Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 1 | /* Copyright (c) 2015, Google Inc. |
| 2 | * |
| 3 | * Permission to use, copy, modify, and/or distribute this software for any |
| 4 | * purpose with or without fee is hereby granted, provided that the above |
| 5 | * copyright notice and this permission notice appear in all copies. |
| 6 | * |
| 7 | * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES |
| 8 | * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF |
| 9 | * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY |
| 10 | * SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES |
| 11 | * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION |
| 12 | * OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN |
| 13 | * CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. */ |
| 14 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 15 | // A 64-bit implementation of the NIST P-224 elliptic curve point multiplication |
| 16 | // |
| 17 | // Inspired by Daniel J. Bernstein's public domain nistp224 implementation |
| 18 | // and Adam Langley's public domain 64-bit C implementation of curve25519. |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 19 | |
| 20 | #include <openssl/base.h> |
| 21 | |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 22 | #include <openssl/bn.h> |
| 23 | #include <openssl/ec.h> |
| 24 | #include <openssl/err.h> |
| 25 | #include <openssl/mem.h> |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 26 | |
| 27 | #include <string.h> |
| 28 | |
| 29 | #include "internal.h" |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 30 | #include "../delocate.h" |
| 31 | #include "../../internal.h" |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 32 | |
| 33 | |
Robert Sloan | 5581810 | 2017-12-18 11:26:17 -0800 | [diff] [blame] | 34 | #if defined(BORINGSSL_HAS_UINT128) && !defined(OPENSSL_SMALL) |
| 35 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 36 | // Field elements are represented as a_0 + 2^56*a_1 + 2^112*a_2 + 2^168*a_3 |
| 37 | // using 64-bit coefficients called 'limbs', and sometimes (for multiplication |
| 38 | // results) as b_0 + 2^56*b_1 + 2^112*b_2 + 2^168*b_3 + 2^224*b_4 + 2^280*b_5 + |
| 39 | // 2^336*b_6 using 128-bit coefficients called 'widelimbs'. A 4-p224_limb |
| 40 | // representation is an 'p224_felem'; a 7-p224_widelimb representation is a |
| 41 | // 'p224_widefelem'. Even within felems, bits of adjacent limbs overlap, and we |
| 42 | // don't always reduce the representations: we ensure that inputs to each |
| 43 | // p224_felem multiplication satisfy a_i < 2^60, so outputs satisfy b_i < |
| 44 | // 4*2^60*2^60, and fit into a 128-bit word without overflow. The coefficients |
| 45 | // are then again partially reduced to obtain an p224_felem satisfying a_i < |
| 46 | // 2^57. We only reduce to the unique minimal representation at the end of the |
| 47 | // computation. |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 48 | |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 49 | typedef uint64_t p224_limb; |
| 50 | typedef uint128_t p224_widelimb; |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 51 | |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 52 | typedef p224_limb p224_felem[4]; |
| 53 | typedef p224_widelimb p224_widefelem[7]; |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 54 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 55 | // Field element represented as a byte arrary. 28*8 = 224 bits is also the |
| 56 | // group order size for the elliptic curve, and we also use this type for |
| 57 | // scalars for point multiplication. |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 58 | typedef uint8_t p224_felem_bytearray[28]; |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 59 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 60 | // Precomputed multiples of the standard generator |
| 61 | // Points are given in coordinates (X, Y, Z) where Z normally is 1 |
| 62 | // (0 for the point at infinity). |
| 63 | // For each field element, slice a_0 is word 0, etc. |
| 64 | // |
| 65 | // The table has 2 * 16 elements, starting with the following: |
| 66 | // index | bits | point |
| 67 | // ------+---------+------------------------------ |
| 68 | // 0 | 0 0 0 0 | 0G |
| 69 | // 1 | 0 0 0 1 | 1G |
| 70 | // 2 | 0 0 1 0 | 2^56G |
| 71 | // 3 | 0 0 1 1 | (2^56 + 1)G |
| 72 | // 4 | 0 1 0 0 | 2^112G |
| 73 | // 5 | 0 1 0 1 | (2^112 + 1)G |
| 74 | // 6 | 0 1 1 0 | (2^112 + 2^56)G |
| 75 | // 7 | 0 1 1 1 | (2^112 + 2^56 + 1)G |
| 76 | // 8 | 1 0 0 0 | 2^168G |
| 77 | // 9 | 1 0 0 1 | (2^168 + 1)G |
| 78 | // 10 | 1 0 1 0 | (2^168 + 2^56)G |
| 79 | // 11 | 1 0 1 1 | (2^168 + 2^56 + 1)G |
| 80 | // 12 | 1 1 0 0 | (2^168 + 2^112)G |
| 81 | // 13 | 1 1 0 1 | (2^168 + 2^112 + 1)G |
| 82 | // 14 | 1 1 1 0 | (2^168 + 2^112 + 2^56)G |
| 83 | // 15 | 1 1 1 1 | (2^168 + 2^112 + 2^56 + 1)G |
| 84 | // followed by a copy of this with each element multiplied by 2^28. |
| 85 | // |
| 86 | // The reason for this is so that we can clock bits into four different |
| 87 | // locations when doing simple scalar multiplies against the base point, |
| 88 | // and then another four locations using the second 16 elements. |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 89 | static const p224_felem g_p224_pre_comp[2][16][3] = { |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 90 | {{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}, |
| 91 | {{0x3280d6115c1d21, 0xc1d356c2112234, 0x7f321390b94a03, 0xb70e0cbd6bb4bf}, |
| 92 | {0xd5819985007e34, 0x75a05a07476444, 0xfb4c22dfe6cd43, 0xbd376388b5f723}, |
| 93 | {1, 0, 0, 0}}, |
| 94 | {{0xfd9675666ebbe9, 0xbca7664d40ce5e, 0x2242df8d8a2a43, 0x1f49bbb0f99bc5}, |
| 95 | {0x29e0b892dc9c43, 0xece8608436e662, 0xdc858f185310d0, 0x9812dd4eb8d321}, |
| 96 | {1, 0, 0, 0}}, |
| 97 | {{0x6d3e678d5d8eb8, 0x559eed1cb362f1, 0x16e9a3bbce8a3f, 0xeedcccd8c2a748}, |
| 98 | {0xf19f90ed50266d, 0xabf2b4bf65f9df, 0x313865468fafec, 0x5cb379ba910a17}, |
| 99 | {1, 0, 0, 0}}, |
| 100 | {{0x0641966cab26e3, 0x91fb2991fab0a0, 0xefec27a4e13a0b, 0x0499aa8a5f8ebe}, |
| 101 | {0x7510407766af5d, 0x84d929610d5450, 0x81d77aae82f706, 0x6916f6d4338c5b}, |
| 102 | {1, 0, 0, 0}}, |
| 103 | {{0xea95ac3b1f15c6, 0x086000905e82d4, 0xdd323ae4d1c8b1, 0x932b56be7685a3}, |
| 104 | {0x9ef93dea25dbbf, 0x41665960f390f0, 0xfdec76dbe2a8a7, 0x523e80f019062a}, |
| 105 | {1, 0, 0, 0}}, |
| 106 | {{0x822fdd26732c73, 0xa01c83531b5d0f, 0x363f37347c1ba4, 0xc391b45c84725c}, |
| 107 | {0xbbd5e1b2d6ad24, 0xddfbcde19dfaec, 0xc393da7e222a7f, 0x1efb7890ede244}, |
| 108 | {1, 0, 0, 0}}, |
| 109 | {{0x4c9e90ca217da1, 0xd11beca79159bb, 0xff8d33c2c98b7c, 0x2610b39409f849}, |
| 110 | {0x44d1352ac64da0, 0xcdbb7b2c46b4fb, 0x966c079b753c89, 0xfe67e4e820b112}, |
| 111 | {1, 0, 0, 0}}, |
| 112 | {{0xe28cae2df5312d, 0xc71b61d16f5c6e, 0x79b7619a3e7c4c, 0x05c73240899b47}, |
| 113 | {0x9f7f6382c73e3a, 0x18615165c56bda, 0x641fab2116fd56, 0x72855882b08394}, |
| 114 | {1, 0, 0, 0}}, |
| 115 | {{0x0469182f161c09, 0x74a98ca8d00fb5, 0xb89da93489a3e0, 0x41c98768fb0c1d}, |
| 116 | {0xe5ea05fb32da81, 0x3dce9ffbca6855, 0x1cfe2d3fbf59e6, 0x0e5e03408738a7}, |
| 117 | {1, 0, 0, 0}}, |
