates_GFp =
254 ec_GFp_simple_set_Jprojective_coordinates_GFp,
255 .point_get_Jprojective_coordinates_GFp =
256 ec_GFp_simple_get_Jprojective_coordinates_GFp,
257 .point_set_affine_coordinates =
258 ec_GFp_simple_point_set_affine_coordinates,
259 .point_get_affine_coordinates =
260 ec_GFp_nistp224_point_get_affine_coordinates,
261 .add = ec_GFp_simple_add,
262 .dbl = ec_GFp_simple_dbl,
263 .invert = ec_GFp_simple_invert,
264 .is_at_infinity = ec_GFp_simple_is_at_infinity,
265 .is_on_curve = ec_GFp_simple_is_on_curve,
266 .point_cmp = ec_GFp_simple_cmp,
267 .make_affine = ec_GFp_simple_make_affine,
268 .points_make_affine = ec_GFp_simple_points_make_affine,
269 .mul = ec_GFp_nistp224_points_mul,
270 .precompute_mult = ec_GFp_nistp224_precompute_mult,
271 .have_precompute_mult = ec_GFp_nistp224_have_precompute_mult,
272 .field_mul = ec_GFp_nist_field_mul,
273 .field_sqr = ec_GFp_nist_field_sqr
274 };
275
276 return &ret;
277}
278
279/* Helper functions to convert field elements to/from internal representation */
280static void
281bin28_to_felem(felem out, const u8 in[28])
282{
283 out[0] = *((const uint64_t *) (in)) & 0x00ffffffffffffff;
284 out[1] = (*((const uint64_t *) (in + 7))) & 0x00ffffffffffffff;
285 out[2] = (*((const uint64_t *) (in + 14))) & 0x00ffffffffffffff;
286 out[3] = (*((const uint64_t *) (in + 21))) & 0x00ffffffffffffff;
287}
288
289static void
290felem_to_bin28(u8 out[28], const felem in)
291{
292 unsigned i;
293 for (i = 0; i < 7; ++i) {
294 out[i] = in[0] >> (8 * i);
295 out[i + 7] = in[1] >> (8 * i);
296 out[i + 14] = in[2] >> (8 * i);
297 out[i + 21] = in[3] >> (8 * i);
298 }
299}
300
301/* To preserve endianness when using BN_bn2bin and BN_bin2bn */
302static void
303flip_endian(u8 * out, const u8 * in, unsigned len)
304{
305 unsigned i;
306 for (i = 0; i < len; ++i)
307 out[i] = in[len - 1 - i];
308}
309
310/* From OpenSSL BIGNUM to internal representation */
311static int
312BN_to_felem(felem out, const BIGNUM * bn)
313{
314 felem_bytearray b_in;
315 felem_bytearray b_out;
316 unsigned num_bytes;
317
318 /* BN_bn2bin eats leading zeroes */
319 memset(b_out, 0, sizeof b_out);
320 num_bytes = BN_num_bytes(bn);
321 if (num_bytes > sizeof b_out) {
322 ECerr(EC_F_BN_TO_FELEM, EC_R_BIGNUM_OUT_OF_RANGE);
323 return 0;
324 }
325 if (BN_is_negative(bn)) {
326 ECerr(EC_F_BN_TO_FELEM, EC_R_BIGNUM_OUT_OF_RANGE);
327 return 0;
328 }
329 num_bytes = BN_bn2bin(bn, b_in);
330 flip_endian(b_out, b_in, num_bytes);
331 bin28_to_felem(out, b_out);
332 return 1;
333}
334
335/* From internal representation to OpenSSL BIGNUM */
336static BIGNUM *
337felem_to_BN(BIGNUM * out, const felem in)
338{
339 felem_bytearray b_in, b_out;
340 felem_to_bin28(b_in, in);
341 flip_endian(b_out, b_in, sizeof b_out);
342 return BN_bin2bn(b_out, sizeof b_out, out);
343}
344
345/******************************************************************************/
346/* FIELD OPERATIONS
347 *
348 * Field operations, using the internal representation of field elements.
349 * NB! These operations are specific to our point multiplication and cannot be
350 * expected to be correct in general - e.g., multiplication with a large scalar
351 * will cause an overflow.
352 *
353 */
354
355static void
356felem_one(felem out)
357{
358 out[0] = 1;
359 out[1] = 0;
360 out[2] = 0;
361 out[3] = 0;
362}
363
364static void
365felem_assign(felem out, const felem in)
366{
367 out[0] = in[0];
368 out[1] = in[1];
369 out[2] = in[2];
370 out[3] = in[3];
371}
372
373/* Sum two field elements: out += in */
374static void
375felem_sum(felem out, const felem in)
376{
377 out[0] += in[0];
378 out[1] += in[1];
379 out[2] += in[2];
380 out[3] += in[3];
381}
382
383/* Get negative value: out = -in */
384/* Assumes in[i] < 2^57 */
385static void
386felem_neg(felem out, const felem in)
387{
388 static const limb two58p2 = (((limb) 1) << 58) + (((limb) 1) << 2);
389 static const limb two58m2 = (((limb) 1) << 58) - (((limb) 1) << 2);
390 static const limb two58m42m2 = (((limb) 1) << 58) -
391 (((limb) 1) << 42) - (((limb) 1) << 2);
392
393 /* Set to 0 mod 2^224-2^96+1 to ensure out > in */
394 out[0] = two58p2 - in[0];
395 out[1] = two58m42m2 - in[1];
396 out[2] = two58m2 - in[2];
397 out[3] = two58m2 - in[3];
398}
399
400/* Subtract field elements: out -= in */
401/* Assumes in[i] < 2^57 */
402static void
403felem_diff(felem out, const felem in)
404{
405 static const limb two58p2 = (((limb) 1) << 58) + (((limb) 1) << 2);
406 static const limb two58m2 = (((limb) 1) << 58) - (((limb) 1) << 2);
407 static const limb two58m42m2 = (((limb) 1) << 58) -
408 (((limb) 1) << 42) - (((limb) 1) << 2);
409
410 /* Add 0 mod 2^224-2^96+1 to ensure out > in */
411 out[0] += two58p2;
412 out[1] += two58m42m2;
413 out[2] += two58m2;
414 out[3] += two58m2;
415
416 out[0] -= in[0];
417 out[1] -= in[1];
418 out[2] -= in[2];
419 out[3] -= in[3];
420}
421
422/* Subtract in unreduced 128-bit mode: out -= in */
423/* Assumes in[i] < 2^119 */
424static void
425widefelem_diff(widefelem out, const widefelem in)
426{
427 static const widelimb two120 = ((widelimb) 1) << 120;
428 static const widelimb two120m64 = (((widelimb) 1) << 120) -
429 (((widelimb) 1) << 64);
430 static const widelimb two120m104m64 = (((widelimb) 1) << 120) -
431 (((widelimb) 1) << 104) - (((widelimb) 1) << 64);
432
433 /* Add 0 mod 2^224-2^96+1 to ensure out > in */
434 out[0] += two120;
435 out[1] += two120m64;
436 out[2] += two120m64;
437 out[3] += two120;
438 out[4] += two120m104m64;
439 out[5] += two120m64;
440 out[6] += two120m64;
441
442 out[0] -= in[0];
443 out[1] -= in[1];
444 out[2] -= in[2];
445 out[3] -= in[3];
446 out[4] -= in[4];
447 out[5] -= in[5];
448 out[6] -= in[6];
449}
450
451/* Subtract in mixed mode: out128 -= in64 */
452/* in[i] < 2^63 */
453static void
454felem_diff_128_64(widefelem out, const felem in)
455{
456 static const widelimb two64p8 = (((widelimb) 1) << 64) +
457 (((widelimb) 1) << 8);
458 static const widelimb two64m8 = (((widelimb) 1) << 64) -
459 (((widelimb) 1) << 8);
460 static const widelimb two64m48m8 = (((widelimb) 1) << 64) -
461 (((widelimb) 1) << 48) - (((widelimb) 1) << 8);
462
463 /* Add 0 mod 2^224-2^96+1 to ensure out > in */
464 out[0] += two64p8;
465 out[1] += two64m48m8;
466 out[2] += two64m8;
467 out[3] += two64m8;
