1 /* crypto/ec/ecp_nistp224.c */
3 * Written by Emilia Kasper (Google) for the OpenSSL project.
5 /* Copyright 2011 Google Inc.
7 * Licensed under the Apache License, Version 2.0 (the "License");
9 * you may not use this file except in compliance with the License.
10 * You may obtain a copy of the License at
12 * http://www.apache.org/licenses/LICENSE-2.0
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.
22 * A 64-bit implementation of the NIST P-224 elliptic curve point multiplication
24 * Inspired by Daniel J. Bernstein's public domain nistp224 implementation
25 * and Adam Langley's public domain 64-bit C implementation of curve25519
28 #include <openssl/opensslconf.h>
29 #ifndef OPENSSL_NO_EC_NISTP_64_GCC_128
31 # ifndef OPENSSL_SYS_VMS
34 # include <inttypes.h>
38 # include <openssl/err.h>
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
46 # error "Need GCC 3.1 or later to define type uint128_t"
53 /******************************************************************************/
55 * INTERNAL REPRESENTATION OF FIELD ELEMENTS
57 * Field elements are represented as a_0 + 2^56*a_1 + 2^112*a_2 + 2^168*a_3
58 * using 64-bit coefficients called 'limbs',
59 * and sometimes (for multiplication results) as
60 * 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
61 * using 128-bit coefficients called 'widelimbs'.
62 * A 4-limb representation is an 'felem';
63 * a 7-widelimb representation is a 'widefelem'.
64 * Even within felems, bits of adjacent limbs overlap, and we don't always
65 * reduce the representations: we ensure that inputs to each felem
66 * multiplication satisfy a_i < 2^60, so outputs satisfy b_i < 4*2^60*2^60,
67 * and fit into a 128-bit word without overflow. The coefficients are then
68 * again partially reduced to obtain an felem satisfying a_i < 2^57.
69 * We only reduce to the unique minimal representation at the end of the
73 typedef uint64_t limb
;
74 typedef uint128_t widelimb
;
76 typedef limb felem
[4];
77 typedef widelimb widefelem
[7];
80 * Field element represented as a byte arrary. 28*8 = 224 bits is also the
81 * group order size for the elliptic curve, and we also use this type for
82 * scalars for point multiplication.
84 typedef u8 felem_bytearray
[28];
86 static const felem_bytearray nistp224_curve_params
[5] = {
87 {0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* p */
88 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x00,
89 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01},
90 {0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* a */
91 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF, 0xFF,
92 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFE},
93 {0xB4, 0x05, 0x0A, 0x85, 0x0C, 0x04, 0xB3, 0xAB, 0xF5, 0x41, /* b */
94 0x32, 0x56, 0x50, 0x44, 0xB0, 0xB7, 0xD7, 0xBF, 0xD8, 0xBA,
95 0x27, 0x0B, 0x39, 0x43, 0x23, 0x55, 0xFF, 0xB4},
96 {0xB7, 0x0E, 0x0C, 0xBD, 0x6B, 0xB4, 0xBF, 0x7F, 0x32, 0x13, /* x */
97 0x90, 0xB9, 0x4A, 0x03, 0xC1, 0xD3, 0x56, 0xC2, 0x11, 0x22,
98 0x34, 0x32, 0x80, 0xD6, 0x11, 0x5C, 0x1D, 0x21},
99 {0xbd, 0x37, 0x63, 0x88, 0xb5, 0xf7, 0x23, 0xfb, 0x4c, 0x22, /* y */
100 0xdf, 0xe6, 0xcd, 0x43, 0x75, 0xa0, 0x5a, 0x07, 0x47, 0x64,
101 0x44, 0xd5, 0x81, 0x99, 0x85, 0x00, 0x7e, 0x34}
105 * Precomputed multiples of the standard generator
106 * Points are given in coordinates (X, Y, Z) where Z normally is 1
107 * (0 for the point at infinity).
108 * For each field element, slice a_0 is word 0, etc.
110 * The table has 2 * 16 elements, starting with the following:
111 * index | bits | point
112 * ------+---------+------------------------------
115 * 2 | 0 0 1 0 | 2^56G
116 * 3 | 0 0 1 1 | (2^56 + 1)G
117 * 4 | 0 1 0 0 | 2^112G
118 * 5 | 0 1 0 1 | (2^112 + 1)G
119 * 6 | 0 1 1 0 | (2^112 + 2^56)G
120 * 7 | 0 1 1 1 | (2^112 + 2^56 + 1)G
121 * 8 | 1 0 0 0 | 2^168G
122 * 9 | 1 0 0 1 | (2^168 + 1)G
123 * 10 | 1 0 1 0 | (2^168 + 2^56)G
124 * 11 | 1 0 1 1 | (2^168 + 2^56 + 1)G
125 * 12 | 1 1 0 0 | (2^168 + 2^112)G
126 * 13 | 1 1 0 1 | (2^168 + 2^112 + 1)G
127 * 14 | 1 1 1 0 | (2^168 + 2^112 + 2^56)G
128 * 15 | 1 1 1 1 | (2^168 + 2^112 + 2^56 + 1)G
129 * followed by a copy of this with each element multiplied by 2^28.
131 * The reason for this is so that we can clock bits into four different
132 * locations when doing simple scalar multiplies against the base point,
133 * and then another four locations using the second 16 elements.
135 static const felem gmul
[2][16][3] = { {{{0, 0, 0, 0},
138 {{0x3280d6115c1d21, 0xc1d356c2112234,
139 0x7f321390b94a03, 0xb70e0cbd6bb4bf},
140 {0xd5819985007e34, 0x75a05a07476444,
141 0xfb4c22dfe6cd43, 0xbd376388b5f723},
143 {{0xfd9675666ebbe9, 0xbca7664d40ce5e,
144 0x2242df8d8a2a43, 0x1f49bbb0f99bc5},
145 {0x29e0b892dc9c43, 0xece8608436e662,
146 0xdc858f185310d0, 0x9812dd4eb8d321},
148 {{0x6d3e678d5d8eb8, 0x559eed1cb362f1,
149 0x16e9a3bbce8a3f, 0xeedcccd8c2a748},
150 {0xf19f90ed50266d, 0xabf2b4bf65f9df,
151 0x313865468fafec, 0x5cb379ba910a17},
153 {{0x0641966cab26e3, 0x91fb2991fab0a0,
154 0xefec27a4e13a0b, 0x0499aa8a5f8ebe},
155 {0x7510407766af5d, 0x84d929610d5450,
156 0x81d77aae82f706, 0x6916f6d4338c5b},
158 {{0xea95ac3b1f15c6, 0x086000905e82d4,
159 0xdd323ae4d1c8b1, 0x932b56be7685a3},
160 {0x9ef93dea25dbbf, 0x41665960f390f0,
161 0xfdec76dbe2a8a7, 0x523e80f019062a},
163 {{0x822fdd26732c73, 0xa01c83531b5d0f,
164 0x363f37347c1ba4, 0xc391b45c84725c},
165 {0xbbd5e1b2d6ad24, 0xddfbcde19dfaec,
166 0xc393da7e222a7f, 0x1efb7890ede244},
168 {{0x4c9e90ca217da1, 0xd11beca79159bb,
169 0xff8d33c2c98b7c, 0x2610b39409f849},
170 {0x44d1352ac64da0, 0xcdbb7b2c46b4fb,
171 0x966c079b753c89, 0xfe67e4e820b112},
173 {{0xe28cae2df5312d, 0xc71b61d16f5c6e,
174 0x79b7619a3e7c4c, 0x05c73240899b47},
175 {0x9f7f6382c73e3a, 0x18615165c56bda,
176 0x641fab2116fd56, 0x72855882b08394},
178 {{0x0469182f161c09, 0x74a98ca8d00fb5,
179 0xb89da93489a3e0, 0x41c98768fb0c1d},
180 {0xe5ea05fb32da81, 0x3dce9ffbca6855,
181 0x1cfe2d3fbf59e6, 0x0e5e03408738a7},
183 {{0xdab22b2333e87f, 0x4430137a5dd2f6,
184 0xe03ab9f738beb8, 0xcb0c5d0dc34f24},
185 {0x764a7df0c8fda5, 0x185ba5c3fa2044,
186 0x9281d688bcbe50, 0xc40331df893881},
188 {{0xb89530796f0f60, 0xade92bd26909a3,
189 0x1a0c83fb4884da, 0x1765bf22a5a984},
190 {0x772a9ee75db09e, 0x23bc6c67cec16f,
191 0x4c1edba8b14e2f, 0xe2a215d9611369},
193 {{0x571e509fb5efb3, 0xade88696410552,
194 0xc8ae85fada74fe, 0x6c7e4be83bbde3},