| 118 | {{0xdab22b2333e87f, 0x4430137a5dd2f6, 0xe03ab9f738beb8, 0xcb0c5d0dc34f24}, |
| 119 | {0x764a7df0c8fda5, 0x185ba5c3fa2044, 0x9281d688bcbe50, 0xc40331df893881}, |
| 120 | {1, 0, 0, 0}}, |
| 121 | {{0xb89530796f0f60, 0xade92bd26909a3, 0x1a0c83fb4884da, 0x1765bf22a5a984}, |
| 122 | {0x772a9ee75db09e, 0x23bc6c67cec16f, 0x4c1edba8b14e2f, 0xe2a215d9611369}, |
| 123 | {1, 0, 0, 0}}, |
| 124 | {{0x571e509fb5efb3, 0xade88696410552, 0xc8ae85fada74fe, 0x6c7e4be83bbde3}, |
| 125 | {0xff9f51160f4652, 0xb47ce2495a6539, 0xa2946c53b582f4, 0x286d2db3ee9a60}, |
| 126 | {1, 0, 0, 0}}, |
| 127 | {{0x40bbd5081a44af, 0x0995183b13926c, 0xbcefba6f47f6d0, 0x215619e9cc0057}, |
| 128 | {0x8bc94d3b0df45e, 0xf11c54a3694f6f, 0x8631b93cdfe8b5, 0xe7e3f4b0982db9}, |
| 129 | {1, 0, 0, 0}}, |
| 130 | {{0xb17048ab3e1c7b, 0xac38f36ff8a1d8, 0x1c29819435d2c6, 0xc813132f4c07e9}, |
| 131 | {0x2891425503b11f, 0x08781030579fea, 0xf5426ba5cc9674, 0x1e28ebf18562bc}, |
| 132 | {1, 0, 0, 0}}, |
| 133 | {{0x9f31997cc864eb, 0x06cd91d28b5e4c, 0xff17036691a973, 0xf1aef351497c58}, |
| 134 | {0xdd1f2d600564ff, 0xdead073b1402db, 0x74a684435bd693, 0xeea7471f962558}, |
| 135 | {1, 0, 0, 0}}}, |
| 136 | {{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}, |
| 137 | {{0x9665266dddf554, 0x9613d78b60ef2d, 0xce27a34cdba417, 0xd35ab74d6afc31}, |
| 138 | {0x85ccdd22deb15e, 0x2137e5783a6aab, 0xa141cffd8c93c6, 0x355a1830e90f2d}, |
| 139 | {1, 0, 0, 0}}, |
| 140 | {{0x1a494eadaade65, 0xd6da4da77fe53c, 0xe7992996abec86, 0x65c3553c6090e3}, |
| 141 | {0xfa610b1fb09346, 0xf1c6540b8a4aaf, 0xc51a13ccd3cbab, 0x02995b1b18c28a}, |
| 142 | {1, 0, 0, 0}}, |
| 143 | {{0x7874568e7295ef, 0x86b419fbe38d04, 0xdc0690a7550d9a, 0xd3966a44beac33}, |
| 144 | {0x2b7280ec29132f, 0xbeaa3b6a032df3, 0xdc7dd88ae41200, 0xd25e2513e3a100}, |
| 145 | {1, 0, 0, 0}}, |
| 146 | {{0x924857eb2efafd, 0xac2bce41223190, 0x8edaa1445553fc, 0x825800fd3562d5}, |
| 147 | {0x8d79148ea96621, 0x23a01c3dd9ed8d, 0xaf8b219f9416b5, 0xd8db0cc277daea}, |
| 148 | {1, 0, 0, 0}}, |
| 149 | {{0x76a9c3b1a700f0, 0xe9acd29bc7e691, 0x69212d1a6b0327, 0x6322e97fe154be}, |
| 150 | {0x469fc5465d62aa, 0x8d41ed18883b05, 0x1f8eae66c52b88, 0xe4fcbe9325be51}, |
| 151 | {1, 0, 0, 0}}, |
| 152 | {{0x825fdf583cac16, 0x020b857c7b023a, 0x683c17744b0165, 0x14ffd0a2daf2f1}, |
| 153 | {0x323b36184218f9, 0x4944ec4e3b47d4, 0xc15b3080841acf, 0x0bced4b01a28bb}, |
| 154 | {1, 0, 0, 0}}, |
| 155 | {{0x92ac22230df5c4, 0x52f33b4063eda8, 0xcb3f19870c0c93, 0x40064f2ba65233}, |
| 156 | {0xfe16f0924f8992, 0x012da25af5b517, 0x1a57bb24f723a6, 0x06f8bc76760def}, |
| 157 | {1, 0, 0, 0}}, |
| 158 | {{0x4a7084f7817cb9, 0xbcab0738ee9a78, 0x3ec11e11d9c326, 0xdc0fe90e0f1aae}, |
| 159 | {0xcf639ea5f98390, 0x5c350aa22ffb74, 0x9afae98a4047b7, 0x956ec2d617fc45}, |
| 160 | {1, 0, 0, 0}}, |
| 161 | {{0x4306d648c1be6a, 0x9247cd8bc9a462, 0xf5595e377d2f2e, 0xbd1c3caff1a52e}, |
| 162 | {0x045e14472409d0, 0x29f3e17078f773, 0x745a602b2d4f7d, 0x191837685cdfbb}, |
| 163 | {1, 0, 0, 0}}, |
| 164 | {{0x5b6ee254a8cb79, 0x4953433f5e7026, 0xe21faeb1d1def4, 0xc4c225785c09de}, |
| 165 | {0x307ce7bba1e518, 0x31b125b1036db8, 0x47e91868839e8f, 0xc765866e33b9f3}, |
| 166 | {1, 0, 0, 0}}, |
| 167 | {{0x3bfece24f96906, 0x4794da641e5093, 0xde5df64f95db26, 0x297ecd89714b05}, |
| 168 | {0x701bd3ebb2c3aa, 0x7073b4f53cb1d5, 0x13c5665658af16, 0x9895089d66fe58}, |
| 169 | {1, 0, 0, 0}}, |
| 170 | {{0x0fef05f78c4790, 0x2d773633b05d2e, 0x94229c3a951c94, 0xbbbd70df4911bb}, |
| 171 | {0xb2c6963d2c1168, 0x105f47a72b0d73, 0x9fdf6111614080, 0x7b7e94b39e67b0}, |
| 172 | {1, 0, 0, 0}}, |
| 173 | {{0xad1a7d6efbe2b3, 0xf012482c0da69d, 0x6b3bdf12438345, 0x40d7558d7aa4d9}, |
| 174 | {0x8a09fffb5c6d3d, 0x9a356e5d9ffd38, 0x5973f15f4f9b1c, 0xdcd5f59f63c3ea}, |
| 175 | {1, 0, 0, 0}}, |
| 176 | {{0xacf39f4c5ca7ab, 0x4c8071cc5fd737, 0xc64e3602cd1184, 0x0acd4644c9abba}, |
| 177 | {0x6c011a36d8bf6e, 0xfecd87ba24e32a, 0x19f6f56574fad8, 0x050b204ced9405}, |
| 178 | {1, 0, 0, 0}}, |
| 179 | {{0xed4f1cae7d9a96, 0x5ceef7ad94c40a, 0x778e4a3bf3ef9b, 0x7405783dc3b55e}, |
| 180 | {0x32477c61b6e8c6, 0xb46a97570f018b, 0x91176d0a7e95d1, 0x3df90fbc4c7d0e}, |
| 181 | {1, 0, 0, 0}}}}; |
| 182 | |
Robert Sloan | a12bf46 | 2017-07-17 07:08:26 -0700 | [diff] [blame] | 183 | static uint64_t p224_load_u64(const uint8_t in[8]) { |
| 184 | uint64_t ret; |
| 185 | OPENSSL_memcpy(&ret, in, sizeof(ret)); |
| 186 | return ret; |
| 187 | } |
| 188 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 189 | // Helper functions to convert field elements to/from internal representation |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 190 | static void p224_bin28_to_felem(p224_felem out, const uint8_t in[28]) { |
Robert Sloan | a12bf46 | 2017-07-17 07:08:26 -0700 | [diff] [blame] | 191 | out[0] = p224_load_u64(in) & 0x00ffffffffffffff; |
| 192 | out[1] = p224_load_u64(in + 7) & 0x00ffffffffffffff; |
| 193 | out[2] = p224_load_u64(in + 14) & 0x00ffffffffffffff; |
| 194 | out[3] = p224_load_u64(in + 20) >> 8; |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 195 | } |
| 196 | |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 197 | static void p224_felem_to_bin28(uint8_t out[28], const p224_felem in) { |
David Benjamin | 7c0d06c | 2016-08-11 13:26:41 -0400 | [diff] [blame] | 198 | for (size_t i = 0; i < 7; ++i) { |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 199 | out[i] = in[0] >> (8 * i); |
| 200 | out[i + 7] = in[1] >> (8 * i); |
| 201 | out[i + 14] = in[2] >> (8 * i); |
| 202 | out[i + 21] = in[3] >> (8 * i); |
| 203 | } |
| 204 | } |
| 205 | |
Robert Sloan | c6ebb28 | 2018-04-30 10:10:26 -0700 | [diff] [blame] | 206 | static void p224_generic_to_felem(p224_felem out, const EC_FELEM *in) { |
| 207 | p224_bin28_to_felem(out, in->bytes); |
| 208 | } |
| 209 | |
Robert Sloan | c9abfe4 | 2018-11-26 12:19:07 -0800 | [diff] [blame] | 210 | // Requires 0 <= in < 2*p (always call p224_felem_reduce first) |
Robert Sloan | c6ebb28 | 2018-04-30 10:10:26 -0700 | [diff] [blame] | 211 | static void p224_felem_to_generic(EC_FELEM *out, const p224_felem in) { |
Robert Sloan | c9abfe4 | 2018-11-26 12:19:07 -0800 | [diff] [blame] | 212 | // Reduce to unique minimal representation. |
| 213 | static const int64_t two56 = ((p224_limb)1) << 56; |
| 214 | // 0 <= in < 2*p, p = 2^224 - 2^96 + 1 |
| 215 | // if in > p , reduce in = in - 2^224 + 2^96 - 1 |
| 216 | int64_t tmp[4], a; |
| 217 | tmp[0] = in[0]; |
| 218 | tmp[1] = in[1]; |
| 219 | tmp[2] = in[2]; |
| 220 | tmp[3] = in[3]; |
| 221 | // Case 1: a = 1 iff in >= 2^224 |
| 222 | a = (in[3] >> 56); |
| 223 | tmp[0] -= a; |
| 224 | tmp[1] += a << 40; |
| 225 | tmp[3] &= 0x00ffffffffffffff; |
| 226 | // Case 2: a = 0 iff p <= in < 2^224, i.e., the high 128 bits are all 1 and |
| 227 | // the lower part is non-zero |
| 228 | a = ((in[3] & in[2] & (in[1] | 0x000000ffffffffff)) + 1) | |
| 229 | (((int64_t)(in[0] + (in[1] & 0x000000ffffffffff)) - 1) >> 63); |
| 230 | a &= 0x00ffffffffffffff; |
| 231 | // turn a into an all-one mask (if a = 0) or an all-zero mask |
| 232 | a = (a - 1) >> 63; |
| 233 | // subtract 2^224 - 2^96 + 1 if a is all-one |
| 234 | tmp[3] &= a ^ 0xffffffffffffffff; |
| 235 | tmp[2] &= a ^ 0xffffffffffffffff; |
| 236 | tmp[1] &= (a ^ 0xffffffffffffffff) | 0x000000ffffffffff; |
| 237 | tmp[0] -= 1 & a; |