468
469 out[0] -= in[0];
470 out[1] -= in[1];
471 out[2] -= in[2];
472 out[3] -= in[3];
473}
474
475/* Multiply a field element by a scalar: out = out * scalar
476 * The scalars we actually use are small, so results fit without overflow */
477static void
478felem_scalar(felem out, const limb scalar)
479{
480 out[0] *= scalar;
481 out[1] *= scalar;
482 out[2] *= scalar;
483 out[3] *= scalar;
484}
485
486/* Multiply an unreduced field element by a scalar: out = out * scalar
487 * The scalars we actually use are small, so results fit without overflow */
488static void
489widefelem_scalar(widefelem out, const widelimb scalar)
490{
491 out[0] *= scalar;
492 out[1] *= scalar;
493 out[2] *= scalar;
494 out[3] *= scalar;
495 out[4] *= scalar;
496 out[5] *= scalar;
497 out[6] *= scalar;
498}
499
500/* Square a field element: out = in^2 */
501static void
502felem_square(widefelem out, const felem in)
503{
504 limb tmp0, tmp1, tmp2;
505 tmp0 = 2 * in[0];
506 tmp1 = 2 * in[1];
507 tmp2 = 2 * in[2];
508 out[0] = ((widelimb) in[0]) * in[0];
509 out[1] = ((widelimb) in[0]) * tmp1;
510 out[2] = ((widelimb) in[0]) * tmp2 + ((widelimb) in[1]) * in[1];
511 out[3] = ((widelimb) in[3]) * tmp0 +
512 ((widelimb) in[1]) * tmp2;
513 out[4] = ((widelimb) in[3]) * tmp1 + ((widelimb) in[2]) * in[2];
514 out[5] = ((widelimb) in[3]) * tmp2;
515 out[6] = ((widelimb) in[3]) * in[3];
516}
517
518/* Multiply two field elements: out = in1 * in2 */
519static void
520felem_mul(widefelem out, const felem in1, const felem in2)
521{
522 out[0] = ((widelimb) in1[0]) * in2[0];
523 out[1] = ((widelimb) in1[0]) * in2[1] + ((widelimb) in1[1]) * in2[0];
524 out[2] = ((widelimb) in1[0]) * in2[2] + ((widelimb) in1[1]) * in2[1] +
525 ((widelimb) in1[2]) * in2[0];
526 out[3] = ((widelimb) in1[0]) * in2[3] + ((widelimb) in1[1]) * in2[2] +
527 ((widelimb) in1[2]) * in2[1] + ((widelimb) in1[3]) * in2[0];
528 out[4] = ((widelimb) in1[1]) * in2[3] + ((widelimb) in1[2]) * in2[2] +
529 ((widelimb) in1[3]) * in2[1];
530 out[5] = ((widelimb) in1[2]) * in2[3] + ((widelimb) in1[3]) * in2[2];
531 out[6] = ((widelimb) in1[3]) * in2[3];
532}
533
534/* Reduce seven 128-bit coefficients to four 64-bit coefficients.
535 * Requires in[i] < 2^126,
536 * ensures out[0] < 2^56, out[1] < 2^56, out[2] < 2^56, out[3] <= 2^56 + 2^16 */
537static void
538felem_reduce(felem out, const widefelem in)
539{
540 static const widelimb two127p15 = (((widelimb) 1) << 127) +
541 (((widelimb) 1) << 15);
542 static const widelimb two127m71 = (((widelimb) 1) << 127) -
543 (((widelimb) 1) << 71);
544 static const widelimb two127m71m55 = (((widelimb) 1) << 127) -
545 (((widelimb) 1) << 71) - (((widelimb) 1) << 55);
546 widelimb output[5];
547
548 /* Add 0 mod 2^224-2^96+1 to ensure all differences are positive */
549 output[0] = in[0] + two127p15;
550 output[1] = in[1] + two127m71m55;
551 output[2] = in[2] + two127m71;
552 output[3] = in[3];
553 output[4] = in[4];
554
555 /* Eliminate in[4], in[5], in[6] */
556 output[4] += in[6] >> 16;
557 output[3] += (in[6] & 0xffff) << 40;
558 output[2] -= in[6];
559
560 output[3] += in[5] >> 16;
561 output[2] += (in[5] & 0xffff) << 40;
562 output[1] -= in[5];
563
564 output[2] += output[4] >> 16;
565 output[1] += (output[4] & 0xffff) << 40;
566 output[0] -= output[4];
567
568 /* Carry 2 -> 3 -> 4 */
569 output[3] += output[2] >> 56;
570 output[2] &= 0x00ffffffffffffff;
571
572 output[4] = output[3] >> 56;
573 output[3] &= 0x00ffffffffffffff;
574
575 /* Now output[2] < 2^56, output[3] < 2^56, output[4] < 2^72 */
576
577 /* Eliminate output[4] */
578 output[2] += output[4] >> 16;
579 /* output[2] < 2^56 + 2^56 = 2^57 */
580 output[1] += (output[4] & 0xffff) << 40;
581 output[0] -= output[4];
582
583 /* Carry 0 -> 1 -> 2 -> 3 */
584 output[1] += output[0] >> 56;
585 out[0] = output[0] & 0x00ffffffffffffff;
586
587 output[2] += output[1] >> 56;
588 /* output[2] < 2^57 + 2^72 */
589 out[1] = output[1] & 0x00ffffffffffffff;
590 output[3] += output[2] >> 56;
591 /* output[3] <= 2^56 + 2^16 */
592 out[2] = output[2] & 0x00ffffffffffffff;
593
594 /*
595 * out[0] < 2^56, out[1] < 2^56, out[2] < 2^56, out[3] <= 2^56 + 2^16
596 * (due to final carry), so out < 2*p
597 */
598 out[3] = output[3];
599}
600
601static void
602felem_square_reduce(felem out, const felem in)
603{
604 widefelem tmp;
605 felem_square(tmp, in);
606 felem_reduce(out, tmp);
607}
608
609static void
610felem_mul_reduce(felem out, const felem in1, const felem in2)
611{
612 widefelem tmp;
613 felem_mul(tmp, in1, in2);
614 felem_reduce(out, tmp);
615}
616
617/* Reduce to unique minimal representation.
618 * Requires 0 <= in < 2*p (always call felem_reduce first) */
619static void
620felem_contract(felem out, const felem in)
621{
622 static const int64_t two56 = ((limb) 1) << 56;
623 /* 0 <= in < 2*p, p = 2^224 - 2^96 + 1 */
624 /* if in > p , reduce in = in - 2^224 + 2^96 - 1 */
625 int64_t tmp[4], a;
626 tmp[0] = in[0];
627 tmp[1] = in[1];
628 tmp[2] = in[2];
629 tmp[3] = in[3];
630 /* Case 1: a = 1 iff in >= 2^224 */
631 a = (in[3] >> 56);
632 tmp[0] -= a;
633 tmp[1] += a << 40;
634 tmp[3] &= 0x00ffffffffffffff;
635 /*
636 * Case 2: a = 0 iff p <= in < 2^224, i.e., the high 128 bits are all
637 * 1 and the lower part is non-zero
638 */
639 a = ((in[3] & in[2] & (in[1] | 0x000000ffffffffff)) + 1) |
640 (((int64_t) (in[0] + (in[1] & 0x000000ffffffffff)) - 1) >> 63);
641 a &= 0x00ffffffffffffff;
642 /* turn a into an all-one mask (if a = 0) or an all-zero mask */
643 a = (a - 1) >> 63;
644 /* subtract 2^224 - 2^96 + 1 if a is all-one */
645 tmp[3] &= a ^ 0xffffffffffffffff;
646 tmp[2] &= a ^ 0xffffffffffffffff;
647 tmp[1] &= (a ^ 0xffffffffffffffff) | 0x000000ffffffffff;
648 tmp[0] -= 1 & a;
649
650 /*
651 * eliminate negative coefficients: if tmp[0] is negative, tmp[1]
652 * must be non-zero, so we only need one step
653 */
654 a = tmp[0] >> 63;
655 tmp[0] += two56 & a;
656 tmp[1] -= 1 & a;
657
658 /* carry 1 -> 2 -> 3 */
659 tmp[2] += tmp[1] >> 56;
660 tmp[1] &= 0x00ffffffffffffff;
661
662 tmp[3] += tmp[2] >> 56;
663 tmp[2] &= 0x00ffffffffffffff;
664
665 /* Now 0 <= out < p */
666 out[0] = tmp[0];
667 out[1] = tmp[1];
668 out[2] = tmp[2];
669 out[3] = tmp[3];
670}
671
672/* Zero-check: returns 1 if input is 0, and 0 otherwise.
