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1/* crypto/ec/ecp_nistp224.c */
2/*
3 * Written by Emilia Kasper (Google) for the OpenSSL project.
4 */
5/* Copyright 2011 Google Inc.
6 *
7 * Licensed under the Apache License, Version 2.0 (the "License");
8 *
9 * you may not use this file except in compliance with the License.
10 * You may obtain a copy of the License at
11 *
12 * http://www.apache.org/licenses/LICENSE-2.0
13 *
14 * Unless required by applicable law or agreed to in writing, software
15 * distributed under the License is distributed on an "AS IS" BASIS,
16 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
17 * See the License for the specific language governing permissions and
18 * limitations under the License.
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 <openssl/opensslconf.h>
29#ifndef OPENSSL_NO_EC_NISTP_64_GCC_128
30
31#ifndef OPENSSL_SYS_VMS
32#include <stdint.h>
33#else
34#include <inttypes.h>
35#endif
36
37#include <string.h>
38#include <openssl/err.h>
39#include "ec_lcl.h"
40
41#if defined(__GNUC__) && (__GNUC__ > 3 || (__GNUC__ == 3 && __GNUC_MINOR__ >= 1))
42 /* even with gcc, the typedef won't work for 32-bit platforms */
43 typedef __uint128_t uint128_t; /* nonstandard; implemented by gcc on 64-bit platforms */
44#else
45 #error "Need GCC 3.1 or later to define type uint128_t"
46#endif
47
48typedef uint8_t u8;
49typedef uint64_t u64;
50typedef int64_t s64;
51
52
53/******************************************************************************/
54/* INTERNAL REPRESENTATION OF FIELD ELEMENTS
55 *
56 * Field elements are represented as a_0 + 2^56*a_1 + 2^112*a_2 + 2^168*a_3
57 * using 64-bit coefficients called 'limbs',
58 * and sometimes (for multiplication results) as
59 * 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
60 * using 128-bit coefficients called 'widelimbs'.
61 * A 4-limb representation is an 'felem';
62 * a 7-widelimb representation is a 'widefelem'.
63 * Even within felems, bits of adjacent limbs overlap, and we don't always
64 * reduce the representations: we ensure that inputs to each felem
65 * multiplication satisfy a_i < 2^60, so outputs satisfy b_i < 4*2^60*2^60,
66 * and fit into a 128-bit word without overflow. The coefficients are then
67 * again partially reduced to obtain an felem satisfying a_i < 2^57.
68 * We only reduce to the unique minimal representation at the end of the
69 * computation.
70 */
71
72typedef uint64_t limb;
73typedef uint128_t widelimb;
74
75typedef limb felem[4];
76typedef widelimb widefelem[7];
77
78/* Field element represented as a byte arrary.
79 * 28*8 = 224 bits is also the group order size for the elliptic curve,
80 * and we also use this type for scalars for point multiplication.
81 */
82typedef u8 felem_bytearray[28];
83
84static const felem_bytearray nistp224_curve_params[5] = {
85 {0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* p */
86 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0x00,0x00,0x00,0x00,
87 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x01},
88 {0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* a */
89 0xFF,0xFF,0xFF,0xFF,0xFF,0xFE,0xFF,0xFF,0xFF,0xFF,
90 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFE},
91 {0xB4,0x05,0x0A,0x85,0x0C,0x04,0xB3,0xAB,0xF5,0x41, /* b */
92 0x32,0x56,0x50,0x44,0xB0,0xB7,0xD7,0xBF,0xD8,0xBA,
93 0x27,0x0B,0x39,0x43,0x23,0x55,0xFF,0xB4},
94 {0xB7,0x0E,0x0C,0xBD,0x6B,0xB4,0xBF,0x7F,0x32,0x13, /* x */
95 0x90,0xB9,0x4A,0x03,0xC1,0xD3,0x56,0xC2,0x11,0x22,
96 0x34,0x32,0x80,0xD6,0x11,0x5C,0x1D,0x21},
97 {0xbd,0x37,0x63,0x88,0xb5,0xf7,0x23,0xfb,0x4c,0x22, /* y */
98 0xdf,0xe6,0xcd,0x43,0x75,0xa0,0x5a,0x07,0x47,0x64,
99 0x44,0xd5,0x81,0x99,0x85,0x00,0x7e,0x34}
100};
101
102/* Precomputed multiples of the standard generator
103 * Points are given in coordinates (X, Y, Z) where Z normally is 1
104 * (0 for the point at infinity).
105 * For each field element, slice a_0 is word 0, etc.
106 *
107 * The table has 2 * 16 elements, starting with the following:
108 * index | bits | point
109 * ------+---------+------------------------------
110 * 0 | 0 0 0 0 | 0G
111 * 1 | 0 0 0 1 | 1G
112 * 2 | 0 0 1 0 | 2^56G
113 * 3 | 0 0 1 1 | (2^56 + 1)G
114 * 4 | 0 1 0 0 | 2^112G
115 * 5 | 0 1 0 1 | (2^112 + 1)G
116 * 6 | 0 1 1 0 | (2^112 + 2^56)G
117 * 7 | 0 1 1 1 | (2^112 + 2^56 + 1)G
118 * 8 | 1 0 0 0 | 2^168G
119 * 9 | 1 0 0 1 | (2^168 + 1)G
120 * 10 | 1 0 1 0 | (2^168 + 2^56)G
121 * 11 | 1 0 1 1 | (2^168 + 2^56 + 1)G
122 * 12 | 1 1 0 0 | (2^168 + 2^112)G
123 * 13 | 1 1 0 1 | (2^168 + 2^112 + 1)G
124 * 14 | 1 1 1 0 | (2^168 + 2^112 + 2^56)G
125 * 15 | 1 1 1 1 | (2^168 + 2^112 + 2^56 + 1)G
126 * followed by a copy of this with each element multiplied by 2^28.
127 *
128 * The reason for this is so that we can clock bits into four different
129 * locations when doing simple scalar multiplies against the base point,
130 * and then another four locations using the second 16 elements.
131 */
132static const felem gmul[2][16][3] =
133{{{{0, 0, 0, 0},
134 {0, 0, 0, 0},
135 {0, 0, 0, 0}},
136 {{0x3280d6115c1d21, 0xc1d356c2112234, 0x7f321390b94a03, 0xb70e0cbd6bb4bf},
137 {0xd5819985007e34, 0x75a05a07476444, 0xfb4c22dfe6cd43, 0xbd376388b5f723},
138 {1, 0, 0, 0}},
139 {{0xfd9675666ebbe9, 0xbca7664d40ce5e, 0x2242df8d8a2a43, 0x1f49bbb0f99bc5},
140 {0x29e0b892dc9c43, 0xece8608436e662, 0xdc858f185310d0, 0x9812dd4eb8d321},
141 {1, 0, 0, 0}},
142 {{0x6d3e678d5d8eb8, 0x559eed1cb362f1, 0x16e9a3bbce8a3f, 0xeedcccd8c2a748},
143 {0xf19f90ed50266d, 0xabf2b4bf65f9df, 0x313865468fafec, 0x5cb379ba910a17},
144 {1, 0, 0, 0}},
145 {{0x0641966cab26e3, 0x91fb2991fab0a0, 0xefec27a4e13a0b, 0x0499aa8a5f8ebe},
146 {0x7510407766af5d, 0x84d929610d5450, 0x81d77aae82f706, 0x6916f6d4338c5b},
147 {1, 0, 0, 0}},
148 {{0xea95ac3b1f15c6, 0x086000905e82d4, 0xdd323ae4d1c8b1, 0x932b56be7685a3},
149 {0x9ef93dea25dbbf, 0x41665960f390f0, 0xfdec76dbe2a8a7, 0x523e80f019062a},
150 {1, 0, 0, 0}},
151 {{0x822fdd26732c73, 0xa01c83531b5d0f, 0x363f37347c1ba4, 0xc391b45c84725c},
152 {0xbbd5e1b2d6ad24, 0xddfbcde19dfaec, 0xc393da7e222a7f, 0x1efb7890ede244},
153 {1, 0, 0, 0}},
154 {{0x4c9e90ca217da1, 0xd11beca79159bb, 0xff8d33c2c98b7c, 0x2610b39409f849},
155 {0x44d1352ac64da0, 0xcdbb7b2c46b4fb, 0x966c079b753c89, 0xfe67e4e820b112},
156 {1, 0, 0, 0}},
157 {{0xe28cae2df5312d, 0xc71b61d16f5c6e, 0x79b7619a3e7c4c, 0x05c73240899b47},
158 {0x9f7f6382c73e3a, 0x18615165c56bda, 0x641fab2116fd56, 0x72855882b08394},
159 {1, 0, 0, 0}},
160 {{0x0469182f161c09, 0x74a98ca8d00fb5, 0xb89da93489a3e0, 0x41c98768fb0c1d},
161 {0xe5ea05fb32da81, 0x3dce9ffbca6855, 0x1cfe2d3fbf59e6, 0x0e5e03408738a7},
162 {1, 0, 0, 0}},