| 238 | |
| 239 | // eliminate negative coefficients: if tmp[0] is negative, tmp[1] must |
| 240 | // be non-zero, so we only need one step |
| 241 | a = tmp[0] >> 63; |
| 242 | tmp[0] += two56 & a; |
| 243 | tmp[1] -= 1 & a; |
| 244 | |
| 245 | // carry 1 -> 2 -> 3 |
| 246 | tmp[2] += tmp[1] >> 56; |
| 247 | tmp[1] &= 0x00ffffffffffffff; |
| 248 | |
| 249 | tmp[3] += tmp[2] >> 56; |
| 250 | tmp[2] &= 0x00ffffffffffffff; |
| 251 | |
| 252 | // Now 0 <= tmp < p |
| 253 | p224_felem tmp2; |
| 254 | tmp2[0] = tmp[0]; |
| 255 | tmp2[1] = tmp[1]; |
| 256 | tmp2[2] = tmp[2]; |
| 257 | tmp2[3] = tmp[3]; |
| 258 | |
| 259 | p224_felem_to_bin28(out->bytes, tmp2); |
Robert Sloan | c6ebb28 | 2018-04-30 10:10:26 -0700 | [diff] [blame] | 260 | // 224 is not a multiple of 64, so zero the remaining bytes. |
| 261 | OPENSSL_memset(out->bytes + 28, 0, 32 - 28); |
| 262 | } |
| 263 | |
| 264 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 265 | // Field operations, using the internal representation of field elements. |
| 266 | // NB! These operations are specific to our point multiplication and cannot be |
| 267 | // expected to be correct in general - e.g., multiplication with a large scalar |
| 268 | // will cause an overflow. |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 269 | |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 270 | static void p224_felem_assign(p224_felem out, const p224_felem in) { |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 271 | out[0] = in[0]; |
| 272 | out[1] = in[1]; |
| 273 | out[2] = in[2]; |
| 274 | out[3] = in[3]; |
| 275 | } |
| 276 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 277 | // Sum two field elements: out += in |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 278 | static void p224_felem_sum(p224_felem out, const p224_felem in) { |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 279 | out[0] += in[0]; |
| 280 | out[1] += in[1]; |
| 281 | out[2] += in[2]; |
| 282 | out[3] += in[3]; |
| 283 | } |
| 284 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 285 | // Subtract field elements: out -= in |
| 286 | // Assumes in[i] < 2^57 |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 287 | static void p224_felem_diff(p224_felem out, const p224_felem in) { |
| 288 | static const p224_limb two58p2 = |
| 289 | (((p224_limb)1) << 58) + (((p224_limb)1) << 2); |
| 290 | static const p224_limb two58m2 = |
| 291 | (((p224_limb)1) << 58) - (((p224_limb)1) << 2); |
| 292 | static const p224_limb two58m42m2 = |
| 293 | (((p224_limb)1) << 58) - (((p224_limb)1) << 42) - (((p224_limb)1) << 2); |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 294 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 295 | // Add 0 mod 2^224-2^96+1 to ensure out > in |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 296 | out[0] += two58p2; |
| 297 | out[1] += two58m42m2; |
| 298 | out[2] += two58m2; |
| 299 | out[3] += two58m2; |
| 300 | |
| 301 | out[0] -= in[0]; |
| 302 | out[1] -= in[1]; |
| 303 | out[2] -= in[2]; |
| 304 | out[3] -= in[3]; |
| 305 | } |
| 306 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 307 | // Subtract in unreduced 128-bit mode: out -= in |
| 308 | // Assumes in[i] < 2^119 |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 309 | static void p224_widefelem_diff(p224_widefelem out, const p224_widefelem in) { |
| 310 | static const p224_widelimb two120 = ((p224_widelimb)1) << 120; |
| 311 | static const p224_widelimb two120m64 = |
| 312 | (((p224_widelimb)1) << 120) - (((p224_widelimb)1) << 64); |
| 313 | static const p224_widelimb two120m104m64 = (((p224_widelimb)1) << 120) - |
| 314 | (((p224_widelimb)1) << 104) - |
| 315 | (((p224_widelimb)1) << 64); |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 316 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 317 | // Add 0 mod 2^224-2^96+1 to ensure out > in |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 318 | out[0] += two120; |
| 319 | out[1] += two120m64; |
| 320 | out[2] += two120m64; |
| 321 | out[3] += two120; |
| 322 | out[4] += two120m104m64; |
| 323 | out[5] += two120m64; |
| 324 | out[6] += two120m64; |
| 325 | |
| 326 | out[0] -= in[0]; |
| 327 | out[1] -= in[1]; |
| 328 | out[2] -= in[2]; |
| 329 | out[3] -= in[3]; |
| 330 | out[4] -= in[4]; |
| 331 | out[5] -= in[5]; |
| 332 | out[6] -= in[6]; |
| 333 | } |
| 334 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 335 | // Subtract in mixed mode: out128 -= in64 |
| 336 | // in[i] < 2^63 |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 337 | static void p224_felem_diff_128_64(p224_widefelem out, const p224_felem in) { |
| 338 | static const p224_widelimb two64p8 = |
| 339 | (((p224_widelimb)1) << 64) + (((p224_widelimb)1) << 8); |
| 340 | static const p224_widelimb two64m8 = |
| 341 | (((p224_widelimb)1) << 64) - (((p224_widelimb)1) << 8); |
| 342 | static const p224_widelimb two64m48m8 = (((p224_widelimb)1) << 64) - |
| 343 | (((p224_widelimb)1) << 48) - |
| 344 | (((p224_widelimb)1) << 8); |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 345 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 346 | // Add 0 mod 2^224-2^96+1 to ensure out > in |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 347 | out[0] += two64p8; |
| 348 | out[1] += two64m48m8; |
| 349 | out[2] += two64m8; |
| 350 | out[3] += two64m8; |
| 351 | |
| 352 | out[0] -= in[0]; |
| 353 | out[1] -= in[1]; |
| 354 | out[2] -= in[2]; |
| 355 | out[3] -= in[3]; |
| 356 | } |
| 357 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 358 | // Multiply a field element by a scalar: out = out * scalar |
| 359 | // The scalars we actually use are small, so results fit without overflow |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 360 | static void p224_felem_scalar(p224_felem out, const p224_limb scalar) { |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 361 | out[0] *= scalar; |
| 362 | out[1] *= scalar; |
| 363 | out[2] *= scalar; |
| 364 | out[3] *= scalar; |
| 365 | } |
| 366 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 367 | // Multiply an unreduced field element by a scalar: out = out * scalar |
| 368 | // The scalars we actually use are small, so results fit without overflow |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 369 | static void p224_widefelem_scalar(p224_widefelem out, |
| 370 | const p224_widelimb scalar) { |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 371 | out[0] *= scalar; |
| 372 | out[1] *= scalar; |
| 373 | out[2] *= scalar; |
| 374 | out[3] *= scalar; |
| 375 | out[4] *= scalar; |
| 376 | out[5] *= scalar; |
| 377 | out[6] *= scalar; |
| 378 | } |
| 379 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 380 | // Square a field element: out = in^2 |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 381 | static void p224_felem_square(p224_widefelem out, const p224_felem in) { |
| 382 | p224_limb tmp0, tmp1, tmp2; |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 383 | tmp0 = 2 * in[0]; |
| 384 | tmp1 = 2 * in[1]; |
| 385 | tmp2 = 2 * in[2]; |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 386 | out[0] = ((p224_widelimb)in[0]) * in[0]; |
| 387 | out[1] = ((p224_widelimb)in[0]) * tmp1; |