673 * We know that field elements are reduced to in < 2^225,
674 * so we only need to check three cases: 0, 2^224 - 2^96 + 1,
675 * and 2^225 - 2^97 + 2 */
676static limb
677felem_is_zero(const felem in)
678{
679 limb zero, two224m96p1, two225m97p2;
680
681 zero = in[0] | in[1] | in[2] | in[3];
682 zero = (((int64_t) (zero) - 1) >> 63) & 1;
683 two224m96p1 = (in[0] ^ 1) | (in[1] ^ 0x00ffff0000000000)
684 | (in[2] ^ 0x00ffffffffffffff) | (in[3] ^ 0x00ffffffffffffff);
685 two224m96p1 = (((int64_t) (two224m96p1) - 1) >> 63) & 1;
686 two225m97p2 = (in[0] ^ 2) | (in[1] ^ 0x00fffe0000000000)
687 | (in[2] ^ 0x00ffffffffffffff) | (in[3] ^ 0x01ffffffffffffff);
688 two225m97p2 = (((int64_t) (two225m97p2) - 1) >> 63) & 1;
689 return (zero | two224m96p1 | two225m97p2);
690}
691
692static limb
693felem_is_zero_int(const felem in)
694{
695 return (int) (felem_is_zero(in) & ((limb) 1));
696}
697
698/* Invert a field element */
699/* Computation chain copied from djb's code */
700static void
701felem_inv(felem out, const felem in)
702{
703 felem ftmp, ftmp2, ftmp3, ftmp4;
704 widefelem tmp;
705 unsigned i;
706
707 felem_square(tmp, in);
708 felem_reduce(ftmp, tmp);/* 2 */
709 felem_mul(tmp, in, ftmp);
710 felem_reduce(ftmp, tmp);/* 2^2 - 1 */
711 felem_square(tmp, ftmp);
712 felem_reduce(ftmp, tmp);/* 2^3 - 2 */
713 felem_mul(tmp, in, ftmp);
714 felem_reduce(ftmp, tmp);/* 2^3 - 1 */
715 felem_square(tmp, ftmp);
716 felem_reduce(ftmp2, tmp); /* 2^4 - 2 */
717 felem_square(tmp, ftmp2);
718 felem_reduce(ftmp2, tmp); /* 2^5 - 4 */
719 felem_square(tmp, ftmp2);
720 felem_reduce(ftmp2, tmp); /* 2^6 - 8 */
721 felem_mul(tmp, ftmp2, ftmp);
722 felem_reduce(ftmp, tmp);/* 2^6 - 1 */
723 felem_square(tmp, ftmp);
724 felem_reduce(ftmp2, tmp); /* 2^7 - 2 */
725 for (i = 0; i < 5; ++i) { /* 2^12 - 2^6 */
726 felem_square(tmp, ftmp2);
727 felem_reduce(ftmp2, tmp);
728 }
729 felem_mul(tmp, ftmp2, ftmp);
730 felem_reduce(ftmp2, tmp); /* 2^12 - 1 */
731 felem_square(tmp, ftmp2);
732 felem_reduce(ftmp3, tmp); /* 2^13 - 2 */
733 for (i = 0; i < 11; ++i) { /* 2^24 - 2^12 */
734 felem_square(tmp, ftmp3);
735 felem_reduce(ftmp3, tmp);
736 }
737 felem_mul(tmp, ftmp3, ftmp2);
738 felem_reduce(ftmp2, tmp); /* 2^24 - 1 */
739 felem_square(tmp, ftmp2);
740 felem_reduce(ftmp3, tmp); /* 2^25 - 2 */
741 for (i = 0; i < 23; ++i) { /* 2^48 - 2^24 */
742 felem_square(tmp, ftmp3);
743 felem_reduce(ftmp3, tmp);
744 }
745 felem_mul(tmp, ftmp3, ftmp2);
746 felem_reduce(ftmp3, tmp); /* 2^48 - 1 */
747 felem_square(tmp, ftmp3);
748 felem_reduce(ftmp4, tmp); /* 2^49 - 2 */
749 for (i = 0; i < 47; ++i) { /* 2^96 - 2^48 */
750 felem_square(tmp, ftmp4);
751 felem_reduce(ftmp4, tmp);
752 }
753 felem_mul(tmp, ftmp3, ftmp4);
754 felem_reduce(ftmp3, tmp); /* 2^96 - 1 */
755 felem_square(tmp, ftmp3);
756 felem_reduce(ftmp4, tmp); /* 2^97 - 2 */
757 for (i = 0; i < 23; ++i) { /* 2^120 - 2^24 */
758 felem_square(tmp, ftmp4);
759 felem_reduce(ftmp4, tmp);
760 }
761 felem_mul(tmp, ftmp2, ftmp4);
762 felem_reduce(ftmp2, tmp); /* 2^120 - 1 */
763 for (i = 0; i < 6; ++i) { /* 2^126 - 2^6 */
764 felem_square(tmp, ftmp2);
765 felem_reduce(ftmp2, tmp);
766 }
767 felem_mul(tmp, ftmp2, ftmp);
768 felem_reduce(ftmp, tmp);/* 2^126 - 1 */
769 felem_square(tmp, ftmp);
770 felem_reduce(ftmp, tmp);/* 2^127 - 2 */
771 felem_mul(tmp, ftmp, in);
772 felem_reduce(ftmp, tmp);/* 2^127 - 1 */
773 for (i = 0; i < 97; ++i) { /* 2^224 - 2^97 */
774 felem_square(tmp, ftmp);
775 felem_reduce(ftmp, tmp);
776 }
777 felem_mul(tmp, ftmp, ftmp3);
778 felem_reduce(out, tmp); /* 2^224 - 2^96 - 1 */
779}
780
781/* Copy in constant time:
782 * if icopy == 1, copy in to out,
783 * if icopy == 0, copy out to itself. */
784static void
785copy_conditional(felem out, const felem in, limb icopy)
786{
787 unsigned i;
788 /* icopy is a (64-bit) 0 or 1, so copy is either all-zero or all-one */
789 const limb copy = -icopy;
790 for (i = 0; i < 4; ++i) {
791 const limb tmp = copy & (in[i] ^ out[i]);
792 out[i] ^= tmp;
793 }
794}
795
796/******************************************************************************/
797/* ELLIPTIC CURVE POINT OPERATIONS
798 *
799 * Points are represented in Jacobian projective coordinates:
800 * (X, Y, Z) corresponds to the affine point (X/Z^2, Y/Z^3),
801 * or to the point at infinity if Z == 0.