195 {0xff9f51160f4652, 0xb47ce2495a6539,
196 0xa2946c53b582f4, 0x286d2db3ee9a60},
198 {{0x40bbd5081a44af, 0x0995183b13926c,
199 0xbcefba6f47f6d0, 0x215619e9cc0057},
200 {0x8bc94d3b0df45e, 0xf11c54a3694f6f,
201 0x8631b93cdfe8b5, 0xe7e3f4b0982db9},
203 {{0xb17048ab3e1c7b, 0xac38f36ff8a1d8,
204 0x1c29819435d2c6, 0xc813132f4c07e9},
205 {0x2891425503b11f, 0x08781030579fea,
206 0xf5426ba5cc9674, 0x1e28ebf18562bc},
208 {{0x9f31997cc864eb, 0x06cd91d28b5e4c,
209 0xff17036691a973, 0xf1aef351497c58},
210 {0xdd1f2d600564ff, 0xdead073b1402db,
211 0x74a684435bd693, 0xeea7471f962558},
216 {{0x9665266dddf554, 0x9613d78b60ef2d, 0xce27a34cdba417, 0xd35ab74d6afc31},
217 {0x85ccdd22deb15e, 0x2137e5783a6aab, 0xa141cffd8c93c6, 0x355a1830e90f2d},
219 {{0x1a494eadaade65, 0xd6da4da77fe53c, 0xe7992996abec86, 0x65c3553c6090e3},
220 {0xfa610b1fb09346, 0xf1c6540b8a4aaf, 0xc51a13ccd3cbab, 0x02995b1b18c28a},
222 {{0x7874568e7295ef, 0x86b419fbe38d04, 0xdc0690a7550d9a, 0xd3966a44beac33},
223 {0x2b7280ec29132f, 0xbeaa3b6a032df3, 0xdc7dd88ae41200, 0xd25e2513e3a100},
225 {{0x924857eb2efafd, 0xac2bce41223190, 0x8edaa1445553fc, 0x825800fd3562d5},
226 {0x8d79148ea96621, 0x23a01c3dd9ed8d, 0xaf8b219f9416b5, 0xd8db0cc277daea},
228 {{0x76a9c3b1a700f0, 0xe9acd29bc7e691, 0x69212d1a6b0327, 0x6322e97fe154be},
229 {0x469fc5465d62aa, 0x8d41ed18883b05, 0x1f8eae66c52b88, 0xe4fcbe9325be51},
231 {{0x825fdf583cac16, 0x020b857c7b023a, 0x683c17744b0165, 0x14ffd0a2daf2f1},
232 {0x323b36184218f9, 0x4944ec4e3b47d4, 0xc15b3080841acf, 0x0bced4b01a28bb},
234 {{0x92ac22230df5c4, 0x52f33b4063eda8, 0xcb3f19870c0c93, 0x40064f2ba65233},
235 {0xfe16f0924f8992, 0x012da25af5b517, 0x1a57bb24f723a6, 0x06f8bc76760def},
237 {{0x4a7084f7817cb9, 0xbcab0738ee9a78, 0x3ec11e11d9c326, 0xdc0fe90e0f1aae},
238 {0xcf639ea5f98390, 0x5c350aa22ffb74, 0x9afae98a4047b7, 0x956ec2d617fc45},
240 {{0x4306d648c1be6a, 0x9247cd8bc9a462, 0xf5595e377d2f2e, 0xbd1c3caff1a52e},
241 {0x045e14472409d0, 0x29f3e17078f773, 0x745a602b2d4f7d, 0x191837685cdfbb},
243 {{0x5b6ee254a8cb79, 0x4953433f5e7026, 0xe21faeb1d1def4, 0xc4c225785c09de},
244 {0x307ce7bba1e518, 0x31b125b1036db8, 0x47e91868839e8f, 0xc765866e33b9f3},
246 {{0x3bfece24f96906, 0x4794da641e5093, 0xde5df64f95db26, 0x297ecd89714b05},
247 {0x701bd3ebb2c3aa, 0x7073b4f53cb1d5, 0x13c5665658af16, 0x9895089d66fe58},
249 {{0x0fef05f78c4790, 0x2d773633b05d2e, 0x94229c3a951c94, 0xbbbd70df4911bb},
250 {0xb2c6963d2c1168, 0x105f47a72b0d73, 0x9fdf6111614080, 0x7b7e94b39e67b0},
252 {{0xad1a7d6efbe2b3, 0xf012482c0da69d, 0x6b3bdf12438345, 0x40d7558d7aa4d9},
253 {0x8a09fffb5c6d3d, 0x9a356e5d9ffd38, 0x5973f15f4f9b1c, 0xdcd5f59f63c3ea},
255 {{0xacf39f4c5ca7ab, 0x4c8071cc5fd737, 0xc64e3602cd1184, 0x0acd4644c9abba},
256 {0x6c011a36d8bf6e, 0xfecd87ba24e32a, 0x19f6f56574fad8, 0x050b204ced9405},
258 {{0xed4f1cae7d9a96, 0x5ceef7ad94c40a, 0x778e4a3bf3ef9b, 0x7405783dc3b55e},
259 {0x32477c61b6e8c6, 0xb46a97570f018b, 0x91176d0a7e95d1, 0x3df90fbc4c7d0e},
263 /* Precomputation for the group generator. */
265 felem g_pre_comp
[2][16][3];
269 const EC_METHOD
*EC_GFp_nistp224_method(void)
271 static const EC_METHOD ret
= {
272 EC_FLAGS_DEFAULT_OCT
,
273 NID_X9_62_prime_field
,
274 ec_GFp_nistp224_group_init
,
275 ec_GFp_simple_group_finish
,
276 ec_GFp_simple_group_clear_finish
,
277 ec_GFp_nist_group_copy
,
278 ec_GFp_nistp224_group_set_curve
,
279 ec_GFp_simple_group_get_curve
,
280 ec_GFp_simple_group_get_degree
,
281 ec_GFp_simple_group_check_discriminant
,
282 ec_GFp_simple_point_init
,
283 ec_GFp_simple_point_finish
,
284 ec_GFp_simple_point_clear_finish
,
285 ec_GFp_simple_point_copy
,
286 ec_GFp_simple_point_set_to_infinity
,
287 ec_GFp_simple_set_Jprojective_coordinates_GFp
,
288 ec_GFp_simple_get_Jprojective_coordinates_GFp
,
289 ec_GFp_simple_point_set_affine_coordinates
,
290 ec_GFp_nistp224_point_get_affine_coordinates
,
291 0 /* point_set_compressed_coordinates */ ,
296 ec_GFp_simple_invert
,
297 ec_GFp_simple_is_at_infinity
,
298 ec_GFp_simple_is_on_curve
,
300 ec_GFp_simple_make_affine
,
301 ec_GFp_simple_points_make_affine
,
302 ec_GFp_nistp224_points_mul
,
303 ec_GFp_nistp224_precompute_mult
,
304 ec_GFp_nistp224_have_precompute_mult
,
305 ec_GFp_nist_field_mul
,
306 ec_GFp_nist_field_sqr
,
308 0 /* field_encode */ ,
309 0 /* field_decode */ ,
310 0 /* field_set_to_one */
317 * Helper functions to convert field elements to/from internal representation
319 static void bin28_to_felem(felem out
, const u8 in
[28])
321 out
[0] = *((const uint64_t *)(in
)) & 0x00ffffffffffffff;
322 out
[1] = (*((const uint64_t *)(in
+ 7))) & 0x00ffffffffffffff;
323 out
[2] = (*((const uint64_t *)(in
+ 14))) & 0x00ffffffffffffff;
324 out
[3] = (*((const uint64_t *)(in
+20))) >> 8;
327 static void felem_to_bin28(u8 out
[28], const felem in
)
330 for (i
= 0; i
< 7; ++i
) {
331 out
[i
] = in
[0] >> (8 * i
);
332 out
[i
+ 7] = in
[1] >> (8 * i
);
333 out
[i
+ 14] = in
[2] >> (8 * i
);
334 out
[i
+ 21] = in
[3] >> (8 * i
);
338 /* To preserve endianness when using BN_bn2bin and BN_bin2bn */
339 static void flip_endian(u8
*out
, const u8
*in
, unsigned len
)
342 for (i
= 0; i
< len
; ++i
)
343 out
[i
] = in
[len
- 1 - i
];
346 /* From OpenSSL BIGNUM to internal representation */
347 static int BN_to_felem(felem out
, const BIGNUM
*bn
)
349 felem_bytearray b_in
;
350 felem_bytearray b_out
;
353 /* BN_bn2bin eats leading zeroes */
354 memset(b_out
, 0, sizeof b_out
);
355 num_bytes
= BN_num_bytes(bn
);
356 if (num_bytes
> sizeof b_out
) {
357 ECerr(EC_F_BN_TO_FELEM
, EC_R_BIGNUM_OUT_OF_RANGE
);
360 if (BN_is_negative(bn
)) {
361 ECerr(EC_F_BN_TO_FELEM
, EC_R_BIGNUM_OUT_OF_RANGE
);
364 num_bytes
= BN_bn2bin(bn
, b_in
);
365 flip_endian(b_out
, b_in
, num_bytes
);
366 bin28_to_felem(out
, b_out
);
370 /* From internal representation to OpenSSL BIGNUM */
371 static BIGNUM
*felem_to_BN(BIGNUM
*out
, const felem in
)
373 felem_bytearray b_in
, b_out
;
374 felem_to_bin28(b_in
, in
);
375 flip_endian(b_out
, b_in
, sizeof b_out
);
376 return BN_bin2bn(b_out
, sizeof b_out
, out
);
379 /******************************************************************************/
383 * Field operations, using the internal representation of field elements.
384 * NB! These operations are specific to our point multiplication and cannot be
385 * expected to be correct in general - e.g., multiplication with a large scalar
386 * will cause an overflow.