| 388 | out[2] = ((p224_widelimb)in[0]) * tmp2 + ((p224_widelimb)in[1]) * in[1]; |
| 389 | out[3] = ((p224_widelimb)in[3]) * tmp0 + ((p224_widelimb)in[1]) * tmp2; |
| 390 | out[4] = ((p224_widelimb)in[3]) * tmp1 + ((p224_widelimb)in[2]) * in[2]; |
| 391 | out[5] = ((p224_widelimb)in[3]) * tmp2; |
| 392 | out[6] = ((p224_widelimb)in[3]) * in[3]; |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 393 | } |
| 394 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 395 | // Multiply two field elements: out = in1 * in2 |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 396 | static void p224_felem_mul(p224_widefelem out, const p224_felem in1, |
| 397 | const p224_felem in2) { |
| 398 | out[0] = ((p224_widelimb)in1[0]) * in2[0]; |
| 399 | out[1] = ((p224_widelimb)in1[0]) * in2[1] + ((p224_widelimb)in1[1]) * in2[0]; |
| 400 | out[2] = ((p224_widelimb)in1[0]) * in2[2] + ((p224_widelimb)in1[1]) * in2[1] + |
| 401 | ((p224_widelimb)in1[2]) * in2[0]; |
| 402 | out[3] = ((p224_widelimb)in1[0]) * in2[3] + ((p224_widelimb)in1[1]) * in2[2] + |
| 403 | ((p224_widelimb)in1[2]) * in2[1] + ((p224_widelimb)in1[3]) * in2[0]; |
| 404 | out[4] = ((p224_widelimb)in1[1]) * in2[3] + ((p224_widelimb)in1[2]) * in2[2] + |
| 405 | ((p224_widelimb)in1[3]) * in2[1]; |
| 406 | out[5] = ((p224_widelimb)in1[2]) * in2[3] + ((p224_widelimb)in1[3]) * in2[2]; |
| 407 | out[6] = ((p224_widelimb)in1[3]) * in2[3]; |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 408 | } |
| 409 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 410 | // Reduce seven 128-bit coefficients to four 64-bit coefficients. |
| 411 | // Requires in[i] < 2^126, |
| 412 | // ensures out[0] < 2^56, out[1] < 2^56, out[2] < 2^56, out[3] <= 2^56 + 2^16 |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 413 | static void p224_felem_reduce(p224_felem out, const p224_widefelem in) { |
| 414 | static const p224_widelimb two127p15 = |
| 415 | (((p224_widelimb)1) << 127) + (((p224_widelimb)1) << 15); |
| 416 | static const p224_widelimb two127m71 = |
| 417 | (((p224_widelimb)1) << 127) - (((p224_widelimb)1) << 71); |
| 418 | static const p224_widelimb two127m71m55 = (((p224_widelimb)1) << 127) - |
| 419 | (((p224_widelimb)1) << 71) - |
| 420 | (((p224_widelimb)1) << 55); |
| 421 | p224_widelimb output[5]; |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 422 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 423 | // Add 0 mod 2^224-2^96+1 to ensure all differences are positive |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 424 | output[0] = in[0] + two127p15; |
| 425 | output[1] = in[1] + two127m71m55; |
| 426 | output[2] = in[2] + two127m71; |
| 427 | output[3] = in[3]; |
| 428 | output[4] = in[4]; |
| 429 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 430 | // Eliminate in[4], in[5], in[6] |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 431 | output[4] += in[6] >> 16; |
| 432 | output[3] += (in[6] & 0xffff) << 40; |
| 433 | output[2] -= in[6]; |
| 434 | |
| 435 | output[3] += in[5] >> 16; |
| 436 | output[2] += (in[5] & 0xffff) << 40; |
| 437 | output[1] -= in[5]; |
| 438 | |
| 439 | output[2] += output[4] >> 16; |
| 440 | output[1] += (output[4] & 0xffff) << 40; |
| 441 | output[0] -= output[4]; |
| 442 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 443 | // Carry 2 -> 3 -> 4 |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 444 | output[3] += output[2] >> 56; |
| 445 | output[2] &= 0x00ffffffffffffff; |
| 446 | |
| 447 | output[4] = output[3] >> 56; |
| 448 | output[3] &= 0x00ffffffffffffff; |
| 449 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 450 | // Now output[2] < 2^56, output[3] < 2^56, output[4] < 2^72 |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 451 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 452 | // Eliminate output[4] |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 453 | output[2] += output[4] >> 16; |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 454 | // output[2] < 2^56 + 2^56 = 2^57 |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 455 | output[1] += (output[4] & 0xffff) << 40; |
| 456 | output[0] -= output[4]; |
| 457 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 458 | // Carry 0 -> 1 -> 2 -> 3 |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 459 | output[1] += output[0] >> 56; |
| 460 | out[0] = output[0] & 0x00ffffffffffffff; |
| 461 | |
| 462 | output[2] += output[1] >> 56; |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 463 | // output[2] < 2^57 + 2^72 |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 464 | out[1] = output[1] & 0x00ffffffffffffff; |
| 465 | output[3] += output[2] >> 56; |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 466 | // output[3] <= 2^56 + 2^16 |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 467 | out[2] = output[2] & 0x00ffffffffffffff; |
| 468 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 469 | // out[0] < 2^56, out[1] < 2^56, out[2] < 2^56, |
| 470 | // out[3] <= 2^56 + 2^16 (due to final carry), |
| 471 | // so out < 2*p |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 472 | out[3] = output[3]; |
| 473 | } |
| 474 | |
Robert Sloan | 49d063b | 2018-04-03 11:30:38 -0700 | [diff] [blame] | 475 | // Get negative value: out = -in |
| 476 | // Requires in[i] < 2^63, |
| 477 | // ensures out[0] < 2^56, out[1] < 2^56, out[2] < 2^56, out[3] <= 2^56 + 2^16 |
| 478 | static void p224_felem_neg(p224_felem out, const p224_felem in) { |
| 479 | p224_widefelem tmp = {0}; |
| 480 | p224_felem_diff_128_64(tmp, in); |
| 481 | p224_felem_reduce(out, tmp); |
| 482 | } |
| 483 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 484 | // Zero-check: returns 1 if input is 0, and 0 otherwise. We know that field |
| 485 | // elements are reduced to in < 2^225, so we only need to check three cases: 0, |
| 486 | // 2^224 - 2^96 + 1, and 2^225 - 2^97 + 2 |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 487 | static p224_limb p224_felem_is_zero(const p224_felem in) { |
| 488 | p224_limb zero = in[0] | in[1] | in[2] | in[3]; |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 489 | zero = (((int64_t)(zero)-1) >> 63) & 1; |
| 490 | |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 491 | p224_limb two224m96p1 = (in[0] ^ 1) | (in[1] ^ 0x00ffff0000000000) | |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 492 | (in[2] ^ 0x00ffffffffffffff) | |
| 493 | (in[3] ^ 0x00ffffffffffffff); |
| 494 | two224m96p1 = (((int64_t)(two224m96p1)-1) >> 63) & 1; |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 495 | p224_limb two225m97p2 = (in[0] ^ 2) | (in[1] ^ 0x00fffe0000000000) | |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 496 | (in[2] ^ 0x00ffffffffffffff) | |
| 497 | (in[3] ^ 0x01ffffffffffffff); |
| 498 | two225m97p2 = (((int64_t)(two225m97p2)-1) >> 63) & 1; |
| 499 | return (zero | two224m96p1 | two225m97p2); |
| 500 | } |
| 501 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 502 | // Invert a field element |
| 503 | // Computation chain copied from djb's code |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 504 | static void p224_felem_inv(p224_felem out, const p224_felem in) { |
| 505 | p224_felem ftmp, ftmp2, ftmp3, ftmp4; |