802 *
803 */
804
805/* Double an elliptic curve point:
806 * (X', Y', Z') = 2 * (X, Y, Z), where
807 * X' = (3 * (X - Z^2) * (X + Z^2))^2 - 8 * X * Y^2
808 * Y' = 3 * (X - Z^2) * (X + Z^2) * (4 * X * Y^2 - X') - 8 * Y^2
809 * Z' = (Y + Z)^2 - Y^2 - Z^2 = 2 * Y * Z
810 * Outputs can equal corresponding inputs, i.e., x_out == x_in is allowed,
811 * while x_out == y_in is not (maybe this works, but it's not tested). */
812static void
813point_double(felem x_out, felem y_out, felem z_out,
814 const felem x_in, const felem y_in, const felem z_in)
815{
816 widefelem tmp, tmp2;
817 felem delta, gamma, beta, alpha, ftmp, ftmp2;
818
819 felem_assign(ftmp, x_in);
820 felem_assign(ftmp2, x_in);
821
822 /* delta = z^2 */
823 felem_square(tmp, z_in);
824 felem_reduce(delta, tmp);
825
826 /* gamma = y^2 */
827 felem_square(tmp, y_in);
828 felem_reduce(gamma, tmp);
829
830 /* beta = x*gamma */
831 felem_mul(tmp, x_in, gamma);
832 felem_reduce(beta, tmp);
833
834 /* alpha = 3*(x-delta)*(x+delta) */
835 felem_diff(ftmp, delta);
836 /* ftmp[i] < 2^57 + 2^58 + 2 < 2^59 */
837 felem_sum(ftmp2, delta);
838 /* ftmp2[i] < 2^57 + 2^57 = 2^58 */
839 felem_scalar(ftmp2, 3);
840 /* ftmp2[i] < 3 * 2^58 < 2^60 */
841 felem_mul(tmp, ftmp, ftmp2);
842 /* tmp[i] < 2^60 * 2^59 * 4 = 2^121 */
843 felem_reduce(alpha, tmp);
844
845 /* x' = alpha^2 - 8*beta */
846 felem_square(tmp, alpha);
847 /* tmp[i] < 4 * 2^57 * 2^57 = 2^116 */
848 felem_assign(ftmp, beta);
849 felem_scalar(ftmp, 8);
850 /* ftmp[i] < 8 * 2^57 = 2^60 */
851 felem_diff_128_64(tmp, ftmp);
852 /* tmp[i] < 2^116 + 2^64 + 8 < 2^117 */
853 felem_reduce(x_out, tmp);
854
855 /* z' = (y + z)^2 - gamma - delta */
856 felem_sum(delta, gamma);
857 /* delta[i] < 2^57 + 2^57 = 2^58 */
858 felem_assign(ftmp, y_in);
859 felem_sum(ftmp, z_in);
860 /* ftmp[i] < 2^57 + 2^57 = 2^58 */
861 felem_square(tmp, ftmp);
862 /* tmp[i] < 4 * 2^58 * 2^58 = 2^118 */
863 felem_diff_128_64(tmp, delta);
864 /* tmp[i] < 2^118 + 2^64 + 8 < 2^119 */
865 felem_reduce(z_out, tmp);
866
867 /* y' = alpha*(4*beta - x') - 8*gamma^2 */
868 felem_scalar(beta, 4);
869 /* beta[i] < 4 * 2^57 = 2^59 */
870 felem_diff(beta, x_out);
871 /* beta[i] < 2^59 + 2^58 + 2 < 2^60 */
872 felem_mul(tmp, alpha, beta);
873 /* tmp[i] < 4 * 2^57 * 2^60 = 2^119 */
874 felem_square(tmp2, gamma);
875 /* tmp2[i] < 4 * 2^57 * 2^57 = 2^116 */
876 widefelem_scalar(tmp2, 8);
877 /* tmp2[i] < 8 * 2^116 = 2^119 */
878 widefelem_diff(tmp, tmp2);
879 /* tmp[i] < 2^119 + 2^120 < 2^121 */
880 felem_reduce(y_out, tmp);
881}
882
883/* Add two elliptic curve points:
884 * (X_1, Y_1, Z_1) + (X_2, Y_2, Z_2) = (X_3, Y_3, Z_3), where
885 * X_3 = (Z_1^3 * Y_2 - Z_2^3 * Y_1)^2 - (Z_1^2 * X_2 - Z_2^2 * X_1)^3 -
886 * 2 * Z_2^2 * X_1 * (Z_1^2 * X_2 - Z_2^2 * X_1)^2
887 * 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) -
888 * Z_2^3 * Y_1 * (Z_1^2 * X_2 - Z_2^2 * X_1)^3
889 * Z_3 = (Z_1^2 * X_2 - Z_2^2 * X_1) * (Z_1 * Z_2)
890 *
891 * This runs faster if 'mixed' is set, which requires Z_2 = 1 or Z_2 = 0.
892 */
893
894/* This function is not entirely constant-time:
895 * it includes a branch for checking whether the two input points are equal,
896 * (while not equal to the point at infinity).
897 * This case never happens during single point multiplication,
898 * so there is no timing leak for ECDH or ECDSA signing. */
899static void
900point_add(felem x3, felem y3, felem z3,
901 const felem x1, const felem y1, const felem z1,
902 const int mixed, const felem x2, const felem y2, const felem z2)
903{
904 felem ftmp, ftmp2, ftmp3, ftmp4, ftmp5, x_out, y_out, z_out;
905 widefelem tmp, tmp2;
906 limb z1_is_zero, z2_is_zero, x_equal, y_equal;
907
908 if (!mixed) {
909 /* ftmp2 = z2^2 */
910 felem_square(tmp, z2);
911 felem_reduce(ftmp2, tmp);
912
913 /* ftmp4 = z2^3 */
914 felem_mul(tmp, ftmp2, z2);
915 felem_reduce(ftmp4, tmp);
916
917 /* ftmp4 = z2^3*y1 */
918 felem_mul(tmp2, ftmp4, y1);
919 felem_reduce(ftmp4, tmp2);
920
921 /* ftmp2 = z2^2*x1 */
922 felem_mul(tmp2, ftmp2, x1);
923 felem_reduce(ftmp2, tmp2);
924 } else {
925 /* We'll assume z2 = 1 (special case z2 = 0 is handled later) */
926
927 /* ftmp4 = z2^3*y1 */
928 felem_assign(ftmp4, y1);
929
930 /* ftmp2 = z2^2*x1 */
931 felem_assign(ftmp2, x1);
932 }
933
934 /* ftmp = z1^2 */
935 felem_square(tmp, z1);
936 felem_reduce(ftmp, tmp);
937
938 /* ftmp3 = z1^3 */
939 felem_mul(tmp, ftmp, z1);
940 felem_reduce(ftmp3, tmp);
941
942 /* tmp = z1^3*y2 */
943 felem_mul(tmp, ftmp3, y2);
944 /* tmp[i] < 4 * 2^57 * 2^57 = 2^116 */
945
946 /* ftmp3 = z1^3*y2 - z2^3*y1 */
947 felem_diff_128_64(tmp, ftmp4);
948 /* tmp[i] < 2^116 + 2^64 + 8 < 2^117 */
949 felem_reduce(ftmp3, tmp);
950
951 /* tmp = z1^2*x2 */
952 felem_mul(tmp, ftmp, x2);
953 /* tmp[i] < 4 * 2^57 * 2^57 = 2^116 */
954
955 /* ftmp = z1^2*x2 - z2^2*x1 */
956 felem_diff_128_64(tmp, ftmp2);
957 /* tmp[i] < 2^116 + 2^64 + 8 < 2^117 */
958 felem_reduce(ftmp, tmp);
959
960 /*