390 static void felem_one(felem out
)
398 static void felem_assign(felem out
, const felem in
)
406 /* Sum two field elements: out += in */
407 static void felem_sum(felem out
, const felem in
)
415 /* Get negative value: out = -in */
416 /* Assumes in[i] < 2^57 */
417 static void felem_neg(felem out
, const felem in
)
419 static const limb two58p2
= (((limb
) 1) << 58) + (((limb
) 1) << 2);
420 static const limb two58m2
= (((limb
) 1) << 58) - (((limb
) 1) << 2);
421 static const limb two58m42m2
= (((limb
) 1) << 58) -
422 (((limb
) 1) << 42) - (((limb
) 1) << 2);
424 /* Set to 0 mod 2^224-2^96+1 to ensure out > in */
425 out
[0] = two58p2
- in
[0];
426 out
[1] = two58m42m2
- in
[1];
427 out
[2] = two58m2
- in
[2];
428 out
[3] = two58m2
- in
[3];
431 /* Subtract field elements: out -= in */
432 /* Assumes in[i] < 2^57 */
433 static void felem_diff(felem out
, const felem in
)
435 static const limb two58p2
= (((limb
) 1) << 58) + (((limb
) 1) << 2);
436 static const limb two58m2
= (((limb
) 1) << 58) - (((limb
) 1) << 2);
437 static const limb two58m42m2
= (((limb
) 1) << 58) -
438 (((limb
) 1) << 42) - (((limb
) 1) << 2);
440 /* Add 0 mod 2^224-2^96+1 to ensure out > in */
442 out
[1] += two58m42m2
;
452 /* Subtract in unreduced 128-bit mode: out -= in */
453 /* Assumes in[i] < 2^119 */
454 static void widefelem_diff(widefelem out
, const widefelem in
)
456 static const widelimb two120
= ((widelimb
) 1) << 120;
457 static const widelimb two120m64
= (((widelimb
) 1) << 120) -
458 (((widelimb
) 1) << 64);
459 static const widelimb two120m104m64
= (((widelimb
) 1) << 120) -
460 (((widelimb
) 1) << 104) - (((widelimb
) 1) << 64);
462 /* Add 0 mod 2^224-2^96+1 to ensure out > in */
467 out
[4] += two120m104m64
;
480 /* Subtract in mixed mode: out128 -= in64 */
482 static void felem_diff_128_64(widefelem out
, const felem in
)
484 static const widelimb two64p8
= (((widelimb
) 1) << 64) +
485 (((widelimb
) 1) << 8);
486 static const widelimb two64m8
= (((widelimb
) 1) << 64) -
487 (((widelimb
) 1) << 8);
488 static const widelimb two64m48m8
= (((widelimb
) 1) << 64) -
489 (((widelimb
) 1) << 48) - (((widelimb
) 1) << 8);
491 /* Add 0 mod 2^224-2^96+1 to ensure out > in */
493 out
[1] += two64m48m8
;
504 * Multiply a field element by a scalar: out = out * scalar The scalars we
505 * actually use are small, so results fit without overflow
507 static void felem_scalar(felem out
, const limb scalar
)
516 * Multiply an unreduced field element by a scalar: out = out * scalar The
517 * scalars we actually use are small, so results fit without overflow
519 static void widefelem_scalar(widefelem out
, const widelimb scalar
)
530 /* Square a field element: out = in^2 */
531 static void felem_square(widefelem out
, const felem in
)
533 limb tmp0
, tmp1
, tmp2
;
537 out
[0] = ((widelimb
) in
[0]) * in
[0];
538 out
[1] = ((widelimb
) in
[0]) * tmp1
;
539 out
[2] = ((widelimb
) in
[0]) * tmp2
+ ((widelimb
) in
[1]) * in
[1];
540 out
[3] = ((widelimb
) in
[3]) * tmp0
+ ((widelimb
) in
[1]) * tmp2
;
541 out
[4] = ((widelimb
) in
[3]) * tmp1
+ ((widelimb
) in
[2]) * in
[2];
542 out
[5] = ((widelimb
) in
[3]) * tmp2
;
543 out
[6] = ((widelimb
) in
[3]) * in
[3];
546 /* Multiply two field elements: out = in1 * in2 */
547 static void felem_mul(widefelem out
, const felem in1
, const felem in2
)
549 out
[0] = ((widelimb
) in1
[0]) * in2
[0];
550 out
[1] = ((widelimb
) in1
[0]) * in2
[1] + ((widelimb
) in1
[1]) * in2
[0];
551 out
[2] = ((widelimb
) in1
[0]) * in2
[2] + ((widelimb
) in1
[1]) * in2
[1] +
552 ((widelimb
) in1
[2]) * in2
[0];
553 out
[3] = ((widelimb
) in1
[0]) * in2
[3] + ((widelimb
) in1
[1]) * in2
[2] +
554 ((widelimb
) in1
[2]) * in2
[1] + ((widelimb
) in1
[3]) * in2
[0];
555 out
[4] = ((widelimb
) in1
[1]) * in2
[3] + ((widelimb
) in1
[2]) * in2
[2] +
556 ((widelimb
) in1
[3]) * in2
[1];
557 out
[5] = ((widelimb
) in1
[2]) * in2
[3] + ((widelimb
) in1
[3]) * in2
[2];
558 out
[6] = ((widelimb
) in1
[3]) * in2
[3];
562 * Reduce seven 128-bit coefficients to four 64-bit coefficients.
563 * Requires in[i] < 2^126,
564 * ensures out[0] < 2^56, out[1] < 2^56, out[2] < 2^56, out[3] <= 2^56 + 2^16 */
565 static void felem_reduce(felem out
, const widefelem in
)
567 static const widelimb two127p15
= (((widelimb
) 1) << 127) +
568 (((widelimb
) 1) << 15);
569 static const widelimb two127m71
= (((widelimb
) 1) << 127) -
570 (((widelimb
) 1) << 71);
571 static const widelimb two127m71m55
= (((widelimb
) 1) << 127) -
572 (((widelimb
) 1) << 71) - (((widelimb
) 1) << 55);
575 /* Add 0 mod 2^224-2^96+1 to ensure all differences are positive */
576 output
[0] = in
[0] + two127p15
;
577 output
[1] = in
[1] + two127m71m55
;
578 output
[2] = in
[2] + two127m71
;
582 /* Eliminate in[4], in[5], in[6] */
583 output
[4] += in
[6] >> 16;
584 output
[3] += (in
[6] & 0xffff) << 40;
587 output
[3] += in
[5] >> 16;
588 output
[2] += (in
[5] & 0xffff) << 40;
591 output
[2] += output
[4] >> 16;
592 output
[1] += (output
[4] & 0xffff) << 40;
593 output
[0] -= output
[4];
595 /* Carry 2 -> 3 -> 4 */
596 output
[3] += output
[2] >> 56;
597 output
[2] &= 0x00ffffffffffffff;
599 output
[4] = output
[3] >> 56;
600 output
[3] &= 0x00ffffffffffffff;
602 /* Now output[2] < 2^56, output[3] < 2^56, output[4] < 2^72 */
604 /* Eliminate output[4] */
605 output
[2] += output
[4] >> 16;
606 /* output[2] < 2^56 + 2^56 = 2^57 */
607 output
[1] += (output
[4] & 0xffff) << 40;
608 output
[0] -= output
[4];
610 /* Carry 0 -> 1 -> 2 -> 3 */
611 output
[1] += output
[0] >> 56;
612 out
[0] = output
[0] & 0x00ffffffffffffff;
614 output
[2] += output
[1] >> 56;
615 /* output[2] < 2^57 + 2^72 */
616 out
[1] = output
[1] & 0x00ffffffffffffff;
617 output
[3] += output
[2] >> 56;
618 /* output[3] <= 2^56 + 2^16 */
619 out
[2] = output
[2] & 0x00ffffffffffffff;
622 * out[0] < 2^56, out[1] < 2^56, out[2] < 2^56,
623 * out[3] <= 2^56 + 2^16 (due to final carry),
629 static void felem_square_reduce(felem out
, const felem in
)
632 felem_square(tmp
, in
);
633 felem_reduce(out
, tmp
);
636 static void felem_mul_reduce(felem out