| 506 | p224_widefelem tmp; |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 507 | |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 508 | p224_felem_square(tmp, in); |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 509 | p224_felem_reduce(ftmp, tmp); // 2 |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 510 | p224_felem_mul(tmp, in, ftmp); |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 511 | p224_felem_reduce(ftmp, tmp); // 2^2 - 1 |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 512 | p224_felem_square(tmp, ftmp); |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 513 | p224_felem_reduce(ftmp, tmp); // 2^3 - 2 |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 514 | p224_felem_mul(tmp, in, ftmp); |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 515 | p224_felem_reduce(ftmp, tmp); // 2^3 - 1 |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 516 | p224_felem_square(tmp, ftmp); |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 517 | p224_felem_reduce(ftmp2, tmp); // 2^4 - 2 |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 518 | p224_felem_square(tmp, ftmp2); |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 519 | p224_felem_reduce(ftmp2, tmp); // 2^5 - 4 |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 520 | p224_felem_square(tmp, ftmp2); |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 521 | p224_felem_reduce(ftmp2, tmp); // 2^6 - 8 |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 522 | p224_felem_mul(tmp, ftmp2, ftmp); |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 523 | p224_felem_reduce(ftmp, tmp); // 2^6 - 1 |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 524 | p224_felem_square(tmp, ftmp); |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 525 | p224_felem_reduce(ftmp2, tmp); // 2^7 - 2 |
| 526 | for (size_t i = 0; i < 5; ++i) { // 2^12 - 2^6 |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 527 | p224_felem_square(tmp, ftmp2); |
| 528 | p224_felem_reduce(ftmp2, tmp); |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 529 | } |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 530 | p224_felem_mul(tmp, ftmp2, ftmp); |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 531 | p224_felem_reduce(ftmp2, tmp); // 2^12 - 1 |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 532 | p224_felem_square(tmp, ftmp2); |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 533 | p224_felem_reduce(ftmp3, tmp); // 2^13 - 2 |
| 534 | for (size_t i = 0; i < 11; ++i) { // 2^24 - 2^12 |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 535 | p224_felem_square(tmp, ftmp3); |
| 536 | p224_felem_reduce(ftmp3, tmp); |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 537 | } |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 538 | p224_felem_mul(tmp, ftmp3, ftmp2); |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 539 | p224_felem_reduce(ftmp2, tmp); // 2^24 - 1 |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 540 | p224_felem_square(tmp, ftmp2); |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 541 | p224_felem_reduce(ftmp3, tmp); // 2^25 - 2 |
| 542 | for (size_t i = 0; i < 23; ++i) { // 2^48 - 2^24 |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 543 | p224_felem_square(tmp, ftmp3); |
| 544 | p224_felem_reduce(ftmp3, tmp); |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 545 | } |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 546 | p224_felem_mul(tmp, ftmp3, ftmp2); |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 547 | p224_felem_reduce(ftmp3, tmp); // 2^48 - 1 |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 548 | p224_felem_square(tmp, ftmp3); |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 549 | p224_felem_reduce(ftmp4, tmp); // 2^49 - 2 |
| 550 | for (size_t i = 0; i < 47; ++i) { // 2^96 - 2^48 |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 551 | p224_felem_square(tmp, ftmp4); |
| 552 | p224_felem_reduce(ftmp4, tmp); |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 553 | } |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 554 | p224_felem_mul(tmp, ftmp3, ftmp4); |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 555 | p224_felem_reduce(ftmp3, tmp); // 2^96 - 1 |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 556 | p224_felem_square(tmp, ftmp3); |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 557 | p224_felem_reduce(ftmp4, tmp); // 2^97 - 2 |
| 558 | for (size_t i = 0; i < 23; ++i) { // 2^120 - 2^24 |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 559 | p224_felem_square(tmp, ftmp4); |
| 560 | p224_felem_reduce(ftmp4, tmp); |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 561 | } |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 562 | p224_felem_mul(tmp, ftmp2, ftmp4); |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 563 | p224_felem_reduce(ftmp2, tmp); // 2^120 - 1 |
| 564 | for (size_t i = 0; i < 6; ++i) { // 2^126 - 2^6 |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 565 | p224_felem_square(tmp, ftmp2); |
| 566 | p224_felem_reduce(ftmp2, tmp); |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 567 | } |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 568 | p224_felem_mul(tmp, ftmp2, ftmp); |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 569 | p224_felem_reduce(ftmp, tmp); // 2^126 - 1 |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 570 | p224_felem_square(tmp, ftmp); |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 571 | p224_felem_reduce(ftmp, tmp); // 2^127 - 2 |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 572 | p224_felem_mul(tmp, ftmp, in); |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 573 | p224_felem_reduce(ftmp, tmp); // 2^127 - 1 |
| 574 | for (size_t i = 0; i < 97; ++i) { // 2^224 - 2^97 |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 575 | p224_felem_square(tmp, ftmp); |
| 576 | p224_felem_reduce(ftmp, tmp); |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 577 | } |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 578 | p224_felem_mul(tmp, ftmp, ftmp3); |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 579 | p224_felem_reduce(out, tmp); // 2^224 - 2^96 - 1 |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 580 | } |
| 581 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 582 | // Copy in constant time: |
| 583 | // if icopy == 1, copy in to out, |
| 584 | // if icopy == 0, copy out to itself. |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 585 | static void p224_copy_conditional(p224_felem out, const p224_felem in, |
| 586 | p224_limb icopy) { |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 587 | // icopy is a (64-bit) 0 or 1, so copy is either all-zero or all-one |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 588 | const p224_limb copy = -icopy; |
David Benjamin | 7c0d06c | 2016-08-11 13:26:41 -0400 | [diff] [blame] | 589 | for (size_t i = 0; i < 4; ++i) { |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 590 | const p224_limb tmp = copy & (in[i] ^ out[i]); |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 591 | out[i] ^= tmp; |
| 592 | } |
| 593 | } |
| 594 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 595 | // ELLIPTIC CURVE POINT OPERATIONS |
| 596 | // |
| 597 | // Points are represented in Jacobian projective coordinates: |