163 {{0xdab22b2333e87f, 0x4430137a5dd2f6, 0xe03ab9f738beb8, 0xcb0c5d0dc34f24},
164 {0x764a7df0c8fda5, 0x185ba5c3fa2044, 0x9281d688bcbe50, 0xc40331df893881},
165 {1, 0, 0, 0}},
166 {{0xb89530796f0f60, 0xade92bd26909a3, 0x1a0c83fb4884da, 0x1765bf22a5a984},
167 {0x772a9ee75db09e, 0x23bc6c67cec16f, 0x4c1edba8b14e2f, 0xe2a215d9611369},
168 {1, 0, 0, 0}},
169 {{0x571e509fb5efb3, 0xade88696410552, 0xc8ae85fada74fe, 0x6c7e4be83bbde3},
170 {0xff9f51160f4652, 0xb47ce2495a6539, 0xa2946c53b582f4, 0x286d2db3ee9a60},
171 {1, 0, 0, 0}},
172 {{0x40bbd5081a44af, 0x0995183b13926c, 0xbcefba6f47f6d0, 0x215619e9cc0057},
173 {0x8bc94d3b0df45e, 0xf11c54a3694f6f, 0x8631b93cdfe8b5, 0xe7e3f4b0982db9},
174 {1, 0, 0, 0}},
175 {{0xb17048ab3e1c7b, 0xac38f36ff8a1d8, 0x1c29819435d2c6, 0xc813132f4c07e9},
176 {0x2891425503b11f, 0x08781030579fea, 0xf5426ba5cc9674, 0x1e28ebf18562bc},
177 {1, 0, 0, 0}},
178 {{0x9f31997cc864eb, 0x06cd91d28b5e4c, 0xff17036691a973, 0xf1aef351497c58},
179 {0xdd1f2d600564ff, 0xdead073b1402db, 0x74a684435bd693, 0xeea7471f962558},
180 {1, 0, 0, 0}}},
181 {{{0, 0, 0, 0},
182 {0, 0, 0, 0},
183 {0, 0, 0, 0}},
184 {{0x9665266dddf554, 0x9613d78b60ef2d, 0xce27a34cdba417, 0xd35ab74d6afc31},
185 {0x85ccdd22deb15e, 0x2137e5783a6aab, 0xa141cffd8c93c6, 0x355a1830e90f2d},
186 {1, 0, 0, 0}},
187 {{0x1a494eadaade65, 0xd6da4da77fe53c, 0xe7992996abec86, 0x65c3553c6090e3},
188 {0xfa610b1fb09346, 0xf1c6540b8a4aaf, 0xc51a13ccd3cbab, 0x02995b1b18c28a},
189 {1, 0, 0, 0}},
190 {{0x7874568e7295ef, 0x86b419fbe38d04, 0xdc0690a7550d9a, 0xd3966a44beac33},
191 {0x2b7280ec29132f, 0xbeaa3b6a032df3, 0xdc7dd88ae41200, 0xd25e2513e3a100},
192 {1, 0, 0, 0}},
193 {{0x924857eb2efafd, 0xac2bce41223190, 0x8edaa1445553fc, 0x825800fd3562d5},
194 {0x8d79148ea96621, 0x23a01c3dd9ed8d, 0xaf8b219f9416b5, 0xd8db0cc277daea},
195 {1, 0, 0, 0}},
196 {{0x76a9c3b1a700f0, 0xe9acd29bc7e691, 0x69212d1a6b0327, 0x6322e97fe154be},
197 {0x469fc5465d62aa, 0x8d41ed18883b05, 0x1f8eae66c52b88, 0xe4fcbe9325be51},
198 {1, 0, 0, 0}},
199 {{0x825fdf583cac16, 0x020b857c7b023a, 0x683c17744b0165, 0x14ffd0a2daf2f1},
200 {0x323b36184218f9, 0x4944ec4e3b47d4, 0xc15b3080841acf, 0x0bced4b01a28bb},
201 {1, 0, 0, 0}},
202 {{0x92ac22230df5c4, 0x52f33b4063eda8, 0xcb3f19870c0c93, 0x40064f2ba65233},
203 {0xfe16f0924f8992, 0x012da25af5b517, 0x1a57bb24f723a6, 0x06f8bc76760def},
204 {1, 0, 0, 0}},
205 {{0x4a7084f7817cb9, 0xbcab0738ee9a78, 0x3ec11e11d9c326, 0xdc0fe90e0f1aae},
206 {0xcf639ea5f98390, 0x5c350aa22ffb74, 0x9afae98a4047b7, 0x956ec2d617fc45},
207 {1, 0, 0, 0}},
208 {{0x4306d648c1be6a, 0x9247cd8bc9a462, 0xf5595e377d2f2e, 0xbd1c3caff1a52e},
209 {0x045e14472409d0, 0x29f3e17078f773, 0x745a602b2d4f7d, 0x191837685cdfbb},
210 {1, 0, 0, 0}},
211 {{0x5b6ee254a8cb79, 0x4953433f5e7026, 0xe21faeb1d1def4, 0xc4c225785c09de},
212 {0x307ce7bba1e518, 0x31b125b1036db8, 0x47e91868839e8f, 0xc765866e33b9f3},
213 {1, 0, 0, 0}},
214 {{0x3bfece24f96906, 0x4794da641e5093, 0xde5df64f95db26, 0x297ecd89714b05},
215 {0x701bd3ebb2c3aa, 0x7073b4f53cb1d5, 0x13c5665658af16, 0x9895089d66fe58},
216 {1, 0, 0, 0}},
217 {{0x0fef05f78c4790, 0x2d773633b05d2e, 0x94229c3a951c94, 0xbbbd70df4911bb},
218 {0xb2c6963d2c1168, 0x105f47a72b0d73, 0x9fdf6111614080, 0x7b7e94b39e67b0},
219 {1, 0, 0, 0}},
220 {{0xad1a7d6efbe2b3, 0xf012482c0da69d, 0x6b3bdf12438345, 0x40d7558d7aa4d9},
221 {0x8a09fffb5c6d3d, 0x9a356e5d9ffd38, 0x5973f15f4f9b1c, 0xdcd5f59f63c3ea},
222 {1, 0, 0, 0}},
223 {{0xacf39f4c5ca7ab, 0x4c8071cc5fd737, 0xc64e3602cd1184, 0x0acd4644c9abba},
224 {0x6c011a36d8bf6e, 0xfecd87ba24e32a, 0x19f6f56574fad8, 0x050b204ced9405},
225 {1, 0, 0, 0}},
226 {{0xed4f1cae7d9a96, 0x5ceef7ad94c40a, 0x778e4a3bf3ef9b, 0x7405783dc3b55e},
227 {0x32477c61b6e8c6, 0xb46a97570f018b, 0x91176d0a7e95d1, 0x3df90fbc4c7d0e},
228 {1, 0, 0, 0}}}};
229
230/* Precomputation for the group generator. */
231typedef struct {
232 felem g_pre_comp[2][16][3];
233 int references;
234} NISTP224_PRE_COMP;
235
236const EC_METHOD *EC_GFp_nistp224_method(void)
237 {
238 static const EC_METHOD ret = {
239 EC_FLAGS_DEFAULT_OCT,
240 NID_X9_62_prime_field,
241 ec_GFp_nistp224_group_init,
242 ec_GFp_simple_group_finish,
243 ec_GFp_simple_group_clear_finish,
244 ec_GFp_nist_group_copy,
245 ec_GFp_nistp224_group_set_curve,
246 ec_GFp_simple_group_get_curve,
247 ec_GFp_simple_group_get_degree,
248 ec_GFp_simple_group_check_discriminant,
249 ec_GFp_simple_point_init,
250 ec_GFp_simple_point_finish,
251 ec_GFp_simple_point_clear_finish,
252 ec_GFp_simple_point_copy,
253 ec_GFp_simple_point_set_to_infinity,
254 ec_GFp_simple_set_Jprojective_coordinates_GFp,
255 ec_GFp_simple_get_Jprojective_coordinates_GFp,
256 ec_GFp_simple_point_set_affine_coordinates,
257 ec_GFp_nistp224_point_get_affine_coordinates,
258 0 /* point_set_compressed_coordinates */,
259 0 /* point2oct */,
260 0 /* oct2point */,
261 ec_GFp_simple_add,
262 ec_GFp_simple_dbl,
263 ec_GFp_simple_invert,
264 ec_GFp_simple_is_at_infinity,
265 ec_GFp_simple_is_on_curve,
266 ec_GFp_simple_cmp,
267 ec_GFp_simple_make_affine,
268 ec_GFp_simple_points_make_affine,
269 ec_GFp_nistp224_points_mul,
270 ec_GFp_nistp224_precompute_mult,
271 ec_GFp_nistp224_have_precompute_mult,
272 ec_GFp_nist_field_mul,
273 ec_GFp_nist_field_sqr,
274 0 /* field_div */,
275 0 /* field_encode */,
276 0 /* field_decode */,
277 0 /* field_set_to_one */ };
278
279 return &ret;
280 }
281
282/* Helper functions to convert field elements to/from internal representation */
283static void bin28_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 felem_to_bin28(u8 out[28], const felem in)
292 {
293 unsigned i;
294 for (i = 0; i < 7; ++i)
295 {
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 flip_endian(u8 *out, const u8 *in, unsigned len)
305 {
306 unsigned i;
307 for (i = 0; i < len; ++i)
308 out[i] = in[len-1-i];
309 }
310
311/* From OpenSSL BIGNUM to internal representation */
312static int BN_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 {
323 ECerr(EC_F_BN_TO_FELEM, EC_R_BIGNUM_OUT_OF_RANGE);
324 return 0;
325 }
326 if (BN_is_negative(bn))
327 {
328 ECerr(EC_F_BN_TO_FELEM, 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 *felem_to_BN(BIGNUM *out, const felem in)
339 {
340 felem_bytearray b_in, b_out;
341 felem_to_bin28(b_in, in);
342 flip_endian(b_out, b_in, sizeof b_out);
343 return BN_bin2bn(b_out, sizeof b_out, out);
344 }
345
346/******************************************************************************/
347/* FIELD OPERATIONS
348 *
349 * Field operations, using the internal representation of field elements.
350 * NB! These operations are specific to our point multiplication and cannot be
351 * expected to be correct in general - e.g., multiplication with a large scalar
352 * will cause an overflow.