961 * the formulae are incorrect if the points are equal so we check for
962 * this and do doubling if this happens
963 */
964 x_equal = felem_is_zero(ftmp);
965 y_equal = felem_is_zero(ftmp3);
966 z1_is_zero = felem_is_zero(z1);
967 z2_is_zero = felem_is_zero(z2);
968 /* In affine coordinates, (X_1, Y_1) == (X_2, Y_2) */
969 if (x_equal && y_equal && !z1_is_zero && !z2_is_zero) {
970 point_double(x3, y3, z3, x1, y1, z1);
971 return;
972 }
973 /* ftmp5 = z1*z2 */
974 if (!mixed) {
975 felem_mul(tmp, z1, z2);
976 felem_reduce(ftmp5, tmp);
977 } else {
978 /* special case z2 = 0 is handled later */
979 felem_assign(ftmp5, z1);
980 }
981
982 /* z_out = (z1^2*x2 - z2^2*x1)*(z1*z2) */
983 felem_mul(tmp, ftmp, ftmp5);
984 felem_reduce(z_out, tmp);
985
986 /* ftmp = (z1^2*x2 - z2^2*x1)^2 */
987 felem_assign(ftmp5, ftmp);
988 felem_square(tmp, ftmp);
989 felem_reduce(ftmp, tmp);
990
991 /* ftmp5 = (z1^2*x2 - z2^2*x1)^3 */
992 felem_mul(tmp, ftmp, ftmp5);
993 felem_reduce(ftmp5, tmp);
994
995 /* ftmp2 = z2^2*x1*(z1^2*x2 - z2^2*x1)^2 */
996 felem_mul(tmp, ftmp2, ftmp);
997 felem_reduce(ftmp2, tmp);
998
999 /* tmp = z2^3*y1*(z1^2*x2 - z2^2*x1)^3 */
1000 felem_mul(tmp, ftmp4, ftmp5);
1001 /* tmp[i] < 4 * 2^57 * 2^57 = 2^116 */
1002
1003 /* tmp2 = (z1^3*y2 - z2^3*y1)^2 */
1004 felem_square(tmp2, ftmp3);
1005 /* tmp2[i] < 4 * 2^57 * 2^57 < 2^116 */
1006
1007 /* tmp2 = (z1^3*y2 - z2^3*y1)^2 - (z1^2*x2 - z2^2*x1)^3 */
1008 felem_diff_128_64(tmp2, ftmp5);
1009 /* tmp2[i] < 2^116 + 2^64 + 8 < 2^117 */
1010
1011 /* ftmp5 = 2*z2^2*x1*(z1^2*x2 - z2^2*x1)^2 */
1012 felem_assign(ftmp5, ftmp2);
1013 felem_scalar(ftmp5, 2);
1014 /* ftmp5[i] < 2 * 2^57 = 2^58 */
1015
1016 /*
1017 * x_out = (z1^3*y2 - z2^3*y1)^2 - (z1^2*x2 - z2^2*x1)^3 -
1018 * 2*z2^2*x1*(z1^2*x2 - z2^2*x1)^2
1019 */
1020 felem_diff_128_64(tmp2, ftmp5);
1021 /* tmp2[i] < 2^117 + 2^64 + 8 < 2^118 */
1022 felem_reduce(x_out, tmp2);
1023
1024 /* ftmp2 = z2^2*x1*(z1^2*x2 - z2^2*x1)^2 - x_out */
1025 felem_diff(ftmp2, x_out);
1026 /* ftmp2[i] < 2^57 + 2^58 + 2 < 2^59 */
1027
1028 /* tmp2 = (z1^3*y2 - z2^3*y1)*(z2^2*x1*(z1^2*x2 - z2^2*x1)^2 - x_out) */
1029 felem_mul(tmp2, ftmp3, ftmp2);
1030 /* tmp2[i] < 4 * 2^57 * 2^59 = 2^118 */
1031
1032 /*
1033 * y_out = (z1^3*y2 - z2^3*y1)*(z2^2*x1*(z1^2*x2 - z2^2*x1)^2 -
1034 * x_out) - z2^3*y1*(z1^2*x2 - z2^2*x1)^3
1035 */
1036 widefelem_diff(tmp2, tmp);
1037 /* tmp2[i] < 2^118 + 2^120 < 2^121 */
1038 felem_reduce(y_out, tmp2);
1039
1040 /*
1041 * the result (x_out, y_out, z_out) is incorrect if one of the inputs
1042 * is the point at infinity, so we need to check for this separately
1043 */
1044
1045 /* if point 1 is at infinity, copy point 2 to output, and vice versa */
1046 copy_conditional(x_out, x2, z1_is_zero);
1047 copy_conditional(x_out, x1, z2_is_zero);
1048 copy_conditional(y_out, y2, z1_is_zero);
1049 copy_conditional(y_out, y1, z2_is_zero);
1050 copy_conditional(z_out, z2, z1_is_zero);
1051 copy_conditional(z_out, z1, z2_is_zero);
1052 felem_assign(x3, x_out);
1053 felem_assign(y3, y_out);
1054 felem_assign(z3, z_out);
1055}
1056
1057/* select_point selects the |idx|th point from a precomputation table and
1058 * copies it to out. */
1059static void
1060select_point(const u64 idx, unsigned int size, const felem pre_comp[ /* size */ ][3], felem out[3])
1061{
1062 unsigned i, j;
1063 limb *outlimbs = &out[0][0];
1064 memset(outlimbs, 0, 3 * sizeof(felem));
1065
1066 for (i = 0; i < size; i++) {
1067 const limb *inlimbs = &pre_comp[i][0][0];
1068 u64 mask = i ^ idx;
1069 mask |= mask >> 4;
1070 mask |= mask >> 2;
1071 mask |= mask >> 1;
1072 mask &= 1;
1073 mask--;
1074 for (j = 0; j < 4 * 3; j++)
1075 outlimbs[j] |= inlimbs[j] & mask;
1076 }
1077}
1078
1079/* get_bit returns the |i|th bit in |in| */
1080static char
1081get_bit(const felem_bytearray in, unsigned i)
1082{
1083 if (i >= 224)
1084 return 0;
1085 return (in[i >> 3] >> (i & 7)) & 1;
1086}
1087
1088/* Interleaved point multiplication using precomputed point multiples:
1089 * The small point multiples 0*P, 1*P, ..., 16*P are in pre_comp[],
1090 * the scalars in scalars[]. If g_scalar is non-NULL, we also add this multiple
1091 * of the generator, using certain (large) precomputed multiples in g_pre_comp.
1092 * Output point (X, Y, Z) is stored in x_out, y_out, z_out */
1093static void
1094batch_mul(felem x_out, felem y_out, felem z_out,
1095 const felem_bytearray scalars[], const unsigned num_points, const u8 * g_scalar,
1096 const int mixed, const felem pre_comp[][17][3], const felem g_pre_comp[2][16][3])
1097{
1098 int i, skip;
1099 unsigned num;
1100 unsigned gen_mul = (g_scalar != NULL);
1101 felem nq[3], tmp[4];
1102 u64 bits;
1103 u8 sign, digit;
1104
1105 /* set nq to the point at infinity */
1106 memset(nq, 0, 3 * sizeof(felem));
1107
1108 /*
1109 * Loop over all scalars msb-to-lsb, interleaving additions of
1110 * multiples of the generator (two in each of the last 28 rounds) and
1111 * additions of other points multiples (every 5th round).