| 598 | // (X, Y, Z) corresponds to the affine point (X/Z^2, Y/Z^3), |
| 599 | // or to the point at infinity if Z == 0. |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 600 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 601 | // Double an elliptic curve point: |
| 602 | // (X', Y', Z') = 2 * (X, Y, Z), where |
| 603 | // X' = (3 * (X - Z^2) * (X + Z^2))^2 - 8 * X * Y^2 |
| 604 | // Y' = 3 * (X - Z^2) * (X + Z^2) * (4 * X * Y^2 - X') - 8 * Y^2 |
| 605 | // Z' = (Y + Z)^2 - Y^2 - Z^2 = 2 * Y * Z |
| 606 | // Outputs can equal corresponding inputs, i.e., x_out == x_in is allowed, |
| 607 | // while x_out == y_in is not (maybe this works, but it's not tested). |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 608 | static void p224_point_double(p224_felem x_out, p224_felem y_out, |
| 609 | p224_felem z_out, const p224_felem x_in, |
| 610 | const p224_felem y_in, const p224_felem z_in) { |
| 611 | p224_widefelem tmp, tmp2; |
| 612 | p224_felem delta, gamma, beta, alpha, ftmp, ftmp2; |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 613 | |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 614 | p224_felem_assign(ftmp, x_in); |
| 615 | p224_felem_assign(ftmp2, x_in); |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 616 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 617 | // delta = z^2 |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 618 | p224_felem_square(tmp, z_in); |
| 619 | p224_felem_reduce(delta, tmp); |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 620 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 621 | // gamma = y^2 |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 622 | p224_felem_square(tmp, y_in); |
| 623 | p224_felem_reduce(gamma, tmp); |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 624 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 625 | // beta = x*gamma |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 626 | p224_felem_mul(tmp, x_in, gamma); |
| 627 | p224_felem_reduce(beta, tmp); |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 628 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 629 | // alpha = 3*(x-delta)*(x+delta) |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 630 | p224_felem_diff(ftmp, delta); |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 631 | // ftmp[i] < 2^57 + 2^58 + 2 < 2^59 |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 632 | p224_felem_sum(ftmp2, delta); |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 633 | // ftmp2[i] < 2^57 + 2^57 = 2^58 |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 634 | p224_felem_scalar(ftmp2, 3); |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 635 | // ftmp2[i] < 3 * 2^58 < 2^60 |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 636 | p224_felem_mul(tmp, ftmp, ftmp2); |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 637 | // tmp[i] < 2^60 * 2^59 * 4 = 2^121 |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 638 | p224_felem_reduce(alpha, tmp); |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 639 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 640 | // x' = alpha^2 - 8*beta |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 641 | p224_felem_square(tmp, alpha); |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 642 | // tmp[i] < 4 * 2^57 * 2^57 = 2^116 |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 643 | p224_felem_assign(ftmp, beta); |
| 644 | p224_felem_scalar(ftmp, 8); |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 645 | // ftmp[i] < 8 * 2^57 = 2^60 |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 646 | p224_felem_diff_128_64(tmp, ftmp); |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 647 | // tmp[i] < 2^116 + 2^64 + 8 < 2^117 |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 648 | p224_felem_reduce(x_out, tmp); |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 649 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 650 | // z' = (y + z)^2 - gamma - delta |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 651 | p224_felem_sum(delta, gamma); |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 652 | // delta[i] < 2^57 + 2^57 = 2^58 |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 653 | p224_felem_assign(ftmp, y_in); |
| 654 | p224_felem_sum(ftmp, z_in); |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 655 | // ftmp[i] < 2^57 + 2^57 = 2^58 |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 656 | p224_felem_square(tmp, ftmp); |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 657 | // tmp[i] < 4 * 2^58 * 2^58 = 2^118 |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 658 | p224_felem_diff_128_64(tmp, delta); |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 659 | // tmp[i] < 2^118 + 2^64 + 8 < 2^119 |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 660 | p224_felem_reduce(z_out, tmp); |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 661 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 662 | // y' = alpha*(4*beta - x') - 8*gamma^2 |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 663 | p224_felem_scalar(beta, 4); |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 664 | // beta[i] < 4 * 2^57 = 2^59 |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 665 | p224_felem_diff(beta, x_out); |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 666 | // beta[i] < 2^59 + 2^58 + 2 < 2^60 |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 667 | p224_felem_mul(tmp, alpha, beta); |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 668 | // tmp[i] < 4 * 2^57 * 2^60 = 2^119 |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 669 | p224_felem_square(tmp2, gamma); |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 670 | // tmp2[i] < 4 * 2^57 * 2^57 = 2^116 |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 671 | p224_widefelem_scalar(tmp2, 8); |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 672 | // tmp2[i] < 8 * 2^116 = 2^119 |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 673 | p224_widefelem_diff(tmp, tmp2); |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 674 | // tmp[i] < 2^119 + 2^120 < 2^121 |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 675 | p224_felem_reduce(y_out, tmp); |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 676 | } |
| 677 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 678 | // Add two elliptic curve points: |
| 679 | // (X_1, Y_1, Z_1) + (X_2, Y_2, Z_2) = (X_3, Y_3, Z_3), where |
| 680 | // X_3 = (Z_1^3 * Y_2 - Z_2^3 * Y_1)^2 - (Z_1^2 * X_2 - Z_2^2 * X_1)^3 - |
| 681 | // 2 * Z_2^2 * X_1 * (Z_1^2 * X_2 - Z_2^2 * X_1)^2 |
| 682 | // 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 * |
| 683 | // X_1)^2 - X_3) - |
| 684 | // Z_2^3 * Y_1 * (Z_1^2 * X_2 - Z_2^2 * X_1)^3 |
| 685 | // Z_3 = (Z_1^2 * X_2 - Z_2^2 * X_1) * (Z_1 * Z_2) |
| 686 | // |
| 687 | // This runs faster if 'mixed' is set, which requires Z_2 = 1 or Z_2 = 0. |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 688 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 689 | // This function is not entirely constant-time: it includes a branch for |
| 690 | // checking whether the two input points are equal, (while not equal to the |