353 *
354 */
355
356static void felem_one(felem out)
357 {
358 out[0] = 1;
359 out[1] = 0;
360 out[2] = 0;
361 out[3] = 0;
362 }
363
364static void felem_assign(felem out, const felem in)
365 {
366 out[0] = in[0];
367 out[1] = in[1];
368 out[2] = in[2];
369 out[3] = in[3];
370 }
371
372/* Sum two field elements: out += in */
373static void felem_sum(felem out, const felem in)
374 {
375 out[0] += in[0];
376 out[1] += in[1];
377 out[2] += in[2];
378 out[3] += in[3];
379 }
380
381/* Get negative value: out = -in */
382/* Assumes in[i] < 2^57 */
383static void felem_neg(felem out, const felem in)
384 {
385 static const limb two58p2 = (((limb) 1) << 58) + (((limb) 1) << 2);
386 static const limb two58m2 = (((limb) 1) << 58) - (((limb) 1) << 2);
387 static const limb two58m42m2 = (((limb) 1) << 58) -
388 (((limb) 1) << 42) - (((limb) 1) << 2);
389
390 /* Set to 0 mod 2^224-2^96+1 to ensure out > in */
391 out[0] = two58p2 - in[0];
392 out[1] = two58m42m2 - in[1];
393 out[2] = two58m2 - in[2];
394 out[3] = two58m2 - in[3];
395 }
396
397/* Subtract field elements: out -= in */
398/* Assumes in[i] < 2^57 */
399static void felem_diff(felem out, const felem in)
400 {
401 static const limb two58p2 = (((limb) 1) << 58) + (((limb) 1) << 2);
402 static const limb two58m2 = (((limb) 1) << 58) - (((limb) 1) << 2);
403 static const limb two58m42m2 = (((limb) 1) << 58) -
404 (((limb) 1) << 42) - (((limb) 1) << 2);
405
406 /* Add 0 mod 2^224-2^96+1 to ensure out > in */
407 out[0] += two58p2;
408 out[1] += two58m42m2;
409 out[2] += two58m2;
410 out[3] += two58m2;
411
412 out[0] -= in[0];
413 out[1] -= in[1];
414 out[2] -= in[2];
415 out[3] -= in[3];
416 }
417
418/* Subtract in unreduced 128-bit mode: out -= in */
419/* Assumes in[i] < 2^119 */
420static void widefelem_diff(widefelem out, const widefelem in)
421 {
422 static const widelimb two120 = ((widelimb) 1) << 120;
423 static const widelimb two120m64 = (((widelimb) 1) << 120) -
424 (((widelimb) 1) << 64);
425 static const widelimb two120m104m64 = (((widelimb) 1) << 120) -
426 (((widelimb) 1) << 104) - (((widelimb) 1) << 64);
427
428 /* Add 0 mod 2^224-2^96+1 to ensure out > in */
429 out[0] += two120;
430 out[1] += two120m64;
431 out[2] += two120m64;
432 out[3] += two120;
433 out[4] += two120m104m64;
434 out[5] += two120m64;
435 out[6] += two120m64;
436
437 out[0] -= in[0];
438 out[1] -= in[1];
439 out[2] -= in[2];
440 out[3] -= in[3];
441 out[4] -= in[4];
442 out[5] -= in[5];
443 out[6] -= in[6];
444 }
445
446/* Subtract in mixed mode: out128 -= in64 */
447/* in[i] < 2^63 */
448static void felem_diff_128_64(widefelem out, const felem in)
449 {
450 static const widelimb two64p8 = (((widelimb) 1) << 64) +
451 (((widelimb) 1) << 8);
452 static const widelimb two64m8 = (((widelimb) 1) << 64) -
453 (((widelimb) 1) << 8);
454 static const widelimb two64m48m8 = (((widelimb) 1) << 64) -
455 (((widelimb) 1) << 48) - (((widelimb) 1) << 8);
456
457 /* Add 0 mod 2^224-2^96+1 to ensure out > in */
458 out[0] += two64p8;
459 out[1] += two64m48m8;
460 out[2] += two64m8;
461 out[3] += two64m8;
462
463 out[0] -= in[0];
464 out[1] -= in[1];
465 out[2] -= in[2];
466 out[3] -= in[3];
467 }
468
469/* Multiply a field element by a scalar: out = out * scalar
470 * The scalars we actually use are small, so results fit without overflow */
471static void felem_scalar(felem out, const limb scalar)
472 {
473 out[0] *= scalar;
474 out[1] *= scalar;
475 out[2] *= scalar;
476 out[3] *= scalar;
477 }
478
479/* Multiply an unreduced field element by a scalar: out = out * scalar
480 * The scalars we actually use are small, so results fit without overflow */
481static void widefelem_scalar(widefelem out, const widelimb scalar)
482 {
483 out[0] *= scalar;
484 out[1] *= scalar;
485 out[2] *= scalar;
486 out[3] *= scalar;
487 out[4] *= scalar;
488 out[5] *= scalar;
489 out[6] *= scalar;
490 }
491
492/* Square a field element: out = in^2 */
493static void felem_square(widefelem out, const felem in)
494 {
495 limb tmp0, tmp1, tmp2;
496 tmp0 = 2 * in[0]; tmp1 = 2 * in[1]; tmp2 = 2 * in[2];
497 out[0] = ((widelimb) in[0]) * in[0];
498 out[1] = ((widelimb) in[0]) * tmp1;
499 out[2] = ((widelimb) in[0]) * tmp2 + ((widelimb) in[1]) * in[1];
500 out[3] = ((widelimb) in[3]) * tmp0 +
501 ((widelimb) in[1]) * tmp2;
502 out[4] = ((widelimb) in[3]) * tmp1 + ((widelimb) in[2]) * in[2];
503 out[5] = ((widelimb) in[3]) * tmp2;
504 out[6] = ((widelimb) in[3]) * in[3];
505 }
506
507/* Multiply two field elements: out = in1 * in2 */
508static void felem_mul(widefelem out, const felem in1, const felem in2)
509 {
510 out[0] = ((widelimb) in1[0]) * in2[0];
511 out[1] = ((widelimb) in1[0]) * in2[1] + ((widelimb) in1[1]) * in2[0];
512 out[2] = ((widelimb) in1[0]) * in2[2] + ((widelimb) in1[1]) * in2[1] +
513 ((widelimb) in1[2]) * in2[0];
514 out[3] = ((widelimb) in1[0]) * in2[3] + ((widelimb) in1[1]) * in2[2] +
515 ((widelimb) in1[2]) * in2[1] + ((widelimb) in1[3]) * in2[0];
516 out[4] = ((widelimb) in1[1]) * in2[3] + ((widelimb) in1[2]) * in2[2] +
517 ((widelimb) in1[3]) * in2[1];
518 out[5] = ((widelimb) in1[2]) * in2[3] + ((widelimb) in1[3]) * in2[2];
519 out[6] = ((widelimb) in1[3]) * in2[3];
520 }
521
522/* Reduce seven 128-bit coefficients to four 64-bit coefficients.
523 * Requires in[i] < 2^126,
524 * ensures out[0] < 2^56, out[1] < 2^56, out[2] < 2^56, out[3] <= 2^56 + 2^16 */
525static void felem_reduce(felem out, const widefelem in)
526 {
527 static const widelimb two127p15 = (((widelimb) 1) << 127) +
528 (((widelimb) 1) << 15);
529 static const widelimb two127m71 = (((widelimb) 1) << 127) -
530 (((widelimb) 1) << 71);
531 static const widelimb two127m71m55 = (((widelimb) 1) << 127) -
532 (((widelimb) 1) << 71) - (((widelimb) 1) << 55);
533 widelimb output[5];
534
535 /* Add 0 mod 2^224-2^96+1 to ensure all differences are positive */
536 output[0] = in[0] + two127p15;
537 output[1] = in[1] + two127m71m55;
538 output[2] = in[2] + two127m71;
539 output[3] = in[3];
540 output[4] = in[4];
541
542 /* Eliminate in[4], in[5], in[6] */
543 output[4] += in[6] >> 16;
544 output[3] += (in[6] & 0xffff) << 40;
545 output[2] -= in[6];
546
547 output[3] += in[5] >> 16;
548 output[2] += (in[5] & 0xffff) << 40;
549 output[1] -= in[5];
550
551 output[2] += output[4] >> 16;
552 output[1] += (output[4] & 0xffff) << 40;
553 output[0] -= output[4];
554
555 /* Carry 2 -> 3 -> 4 */
556 output[3] += output[2] >> 56;
557 output[2] &= 0x00ffffffffffffff;
558
559 output[4] = output[3] >> 56;
560 output[3] &= 0x00ffffffffffffff;
561
562 /* Now output[2] < 2^56, output[3] < 2^56, output[4] < 2^72 */
563
564 /* Eliminate output[4] */
565 output[2] += output[4] >> 16;
566 /* output[2] < 2^56 + 2^56 = 2^57 */
567 output[1] += (output[4] & 0xffff) << 40;
568 output[0] -= output[4];
569
570 /* Carry 0 -> 1 -> 2 -> 3 */
571 output[1] += output[0] >> 56;
572 out[0] = output[0] & 0x00ffffffffffffff;
573
574 output[2] += output[1] >> 56;
575 /* output[2] < 2^57 + 2^72 */
576 out[1] = output[1] & 0x00ffffffffffffff;
577 output[3] += output[2] >> 56;
578 /* output[3] <= 2^56 + 2^16 */
579 out[2] = output[2] & 0x00ffffffffffffff;
580
581 /* out[0] < 2^56, out[1] < 2^56, out[2] < 2^56,
582 * out[3] <= 2^56 + 2^16 (due to final carry),
583 * so out < 2*p */
584 out[3] = output[3];
585 }
586
587static void felem_square_reduce(felem out, const felem in)
588 {
589 widefelem tmp;
590 felem_square(tmp, in);
591 felem_reduce(out, tmp);
592 }
593
594static void felem_mul_reduce(felem out, const felem in1, const felem in2)
595 {
596 widefelem tmp;
597 felem_mul(tmp, in1, in2);
598 felem_reduce(out, tmp);
599 }
600
601/* Reduce to unique minimal representation.