1112 */
1113 skip = 1; /* save two point operations in the first
1114 * round */
1115 for (i = (num_points ? 220 : 27); i >= 0; --i) {
1116 /* double */
1117 if (!skip)
1118 point_double(nq[0], nq[1], nq[2], nq[0], nq[1], nq[2]);
1119
1120 /* add multiples of the generator */
1121 if (gen_mul && (i <= 27)) {
1122 /* first, look 28 bits upwards */
1123 bits = get_bit(g_scalar, i + 196) << 3;
1124 bits |= get_bit(g_scalar, i + 140) << 2;
1125 bits |= get_bit(g_scalar, i + 84) << 1;
1126 bits |= get_bit(g_scalar, i + 28);
1127 /* select the point to add, in constant time */
1128 select_point(bits, 16, g_pre_comp[1], tmp);
1129
1130 if (!skip) {
1131 point_add(nq[0], nq[1], nq[2],
1132 nq[0], nq[1], nq[2],
1133 1 /* mixed */ , tmp[0], tmp[1], tmp[2]);
1134 } else {
1135 memcpy(nq, tmp, 3 * sizeof(felem));
1136 skip = 0;
1137 }
1138
1139 /* second, look at the current position */
1140 bits = get_bit(g_scalar, i + 168) << 3;
1141 bits |= get_bit(g_scalar, i + 112) << 2;
1142 bits |= get_bit(g_scalar, i + 56) << 1;
1143 bits |= get_bit(g_scalar, i);
1144 /* select the point to add, in constant time */
1145 select_point(bits, 16, g_pre_comp[0], tmp);
1146 point_add(nq[0], nq[1], nq[2],
1147 nq[0], nq[1], nq[2],
1148 1 /* mixed */ , tmp[0], tmp[1], tmp[2]);
1149 }
1150 /* do other additions every 5 doublings */
1151 if (num_points && (i % 5 == 0)) {
1152 /* loop over all scalars */
1153 for (num = 0; num < num_points; ++num) {
1154 bits = get_bit(scalars[num], i + 4) << 5;
1155 bits |= get_bit(scalars[num], i + 3) << 4;
1156 bits |= get_bit(scalars[num], i + 2) << 3;
1157 bits |= get_bit(scalars[num], i + 1) << 2;
1158 bits |= get_bit(scalars[num], i) << 1;
1159 bits |= get_bit(scalars[num], i - 1);
1160 ec_GFp_nistp_recode_scalar_bits(&sign, &digit, bits);
1161
1162 /* select the point to add or subtract */
1163 select_point(digit, 17, pre_comp[num], tmp);
1164 felem_neg(tmp[3], tmp[1]); /* (X, -Y, Z) is the
1165 * negative point */
1166 copy_conditional(tmp[1], tmp[3], sign);
1167
1168 if (!skip) {
1169 point_add(nq[0], nq[1], nq[2],
1170 nq[0], nq[1], nq[2],
1171 mixed, tmp[0], tmp[1], tmp[2]);
1172 } else {
1173 memcpy(nq, tmp, 3 * sizeof(felem));
1174 skip = 0;
1175 }
1176 }
1177 }
1178 }
1179 felem_assign(x_out, nq[0]);
1180 felem_assign(y_out, nq[1]);
1181 felem_assign(z_out, nq[2]);
1182}
1183
1184/******************************************************************************/
1185/* FUNCTIONS TO MANAGE PRECOMPUTATION
1186 */
1187
1188static NISTP224_PRE_COMP *
1189nistp224_pre_comp_new()
1190{
1191 NISTP224_PRE_COMP *ret = NULL;
1192 ret = malloc(sizeof *ret);
1193 if (!ret) {
1194 ECerr(EC_F_NISTP224_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE);
1195 return ret;
1196 }
1197 memset(ret->g_pre_comp, 0, sizeof(ret->g_pre_comp));
1198 ret->references = 1;
1199 return ret;
1200}
1201
1202static void *
1203nistp224_pre_comp_dup(void *src_)
1204{
1205 NISTP224_PRE_COMP *src = src_;
1206
1207 /* no need to actually copy, these objects never change! */
1208 CRYPTO_add(&src->references, 1, CRYPTO_LOCK_EC_PRE_COMP);
1209
1210 return src_;
1211}
1212
1213static void
1214nistp224_pre_comp_free(void *pre_)
1215{
1216 int i;
1217 NISTP224_PRE_COMP *pre = pre_;
1218
1219 if (!pre)
1220 return;
1221
1222 i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP);
1223 if (i > 0)
1224 return;
1225
1226 free(pre);
1227}
1228
1229static void
1230nistp224_pre_comp_clear_free(void *pre_)
1231{
1232 int i;
1233 NISTP224_PRE_COMP *pre = pre_;
1234
1235 if (!pre)
1236 return;
1237
1238 i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP);
1239 if (i > 0)
1240 return;
1241
1242 explicit_bzero(pre, sizeof *pre);
1243 free(pre);
1244}
1245
1246/******************************************************************************/
1247/* OPENSSL EC_METHOD FUNCTIONS
1248 */
1249
1250int
1251ec_GFp_nistp224_group_init(EC_GROUP * group)
1252{
1253 int ret;
1254 ret = ec_GFp_simple_group_init(group);
1255 group->a_is_minus3 = 1;
1256 return ret;
1257}
1258
1259int
1260ec_GFp_nistp224_group_set_curve(EC_GROUP * group, const BIGNUM * p,
1261 const BIGNUM * a, const BIGNUM * b, BN_CTX * ctx)
1262{
1263 int ret = 0;
1264 BN_CTX *new_ctx = NULL;
1265 BIGNUM *curve_p, *curve_a, *curve_b;
1266
1267 if (ctx == NULL)
1268 if ((ctx = new_ctx = BN_CTX_new()) == NULL)
1269 return 0;
1270 BN_CTX_start(ctx);
1271 if (((curve_p = BN_CTX_get(ctx)) == NULL) ||
1272 ((curve_a = BN_CTX_get(ctx)) == NULL) ||
1273 ((curve_b = BN_CTX_get(ctx)) == NULL))
1274 goto err;
1275 BN_bin2bn(nistp224_curve_params[0], sizeof(felem_bytearray), curve_p);
1276 BN_bin2bn(nistp224_curve_params[1], sizeof(felem_bytearray), curve_a);
1277 BN_bin2bn(nistp224_curve_params[2], sizeof(felem_bytearray), curve_b);
1278 if ((BN_cmp(curve_p, p)) || (BN_cmp(curve_a, a)) ||
1279 (BN_cmp(curve_b, b))) {
1280 ECerr(EC_F_EC_GFP_NISTP224_GROUP_SET_CURVE,
1281 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);
1286err:
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 ECerr(EC_F_EC_GFP_NISTP224_POINT_GET_AFFINE_COORDINATES,
1303 EC_R_POINT_AT_INFINITY);
1304 return 0;
1305 }
1306 if ((!BN_to_felem(x_in, &point->X)) || (!BN_to_felem(y_in, &point->Y)) ||
1307 (!BN_to_felem(z1, &point->Z)))
1308 return 0;
1309 felem_inv(z2, z1);
1310 felem_square(tmp, z2);
1311 felem_reduce(z1, tmp);
1312 felem_mul(tmp, x_in, z1);
1313 felem_reduce(x_in, tmp);
1314 felem_contract(x_out, x_in);
1315 if (x != NULL) {
1316 if (!felem_to_BN(x, x_out)) {
1317 ECerr(EC_F_EC_GFP_NISTP224_POINT_GET_AFFINE_COORDINATES,
1318 ERR_R_BN_LIB);
1319 return 0;
1320 }
1321 }
1322 felem_mul(tmp, z1, z2);
1323 felem_reduce(z1, tmp);
1324 felem_mul(tmp, y_in, z1);
1325 felem_reduce(y_in, tmp);
1326 felem_contract(y_out, y_in);
1327 if (y != NULL) {
1328 if (!felem_to_BN(y, y_out)) {
1329 ECerr(EC_F_EC_GFP_NISTP224_POINT_GET_AFFINE_COORDINATES,
1330 ERR_R_BN_LIB);
1331 return 0;
1332 }
1333 }
1334 return 1;
1335}
1336
1337static void
1338make_points_affine(size_t num, felem points[ /* num */ ][3], felem tmp_felems[ /* num+1 */ ])
1339{
1340 /*
1341 * Runs in constant time, unless an input is the point at infinity
1342 * (which normally shouldn't happen).