| 691 | // point at infinity). This case never happens during single point |
| 692 | // multiplication, so there is no timing leak for ECDH or ECDSA signing. |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 693 | static void p224_point_add(p224_felem x3, p224_felem y3, p224_felem z3, |
| 694 | const p224_felem x1, const p224_felem y1, |
| 695 | const p224_felem z1, const int mixed, |
| 696 | const p224_felem x2, const p224_felem y2, |
| 697 | const p224_felem z2) { |
| 698 | p224_felem ftmp, ftmp2, ftmp3, ftmp4, ftmp5, x_out, y_out, z_out; |
| 699 | p224_widefelem tmp, tmp2; |
| 700 | p224_limb z1_is_zero, z2_is_zero, x_equal, y_equal; |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 701 | |
| 702 | if (!mixed) { |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 703 | // ftmp2 = z2^2 |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 704 | p224_felem_square(tmp, z2); |
| 705 | p224_felem_reduce(ftmp2, tmp); |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 706 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 707 | // ftmp4 = z2^3 |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 708 | p224_felem_mul(tmp, ftmp2, z2); |
| 709 | p224_felem_reduce(ftmp4, tmp); |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 710 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 711 | // ftmp4 = z2^3*y1 |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 712 | p224_felem_mul(tmp2, ftmp4, y1); |
| 713 | p224_felem_reduce(ftmp4, tmp2); |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 714 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 715 | // ftmp2 = z2^2*x1 |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 716 | p224_felem_mul(tmp2, ftmp2, x1); |
| 717 | p224_felem_reduce(ftmp2, tmp2); |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 718 | } else { |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 719 | // We'll assume z2 = 1 (special case z2 = 0 is handled later) |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 720 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 721 | // ftmp4 = z2^3*y1 |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 722 | p224_felem_assign(ftmp4, y1); |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 723 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 724 | // ftmp2 = z2^2*x1 |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 725 | p224_felem_assign(ftmp2, x1); |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 726 | } |
| 727 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 728 | // ftmp = z1^2 |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 729 | p224_felem_square(tmp, z1); |
| 730 | p224_felem_reduce(ftmp, tmp); |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 731 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 732 | // ftmp3 = z1^3 |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 733 | p224_felem_mul(tmp, ftmp, z1); |
| 734 | p224_felem_reduce(ftmp3, tmp); |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 735 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 736 | // tmp = z1^3*y2 |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 737 | p224_felem_mul(tmp, ftmp3, y2); |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 738 | // tmp[i] < 4 * 2^57 * 2^57 = 2^116 |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 739 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 740 | // ftmp3 = z1^3*y2 - z2^3*y1 |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 741 | p224_felem_diff_128_64(tmp, ftmp4); |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 742 | // tmp[i] < 2^116 + 2^64 + 8 < 2^117 |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 743 | p224_felem_reduce(ftmp3, tmp); |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 744 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 745 | // tmp = z1^2*x2 |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 746 | p224_felem_mul(tmp, ftmp, x2); |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 747 | // tmp[i] < 4 * 2^57 * 2^57 = 2^116 |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 748 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 749 | // ftmp = z1^2*x2 - z2^2*x1 |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 750 | p224_felem_diff_128_64(tmp, ftmp2); |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 751 | // tmp[i] < 2^116 + 2^64 + 8 < 2^117 |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 752 | p224_felem_reduce(ftmp, tmp); |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 753 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 754 | // the formulae are incorrect if the points are equal |
| 755 | // so we check for this and do doubling if this happens |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 756 | x_equal = p224_felem_is_zero(ftmp); |
| 757 | y_equal = p224_felem_is_zero(ftmp3); |
| 758 | z1_is_zero = p224_felem_is_zero(z1); |
| 759 | z2_is_zero = p224_felem_is_zero(z2); |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 760 | // In affine coordinates, (X_1, Y_1) == (X_2, Y_2) |
Pete Bentley | 0c61efe | 2019-08-13 09:32:23 +0100 | [diff] [blame^] | 761 | p224_limb is_nontrivial_double = |
| 762 | x_equal & y_equal & (1 - z1_is_zero) & (1 - z2_is_zero); |
| 763 | if (is_nontrivial_double) { |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 764 | p224_point_double(x3, y3, z3, x1, y1, z1); |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 765 | return; |
| 766 | } |
| 767 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 768 | // ftmp5 = z1*z2 |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 769 | if (!mixed) { |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 770 | p224_felem_mul(tmp, z1, z2); |
| 771 | p224_felem_reduce(ftmp5, tmp); |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 772 | } else { |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 773 | // special case z2 = 0 is handled later |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 774 | p224_felem_assign(ftmp5, z1); |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 775 | } |
| 776 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 777 | // z_out = (z1^2*x2 - z2^2*x1)*(z1*z2) |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 778 | p224_felem_mul(tmp, ftmp, ftmp5); |
| 779 | p224_felem_reduce(z_out, tmp); |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 780 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 781 | // ftmp = (z1^2*x2 - z2^2*x1)^2 |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 782 | p224_felem_assign(ftmp5, ftmp); |
| 783 | p224_felem_square(tmp, ftmp); |
| 784 | p224_felem_reduce(ftmp, tmp); |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 785 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 786 | // ftmp5 = (z1^2*x2 - z2^2*x1)^3 |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 787 | p224_felem_mul(tmp, ftmp, ftmp5); |
| 788 | p224_felem_reduce(ftmp5, tmp); |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 789 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 790 | // ftmp2 = z2^2*x1*(z1^2*x2 - z2^2*x1)^2 |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 791 | p224_felem_mul(tmp, ftmp2, ftmp); |