, const felem in1
, const felem in2
)
639 felem_mul(tmp
, in1
, in2
);
640 felem_reduce(out
, tmp
);
644 * Reduce to unique minimal representation. Requires 0 <= in < 2*p (always
645 * call felem_reduce first)
647 static void felem_contract(felem out
, const felem in
)
649 static const int64_t two56
= ((limb
) 1) << 56;
650 /* 0 <= in < 2*p, p = 2^224 - 2^96 + 1 */
651 /* if in > p , reduce in = in - 2^224 + 2^96 - 1 */
657 /* Case 1: a = 1 iff in >= 2^224 */
661 tmp
[3] &= 0x00ffffffffffffff;
663 * Case 2: a = 0 iff p <= in < 2^224, i.e., the high 128 bits are all 1
664 * and the lower part is non-zero
666 a
= ((in
[3] & in
[2] & (in
[1] | 0x000000ffffffffff)) + 1) |
667 (((int64_t) (in
[0] + (in
[1] & 0x000000ffffffffff)) - 1) >> 63);
668 a
&= 0x00ffffffffffffff;
669 /* turn a into an all-one mask (if a = 0) or an all-zero mask */
671 /* subtract 2^224 - 2^96 + 1 if a is all-one */
672 tmp
[3] &= a
^ 0xffffffffffffffff;
673 tmp
[2] &= a
^ 0xffffffffffffffff;
674 tmp
[1] &= (a
^ 0xffffffffffffffff) | 0x000000ffffffffff;
678 * eliminate negative coefficients: if tmp[0] is negative, tmp[1] must be
679 * non-zero, so we only need one step
685 /* carry 1 -> 2 -> 3 */
686 tmp
[2] += tmp
[1] >> 56;
687 tmp
[1] &= 0x00ffffffffffffff;
689 tmp
[3] += tmp
[2] >> 56;
690 tmp
[2] &= 0x00ffffffffffffff;
692 /* Now 0 <= out < p */
700 * Zero-check: returns 1 if input is 0, and 0 otherwise. We know that field
701 * elements are reduced to in < 2^225, so we only need to check three cases:
702 * 0, 2^224 - 2^96 + 1, and 2^225 - 2^97 + 2
704 static limb
felem_is_zero(const felem in
)
706 limb zero
, two224m96p1
, two225m97p2
;
708 zero
= in
[0] | in
[1] | in
[2] | in
[3];
709 zero
= (((int64_t) (zero
) - 1) >> 63) & 1;
710 two224m96p1
= (in
[0] ^ 1) | (in
[1] ^ 0x00ffff0000000000)
711 | (in
[2] ^ 0x00ffffffffffffff) | (in
[3] ^ 0x00ffffffffffffff);
712 two224m96p1
= (((int64_t) (two224m96p1
) - 1) >> 63) & 1;
713 two225m97p2
= (in
[0] ^ 2) | (in
[1] ^ 0x00fffe0000000000)
714 | (in
[2] ^ 0x00ffffffffffffff) | (in
[3] ^ 0x01ffffffffffffff);
715 two225m97p2
= (((int64_t) (two225m97p2
) - 1) >> 63) & 1;
716 return (zero
| two224m96p1
| two225m97p2
);
719 static limb
felem_is_zero_int(const felem in
)
721 return (int)(felem_is_zero(in
) & ((limb
) 1));
724 /* Invert a field element */
725 /* Computation chain copied from djb's code */
726 static void felem_inv(felem out
, const felem in
)
728 felem ftmp
, ftmp2
, ftmp3
, ftmp4
;
732 felem_square(tmp
, in
);
733 felem_reduce(ftmp
, tmp
); /* 2 */
734 felem_mul(tmp
, in
, ftmp
);
735 felem_reduce(ftmp
, tmp
); /* 2^2 - 1 */
736 felem_square(tmp
, ftmp
);
737 felem_reduce(ftmp
, tmp
); /* 2^3 - 2 */
738 felem_mul(tmp
, in
, ftmp
);
739 felem_reduce(ftmp
, tmp
); /* 2^3 - 1 */
740 felem_square(tmp
, ftmp
);
741 felem_reduce(ftmp2
, tmp
); /* 2^4 - 2 */
742 felem_square(tmp
, ftmp2
);
743 felem_reduce(ftmp2
, tmp
); /* 2^5 - 4 */
744 felem_square(tmp
, ftmp2
);
745 felem_reduce(ftmp2
, tmp
); /* 2^6 - 8 */
746 felem_mul(tmp
, ftmp2
, ftmp
);
747 felem_reduce(ftmp
, tmp
); /* 2^6 - 1 */
748 felem_square(tmp
, ftmp
);
749 felem_reduce(ftmp2
, tmp
); /* 2^7 - 2 */
750 for (i
= 0; i
< 5; ++i
) { /* 2^12 - 2^6 */
751 felem_square(tmp
, ftmp2
);
752 felem_reduce(ftmp2
, tmp
);
754 felem_mul(tmp
, ftmp2
, ftmp
);
755 felem_reduce(ftmp2
, tmp
); /* 2^12 - 1 */
756 felem_square(tmp
, ftmp2
);
757 felem_reduce(ftmp3
, tmp
); /* 2^13 - 2 */
758 for (i
= 0; i
< 11; ++i
) { /* 2^24 - 2^12 */
759 felem_square(tmp
, ftmp3
);
760 felem_reduce(ftmp3
, tmp
);
762 felem_mul(tmp
, ftmp3
, ftmp2
);
763 felem_reduce(ftmp2
, tmp
); /* 2^24 - 1 */
764 felem_square(tmp
, ftmp2
);
765 felem_reduce(ftmp3
, tmp
); /* 2^25 - 2 */
766 for (i
= 0; i
< 23; ++i
) { /* 2^48 - 2^24 */
767 felem_square(tmp
, ftmp3
);
768 felem_reduce(ftmp3
, tmp
);
770 felem_mul(tmp
, ftmp3
, ftmp2
);
771 felem_reduce(ftmp3
, tmp
); /* 2^48 - 1 */
772 felem_square(tmp
, ftmp3
);
773 felem_reduce(ftmp4
, tmp
); /* 2^49 - 2 */
774 for (i
= 0; i
< 47; ++i
) { /* 2^96 - 2^48 */
775 felem_square(tmp
, ftmp4
);
776 felem_reduce(ftmp4
, tmp
);
778 felem_mul(tmp
, ftmp3
, ftmp4
);
779 felem_reduce(ftmp3
, tmp
); /* 2^96 - 1 */
780 felem_square(tmp
, ftmp3
);
781 felem_reduce(ftmp4
, tmp
); /* 2^97 - 2 */
782 for (i
= 0; i
< 23; ++i
) { /* 2^120 - 2^24 */
783 felem_square(tmp
, ftmp4
);
784 felem_reduce(ftmp4
, tmp
);
786 felem_mul(tmp
, ftmp2
, ftmp4
);
787 felem_reduce(ftmp2
, tmp
); /* 2^120 - 1 */
788 for (i
= 0; i
< 6; ++i
) { /* 2^126 - 2^6 */
789 felem_square(tmp
, ftmp2
);
790 felem_reduce(ftmp2
, tmp
);
792 felem_mul(tmp
, ftmp2
, ftmp
);
793 felem_reduce(ftmp
, tmp
); /* 2^126 - 1 */
794 felem_square(tmp
, ftmp
);
795 felem_reduce(ftmp
, tmp
); /* 2^127 - 2 */
796 felem_mul(tmp
, ftmp
, in
);
797 felem_reduce(ftmp
, tmp
); /* 2^127 - 1 */
798 for (i
= 0; i
< 97; ++i
) { /* 2^224 - 2^97 */
799 felem_square(tmp
, ftmp
);
800 felem_reduce(ftmp
, tmp
);
802 felem_mul(tmp
, ftmp
, ftmp3
);
803 felem_reduce(out
, tmp
); /* 2^224 - 2^96 - 1 */
807 * Copy in constant time: if icopy == 1, copy in to out, if icopy == 0, copy
810 static void copy_conditional(felem out
, const felem in
, limb icopy
)
814 * icopy is a (64-bit) 0 or 1, so copy is either all-zero or all-one
816 const limb copy
= -icopy
;
817 for (i
= 0; i
< 4; ++i
) {
818 const limb tmp
= copy
& (in
[i
] ^ out
[i
]);
823 /******************************************************************************/
825 * ELLIPTIC CURVE POINT OPERATIONS
827 * Points are represented in Jacobian projective coordinates:
828 * (X, Y, Z) corresponds to the affine point (X/Z^2, Y/Z^3),
829 * or to the point at infinity if Z == 0.
834 * Double an elliptic curve point:
835 * (X', Y', Z') = 2 * (X, Y, Z), where
836 * X' = (3 * (X - Z^2) * (X + Z^2))^2 - 8 * X * Y^2
837 * Y' = 3 * (X - Z^2) * (X + Z^2) * (4 * X * Y^2 - X') - 8 * Y^2
838 * Z' = (Y + Z)^2 - Y^2 - Z^2 = 2 * Y * Z
839 * Outputs can equal corresponding inputs, i.e., x_out == x_in is allowed,
840 * while x_out == y_in is not (maybe this works, but it's not tested).