602 * Requires 0 <= in < 2*p (always call felem_reduce first) */
603static void felem_contract(felem out, const felem in)
604 {
605 static const int64_t two56 = ((limb) 1) << 56;
606 /* 0 <= in < 2*p, p = 2^224 - 2^96 + 1 */
607 /* if in > p , reduce in = in - 2^224 + 2^96 - 1 */
608 int64_t tmp[4], a;
609 tmp[0] = in[0];
610 tmp[1] = in[1];
611 tmp[2] = in[2];
612 tmp[3] = in[3];
613 /* Case 1: a = 1 iff in >= 2^224 */
614 a = (in[3] >> 56);
615 tmp[0] -= a;
616 tmp[1] += a << 40;
617 tmp[3] &= 0x00ffffffffffffff;
618 /* Case 2: a = 0 iff p <= in < 2^224, i.e.,
619 * the high 128 bits are all 1 and the lower part is non-zero */
620 a = ((in[3] & in[2] & (in[1] | 0x000000ffffffffff)) + 1) |
621 (((int64_t)(in[0] + (in[1] & 0x000000ffffffffff)) - 1) >> 63);
622 a &= 0x00ffffffffffffff;
623 /* turn a into an all-one mask (if a = 0) or an all-zero mask */
624 a = (a - 1) >> 63;
625 /* subtract 2^224 - 2^96 + 1 if a is all-one*/
626 tmp[3] &= a ^ 0xffffffffffffffff;
627 tmp[2] &= a ^ 0xffffffffffffffff;
628 tmp[1] &= (a ^ 0xffffffffffffffff) | 0x000000ffffffffff;
629 tmp[0] -= 1 & a;
630
631 /* eliminate negative coefficients: if tmp[0] is negative, tmp[1] must
632 * be non-zero, so we only need one step */
633 a = tmp[0] >> 63;
634 tmp[0] += two56 & a;
635 tmp[1] -= 1 & a;
636
637 /* carry 1 -> 2 -> 3 */
638 tmp[2] += tmp[1] >> 56;
639 tmp[1] &= 0x00ffffffffffffff;
640
641 tmp[3] += tmp[2] >> 56;
642 tmp[2] &= 0x00ffffffffffffff;
643
644 /* Now 0 <= out < p */
645 out[0] = tmp[0];
646 out[1] = tmp[1];
647 out[2] = tmp[2];
648 out[3] = tmp[3];
649 }
650
651/* Zero-check: returns 1 if input is 0, and 0 otherwise.
652 * We know that field elements are reduced to in < 2^225,
653 * so we only need to check three cases: 0, 2^224 - 2^96 + 1,
654 * and 2^225 - 2^97 + 2 */
655static limb felem_is_zero(const felem in)
656 {
657 limb zero, two224m96p1, two225m97p2;
658
659 zero = in[0] | in[1] | in[2] | in[3];
660 zero = (((int64_t)(zero) - 1) >> 63) & 1;
661 two224m96p1 = (in[0] ^ 1) | (in[1] ^ 0x00ffff0000000000)
662 | (in[2] ^ 0x00ffffffffffffff) | (in[3] ^ 0x00ffffffffffffff);
663 two224m96p1 = (((int64_t)(two224m96p1) - 1) >> 63) & 1;
664 two225m97p2 = (in[0] ^ 2) | (in[1] ^ 0x00fffe0000000000)
665 | (in[2] ^ 0x00ffffffffffffff) | (in[3] ^ 0x01ffffffffffffff);
666 two225m97p2 = (((int64_t)(two225m97p2) - 1) >> 63) & 1;
667 return (zero | two224m96p1 | two225m97p2);
668 }
669
670static limb felem_is_zero_int(const felem in)
671 {
672 return (int) (felem_is_zero(in) & ((limb)1));
673 }
674
675/* Invert a field element */
676/* Computation chain copied from djb's code */
677static void felem_inv(felem out, const felem in)
678 {
679 felem ftmp, ftmp2, ftmp3, ftmp4;
680 widefelem tmp;
681 unsigned i;
682
683 felem_square(tmp, in); felem_reduce(ftmp, tmp); /* 2 */
684 felem_mul(tmp, in, ftmp); felem_reduce(ftmp, tmp); /* 2^2 - 1 */
685 felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); /* 2^3 - 2 */
686 felem_mul(tmp, in, ftmp); felem_reduce(ftmp, tmp); /* 2^3 - 1 */
687 felem_square(tmp, ftmp); felem_reduce(ftmp2, tmp); /* 2^4 - 2 */
688 felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); /* 2^5 - 4 */
689 felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); /* 2^6 - 8 */
690 felem_mul(tmp, ftmp2, ftmp); felem_reduce(ftmp, tmp); /* 2^6 - 1 */
691 felem_square(tmp, ftmp); felem_reduce(ftmp2, tmp); /* 2^7 - 2 */
692 for (i = 0; i < 5; ++i) /* 2^12 - 2^6 */
693 {
694 felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp);
695 }
696 felem_mul(tmp, ftmp2, ftmp); felem_reduce(ftmp2, tmp); /* 2^12 - 1 */
697 felem_square(tmp, ftmp2); felem_reduce(ftmp3, tmp); /* 2^13 - 2 */
698 for (i = 0; i < 11; ++i) /* 2^24 - 2^12 */
699 {
700 felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp);
701 }
702 felem_mul(tmp, ftmp3, ftmp2); felem_reduce(ftmp2, tmp); /* 2^24 - 1 */
703 felem_square(tmp, ftmp2); felem_reduce(ftmp3, tmp); /* 2^25 - 2 */
704 for (i = 0; i < 23; ++i) /* 2^48 - 2^24 */
705 {
706 felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp);
707 }
708 felem_mul(tmp, ftmp3, ftmp2); felem_reduce(ftmp3, tmp); /* 2^48 - 1 */
709 felem_square(tmp, ftmp3); felem_reduce(ftmp4, tmp); /* 2^49 - 2 */
710 for (i = 0; i < 47; ++i) /* 2^96 - 2^48 */
711 {
712 felem_square(tmp, ftmp4); felem_reduce(ftmp4, tmp);
713 }
714 felem_mul(tmp, ftmp3, ftmp4); felem_reduce(ftmp3, tmp); /* 2^96 - 1 */
715 felem_square(tmp, ftmp3); felem_reduce(ftmp4, tmp); /* 2^97 - 2 */
716 for (i = 0; i < 23; ++i) /* 2^120 - 2^24 */
717 {
718 felem_square(tmp, ftmp4); felem_reduce(ftmp4, tmp);
719 }
720 felem_mul(tmp, ftmp2, ftmp4); felem_reduce(ftmp2, tmp); /* 2^120 - 1 */
721 for (i = 0; i < 6; ++i) /* 2^126 - 2^6 */
722 {
723 felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp);
724 }
725 felem_mul(tmp, ftmp2, ftmp); felem_reduce(ftmp, tmp); /* 2^126 - 1 */
726 felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); /* 2^127 - 2 */
727 felem_mul(tmp, ftmp, in); felem_reduce(ftmp, tmp); /* 2^127 - 1 */
728 for (i = 0; i < 97; ++i) /* 2^224 - 2^97 */
729 {
730 felem_square(tmp, ftmp); felem_reduce(ftmp, tmp);
731 }
732 felem_mul(tmp, ftmp, ftmp3); felem_reduce(out, tmp); /* 2^224 - 2^96 - 1 */
733 }
734
735/* Copy in constant time:
736 * if icopy == 1, copy in to out,
737 * if icopy == 0, copy out to itself. */
738static void
739copy_conditional(felem out, const felem in, limb icopy)
740 {
741 unsigned i;
742 /* icopy is a (64-bit) 0 or 1, so copy is either all-zero or all-one */
743 const limb copy = -icopy;
744 for (i = 0; i < 4; ++i)
745 {
746 const limb tmp = copy & (in[i] ^ out[i]);
747 out[i] ^= tmp;
748 }
749 }
750
751/******************************************************************************/
752/* ELLIPTIC CURVE POINT OPERATIONS
753 *
754 * Points are represented in Jacobian projective coordinates:
755 * (X, Y, Z) corresponds to the affine point (X/Z^2, Y/Z^3),
756 * or to the point at infinity if Z == 0.