1343 */
1344 ec_GFp_nistp_points_make_affine_internal(
1345 num,
1346 points,
1347 sizeof(felem),
1348 tmp_felems,
1349 (void (*) (void *)) felem_one,
1350 (int (*) (const void *)) felem_is_zero_int,
1351 (void (*) (void *, const void *)) felem_assign,
1352 (void (*) (void *, const void *)) felem_square_reduce,
1353 (void (*) (void *, const void *, const void *)) felem_mul_reduce,
1354 (void (*) (void *, const void *)) felem_inv,
1355 (void (*) (void *, const void *)) felem_contract);
1356}
1357
1358/* Computes scalar*generator + \sum scalars[i]*points[i], ignoring NULL values
1359 * Result is stored in r (r can equal one of the inputs). */
1360int
1361ec_GFp_nistp224_points_mul(const EC_GROUP * group, EC_POINT * r,
1362 const BIGNUM * scalar, size_t num, const EC_POINT * points[],
1363 const BIGNUM * scalars[], BN_CTX * ctx)
1364{
1365 int ret = 0;
1366 int j;
1367 unsigned i;
1368 int mixed = 0;
1369 BN_CTX *new_ctx = NULL;
1370 BIGNUM *x, *y, *z, *tmp_scalar;
1371 felem_bytearray g_secret;
1372 felem_bytearray *secrets = NULL;
1373 felem(*pre_comp)[17][3] = NULL;
1374 felem *tmp_felems = NULL;
1375 felem_bytearray tmp;
1376 unsigned num_bytes;
1377 int have_pre_comp = 0;
1378 size_t num_points = num;
1379 felem x_in, y_in, z_in, x_out, y_out, z_out;
1380 NISTP224_PRE_COMP *pre = NULL;
1381 const felem(*g_pre_comp)[16][3] = NULL;
1382 EC_POINT *generator = NULL;
1383 const EC_POINT *p = NULL;
1384 const BIGNUM *p_scalar = NULL;
1385
1386 if (ctx == NULL)
1387 if ((ctx = new_ctx = BN_CTX_new()) == NULL)
1388 return 0;
1389 BN_CTX_start(ctx);
1390 if (((x = BN_CTX_get(ctx)) == NULL) ||
1391 ((y = BN_CTX_get(ctx)) == NULL) ||
1392 ((z = BN_CTX_get(ctx)) == NULL) ||
1393 ((tmp_scalar = BN_CTX_get(ctx)) == NULL))
1394 goto err;
1395
1396 if (scalar != NULL) {
1397 pre = EC_EX_DATA_get_data(group->extra_data,
1398 nistp224_pre_comp_dup, nistp224_pre_comp_free,
1399 nistp224_pre_comp_clear_free);
1400 if (pre)
1401 /* we have precomputation, try to use it */
1402 g_pre_comp = (const felem(*)[16][3]) pre->g_pre_comp;
1403 else
1404 /* try to use the standard precomputation */
1405 g_pre_comp = &gmul[0];
1406 generator = EC_POINT_new(group);
1407 if (generator == NULL)
1408 goto err;
1409 /* get the generator from precomputation */
1410 if (!felem_to_BN(x, g_pre_comp[0][1][0]) ||
1411 !felem_to_BN(y, g_pre_comp[0][1][1]) ||
1412 !felem_to_BN(z, g_pre_comp[0][1][2])) {
1413 ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_BN_LIB);
1414 goto err;
1415 }
1416 if (!EC_POINT_set_Jprojective_coordinates_GFp(group,
1417 generator, x, y, z, ctx))
1418 goto err;
1419 if (0 == EC_POINT_cmp(group, generator, group->generator, ctx))
1420 /* precomputation matches generator */
1421 have_pre_comp = 1;
1422 else
1423 /*
1424 * we don't have valid precomputation: treat the
1425 * generator as a random point
1426 */
1427 num_points = num_points + 1;
1428 }
1429 if (num_points > 0) {
1430 if (num_points >= 3) {
1431 /*
1432 * unless we precompute multiples for just one or two
1433 * points, converting those into affine form is time
1434 * well spent
1435 */
1436 mixed = 1;
1437 }
1438 secrets = calloc(num_points, sizeof(felem_bytearray));
1439 pre_comp = calloc(num_points, 17 * 3 * sizeof(felem));
1440 if (mixed) {
1441 /* XXX should do more int overflow checking */
1442 tmp_felems = reallocarray(NULL,
1443 (num_points * 17 + 1), sizeof(felem));
1444 }
1445 if ((secrets == NULL) || (pre_comp == NULL) || (mixed && (tmp_felems == NULL))) {
1446 ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_MALLOC_FAILURE);
1447 goto err;
1448 }
1449 /*
1450 * we treat NULL scalars as 0, and NULL points as points at
1451 * infinity, i.e., they contribute nothing to the linear
1452 * combination
1453 */
1454 for (i = 0; i < num_points; ++i) {
1455 if (i == num)
1456 /* the generator */
1457 {
1458 p = EC_GROUP_get0_generator(group);
1459 p_scalar = scalar;
1460 } else
1461 /* the i^th point */
1462 {
1463 p = points[i];
1464 p_scalar = scalars[i];
1465 }
1466 if ((p_scalar != NULL) && (p != NULL)) {
1467 /* reduce scalar to 0 <= scalar < 2^224 */
1468 if ((BN_num_bits(p_scalar) > 224) || (BN_is_negative(p_scalar))) {
1469 /*
1470 * this is an unusual input, and we
1471 * don't guarantee constant-timeness
1472 */
1473 if (!BN_nnmod(tmp_scalar, p_scalar, &group->order, ctx)) {
1474 ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_BN_LIB);
1475 goto err;
1476 }
1477 num_bytes = BN_bn2bin(tmp_scalar, tmp);
1478 } else
1479 num_bytes = BN_bn2bin(p_scalar, tmp);
1480 flip_endian(secrets[i], tmp, num_bytes);
1481 /* precompute multiples */
1482 if ((!BN_to_felem(x_out, &p->X)) ||
1483 (!BN_to_felem(y_out, &p->Y)) ||
1484 (!BN_to_felem(z_out, &p->Z)))
1485 goto err;
1486 felem_assign(pre_comp[i][1][0], x_out);
1487 felem_assign(pre_comp[i][1][1], y_out);
1488 felem_assign(pre_comp[i][1][2], z_out);
1489 for (j = 2; j <= 16; ++j) {
1490 if (j & 1) {
1491 point_add(
1492 pre_comp[i][j][0], pre_comp[i][j][1], pre_comp[i][j][2],
1493 pre_comp[i][1][0], pre_comp[i][1][1], pre_comp[i][1][2],
1494 0, pre_comp[i][j - 1][0], pre_comp[i][j - 1][1], pre_comp[i][j - 1][2]);
1495 } else {
1496 point_double(
1497 pre_comp[i][j][0], pre_comp[i][j][1], pre_comp[i][j][2],
1498 pre_comp[i][j / 2][0], pre_comp[i][j / 2][1], pre_comp[i][j / 2][2]);
1499 }
1500 }
1501 }
1502 }
1503 if (mixed)
1504 make_points_affine(num_points * 17, pre_comp[0], tmp_felems);
1505 }
1506 /* the scalar for the generator */
1507 if ((scalar != NULL) && (have_pre_comp)) {
1508 memset(g_secret, 0, sizeof g_secret);
1509 /* reduce scalar to 0 <= scalar < 2^224 */
1510 if ((BN_num_bits(scalar) > 224) || (BN_is_negative(scalar))) {
1511 /*
1512 * this is an unusual input, and we don't guarantee
1513 * constant-timeness
1514 */
1515 if (!BN_nnmod(tmp_scalar, scalar, &group->order, ctx)) {
1516 ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_BN_LIB);
1517 goto err;
1518 }
1519 num_bytes = BN_bn2bin(tmp_scalar, tmp);
1520 } else
1521 num_bytes = BN_bn2bin(scalar, tmp);
1522 flip_endian(g_secret, tmp, num_bytes);
1523 /* do the multiplication with generator precomputation */
1524 batch_mul(x_out, y_out, z_out,
1525 (const felem_bytearray(*)) secrets, num_points,
1526 g_secret,