843 point_double(felem x_out
, felem y_out
, felem z_out
,
844 const felem x_in
, const felem y_in
, const felem z_in
)
847 felem delta
, gamma
, beta
, alpha
, ftmp
, ftmp2
;
849 felem_assign(ftmp
, x_in
);
850 felem_assign(ftmp2
, x_in
);
853 felem_square(tmp
, z_in
);
854 felem_reduce(delta
, tmp
);
857 felem_square(tmp
, y_in
);
858 felem_reduce(gamma
, tmp
);
861 felem_mul(tmp
, x_in
, gamma
);
862 felem_reduce(beta
, tmp
);
864 /* alpha = 3*(x-delta)*(x+delta) */
865 felem_diff(ftmp
, delta
);
866 /* ftmp[i] < 2^57 + 2^58 + 2 < 2^59 */
867 felem_sum(ftmp2
, delta
);
868 /* ftmp2[i] < 2^57 + 2^57 = 2^58 */
869 felem_scalar(ftmp2
, 3);
870 /* ftmp2[i] < 3 * 2^58 < 2^60 */
871 felem_mul(tmp
, ftmp
, ftmp2
);
872 /* tmp[i] < 2^60 * 2^59 * 4 = 2^121 */
873 felem_reduce(alpha
, tmp
);
875 /* x' = alpha^2 - 8*beta */
876 felem_square(tmp
, alpha
);
877 /* tmp[i] < 4 * 2^57 * 2^57 = 2^116 */
878 felem_assign(ftmp
, beta
);
879 felem_scalar(ftmp
, 8);
880 /* ftmp[i] < 8 * 2^57 = 2^60 */
881 felem_diff_128_64(tmp
, ftmp
);
882 /* tmp[i] < 2^116 + 2^64 + 8 < 2^117 */
883 felem_reduce(x_out
, tmp
);
885 /* z' = (y + z)^2 - gamma - delta */
886 felem_sum(delta
, gamma
);
887 /* delta[i] < 2^57 + 2^57 = 2^58 */
888 felem_assign(ftmp
, y_in
);
889 felem_sum(ftmp
, z_in
);
890 /* ftmp[i] < 2^57 + 2^57 = 2^58 */
891 felem_square(tmp
, ftmp
);
892 /* tmp[i] < 4 * 2^58 * 2^58 = 2^118 */
893 felem_diff_128_64(tmp
, delta
);
894 /* tmp[i] < 2^118 + 2^64 + 8 < 2^119 */
895 felem_reduce(z_out
, tmp
);
897 /* y' = alpha*(4*beta - x') - 8*gamma^2 */
898 felem_scalar(beta
, 4);
899 /* beta[i] < 4 * 2^57 = 2^59 */
900 felem_diff(beta
, x_out
);
901 /* beta[i] < 2^59 + 2^58 + 2 < 2^60 */
902 felem_mul(tmp
, alpha
, beta
);
903 /* tmp[i] < 4 * 2^57 * 2^60 = 2^119 */
904 felem_square(tmp2
, gamma
);
905 /* tmp2[i] < 4 * 2^57 * 2^57 = 2^116 */
906 widefelem_scalar(tmp2
, 8);
907 /* tmp2[i] < 8 * 2^116 = 2^119 */
908 widefelem_diff(tmp
, tmp2
);
909 /* tmp[i] < 2^119 + 2^120 < 2^121 */
910 felem_reduce(y_out
, tmp
);
914 * Add two elliptic curve points:
915 * (X_1, Y_1, Z_1) + (X_2, Y_2, Z_2) = (X_3, Y_3, Z_3), where
916 * X_3 = (Z_1^3 * Y_2 - Z_2^3 * Y_1)^2 - (Z_1^2 * X_2 - Z_2^2 * X_1)^3 -
917 * 2 * Z_2^2 * X_1 * (Z_1^2 * X_2 - Z_2^2 * X_1)^2
918 * 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) -
919 * Z_2^3 * Y_1 * (Z_1^2 * X_2 - Z_2^2 * X_1)^3
920 * Z_3 = (Z_1^2 * X_2 - Z_2^2 * X_1) * (Z_1 * Z_2)
922 * This runs faster if 'mixed' is set, which requires Z_2 = 1 or Z_2 = 0.
926 * This function is not entirely constant-time: it includes a branch for
927 * checking whether the two input points are equal, (while not equal to the
928 * point at infinity). This case never happens during single point
929 * multiplication, so there is no timing leak for ECDH or ECDSA signing.
931 static void point_add(felem x3
, felem y3
, felem z3
,
932 const felem x1
, const felem y1
, const felem z1
,
933 const int mixed
, const felem x2
, const felem y2
,
936 felem ftmp
, ftmp2
, ftmp3
, ftmp4
, ftmp5
, x_out
, y_out
, z_out
;
938 limb z1_is_zero
, z2_is_zero
, x_equal
, y_equal
;
942 felem_square(tmp
, z2
);
943 felem_reduce(ftmp2
, tmp
);
946 felem_mul(tmp
, ftmp2
, z2
);
947 felem_reduce(ftmp4
, tmp
);
949 /* ftmp4 = z2^3*y1 */
950 felem_mul(tmp2
, ftmp4
, y1
);
951 felem_reduce(ftmp4
, tmp2
);
953 /* ftmp2 = z2^2*x1 */
954 felem_mul(tmp2
, ftmp2
, x1
);
955 felem_reduce(ftmp2
, tmp2
);
958 * We'll assume z2 = 1 (special case z2 = 0 is handled later)
961 /* ftmp4 = z2^3*y1 */
962 felem_assign(ftmp4
, y1
);
964 /* ftmp2 = z2^2*x1 */
965 felem_assign(ftmp2
, x1
);
969 felem_square(tmp
, z1
);
970 felem_reduce(ftmp
, tmp
);
973 felem_mul(tmp
, ftmp
, z1
);
974 felem_reduce(ftmp3
, tmp
);
977 felem_mul(tmp
, ftmp3
, y2
);
978 /* tmp[i] < 4 * 2^57 * 2^57 = 2^116 */
980 /* ftmp3 = z1^3*y2 - z2^3*y1 */
981 felem_diff_128_64(tmp
, ftmp4
);
982 /* tmp[i] < 2^116 + 2^64 + 8 < 2^117 */
983 felem_reduce(ftmp3
, tmp
);
986 felem_mul(tmp
, ftmp
, x2
);
987 /* tmp[i] < 4 * 2^57 * 2^57 = 2^116 */
989 /* ftmp = z1^2*x2 - z2^2*x1 */
990 felem_diff_128_64(tmp
, ftmp2
);
991 /* tmp[i] < 2^116 + 2^64 + 8 < 2^117 */
992 felem_reduce(ftmp
, tmp
);
995 * the formulae are incorrect if the points are equal so we check for
996 * this and do doubling if this happens
998 x_equal
= felem_is_zero(ftmp
);
999 y_equal
= felem_is_zero(ftmp3
);
1000 z1_is_zero
= felem_is_zero(z1
);
1001 z2_is_zero
= felem_is_zero(z2
);
1002 /* In affine coordinates, (X_1, Y_1) == (X_2, Y_2) */
1003 if (x_equal
&& y_equal
&& !z1_is_zero
&& !z2_is_zero
) {
1004 point_double(x3
, y3
, z3
, x1
, y1
, z1
);
1010 felem_mul(tmp
, z1
, z2
);
1011 felem_reduce(ftmp5
, tmp
);
1013 /* special case z2 = 0 is handled later */
1014 felem_assign(ftmp5
, z1
);
1017 /* z_out = (z1^2*x2 - z2^2*x1)*(z1*z2) */
1018 felem_mul(tmp
, ftmp
, ftmp5
);
1019 felem_reduce(z_out
, tmp
);
1021 /* ftmp = (z1^2*x2 - z2^2*x1)^2 */
1022 felem_assign(ftmp5
, ftmp
);
1023 felem_square(tmp
, ftmp
);
1024 felem_reduce(ftmp
, tmp
);
1026 /* ftmp5 = (z1^2*x2 - z2^2*x1)^3 */
1027 felem_mul(tmp
, ftmp
, ftmp5
);
1028 felem_reduce(ftmp5
, tmp
);
1030 /* ftmp2 = z2^2*x1*(z1^2*x2 - z2^2*x1)^2 */
1031 felem_mul(tmp
, ftmp2
, ftmp
);
1032 felem_reduce(ftmp2
, tmp
);
1034 /* tmp = z2^3*y1*(z1^2*x2 - z2^2*x1)^3 */
1035 felem_mul(tmp
, ftmp4
, ftmp5
);
1036 /* tmp[i] < 4 * 2^57 * 2^57 = 2^116 */
1038 /* tmp2 = (z1^3*y2 - z2^3*y1)^2 */
1039 felem_square(tmp2
, ftmp3
);
1040 /* tmp2[i] < 4 * 2^57 * 2^57 < 2^116 */
1042 /* tmp2 = (z1^3*y2 - z2^3*y1)^2 - (z1^2*x2 - z2^2*x1)^3 */
1043 felem_diff_128_64(tmp2
, ftmp5
);
1044 /* tmp2[i] < 2^116 + 2^64 + 8 < 2^117 */
1046 /* ftmp5 = 2*z2^2*x1*(z1^2*x2 - z2^2*x1)^2 */
1047 felem_assign(ftmp5
, ftmp2
);
1048 felem_scalar(ftmp5
, 2);
1049 /* ftmp5[i] < 2 * 2^57 = 2^58 */
1052 * x_out = (z1^3*y2 - z2^3*y1)^2 - (z1^2*x2 - z2^2*x1)^3 -
1053 * 2*z2^2*x1*(z1^2*x2 - z2^2*x1)^2
1055 felem_diff_128_64(tmp2
, ftmp5
);
1056 /* tmp2[i] < 2^117 + 2^64 + 8 < 2^118 */
1057 felem_reduce(x_out
, tmp2
);
1059 /* ftmp2 = z2^2*x1*(z1^2*x2 - z2^2*x1)^2 - x_out */
1060 felem_diff(ftmp2
, x_out
);
1061 /* ftmp2[i] < 2^57 + 2^58 + 2 < 2^59 */
1064 * tmp2 = (z1^3*y2 - z2^3*y1)*(z2^2*x1*(z1^2*x2 - z2^2*x1)^2 - x_out)
1066 felem_mul(tmp2
, ftmp3
, ftmp2
);
1067 /* tmp2[i] < 4 * 2^57 * 2^59 = 2^118 */
1070 * y_out = (z1^3*y2 - z2^3*y1)*(z2^2*x1*(z1^2*x2 - z2^2*x1)^2 - x_out) -
1071 * z2^3*y1*(z1^2*x2 - z2^2*x1)^3
1073 widefelem_diff(tmp2
, tmp
);
1074 /* tmp2[i] < 2^118 + 2^120 < 2^121 */
1075 felem_reduce(y_out
, tmp2
);
1078 * the result (x_out, y_out, z_out) is incorrect if one of the inputs is
1079 * the point at infinity, so we need to check for this separately
1083 * if point 1 is at infinity, copy point 2 to output, and vice versa
1085 copy_conditional(x_out
, x2
, z1_is_zero
);
1086 copy_conditional(x_out
, x1
, z2_is_zero
);
1087 copy_conditional(y_out
, y2
, z1_is_zero
);
1088 copy_conditional(y_out
, y1
, z2_is_zero
);
1089 copy_conditional(z_out
, z2
, z1_is_zero
);
1090 copy_conditional(z_out
, z1
, z2_is_zero
);
1091 felem_assign(x3
, x_out
);
1092 felem_assign(y3
, y_out
);
1093 felem_assign(z3
, z_out
);
1097 * select_point selects the |idx|th point from a precomputation table and
1099 * The pre_comp array argument should be size of |size| argument
1101 static void select_point(const u64 idx
, unsigned int size
,
1102 const felem pre_comp
[][3], felem out
[3])
1105 limb
*outlimbs
= &out
[0][0];
1106 memset(outlimbs
, 0, 3 * sizeof(felem
));
1108 for (i
= 0; i
< size
; i
++) {
1109 const limb
*inlimbs
= &pre_comp
[i
][0][0];
1116 for (j
= 0; j
< 4 * 3; j
++)
1117 outlimbs
[j
] |= inlimbs
[j
] & mask
;
1121 /* get_bit returns the |i|th bit in |in| */
1122 static char get_bit(const felem_bytearray in
, unsigned i
)
1126 return (in
[i
>> 3] >> (i
& 7)) & 1;
1130 * Interleaved point multiplication using precomputed point multiples: The
1131 * small point multiples 0*P, 1*P, ..., 16*P are in pre_comp[], the scalars
1132 * in scalars[]. If g_scalar is non-NULL, we also add this multiple of the
1133 * generator, using certain (large) precomputed multiples in g_pre_comp.