757 *
758 */
759
760/* Double an elliptic curve point:
761 * (X', Y', Z') = 2 * (X, Y, Z), where
762 * X' = (3 * (X - Z^2) * (X + Z^2))^2 - 8 * X * Y^2
763 * Y' = 3 * (X - Z^2) * (X + Z^2) * (4 * X * Y^2 - X') - 8 * Y^2
764 * Z' = (Y + Z)^2 - Y^2 - Z^2 = 2 * Y * Z
765 * Outputs can equal corresponding inputs, i.e., x_out == x_in is allowed,
766 * while x_out == y_in is not (maybe this works, but it's not tested). */
767static void
768point_double(felem x_out, felem y_out, felem z_out,
769 const felem x_in, const felem y_in, const felem z_in)
770 {
771 widefelem tmp, tmp2;
772 felem delta, gamma, beta, alpha, ftmp, ftmp2;
773
774 felem_assign(ftmp, x_in);
775 felem_assign(ftmp2, x_in);
776
777 /* delta = z^2 */
778 felem_square(tmp, z_in);
779 felem_reduce(delta, tmp);
780
781 /* gamma = y^2 */
782 felem_square(tmp, y_in);
783 felem_reduce(gamma, tmp);
784
785 /* beta = x*gamma */
786 felem_mul(tmp, x_in, gamma);
787 felem_reduce(beta, tmp);
788
789 /* alpha = 3*(x-delta)*(x+delta) */
790 felem_diff(ftmp, delta);
791 /* ftmp[i] < 2^57 + 2^58 + 2 < 2^59 */
792 felem_sum(ftmp2, delta);
793 /* ftmp2[i] < 2^57 + 2^57 = 2^58 */
794 felem_scalar(ftmp2, 3);
795 /* ftmp2[i] < 3 * 2^58 < 2^60 */
796 felem_mul(tmp, ftmp, ftmp2);
797 /* tmp[i] < 2^60 * 2^59 * 4 = 2^121 */
798 felem_reduce(alpha, tmp);
799
800 /* x' = alpha^2 - 8*beta */
801 felem_square(tmp, alpha);
802 /* tmp[i] < 4 * 2^57 * 2^57 = 2^116 */
803 felem_assign(ftmp, beta);
804 felem_scalar(ftmp, 8);
805 /* ftmp[i] < 8 * 2^57 = 2^60 */
806 felem_diff_128_64(tmp, ftmp);
807 /* tmp[i] < 2^116 + 2^64 + 8 < 2^117 */
808 felem_reduce(x_out, tmp);
809
810 /* z' = (y + z)^2 - gamma - delta */
811 felem_sum(delta, gamma);
812 /* delta[i] < 2^57 + 2^57 = 2^58 */
813 felem_assign(ftmp, y_in);
814 felem_sum(ftmp, z_in);
815 /* ftmp[i] < 2^57 + 2^57 = 2^58 */
816 felem_square(tmp, ftmp);
817 /* tmp[i] < 4 * 2^58 * 2^58 = 2^118 */
818 felem_diff_128_64(tmp, delta);
819 /* tmp[i] < 2^118 + 2^64 + 8 < 2^119 */
820 felem_reduce(z_out, tmp);
821
822 /* y' = alpha*(4*beta - x') - 8*gamma^2 */
823 felem_scalar(beta, 4);
824 /* beta[i] < 4 * 2^57 = 2^59 */
825 felem_diff(beta, x_out);
826 /* beta[i] < 2^59 + 2^58 + 2 < 2^60 */
827 felem_mul(tmp, alpha, beta);
828 /* tmp[i] < 4 * 2^57 * 2^60 = 2^119 */
829 felem_square(tmp2, gamma);
830 /* tmp2[i] < 4 * 2^57 * 2^57 = 2^116 */
831 widefelem_scalar(tmp2, 8);
832 /* tmp2[i] < 8 * 2^116 = 2^119 */
833 widefelem_diff(tmp, tmp2);
834 /* tmp[i] < 2^119 + 2^120 < 2^121 */
835 felem_reduce(y_out, tmp);
836 }
837
838/* Add two elliptic curve points:
839 * (X_1, Y_1, Z_1) + (X_2, Y_2, Z_2) = (X_3, Y_3, Z_3), where
840 * X_3 = (Z_1^3 * Y_2 - Z_2^3 * Y_1)^2 - (Z_1^2 * X_2 - Z_2^2 * X_1)^3 -
841 * 2 * Z_2^2 * X_1 * (Z_1^2 * X_2 - Z_2^2 * X_1)^2
842 * 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) -
843 * Z_2^3 * Y_1 * (Z_1^2 * X_2 - Z_2^2 * X_1)^3
844 * Z_3 = (Z_1^2 * X_2 - Z_2^2 * X_1) * (Z_1 * Z_2)
845 *
846 * This runs faster if 'mixed' is set, which requires Z_2 = 1 or Z_2 = 0.
847 */
848
849/* This function is not entirely constant-time:
850 * it includes a branch for checking whether the two input points are equal,
851 * (while not equal to the point at infinity).
852 * This case never happens during single point multiplication,
853 * so there is no timing leak for ECDH or ECDSA signing. */
854static void point_add(felem x3, felem y3, felem z3,
855 const felem x1, const felem y1, const felem z1,
856 const int mixed, const felem x2, const felem y2, const felem z2)
857 {
858 felem ftmp, ftmp2, ftmp3, ftmp4, ftmp5, x_out, y_out, z_out;
859 widefelem tmp, tmp2;
860 limb z1_is_zero, z2_is_zero, x_equal, y_equal;
861
862 if (!mixed)
863 {
864 /* ftmp2 = z2^2 */
865 felem_square(tmp, z2);
866 felem_reduce(ftmp2, tmp);
867
868 /* ftmp4 = z2^3 */
869 felem_mul(tmp, ftmp2, z2);
870 felem_reduce(ftmp4, tmp);
871
872 /* ftmp4 = z2^3*y1 */
873 felem_mul(tmp2, ftmp4, y1);
874 felem_reduce(ftmp4, tmp2);
875
876 /* ftmp2 = z2^2*x1 */
877 felem_mul(tmp2, ftmp2, x1);
878 felem_reduce(ftmp2, tmp2);
879 }
880 else
881 {
882 /* We'll assume z2 = 1 (special case z2 = 0 is handled later) */
883
884 /* ftmp4 = z2^3*y1 */
885 felem_assign(ftmp4, y1);
886
887 /* ftmp2 = z2^2*x1 */
888 felem_assign(ftmp2, x1);
889 }
890
891 /* ftmp = z1^2 */
892 felem_square(tmp, z1);
893 felem_reduce(ftmp, tmp);
894
895 /* ftmp3 = z1^3 */
896 felem_mul(tmp, ftmp, z1);
897 felem_reduce(ftmp3, tmp);
898
899 /* tmp = z1^3*y2 */
900 felem_mul(tmp, ftmp3, y2);
901 /* tmp[i] < 4 * 2^57 * 2^57 = 2^116 */
902
903 /* ftmp3 = z1^3*y2 - z2^3*y1 */
904 felem_diff_128_64(tmp, ftmp4);
905 /* tmp[i] < 2^116 + 2^64 + 8 < 2^117 */
906 felem_reduce(ftmp3, tmp);
907
908 /* tmp = z1^2*x2 */
909 felem_mul(tmp, ftmp, x2);
910 /* tmp[i] < 4 * 2^57 * 2^57 = 2^116 */
911
912 /* ftmp = z1^2*x2 - z2^2*x1 */
913 felem_diff_128_64(tmp, ftmp2);
914 /* tmp[i] < 2^116 + 2^64 + 8 < 2^117 */
915 felem_reduce(ftmp, tmp);
916
917 /* the formulae are incorrect if the points are equal
918 * so we check for this and do doubling if this happens */
919 x_equal = felem_is_zero(ftmp);
920 y_equal = felem_is_zero(ftmp3);
921 z1_is_zero = felem_is_zero(z1);
922 z2_is_zero = felem_is_zero(z2);
923 /* In affine coordinates, (X_1, Y_1) == (X_2, Y_2) */
924 if (x_equal && y_equal && !z1_is_zero && !z2_is_zero)
925 {
926 point_double(x3, y3, z3, x1, y1, z1);
927 return;
928 }
929
930 /* ftmp5 = z1*z2 */
931 if (!mixed)
932 {
933 felem_mul(tmp, z1, z2);
934 felem_reduce(ftmp5, tmp);
935 }
936 else
937 {
938 /* special case z2 = 0 is handled later */
939 felem_assign(ftmp5, z1);
940 }
941
942 /* z_out = (z1^2*x2 - z2^2*x1)*(z1*z2) */
943 felem_mul(tmp, ftmp, ftmp5);
944 felem_reduce(z_out, tmp);
945
946 /* ftmp = (z1^2*x2 - z2^2*x1)^2 */
947 felem_assign(ftmp5, ftmp);
948 felem_square(tmp, ftmp);
949 felem_reduce(ftmp, tmp);
950
951 /* ftmp5 = (z1^2*x2 - z2^2*x1)^3 */
952 felem_mul(tmp, ftmp, ftmp5);
953 felem_reduce(ftmp5, tmp);
954
955 /* ftmp2 = z2^2*x1*(z1^2*x2 - z2^2*x1)^2 */
956 felem_mul(tmp, ftmp2, ftmp);
957 felem_reduce(ftmp2, tmp);
958
959 /* tmp = z2^3*y1*(z1^2*x2 - z2^2*x1)^3 */
960 felem_mul(tmp, ftmp4, ftmp5);
961 /* tmp[i] < 4 * 2^57 * 2^57 = 2^116 */
962
963 /* tmp2 = (z1^3*y2 - z2^3*y1)^2 */
964 felem_square(tmp2, ftmp3);
965 /* tmp2[i] < 4 * 2^57 * 2^57 < 2^116 */
966
967 /* tmp2 = (z1^3*y2 - z2^3*y1)^2 - (z1^2*x2 - z2^2*x1)^3 */
968 felem_diff_128_64(tmp2, ftmp5);
969 /* tmp2[i] < 2^116 + 2^64 + 8 < 2^117 */
970
971 /* ftmp5 = 2*z2^2*x1*(z1^2*x2 - z2^2*x1)^2 */
972 felem_assign(ftmp5, ftmp2);
973 felem_scalar(ftmp5, 2);
974 /* ftmp5[i] < 2 * 2^57 = 2^58 */
975
976 /* x_out = (z1^3*y2 - z2^3*y1)^2 - (z1^2*x2 - z2^2*x1)^3 -
977 2*z2^2*x1*(z1^2*x2 - z2^2*x1)^2 */
978 felem_diff_128_64(tmp2, ftmp5);
979 /* tmp2[i] < 2^117 + 2^64 + 8 < 2^118 */
980 felem_reduce(x_out, tmp2);
981
982 /* ftmp2 = z2^2*x1*(z1^2*x2 - z2^2*x1)^2 - x_out */
983 felem_diff(ftmp2, x_out);
984 /* ftmp2[i] < 2^57 + 2^58 + 2 < 2^59 */
985
986 /* tmp2 = (z1^3*y2 - z2^3*y1)*(z2^2*x1*(z1^2*x2 - z2^2*x1)^2 - x_out) */
987 felem_mul(tmp2, ftmp3, ftmp2);
988 /* tmp2[i] < 4 * 2^57 * 2^59 = 2^118 */
989
990 /* y_out = (z1^3*y2 - z2^3*y1)*(z2^2*x1*(z1^2*x2 - z2^2*x1)^2 - x_out) -
991 z2^3*y1*(z1^2*x2 - z2^2*x1)^3 */
992 widefelem_diff(tmp2, tmp);
993 /* tmp2[i] < 2^118 + 2^120 < 2^121 */
994 felem_reduce(y_out, tmp2);
995
996 /* the result (x_out, y_out, z_out) is incorrect if one of the inputs is
997 * the point at infinity, so we need to check for this separately */
998
999 /* if point 1 is at infinity, copy point 2 to output, and vice versa */
1000 copy_conditional(x_out, x2, z1_is_zero);
1001 copy_conditional(x_out, x1, z2_is_zero);
1002 copy_conditional(y_out, y2, z1_is_zero);
1003 copy_conditional(y_out, y1, z2_is_zero);
1004 copy_conditional(z_out, z2, z1_is_zero);
1005 copy_conditional(z_out, z1, z2_is_zero);
1006 felem_assign(x3, x_out);
1007 felem_assign(y3, y_out);
1008 felem_assign(z3, z_out);
1009 }
1010
1011/* select_point selects the |idx|th point from a precomputation table and
1012 * copies it to out. */
1013static void select_point(const u64 idx, unsigned int size, const felem pre_comp[/*size*/][3], felem out[3])
1014 {
1015 unsigned i, j;
1016 limb *outlimbs = &out[0][0];
1017 memset(outlimbs, 0, 3 * sizeof(felem));
1018
1019 for (i = 0; i < size; i++)
1020 {
1021 const limb *inlimbs = &pre_comp[i][0][0];
1022 u64 mask = i ^ idx;
1023 mask |= mask >> 4;
1024 mask |= mask >> 2;
1025 mask |= mask >> 1;
1026 mask &= 1;
1027 mask--;
1028 for (j = 0; j < 4 * 3; j++)
1029 outlimbs[j] |= inlimbs[j] & mask;
1030 }
1031 }
1032
1033/* get_bit returns the |i|th bit in |in| */
1034static char get_bit(const felem_bytearray in, unsigned i)
1035 {
1036 if (i >= 224)
1037 return 0;
1038 return (in[i >> 3] >> (i & 7)) & 1;
1039 }
1040
1041/* Interleaved point multiplication using precomputed point multiples:
1042 * The small point multiples 0*P, 1*P, ..., 16*P are in pre_comp[],
1043 * the scalars in scalars[]. If g_scalar is non-NULL, we also add this multiple
1044 * of the generator, using certain (large) precomputed multiples in g_pre_comp.