1527 mixed, (const felem(*)[17][3]) pre_comp,
1528 g_pre_comp);
1529 } else
1530 /* do the multiplication without generator precomputation */
1531 batch_mul(x_out, y_out, z_out,
1532 (const felem_bytearray(*)) secrets, num_points,
1533 NULL, mixed, (const felem(*)[17][3]) pre_comp, NULL);
1534 /* reduce the output to its unique minimal representation */
1535 felem_contract(x_in, x_out);
1536 felem_contract(y_in, y_out);
1537 felem_contract(z_in, z_out);
1538 if ((!felem_to_BN(x, x_in)) || (!felem_to_BN(y, y_in)) ||
1539 (!felem_to_BN(z, z_in))) {
1540 ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_BN_LIB);
1541 goto err;
1542 }
1543 ret = EC_POINT_set_Jprojective_coordinates_GFp(group, r, x, y, z, ctx);
1544
1545err:
1546 BN_CTX_end(ctx);
1547 EC_POINT_free(generator);
1548 BN_CTX_free(new_ctx);
1549 free(secrets);
1550 free(pre_comp);
1551 free(tmp_felems);
1552 return ret;
1553}
1554
1555int
1556ec_GFp_nistp224_precompute_mult(EC_GROUP * group, BN_CTX * ctx)
1557{
1558 int ret = 0;
1559 NISTP224_PRE_COMP *pre = NULL;
1560 int i, j;
1561 BN_CTX *new_ctx = NULL;
1562 BIGNUM *x, *y;
1563 EC_POINT *generator = NULL;
1564 felem tmp_felems[32];
1565
1566 /* throw away old precomputation */
1567 EC_EX_DATA_free_data(&group->extra_data, nistp224_pre_comp_dup,
1568 nistp224_pre_comp_free, nistp224_pre_comp_clear_free);
1569 if (ctx == NULL)
1570 if ((ctx = new_ctx = BN_CTX_new()) == NULL)
1571 return 0;
1572 BN_CTX_start(ctx);
1573 if (((x = BN_CTX_get(ctx)) == NULL) ||
1574 ((y = BN_CTX_get(ctx)) == NULL))
1575 goto err;
1576 /* get the generator */
1577 if (group->generator == NULL)
1578 goto err;
1579 generator = EC_POINT_new(group);
1580 if (generator == NULL)
1581 goto err;
1582 BN_bin2bn(nistp224_curve_params[3], sizeof(felem_bytearray), x);
1583 BN_bin2bn(nistp224_curve_params[4], sizeof(felem_bytearray), y);
1584 if (!EC_POINT_set_affine_coordinates_GFp(group, generator, x, y, ctx))
1585 goto err;
1586 if ((pre = nistp224_pre_comp_new()) == NULL)
1587 goto err;
1588 /* if the generator is the standard one, use built-in precomputation */
1589 if (0 == EC_POINT_cmp(group, generator, group->generator, ctx)) {
1590 memcpy(pre->g_pre_comp, gmul, sizeof(pre->g_pre_comp));
1591 ret = 1;
1592 goto err;
1593 }
1594 if ((!BN_to_felem(pre->g_pre_comp[0][1][0], &group->generator->X)) ||
1595 (!BN_to_felem(pre->g_pre_comp[0][1][1], &group->generator->Y)) ||
1596 (!BN_to_felem(pre->g_pre_comp[0][1][2], &group->generator->Z)))
1597 goto err;
1598 /*
1599 * compute 2^56*G, 2^112*G, 2^168*G for the first table, 2^28*G,
1600 * 2^84*G, 2^140*G, 2^196*G for the second one
1601 */
1602 for (i = 1; i <= 8; i <<= 1) {
1603 point_double(
1604 pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2],
1605 pre->g_pre_comp[0][i][0], pre->g_pre_comp[0][i][1], pre->g_pre_comp[0][i][2]);
1606 for (j = 0; j < 27; ++j) {
1607 point_double(
1608 pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2],
1609 pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2]);
1610 }
1611 if (i == 8)
1612 break;
1613 point_double(
1614 pre->g_pre_comp[0][2 * i][0], pre->g_pre_comp[0][2 * i][1], pre->g_pre_comp[0][2 * i][2],
1615 pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2]);
1616 for (j = 0; j < 27; ++j) {
1617 point_double(
1618 pre->g_pre_comp[0][2 * i][0], pre->g_pre_comp[0][2 * i][1], pre->g_pre_comp[0][2 * i][2],
1619 pre->g_pre_comp[0][2 * i][0], pre->g_pre_comp[0][2 * i][1], pre->g_pre_comp[0][2 * i][2]);
1620 }
1621 }
1622 for (i = 0; i < 2; i++) {
1623 /* g_pre_comp[i][0] is the point at infinity */
1624 memset(pre->g_pre_comp[i][0], 0, sizeof(pre->g_pre_comp[i][0]));
1625 /* the remaining multiples */
1626 /* 2^56*G + 2^112*G resp. 2^84*G + 2^140*G */
1627 point_add(
1628 pre->g_pre_comp[i][6][0], pre->g_pre_comp[i][6][1],
1629 pre->g_pre_comp[i][6][2], pre->g_pre_comp[i][4][0],
1630 pre->g_pre_comp[i][4][1], pre->g_pre_comp[i][4][2],
1631 0, pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1],
1632 pre->g_pre_comp[i][2][2]);
1633 /* 2^56*G + 2^168*G resp. 2^84*G + 2^196*G */
1634 point_add(
1635 pre->g_pre_comp[i][10][0], pre->g_pre_comp[i][10][1],
1636 pre->g_pre_comp[i][10][2], pre->g_pre_comp[i][8][0],
1637 pre->g_pre_comp[i][8][1], pre->g_pre_comp[i][8][2],
1638 0, pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1],
1639 pre->g_pre_comp[i][2][2]);
1640 /* 2^112*G + 2^168*G resp. 2^140*G + 2^196*G */
1641 point_add(
1642 pre->g_pre_comp[i][12][0], pre->g_pre_comp[i][12][1],
1643 pre->g_pre_comp[i][12][2], pre->g_pre_comp[i][8][0],
1644 pre->g_pre_comp[i][8][1], pre->g_pre_comp[i][8][2],
1645 0, pre->g_pre_comp[i][4][0], pre->g_pre_comp[i][4][1],
1646 pre->g_pre_comp[i][4][2]);
1647 /*
1648 * 2^56*G + 2^112*G + 2^168*G resp. 2^84*G + 2^140*G +
1649 * 2^196*G
1650 */
1651 point_add(
1652 pre->g_pre_comp[i][14][0], pre->g_pre_comp[i][14][1],
1653 pre->g_pre_comp[i][14][2], pre->g_pre_comp[i][12][0],
1654 pre->g_pre_comp[i][12][1], pre->g_pre_comp[i][12][2],
1655 0, pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1],
1656 pre->g_pre_comp[i][2][2]);
1657 for (j = 1; j < 8; ++j) {
1658 /* odd multiples: add G resp. 2^28*G */
1659 point_add(
1660 pre->g_pre_comp[i][2 * j + 1][0], pre->g_pre_comp[i][2 * j + 1][1],
1661 pre->g_pre_comp[i][2 * j + 1][2], pre->g_pre_comp[i][2 * j][0],
1662 pre->g_pre_comp[i][2 * j][1], pre->g_pre_comp[i][2 * j][2],
1663 0, pre->g_pre_comp[i][1][0], pre->g_pre_comp[i][1][1],
1664 pre->g_pre_comp[i][1][2]);
1665 }
1666 }
1667 make_points_affine(31, &(pre->g_pre_comp[0][1]), tmp_felems);
1668
1669 if (!EC_EX_DATA_set_data(&group->extra_data, pre, nistp224_pre_comp_dup,
1670 nistp224_pre_comp_free, nistp224_pre_comp_clear_free))
1671 goto err;
1672 ret = 1;
1673 pre = NULL;
1674err:
1675 BN_CTX_end(ctx);
1676 EC_POINT_free(generator);
1677 BN_CTX_free(new_ctx);
1678 nistp224_pre_comp_free(pre);
1679 return ret;
1680}
1681
1682int
1683ec_GFp_nistp224_have_precompute_mult(const EC_GROUP * group)
1684{
1685 if (EC_EX_DATA_get_data(group->extra_data, nistp224_pre_comp_dup,
1686 nistp224_pre_comp_free, nistp224_pre_comp_clear_free)
1687 != NULL)
1688 return 1;
1689 else
1690 return 0;
1691}
1692
1693#endif
generated by cgit v1.2.3-55-g6feb (git 2.39.1) at 2025-08-17 03:36:41 +0000