1134 * Output point (X, Y, Z) is stored in x_out, y_out, z_out
1136 static void batch_mul(felem x_out
, felem y_out
, felem z_out
,
1137 const felem_bytearray scalars
[],
1138 const unsigned num_points
, const u8
*g_scalar
,
1139 const int mixed
, const felem pre_comp
[][17][3],
1140 const felem g_pre_comp
[2][16][3])
1144 unsigned gen_mul
= (g_scalar
!= NULL
);
1145 felem nq
[3], tmp
[4];
1149 /* set nq to the point at infinity */
1150 memset(nq
, 0, 3 * sizeof(felem
));
1153 * Loop over all scalars msb-to-lsb, interleaving additions of multiples
1154 * of the generator (two in each of the last 28 rounds) and additions of
1155 * other points multiples (every 5th round).
1157 skip
= 1; /* save two point operations in the first
1159 for (i
= (num_points
? 220 : 27); i
>= 0; --i
) {
1162 point_double(nq
[0], nq
[1], nq
[2], nq
[0], nq
[1], nq
[2]);
1164 /* add multiples of the generator */
1165 if (gen_mul
&& (i
<= 27)) {
1166 /* first, look 28 bits upwards */
1167 bits
= get_bit(g_scalar
, i
+ 196) << 3;
1168 bits
|= get_bit(g_scalar
, i
+ 140) << 2;
1169 bits
|= get_bit(g_scalar
, i
+ 84) << 1;
1170 bits
|= get_bit(g_scalar
, i
+ 28);
1171 /* select the point to add, in constant time */
1172 select_point(bits
, 16, g_pre_comp
[1], tmp
);
1175 /* value 1 below is argument for "mixed" */
1176 point_add(nq
[0], nq
[1], nq
[2],
1177 nq
[0], nq
[1], nq
[2], 1, tmp
[0], tmp
[1], tmp
[2]);
1179 memcpy(nq
, tmp
, 3 * sizeof(felem
));
1183 /* second, look at the current position */
1184 bits
= get_bit(g_scalar
, i
+ 168) << 3;
1185 bits
|= get_bit(g_scalar
, i
+ 112) << 2;
1186 bits
|= get_bit(g_scalar
, i
+ 56) << 1;
1187 bits
|= get_bit(g_scalar
, i
);
1188 /* select the point to add, in constant time */
1189 select_point(bits
, 16, g_pre_comp
[0], tmp
);
1190 point_add(nq
[0], nq
[1], nq
[2],
1191 nq
[0], nq
[1], nq
[2],
1192 1 /* mixed */ , tmp
[0], tmp
[1], tmp
[2]);
1195 /* do other additions every 5 doublings */
1196 if (num_points
&& (i
% 5 == 0)) {
1197 /* loop over all scalars */
1198 for (num
= 0; num
< num_points
; ++num
) {
1199 bits
= get_bit(scalars
[num
], i
+ 4) << 5;
1200 bits
|= get_bit(scalars
[num
], i
+ 3) << 4;
1201 bits
|= get_bit(scalars
[num
], i
+ 2) << 3;
1202 bits
|= get_bit(scalars
[num
], i
+ 1) << 2;
1203 bits
|= get_bit(scalars
[num
], i
) << 1;
1204 bits
|= get_bit(scalars
[num
], i
- 1);
1205 ec_GFp_nistp_recode_scalar_bits(&sign
, &digit
, bits
);
1207 /* select the point to add or subtract */
1208 select_point(digit
, 17, pre_comp
[num
], tmp
);
1209 felem_neg(tmp
[3], tmp
[1]); /* (X, -Y, Z) is the negative
1211 copy_conditional(tmp
[1], tmp
[3], sign
);
1214 point_add(nq
[0], nq
[1], nq
[2],
1215 nq
[0], nq
[1], nq
[2],
1216 mixed
, tmp
[0], tmp
[1], tmp
[2]);
1218 memcpy(nq
, tmp
, 3 * sizeof(felem
));
1224 felem_assign(x_out
, nq
[0]);
1225 felem_assign(y_out
, nq
[1]);
1226 felem_assign(z_out
, nq
[2]);
1229 /******************************************************************************/
1231 * FUNCTIONS TO MANAGE PRECOMPUTATION
1234 static NISTP224_PRE_COMP
*nistp224_pre_comp_new()
1236 NISTP224_PRE_COMP
*ret
= NULL
;
1237 ret
= (NISTP224_PRE_COMP
*) OPENSSL_malloc(sizeof *ret
);
1239 ECerr(EC_F_NISTP224_PRE_COMP_NEW
, ERR_R_MALLOC_FAILURE
);
1242 memset(ret
->g_pre_comp
, 0, sizeof(ret
->g_pre_comp
));
1243 ret
->references
= 1;
1247 static void *nistp224_pre_comp_dup(void *src_
)
1249 NISTP224_PRE_COMP
*src
= src_
;
1251 /* no need to actually copy, these objects never change! */
1252 CRYPTO_add(&src
->references
, 1, CRYPTO_LOCK_EC_PRE_COMP
);
1257 static void nistp224_pre_comp_free(void *pre_
)
1260 NISTP224_PRE_COMP
*pre
= pre_
;
1265 i
= CRYPTO_add(&pre
->references
, -1, CRYPTO_LOCK_EC_PRE_COMP
);
1272 static void nistp224_pre_comp_clear_free(void *pre_
)
1275 NISTP224_PRE_COMP
*pre
= pre_
;
1280 i
= CRYPTO_add(&pre
->references
, -1, CRYPTO_LOCK_EC_PRE_COMP
);
1284 OPENSSL_cleanse(pre
, sizeof *pre
);
1288 /******************************************************************************/
1290 * OPENSSL EC_METHOD FUNCTIONS
1293 int ec_GFp_nistp224_group_init(EC_GROUP
*group
)
1296 ret
= ec_GFp_simple_group_init(group
);
1297 group
->a_is_minus3
= 1;
1301 int ec_GFp_nistp224_group_set_curve(EC_GROUP
*group
, const BIGNUM
*p
,
1302 const BIGNUM
*a
, const BIGNUM
*b
,
1306 BN_CTX
*new_ctx
= NULL
;
1307 BIGNUM
*curve_p
, *curve_a
, *curve_b
;
1310 if ((ctx
= new_ctx
= BN_CTX_new()) == NULL
)
1313 if (((curve_p
= BN_CTX_get(ctx
)) == NULL
) ||
1314 ((curve_a
= BN_CTX_get(ctx
)) == NULL
) ||
1315 ((curve_b
= BN_CTX_get(ctx
)) == NULL
))
1317 BN_bin2bn(nistp224_curve_params
[0], sizeof(felem_bytearray
), curve_p
);
1318 BN_bin2bn(nistp224_curve_params
[1], sizeof(felem_bytearray
), curve_a
);
1319 BN_bin2bn(nistp224_curve_params
[2], sizeof(felem_bytearray
), curve_b
);
1320 if ((BN_cmp(curve_p
, p
)) || (BN_cmp(curve_a
, a
)) || (BN_cmp(curve_b
, b
))) {
1321 ECerr(EC_F_EC_GFP_NISTP224_GROUP_SET_CURVE
,
1322 EC_R_WRONG_CURVE_PARAMETERS
);
1325 group
->field_mod_func
= BN_nist_mod_224
;
1326 ret
= ec_GFp_simple_group_set_curve(group
, p
, a
, b
, ctx
);
1329 if (new_ctx
!= NULL
)
1330 BN_CTX_free(new_ctx
);
1335 * Takes the Jacobian coordinates (X, Y, Z) of a point and returns (X', Y') =
1338 int ec_GFp_nistp224_point_get_affine_coordinates(const EC_GROUP
*group
,
1339 const EC_POINT
*point
,
1340 BIGNUM
*x
, BIGNUM
*y
,
1343 felem z1
, z2
, x_in
, y_in
, x_out
, y_out
;
1346 if (EC_POINT_is_at_infinity(group
, point
)) {
1347 ECerr(EC_F_EC_GFP_NISTP224_POINT_GET_AFFINE_COORDINATES
,
1348 EC_R_POINT_AT_INFINITY
);
1351 if ((!BN_to_felem(x_in
, &point
->X
)) || (!BN_to_felem(y_in
, &point
->Y
)) ||
1352 (!BN_to_felem(z1
, &point
->Z
)))
1355 felem_square(tmp
, z2
);
1356 felem_reduce(z1
, tmp
);
1357 felem_mul(tmp
, x_in
, z1
);
1358 felem_reduce(x_in
, tmp
);
1359 felem_contract(x_out
, x_in
);
1361 if (!felem_to_BN(x
, x_out
)) {
1362 ECerr(EC_F_EC_GFP_NISTP224_POINT_GET_AFFINE_COORDINATES
,
1367 felem_mul(tmp
, z1
, z2
);
1368 felem_reduce(z1
, tmp
);
1369 felem_mul(tmp
, y_in
, z1
);
1370 felem_reduce(y_in
, tmp
);
1371 felem_contract(y_out
, y_in
);
1373 if (!felem_to_BN(y
, y_out
)) {
1374 ECerr(EC_F_EC_GFP_NISTP224_POINT_GET_AFFINE_COORDINATES
,
1382 static void make_points_affine(size_t num
, felem points
[ /* num */ ][3],
1383 felem tmp_felems
[ /* num+1 */ ])
1386 * Runs in constant time, unless an input is the point at infinity (which
1387 * normally shouldn't happen).