1045 * Output point (X, Y, Z) is stored in x_out, y_out, z_out */
1046static void batch_mul(felem x_out, felem y_out, felem z_out,
1047 const felem_bytearray scalars[], const unsigned num_points, const u8 *g_scalar,
1048 const int mixed, const felem pre_comp[][17][3], const felem g_pre_comp[2][16][3])
1049 {
1050 int i, skip;
1051 unsigned num;
1052 unsigned gen_mul = (g_scalar != NULL);
1053 felem nq[3], tmp[4];
1054 u64 bits;
1055 u8 sign, digit;
1056
1057 /* set nq to the point at infinity */
1058 memset(nq, 0, 3 * sizeof(felem));
1059
1060 /* Loop over all scalars msb-to-lsb, interleaving additions
1061 * of multiples of the generator (two in each of the last 28 rounds)
1062 * and additions of other points multiples (every 5th round).
1063 */
1064 skip = 1; /* save two point operations in the first round */
1065 for (i = (num_points ? 220 : 27); i >= 0; --i)
1066 {
1067 /* double */
1068 if (!skip)
1069 point_double(nq[0], nq[1], nq[2], nq[0], nq[1], nq[2]);
1070
1071 /* add multiples of the generator */
1072 if (gen_mul && (i <= 27))
1073 {
1074 /* first, look 28 bits upwards */
1075 bits = get_bit(g_scalar, i + 196) << 3;
1076 bits |= get_bit(g_scalar, i + 140) << 2;
1077 bits |= get_bit(g_scalar, i + 84) << 1;
1078 bits |= get_bit(g_scalar, i + 28);
1079 /* select the point to add, in constant time */
1080 select_point(bits, 16, g_pre_comp[1], tmp);
1081
1082 if (!skip)
1083 {
1084 point_add(nq[0], nq[1], nq[2],
1085 nq[0], nq[1], nq[2],
1086 1 /* mixed */, tmp[0], tmp[1], tmp[2]);
1087 }
1088 else
1089 {
1090 memcpy(nq, tmp, 3 * sizeof(felem));
1091 skip = 0;
1092 }
1093
1094 /* second, look at the current position */
1095 bits = get_bit(g_scalar, i + 168) << 3;
1096 bits |= get_bit(g_scalar, i + 112) << 2;
1097 bits |= get_bit(g_scalar, i + 56) << 1;
1098 bits |= get_bit(g_scalar, i);
1099 /* select the point to add, in constant time */
1100 select_point(bits, 16, g_pre_comp[0], tmp);
1101 point_add(nq[0], nq[1], nq[2],
1102 nq[0], nq[1], nq[2],
1103 1 /* mixed */, tmp[0], tmp[1], tmp[2]);
1104 }
1105
1106 /* do other additions every 5 doublings */
1107 if (num_points && (i % 5 == 0))
1108 {
1109 /* loop over all scalars */
1110 for (num = 0; num < num_points; ++num)
1111 {
1112 bits = get_bit(scalars[num], i + 4) << 5;
1113 bits |= get_bit(scalars[num], i + 3) << 4;
1114 bits |= get_bit(scalars[num], i + 2) << 3;
1115 bits |= get_bit(scalars[num], i + 1) << 2;
1116 bits |= get_bit(scalars[num], i) << 1;
1117 bits |= get_bit(scalars[num], i - 1);
1118 ec_GFp_nistp_recode_scalar_bits(&sign, &digit, bits);
1119
1120 /* select the point to add or subtract */
1121 select_point(digit, 17, pre_comp[num], tmp);
1122 felem_neg(tmp[3], tmp[1]); /* (X, -Y, Z) is the negative point */
1123 copy_conditional(tmp[1], tmp[3], sign);
1124
1125 if (!skip)
1126 {
1127 point_add(nq[0], nq[1], nq[2],
1128 nq[0], nq[1], nq[2],
1129 mixed, tmp[0], tmp[1], tmp[2]);
1130 }
1131 else
1132 {
1133 memcpy(nq, tmp, 3 * sizeof(felem));
1134 skip = 0;
1135 }
1136 }
1137 }
1138 }
1139 felem_assign(x_out, nq[0]);
1140 felem_assign(y_out, nq[1]);
1141 felem_assign(z_out, nq[2]);
1142 }
1143
1144/******************************************************************************/
1145/* FUNCTIONS TO MANAGE PRECOMPUTATION
1146 */
1147
1148static NISTP224_PRE_COMP *nistp224_pre_comp_new()
1149 {
1150 NISTP224_PRE_COMP *ret = NULL;
1151 ret = (NISTP224_PRE_COMP *) OPENSSL_malloc(sizeof *ret);
1152 if (!ret)
1153 {
1154 ECerr(EC_F_NISTP224_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE);
1155 return ret;
1156 }
1157 memset(ret->g_pre_comp, 0, sizeof(ret->g_pre_comp));
1158 ret->references = 1;
1159 return ret;
1160 }
1161
1162static void *nistp224_pre_comp_dup(void *src_)
1163 {
1164 NISTP224_PRE_COMP *src = src_;
1165
1166 /* no need to actually copy, these objects never change! */
1167 CRYPTO_add(&src->references, 1, CRYPTO_LOCK_EC_PRE_COMP);
1168
1169 return src_;
1170 }
1171
1172static void nistp224_pre_comp_free(void *pre_)
1173 {
1174 int i;
1175 NISTP224_PRE_COMP *pre = pre_;
1176
1177 if (!pre)
1178 return;
1179
1180 i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP);
1181 if (i > 0)
1182 return;
1183
1184 OPENSSL_free(pre);
1185 }
1186
1187static void nistp224_pre_comp_clear_free(void *pre_)
1188 {
1189 int i;
1190 NISTP224_PRE_COMP *pre = pre_;
1191
1192 if (!pre)
1193 return;
1194
1195 i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP);
1196 if (i > 0)
1197 return;
1198
1199 OPENSSL_cleanse(pre, sizeof *pre);
1200 OPENSSL_free(pre);
1201 }
1202
1203/******************************************************************************/
1204/* OPENSSL EC_METHOD FUNCTIONS
1205 */
1206
1207int ec_GFp_nistp224_group_init(EC_GROUP *group)
1208 {
1209 int ret;
1210 ret = ec_GFp_simple_group_init(group);
1211 group->a_is_minus3 = 1;
1212 return ret;
1213 }
1214
1215int ec_GFp_nistp224_group_set_curve(EC_GROUP *group, const BIGNUM *p,
1216 const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
1217 {
1218 int ret = 0;
1219 BN_CTX *new_ctx = NULL;
1220 BIGNUM *curve_p, *curve_a, *curve_b;
1221
1222 if (ctx == NULL)
1223 if ((ctx = new_ctx = BN_CTX_new()) == NULL) return 0;
1224 BN_CTX_start(ctx);
1225 if (((curve_p = BN_CTX_get(ctx)) == NULL) ||
1226 ((curve_a = BN_CTX_get(ctx)) == NULL) ||
1227 ((curve_b = BN_CTX_get(ctx)) == NULL)) goto err;
1228 BN_bin2bn(nistp224_curve_params[0], sizeof(felem_bytearray), curve_p);
1229 BN_bin2bn(nistp224_curve_params[1], sizeof(felem_bytearray), curve_a);
1230 BN_bin2bn(nistp224_curve_params[2], sizeof(felem_bytearray), curve_b);
1231 if ((BN_cmp(curve_p, p)) || (BN_cmp(curve_a, a)) ||
1232 (BN_cmp(curve_b, b)))
1233 {
1234 ECerr(EC_F_EC_GFP_NISTP224_GROUP_SET_CURVE,
1235 EC_R_WRONG_CURVE_PARAMETERS);
1236 goto err;
1237 }
1238 group->field_mod_func = BN_nist_mod_224;
1239 ret = ec_GFp_simple_group_set_curve(group, p, a, b, ctx);
1240err:
1241 BN_CTX_end(ctx);
1242 if (new_ctx != NULL)
1243 BN_CTX_free(new_ctx);
1244 return ret;
1245 }
1246
1247/* Takes the Jacobian coordinates (X, Y, Z) of a point and returns
1248 * (X', Y') = (X/Z^2, Y/Z^3) */
1249int ec_GFp_nistp224_point_get_affine_coordinates(const EC_GROUP *group,
1250 const EC_POINT *point, BIGNUM *x, BIGNUM *y, BN_CTX *ctx)
1251 {
1252 felem z1, z2, x_in, y_in, x_out, y_out;
1253 widefelem tmp;
1254
1255 if (EC_POINT_is_at_infinity(group, point))
1256 {
1257 ECerr(EC_F_EC_GFP_NISTP224_POINT_GET_AFFINE_COORDINATES,
1258 EC_R_POINT_AT_INFINITY);
1259 return 0;
1260 }
1261 if ((!BN_to_felem(x_in, &point->X)) || (!BN_to_felem(y_in, &point->Y)) ||
1262 (!BN_to_felem(z1, &point->Z))) return 0;
1263 felem_inv(z2, z1);
1264 felem_square(tmp, z2); felem_reduce(z1, tmp);
1265 felem_mul(tmp, x_in, z1); felem_reduce(x_in, tmp);
1266 felem_contract(x_out, x_in);
1267 if (x != NULL)
1268 {
1269 if (!felem_to_BN(x, x_out)) {
1270 ECerr(EC_F_EC_GFP_NISTP224_POINT_GET_AFFINE_COORDINATES,
1271 ERR_R_BN_LIB);
1272 return 0;
1273 }
1274 }
1275 felem_mul(tmp, z1, z2); felem_reduce(z1, tmp);
1276 felem_mul(tmp, y_in, z1); felem_reduce(y_in, tmp);
1277 felem_contract(y_out, y_in);
1278 if (y != NULL)
1279 {
1280 if (!felem_to_BN(y, y_out)) {
1281 ECerr(EC_F_EC_GFP_NISTP224_POINT_GET_AFFINE_COORDINATES,
1282 ERR_R_BN_LIB);
1283 return 0;
1284 }
1285 }
1286 return 1;
1287 }
1288
1289static void make_points_affine(size_t num, felem points[/*num*/][3], felem tmp_felems[/*num+1*/])
1290 {
1291 /* Runs in constant time, unless an input is the point at infinity
1292 * (which normally shouldn't happen). */
1293 ec_GFp_nistp_points_make_affine_internal(
1294 num,
1295 points,
1296 sizeof(felem),
1297 tmp_felems,
1298 (void (*)(void *)) felem_one,
1299 (int (*)(const void *)) felem_is_zero_int,
1300 (void (*)(void *, const void *)) felem_assign,
1301 (void (*)(void *, const void *)) felem_square_reduce,
1302 (void (*)(void *, const void *, const void *)) felem_mul_reduce,
1303 (void (*)(void *, const void *)) felem_inv,
1304 (void (*)(void *, const void *)) felem_contract);
1305 }
1306
1307/* Computes scalar*generator + \sum scalars[i]*points[i], ignoring NULL values
1308 * Result is stored in r (r can equal one of the inputs). */
1309int ec_GFp_nistp224_points_mul(const EC_GROUP *group, EC_POINT *r,
1310 const BIGNUM *scalar, size_t num, const EC_POINT *points[],
1311 const BIGNUM *scalars[], BN_CTX *ctx)
1312 {
1313 int ret = 0;
1314 int j;
1315 unsigned i;
1316 int mixed = 0;
1317 BN_CTX *new_ctx = NULL;
1318 BIGNUM *x, *y, *z, *tmp_scalar;
1319 felem_bytearray g_secret;
1320 felem_bytearray *secrets = NULL;
1321 felem (*pre_comp)[17][3] = NULL;
1322 felem *tmp_felems = NULL;
1323 felem_bytearray tmp;
1324 unsigned num_bytes;
1325 int have_pre_comp = 0;
1326 size_t num_points = num;
1327 felem x_in, y_in, z_in, x_out, y_out, z_out;
1328 NISTP224_PRE_COMP *pre = NULL;
1329 const felem (*g_pre_comp)[16][3] = NULL;
1330 EC_POINT *generator = NULL;
1331 const EC_POINT *p = NULL;
1332 const BIGNUM *p_scalar = NULL;
1333
1334 if (ctx == NULL)
1335 if ((ctx = new_ctx = BN_CTX_new()) == NULL) return 0;
1336 BN_CTX_start(ctx);
1337 if (((x = BN_CTX_get(ctx)) == NULL) ||
1338 ((y = BN_CTX_get(ctx)) == NULL) ||
1339 ((z = BN_CTX_get(ctx)) == NULL) ||
1340 ((tmp_scalar = BN_CTX_get(ctx)) == NULL))
1341 goto err;
1342
1343 if (scalar != NULL)
1344 {
1345 pre = EC_EX_DATA_get_data(group->extra_data,
1346 nistp224_pre_comp_dup, nistp224_pre_comp_free,
1347 nistp224_pre_comp_clear_free);
1348 if (pre)
1349 /* we have precomputation, try to use it */
1350 g_pre_comp = (const felem (*)[16][3]) pre->g_pre_comp;
1351 else
1352 /* try to use the standard precomputation */
1353 g_pre_comp = &gmul[0];
1354 generator = EC_POINT_new(group);
1355 if (generator == NULL)
1356 goto err;
1357 /* get the generator from precomputation */
1358 if (!felem_to_BN(x, g_pre_comp[0][1][0]) ||
1359 !felem_to_BN(y, g_pre_comp[0][1][1]) ||
1360 !felem_to_BN(z, g_pre_comp[0][1][2]))
1361 {
1362 ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_BN_LIB);
1363 goto err;
1364 }
1365 if (!EC_POINT_set_Jprojective_coordinates_GFp(group,
1366 generator, x, y, z, ctx))
1367 goto err;
1368 if (0 == EC_POINT_cmp(group, generator, group->generator, ctx))
1369 /* precomputation matches generator */
1370 have_pre_comp = 1;
1371 else
1372 /* we don't have valid precomputation:
1373 * treat the generator as a random point */
1374 num_points = num_points + 1;
1375 }
1376
1377 if (num_points > 0)
1378 {
1379 if (num_points >= 3)
1380 {
1381 /* unless we precompute multiples for just one or two points,
1382 * converting those into affine form is time well spent */
1383 mixed = 1;
1384 }
1385 secrets = OPENSSL_malloc(num_points * sizeof(felem_bytearray));
1386 pre_comp = OPENSSL_malloc(num_points * 17 * 3 * sizeof(felem));
1387 if (mixed)
1388 tmp_felems = OPENSSL_malloc((num_points * 17 + 1) * sizeof(felem));
1389 if ((secrets == NULL) || (pre_comp == NULL) || (mixed && (tmp_felems == NULL)))
1390 {
1391 ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_MALLOC_FAILURE);
1392 goto err;
1393 }
1394
1395 /* we treat NULL scalars as 0, and NULL points as points at infinity,
1396 * i.e., they contribute nothing to the linear combination */
1397 memset(secrets, 0, num_points * sizeof(felem_bytearray));
1398 memset(pre_comp, 0, num_points * 17 * 3 * sizeof(felem));
1399 for (i = 0; i < num_points; ++i)
1400 {
1401 if (i == num)
1402 /* the generator */
1403 {
1404 p = EC_GROUP_get0_generator(group);
1405 p_scalar = scalar;
1406 }
1407 else
1408 /* the i^th point */
1409 {
1410 p = points[i];
1411 p_scalar = scalars[i];
1412 }
1413 if ((p_scalar != NULL) && (p != NULL))
1414 {
1415 /* reduce scalar to 0 <= scalar < 2^224 */
1416 if ((BN_num_bits(p_scalar) > 224) || (BN_is_negative(p_scalar)))
1417 {
1418 /* this is an unusual input, and we don't guarantee
1419 * constant-timeness */
1420 if (!BN_nnmod(tmp_scalar, p_scalar, &group->order, ctx))
1421 {
1422 ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_BN_LIB);
1423 goto err;
1424 }
1425 num_bytes = BN_bn2bin(tmp_scalar, tmp);
1426 }
1427 else
1428 num_bytes = BN_bn2bin(p_scalar, tmp);
1429 flip_endian(secrets[i], tmp, num_bytes);
1430 /* precompute multiples */
1431 if ((!BN_to_felem(x_out, &p->X)) ||
1432 (!BN_to_felem(y_out, &p->Y)) ||
1433 (!BN_to_felem(z_out, &p->Z))) goto err;
1434 felem_assign(pre_comp[i][1][0], x_out);
1435 felem_assign(pre_comp[i][1][1], y_out);
1436 felem_assign(pre_comp[i][1][2], z_out);
1437 for (j = 2; j <= 16; ++j)
1438 {
1439 if (j & 1)
1440 {
1441 point_add(
1442 pre_comp[i][j][0], pre_comp[i][j][1], pre_comp[i][j][2],
1443 pre_comp[i][1][0], pre_comp[i][1][1], pre_comp[i][1][2],
1444 0, pre_comp[i][j-1][0], pre_comp[i][j-1][1], pre_comp[i][j-1][2]);
1445 }
1446 else
1447 {
1448 point_double(
1449 pre_comp[i][j][0], pre_comp[i][j][1], pre_comp[i][j][2],
1450 pre_comp[i][j/2][0], pre_comp[i][j/2][1], pre_comp[i][j/2][2]);
1451 }
1452 }
1453 }
1454 }
1455 if (mixed)
1456 make_points_affine(num_points * 17, pre_comp[0], tmp_felems);
1457 }
1458
1459 /* the scalar for the generator */
1460 if ((scalar != NULL) && (have_pre_comp))
1461 {
1462 memset(g_secret, 0, sizeof g_secret);
1463 /* reduce scalar to 0 <= scalar < 2^224 */
1464 if ((BN_num_bits(scalar) > 224) || (BN_is_negative(scalar)))
1465 {
1466 /* this is an unusual input, and we don't guarantee
1467 * constant-timeness */
1468 if (!BN_nnmod(tmp_scalar, scalar, &group->order, ctx))
1469 {
1470 ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_BN_LIB);
1471 goto err;
1472 }
1473 num_bytes = BN_bn2bin(tmp_scalar, tmp);