1389 ec_GFp_nistp_points_make_affine_internal(num
,
1393 (void (*)(void *))felem_one
,
1394 (int (*)(const void *))
1396 (void (*)(void *, const void *))
1398 (void (*)(void *, const void *))
1399 felem_square_reduce
, (void (*)
1406 (void (*)(void *, const void *))
1408 (void (*)(void *, const void *))
1413 * Computes scalar*generator + \sum scalars[i]*points[i], ignoring NULL
1414 * values Result is stored in r (r can equal one of the inputs).
1416 int ec_GFp_nistp224_points_mul(const EC_GROUP
*group
, EC_POINT
*r
,
1417 const BIGNUM
*scalar
, size_t num
,
1418 const EC_POINT
*points
[],
1419 const BIGNUM
*scalars
[], BN_CTX
*ctx
)
1425 BN_CTX
*new_ctx
= NULL
;
1426 BIGNUM
*x
, *y
, *z
, *tmp_scalar
;
1427 felem_bytearray g_secret
;
1428 felem_bytearray
*secrets
= NULL
;
1429 felem(*pre_comp
)[17][3] = NULL
;
1430 felem
*tmp_felems
= NULL
;
1431 felem_bytearray tmp
;
1433 int have_pre_comp
= 0;
1434 size_t num_points
= num
;
1435 felem x_in
, y_in
, z_in
, x_out
, y_out
, z_out
;
1436 NISTP224_PRE_COMP
*pre
= NULL
;
1437 const felem(*g_pre_comp
)[16][3] = NULL
;
1438 EC_POINT
*generator
= NULL
;
1439 const EC_POINT
*p
= NULL
;
1440 const BIGNUM
*p_scalar
= NULL
;
1443 if ((ctx
= new_ctx
= BN_CTX_new()) == NULL
)
1446 if (((x
= BN_CTX_get(ctx
)) == NULL
) ||
1447 ((y
= BN_CTX_get(ctx
)) == NULL
) ||
1448 ((z
= BN_CTX_get(ctx
)) == NULL
) ||
1449 ((tmp_scalar
= BN_CTX_get(ctx
)) == NULL
))
1452 if (scalar
!= NULL
) {
1453 pre
= EC_EX_DATA_get_data(group
->extra_data
,
1454 nistp224_pre_comp_dup
,
1455 nistp224_pre_comp_free
,
1456 nistp224_pre_comp_clear_free
);
1458 /* we have precomputation, try to use it */
1459 g_pre_comp
= (const felem(*)[16][3])pre
->g_pre_comp
;
1461 /* try to use the standard precomputation */
1462 g_pre_comp
= &gmul
[0];
1463 generator
= EC_POINT_new(group
);
1464 if (generator
== NULL
)
1466 /* get the generator from precomputation */
1467 if (!felem_to_BN(x
, g_pre_comp
[0][1][0]) ||
1468 !felem_to_BN(y
, g_pre_comp
[0][1][1]) ||
1469 !felem_to_BN(z
, g_pre_comp
[0][1][2])) {
1470 ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL
, ERR_R_BN_LIB
);
1473 if (!EC_POINT_set_Jprojective_coordinates_GFp(group
,
1477 if (0 == EC_POINT_cmp(group
, generator
, group
->generator
, ctx
))
1478 /* precomputation matches generator */
1482 * we don't have valid precomputation: treat the generator as a
1485 num_points
= num_points
+ 1;
1488 if (num_points
> 0) {
1489 if (num_points
>= 3) {
1491 * unless we precompute multiples for just one or two points,
1492 * converting those into affine form is time well spent
1496 secrets
= OPENSSL_malloc(num_points
* sizeof(felem_bytearray
));
1497 pre_comp
= OPENSSL_malloc(num_points
* 17 * 3 * sizeof(felem
));
1500 OPENSSL_malloc((num_points
* 17 + 1) * sizeof(felem
));
1501 if ((secrets
== NULL
) || (pre_comp
== NULL
)
1502 || (mixed
&& (tmp_felems
== NULL
))) {
1503 ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL
, ERR_R_MALLOC_FAILURE
);
1508 * we treat NULL scalars as 0, and NULL points as points at infinity,
1509 * i.e., they contribute nothing to the linear combination
1511 memset(secrets
, 0, num_points
* sizeof(felem_bytearray
));
1512 memset(pre_comp
, 0, num_points
* 17 * 3 * sizeof(felem
));
1513 for (i
= 0; i
< num_points
; ++i
) {
1517 p
= EC_GROUP_get0_generator(group
);
1520 /* the i^th point */
1523 p_scalar
= scalars
[i
];
1525 if ((p_scalar
!= NULL
) && (p
!= NULL
)) {
1526 /* reduce scalar to 0 <= scalar < 2^224 */
1527 if ((BN_num_bits(p_scalar
) > 224)
1528 || (BN_is_negative(p_scalar
))) {
1530 * this is an unusual input, and we don't guarantee
1533 if (!BN_nnmod(tmp_scalar
, p_scalar
, &group
->order
, ctx
)) {
1534 ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL
, ERR_R_BN_LIB
);
1537 num_bytes
= BN_bn2bin(tmp_scalar
, tmp
);
1539 num_bytes
= BN_bn2bin(p_scalar
, tmp
);
1540 flip_endian(secrets
[i
], tmp
, num_bytes
);
1541 /* precompute multiples */
1542 if ((!BN_to_felem(x_out
, &p
->X
)) ||
1543 (!BN_to_felem(y_out
, &p
->Y
)) ||
1544 (!BN_to_felem(z_out
, &p
->Z
)))
1546 felem_assign(pre_comp
[i
][1][0], x_out
);
1547 felem_assign(pre_comp
[i
][1][1], y_out
);
1548 felem_assign(pre_comp
[i
][1][2], z_out
);
1549 for (j
= 2; j
<= 16; ++j
) {
1551 point_add(pre_comp
[i
][j
][0], pre_comp
[i
][j
][1],
1552 pre_comp
[i
][j
][2], pre_comp
[i
][1][0],
1553 pre_comp
[i
][1][1], pre_comp
[i
][1][2], 0,
1554 pre_comp
[i
][j
- 1][0],
1555 pre_comp
[i
][j
- 1][1],
1556 pre_comp
[i
][j
- 1][2]);
1558 point_double(pre_comp
[i
][j
][0], pre_comp
[i
][j
][1],
1559 pre_comp
[i
][j
][2], pre_comp
[i
][j
/ 2][0],
1560 pre_comp
[i
][j
/ 2][1],
1561 pre_comp
[i
][j
/ 2][2]);
1567 make_points_affine(num_points
* 17, pre_comp
[0], tmp_felems
);
1570 /* the scalar for the generator */
1571 if ((scalar
!= NULL
) && (have_pre_comp
)) {
1572 memset(g_secret
, 0, sizeof g_secret
);
1573 /* reduce scalar to 0 <= scalar < 2^224 */
1574 if ((BN_num_bits(scalar
) > 224) || (BN_is_negative(scalar
))) {
1576 * this is an unusual input, and we don't guarantee
1579 if (!BN_nnmod(tmp_scalar
, scalar
, &group
->order
, ctx
)) {
1580 ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL
, ERR_R_BN_LIB
);
1583 num_bytes
= BN_bn2bin(tmp_scalar
, tmp
);
1585 num_bytes
= BN_bn2bin(scalar
, tmp
);
1586 flip_endian(g_secret
, tmp
, num_bytes
);
1587 /* do the multiplication with generator precomputation */
1588 batch_mul(x_out
, y_out
, z_out
,
1589 (const felem_bytearray(*))secrets
, num_points
,
1591 mixed
, (const felem(*)[17][3])pre_comp
, g_pre_comp
);
1593 /* do the multiplication without generator precomputation */
1594 batch_mul(x_out
, y_out
, z_out
,
1595 (const felem_bytearray(*))secrets
, num_points
,
1596 NULL
, mixed
, (const felem(*)[17][3])pre_comp
, NULL
);
1597 /* reduce the output to its unique minimal representation */