1474 }
1475 else
1476 num_bytes = BN_bn2bin(scalar, tmp);
1477 flip_endian(g_secret, tmp, num_bytes);
1478 /* do the multiplication with generator precomputation*/
1479 batch_mul(x_out, y_out, z_out,
1480 (const felem_bytearray (*)) secrets, num_points,
1481 g_secret,
1482 mixed, (const felem (*)[17][3]) pre_comp,
1483 g_pre_comp);
1484 }
1485 else
1486 /* do the multiplication without generator precomputation */
1487 batch_mul(x_out, y_out, z_out,
1488 (const felem_bytearray (*)) secrets, num_points,
1489 NULL, mixed, (const felem (*)[17][3]) pre_comp, NULL);
1490 /* reduce the output to its unique minimal representation */
1491 felem_contract(x_in, x_out);
1492 felem_contract(y_in, y_out);
1493 felem_contract(z_in, z_out);
1494 if ((!felem_to_BN(x, x_in)) || (!felem_to_BN(y, y_in)) ||
1495 (!felem_to_BN(z, z_in)))
1496 {
1497 ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_BN_LIB);
1498 goto err;
1499 }
1500 ret = EC_POINT_set_Jprojective_coordinates_GFp(group, r, x, y, z, ctx);
1501
1502err:
1503 BN_CTX_end(ctx);
1504 if (generator != NULL)
1505 EC_POINT_free(generator);
1506 if (new_ctx != NULL)
1507 BN_CTX_free(new_ctx);
1508 if (secrets != NULL)
1509 OPENSSL_free(secrets);
1510 if (pre_comp != NULL)
1511 OPENSSL_free(pre_comp);
1512 if (tmp_felems != NULL)
1513 OPENSSL_free(tmp_felems);
1514 return ret;
1515 }
1516
1517int ec_GFp_nistp224_precompute_mult(EC_GROUP *group, BN_CTX *ctx)
1518 {
1519 int ret = 0;
1520 NISTP224_PRE_COMP *pre = NULL;
1521 int i, j;
1522 BN_CTX *new_ctx = NULL;
1523 BIGNUM *x, *y;
1524 EC_POINT *generator = NULL;
1525 felem tmp_felems[32];
1526
1527 /* throw away old precomputation */
1528 EC_EX_DATA_free_data(&group->extra_data, nistp224_pre_comp_dup,
1529 nistp224_pre_comp_free, nistp224_pre_comp_clear_free);
1530 if (ctx == NULL)
1531 if ((ctx = new_ctx = BN_CTX_new()) == NULL) return 0;
1532 BN_CTX_start(ctx);
1533 if (((x = BN_CTX_get(ctx)) == NULL) ||
1534 ((y = BN_CTX_get(ctx)) == NULL))
1535 goto err;
1536 /* get the generator */
1537 if (group->generator == NULL) goto err;
1538 generator = EC_POINT_new(group);
1539 if (generator == NULL)
1540 goto err;
1541 BN_bin2bn(nistp224_curve_params[3], sizeof (felem_bytearray), x);
1542 BN_bin2bn(nistp224_curve_params[4], sizeof (felem_bytearray), y);
1543 if (!EC_POINT_set_affine_coordinates_GFp(group, generator, x, y, ctx))
1544 goto err;
1545 if ((pre = nistp224_pre_comp_new()) == NULL)
1546 goto err;
1547 /* if the generator is the standard one, use built-in precomputation */
1548 if (0 == EC_POINT_cmp(group, generator, group->generator, ctx))
1549 {
1550 memcpy(pre->g_pre_comp, gmul, sizeof(pre->g_pre_comp));
1551 ret = 1;
1552 goto err;
1553 }
1554 if ((!BN_to_felem(pre->g_pre_comp[0][1][0], &group->generator->X)) ||
1555 (!BN_to_felem(pre->g_pre_comp[0][1][1], &group->generator->Y)) ||
1556 (!BN_to_felem(pre->g_pre_comp[0][1][2], &group->generator->Z)))
1557 goto err;
1558 /* compute 2^56*G, 2^112*G, 2^168*G for the first table,
1559 * 2^28*G, 2^84*G, 2^140*G, 2^196*G for the second one
1560 */
1561 for (i = 1; i <= 8; i <<= 1)
1562 {
1563 point_double(
1564 pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2],
1565 pre->g_pre_comp[0][i][0], pre->g_pre_comp[0][i][1], pre->g_pre_comp[0][i][2]);
1566 for (j = 0; j < 27; ++j)
1567 {
1568 point_double(
1569 pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2],
1570 pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2]);
1571 }
1572 if (i == 8)
1573 break;
1574 point_double(
1575 pre->g_pre_comp[0][2*i][0], pre->g_pre_comp[0][2*i][1], pre->g_pre_comp[0][2*i][2],
1576 pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2]);
1577 for (j = 0; j < 27; ++j)
1578 {
1579 point_double(
1580 pre->g_pre_comp[0][2*i][0], pre->g_pre_comp[0][2*i][1], pre->g_pre_comp[0][2*i][2],
1581 pre->g_pre_comp[0][2*i][0], pre->g_pre_comp[0][2*i][1], pre->g_pre_comp[0][2*i][2]);
1582 }
1583 }
1584 for (i = 0; i < 2; i++)
1585 {
1586 /* g_pre_comp[i][0] is the point at infinity */
1587 memset(pre->g_pre_comp[i][0], 0, sizeof(pre->g_pre_comp[i][0]));
1588 /* the remaining multiples */
1589 /* 2^56*G + 2^112*G resp. 2^84*G + 2^140*G */
1590 point_add(
1591 pre->g_pre_comp[i][6][0], pre->g_pre_comp[i][6][1],
1592 pre->g_pre_comp[i][6][2], pre->g_pre_comp[i][4][0],
1593 pre->g_pre_comp[i][4][1], pre->g_pre_comp[i][4][2],
1594 0, pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1],
1595 pre->g_pre_comp[i][2][2]);
1596 /* 2^56*G + 2^168*G resp. 2^84*G + 2^196*G */
1597 point_add(
1598 pre->g_pre_comp[i][10][0], pre->g_pre_comp[i][10][1],
1599 pre->g_pre_comp[i][10][2], pre->g_pre_comp[i][8][0],
1600 pre->g_pre_comp[i][8][1], pre->g_pre_comp[i][8][2],
1601 0, pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1],
1602 pre->g_pre_comp[i][2][2]);
1603 /* 2^112*G + 2^168*G resp. 2^140*G + 2^196*G */
1604 point_add(
1605 pre->g_pre_comp[i][12][0], pre->g_pre_comp[i][12][1],
1606 pre->g_pre_comp[i][12][2], pre->g_pre_comp[i][8][0],
1607 pre->g_pre_comp[i][8][1], pre->g_pre_comp[i][8][2],
1608 0, pre->g_pre_comp[i][4][0], pre->g_pre_comp[i][4][1],
1609 pre->g_pre_comp[i][4][2]);
1610 /* 2^56*G + 2^112*G + 2^168*G resp. 2^84*G + 2^140*G + 2^196*G */
1611 point_add(
1612 pre->g_pre_comp[i][14][0], pre->g_pre_comp[i][14][1],
1613 pre->g_pre_comp[i][14][2], pre->g_pre_comp[i][12][0],
1614 pre->g_pre_comp[i][12][1], pre->g_pre_comp[i][12][2],
1615 0, pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1],
1616 pre->g_pre_comp[i][2][2]);
1617 for (j = 1; j < 8; ++j)
1618 {
1619 /* odd multiples: add G resp. 2^28*G */
1620 point_add(
1621 pre->g_pre_comp[i][2*j+1][0], pre->g_pre_comp[i][2*j+1][1],
1622 pre->g_pre_comp[i][2*j+1][2], pre->g_pre_comp[i][2*j][0],
1623 pre->g_pre_comp[i][2*j][1], pre->g_pre_comp[i][2*j][2],
1624 0, pre->g_pre_comp[i][1][0], pre->g_pre_comp[i][1][1],
1625 pre->g_pre_comp[i][1][2]);
1626 }
1627 }
1628 make_points_affine(31, &(pre->g_pre_comp[0][1]), tmp_felems);
1629
1630 if (!EC_EX_DATA_set_data(&group->extra_data, pre, nistp224_pre_comp_dup,
1631 nistp224_pre_comp_free, nistp224_pre_comp_clear_free))
1632 goto err;
1633 ret = 1;
1634 pre = NULL;
1635 err:
1636 BN_CTX_end(ctx);
1637 if (generator != NULL)
1638 EC_POINT_free(generator);
1639 if (new_ctx != NULL)
1640 BN_CTX_free(new_ctx);
1641 if (pre)
1642 nistp224_pre_comp_free(pre);
1643 return ret;
1644 }
1645
1646int ec_GFp_nistp224_have_precompute_mult(const EC_GROUP *group)
1647 {
1648 if (EC_EX_DATA_get_data(group->extra_data, nistp224_pre_comp_dup,
1649 nistp224_pre_comp_free, nistp224_pre_comp_clear_free)
1650 != NULL)
1651 return 1;
1652 else
1653 return 0;
1654 }
1655
1656#else
1657static void *dummy=&dummy;
1658#endif
generated by cgit v1.2.3-55-g6feb (git 2.39.1) at 2025-08-04 20:07:18 +0000