1598 felem_contract(x_in
, x_out
);
1599 felem_contract(y_in
, y_out
);
1600 felem_contract(z_in
, z_out
);
1601 if ((!felem_to_BN(x
, x_in
)) || (!felem_to_BN(y
, y_in
)) ||
1602 (!felem_to_BN(z
, z_in
))) {
1603 ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL
, ERR_R_BN_LIB
);
1606 ret
= EC_POINT_set_Jprojective_coordinates_GFp(group
, r
, x
, y
, z
, ctx
);
1610 if (generator
!= NULL
)
1611 EC_POINT_free(generator
);
1612 if (new_ctx
!= NULL
)
1613 BN_CTX_free(new_ctx
);
1614 if (secrets
!= NULL
)
1615 OPENSSL_free(secrets
);
1616 if (pre_comp
!= NULL
)
1617 OPENSSL_free(pre_comp
);
1618 if (tmp_felems
!= NULL
)
1619 OPENSSL_free(tmp_felems
);
1623 int ec_GFp_nistp224_precompute_mult(EC_GROUP
*group
, BN_CTX
*ctx
)
1626 NISTP224_PRE_COMP
*pre
= NULL
;
1628 BN_CTX
*new_ctx
= NULL
;
1630 EC_POINT
*generator
= NULL
;
1631 felem tmp_felems
[32];
1633 /* throw away old precomputation */
1634 EC_EX_DATA_free_data(&group
->extra_data
, nistp224_pre_comp_dup
,
1635 nistp224_pre_comp_free
,
1636 nistp224_pre_comp_clear_free
);
1638 if ((ctx
= new_ctx
= BN_CTX_new()) == NULL
)
1641 if (((x
= BN_CTX_get(ctx
)) == NULL
) || ((y
= BN_CTX_get(ctx
)) == NULL
))
1643 /* get the generator */
1644 if (group
->generator
== NULL
)
1646 generator
= EC_POINT_new(group
);
1647 if (generator
== NULL
)
1649 BN_bin2bn(nistp224_curve_params
[3], sizeof(felem_bytearray
), x
);
1650 BN_bin2bn(nistp224_curve_params
[4], sizeof(felem_bytearray
), y
);
1651 if (!EC_POINT_set_affine_coordinates_GFp(group
, generator
, x
, y
, ctx
))
1653 if ((pre
= nistp224_pre_comp_new()) == NULL
)
1656 * if the generator is the standard one, use built-in precomputation
1658 if (0 == EC_POINT_cmp(group
, generator
, group
->generator
, ctx
)) {
1659 memcpy(pre
->g_pre_comp
, gmul
, sizeof(pre
->g_pre_comp
));
1662 if ((!BN_to_felem(pre
->g_pre_comp
[0][1][0], &group
->generator
->X
)) ||
1663 (!BN_to_felem(pre
->g_pre_comp
[0][1][1], &group
->generator
->Y
)) ||
1664 (!BN_to_felem(pre
->g_pre_comp
[0][1][2], &group
->generator
->Z
)))
1667 * compute 2^56*G, 2^112*G, 2^168*G for the first table, 2^28*G, 2^84*G,
1668 * 2^140*G, 2^196*G for the second one
1670 for (i
= 1; i
<= 8; i
<<= 1) {
1671 point_double(pre
->g_pre_comp
[1][i
][0], pre
->g_pre_comp
[1][i
][1],
1672 pre
->g_pre_comp
[1][i
][2], pre
->g_pre_comp
[0][i
][0],
1673 pre
->g_pre_comp
[0][i
][1], pre
->g_pre_comp
[0][i
][2]);
1674 for (j
= 0; j
< 27; ++j
) {
1675 point_double(pre
->g_pre_comp
[1][i
][0], pre
->g_pre_comp
[1][i
][1],
1676 pre
->g_pre_comp
[1][i
][2], pre
->g_pre_comp
[1][i
][0],
1677 pre
->g_pre_comp
[1][i
][1], pre
->g_pre_comp
[1][i
][2]);
1681 point_double(pre
->g_pre_comp
[0][2 * i
][0],
1682 pre
->g_pre_comp
[0][2 * i
][1],
1683 pre
->g_pre_comp
[0][2 * i
][2], pre
->g_pre_comp
[1][i
][0],
1684 pre
->g_pre_comp
[1][i
][1], pre
->g_pre_comp
[1][i
][2]);
1685 for (j
= 0; j
< 27; ++j
) {
1686 point_double(pre
->g_pre_comp
[0][2 * i
][0],
1687 pre
->g_pre_comp
[0][2 * i
][1],
1688 pre
->g_pre_comp
[0][2 * i
][2],
1689 pre
->g_pre_comp
[0][2 * i
][0],
1690 pre
->g_pre_comp
[0][2 * i
][1],
1691 pre
->g_pre_comp
[0][2 * i
][2]);
1694 for (i
= 0; i
< 2; i
++) {
1695 /* g_pre_comp[i][0] is the point at infinity */
1696 memset(pre
->g_pre_comp
[i
][0], 0, sizeof(pre
->g_pre_comp
[i
][0]));
1697 /* the remaining multiples */
1698 /* 2^56*G + 2^112*G resp. 2^84*G + 2^140*G */
1699 point_add(pre
->g_pre_comp
[i
][6][0], pre
->g_pre_comp
[i
][6][1],
1700 pre
->g_pre_comp
[i
][6][2], pre
->g_pre_comp
[i
][4][0],
1701 pre
->g_pre_comp
[i
][4][1], pre
->g_pre_comp
[i
][4][2],
1702 0, pre
->g_pre_comp
[i
][2][0], pre
->g_pre_comp
[i
][2][1],
1703 pre
->g_pre_comp
[i
][2][2]);
1704 /* 2^56*G + 2^168*G resp. 2^84*G + 2^196*G */
1705 point_add(pre
->g_pre_comp
[i
][10][0], pre
->g_pre_comp
[i
][10][1],
1706 pre
->g_pre_comp
[i
][10][2], pre
->g_pre_comp
[i
][8][0],
1707 pre
->g_pre_comp
[i
][8][1], pre
->g_pre_comp
[i
][8][2],
1708 0, pre
->g_pre_comp
[i
][2][0], pre
->g_pre_comp
[i
][2][1],
1709 pre
->g_pre_comp
[i
][2][2]);
1710 /* 2^112*G + 2^168*G resp. 2^140*G + 2^196*G */
1711 point_add(pre
->g_pre_comp
[i
][12][0], pre
->g_pre_comp
[i
][12][1],
1712 pre
->g_pre_comp
[i
][12][2], pre
->g_pre_comp
[i
][8][0],
1713 pre
->g_pre_comp
[i
][8][1], pre
->g_pre_comp
[i
][8][2],
1714 0, pre
->g_pre_comp
[i
][4][0], pre
->g_pre_comp
[i
][4][1],
1715 pre
->g_pre_comp
[i
][4][2]);
1717 * 2^56*G + 2^112*G + 2^168*G resp. 2^84*G + 2^140*G + 2^196*G
1719 point_add(pre
->g_pre_comp
[i
][14][0], pre
->g_pre_comp
[i
][14][1],
1720 pre
->g_pre_comp
[i
][14][2], pre
->g_pre_comp
[i
][12][0],
1721 pre
->g_pre_comp
[i
][12][1], pre
->g_pre_comp
[i
][12][2],
1722 0, pre
->g_pre_comp
[i
][2][0], pre
->g_pre_comp
[i
][2][1],
1723 pre
->g_pre_comp
[i
][2][2]);
1724 for (j
= 1; j
< 8; ++j
) {
1725 /* odd multiples: add G resp. 2^28*G */
1726 point_add(pre
->g_pre_comp
[i
][2 * j
+ 1][0],
1727 pre
->g_pre_comp
[i
][2 * j
+ 1][1],
1728 pre
->g_pre_comp
[i
][2 * j
+ 1][2],
1729 pre
->g_pre_comp
[i
][2 * j
][0],
1730 pre
->g_pre_comp
[i
][2 * j
][1],
1731 pre
->g_pre_comp
[i
][2 * j
][2], 0,
1732 pre
->g_pre_comp
[i
][1][0], pre
->g_pre_comp
[i
][1][1],
1733 pre
->g_pre_comp
[i
][1][2]);
1736 make_points_affine(31, &(pre
->g_pre_comp
[0][1]), tmp_felems
);
1739 if (!EC_EX_DATA_set_data(&group
->extra_data
, pre
, nistp224_pre_comp_dup
,
1740 nistp224_pre_comp_free
,
1741 nistp224_pre_comp_clear_free
))
1747 if (generator
!= NULL
)
1748 EC_POINT_free(generator
);
1749 if (new_ctx
!= NULL
)
1750 BN_CTX_free(new_ctx
);
1752 nistp224_pre_comp_free(pre
);
1756 int ec_GFp_nistp224_have_precompute_mult(const EC_GROUP
*group
)
1758 if (EC_EX_DATA_get_data(group
->extra_data
, nistp224_pre_comp_dup
,
1759 nistp224_pre_comp_free
,
1760 nistp224_pre_comp_clear_free
)
1768 static void *dummy
= &dummy
;