| 792 | p224_felem_reduce(ftmp2, tmp); |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 793 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 794 | // tmp = z2^3*y1*(z1^2*x2 - z2^2*x1)^3 |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 795 | p224_felem_mul(tmp, ftmp4, ftmp5); |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 796 | // tmp[i] < 4 * 2^57 * 2^57 = 2^116 |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 797 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 798 | // tmp2 = (z1^3*y2 - z2^3*y1)^2 |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 799 | p224_felem_square(tmp2, ftmp3); |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 800 | // tmp2[i] < 4 * 2^57 * 2^57 < 2^116 |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 801 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 802 | // tmp2 = (z1^3*y2 - z2^3*y1)^2 - (z1^2*x2 - z2^2*x1)^3 |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 803 | p224_felem_diff_128_64(tmp2, ftmp5); |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 804 | // tmp2[i] < 2^116 + 2^64 + 8 < 2^117 |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 805 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 806 | // ftmp5 = 2*z2^2*x1*(z1^2*x2 - z2^2*x1)^2 |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 807 | p224_felem_assign(ftmp5, ftmp2); |
| 808 | p224_felem_scalar(ftmp5, 2); |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 809 | // ftmp5[i] < 2 * 2^57 = 2^58 |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 810 | |
| 811 | /* x_out = (z1^3*y2 - z2^3*y1)^2 - (z1^2*x2 - z2^2*x1)^3 - |
| 812 | 2*z2^2*x1*(z1^2*x2 - z2^2*x1)^2 */ |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 813 | p224_felem_diff_128_64(tmp2, ftmp5); |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 814 | // tmp2[i] < 2^117 + 2^64 + 8 < 2^118 |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 815 | p224_felem_reduce(x_out, tmp2); |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 816 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 817 | // ftmp2 = z2^2*x1*(z1^2*x2 - z2^2*x1)^2 - x_out |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 818 | p224_felem_diff(ftmp2, x_out); |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 819 | // ftmp2[i] < 2^57 + 2^58 + 2 < 2^59 |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 820 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 821 | // tmp2 = (z1^3*y2 - z2^3*y1)*(z2^2*x1*(z1^2*x2 - z2^2*x1)^2 - x_out) |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 822 | p224_felem_mul(tmp2, ftmp3, ftmp2); |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 823 | // tmp2[i] < 4 * 2^57 * 2^59 = 2^118 |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 824 | |
| 825 | /* y_out = (z1^3*y2 - z2^3*y1)*(z2^2*x1*(z1^2*x2 - z2^2*x1)^2 - x_out) - |
| 826 | z2^3*y1*(z1^2*x2 - z2^2*x1)^3 */ |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 827 | p224_widefelem_diff(tmp2, tmp); |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 828 | // tmp2[i] < 2^118 + 2^120 < 2^121 |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 829 | p224_felem_reduce(y_out, tmp2); |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 830 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 831 | // the result (x_out, y_out, z_out) is incorrect if one of the inputs is |
| 832 | // the point at infinity, so we need to check for this separately |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 833 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 834 | // if point 1 is at infinity, copy point 2 to output, and vice versa |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 835 | p224_copy_conditional(x_out, x2, z1_is_zero); |
| 836 | p224_copy_conditional(x_out, x1, z2_is_zero); |
| 837 | p224_copy_conditional(y_out, y2, z1_is_zero); |
| 838 | p224_copy_conditional(y_out, y1, z2_is_zero); |
| 839 | p224_copy_conditional(z_out, z2, z1_is_zero); |
| 840 | p224_copy_conditional(z_out, z1, z2_is_zero); |
| 841 | p224_felem_assign(x3, x_out); |
| 842 | p224_felem_assign(y3, y_out); |
| 843 | p224_felem_assign(z3, z_out); |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 844 | } |
| 845 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 846 | // p224_select_point selects the |idx|th point from a precomputation table and |
| 847 | // copies it to out. |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 848 | static void p224_select_point(const uint64_t idx, size_t size, |
| 849 | const p224_felem pre_comp[/*size*/][3], |
| 850 | p224_felem out[3]) { |
| 851 | p224_limb *outlimbs = &out[0][0]; |
| 852 | OPENSSL_memset(outlimbs, 0, 3 * sizeof(p224_felem)); |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 853 | |
David Benjamin | 7c0d06c | 2016-08-11 13:26:41 -0400 | [diff] [blame] | 854 | for (size_t i = 0; i < size; i++) { |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 855 | const p224_limb *inlimbs = &pre_comp[i][0][0]; |
| 856 | uint64_t mask = i ^ idx; |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 857 | mask |= mask >> 4; |
| 858 | mask |= mask >> 2; |
| 859 | mask |= mask >> 1; |
| 860 | mask &= 1; |
| 861 | mask--; |
David Benjamin | 7c0d06c | 2016-08-11 13:26:41 -0400 | [diff] [blame] | 862 | for (size_t j = 0; j < 4 * 3; j++) { |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 863 | outlimbs[j] |= inlimbs[j] & mask; |
| 864 | } |
| 865 | } |
| 866 | } |
| 867 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 868 | // p224_get_bit returns the |i|th bit in |in| |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 869 | static char p224_get_bit(const p224_felem_bytearray in, size_t i) { |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 870 | if (i >= 224) { |
| 871 | return 0; |
| 872 | } |
| 873 | return (in[i >> 3] >> (i & 7)) & 1; |
| 874 | } |
| 875 | |
Robert Sloan | 8f860b1 | 2017-08-28 07:37:06 -0700 | [diff] [blame] | 876 | // Takes the Jacobian coordinates (X, Y, Z) of a point and returns |
| 877 | // (X', Y') = (X/Z^2, Y/Z^3) |
Robert Sloan | c6ebb28 | 2018-04-30 10:10:26 -0700 | [diff] [blame] | 878 | static int ec_GFp_nistp224_point_get_affine_coordinates( |
Robert Sloan | a51059f | 2018-11-12 13:38:50 -0800 | [diff] [blame] | 879 | const EC_GROUP *group, const EC_RAW_POINT *point, EC_FELEM *x, |
| 880 | EC_FELEM *y) { |
Robert Sloan | c6ebb28 | 2018-04-30 10:10:26 -0700 | [diff] [blame] | 881 | if (ec_GFp_simple_is_at_infinity(group, point)) { |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 882 | OPENSSL_PUT_ERROR(EC, EC_R_POINT_AT_INFINITY); |
| 883 | return 0; |
| 884 | } |
| 885 | |
Robert Sloan | c6ebb28 | 2018-04-30 10:10:26 -0700 | [diff] [blame] | 886 | p224_felem z1, z2; |
| 887 | p224_widefelem tmp; |
| 888 | p224_generic_to_felem(z1, &point->Z); |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 889 | p224_felem_inv(z2, z1); |
| 890 | p224_felem_square(tmp, z2); |
| 891 | p224_felem_reduce(z1, tmp); |
Robert Sloan | 0db7f54 | 2018-01-16 15:48:33 -0800 | [diff] [blame] | 892 | |
| 893 | if (x != NULL) { |
Robert Sloan | c6ebb28 | 2018-04-30 10:10:26 -0700 | [diff] [blame] | 894 | p224_felem x_in, x_out; |
| 895 | p224_generic_to_felem(x_in, &point->X); |
Robert Sloan | 0db7f54 | 2018-01-16 15:48:33 -0800 | [diff] [blame] | 896 | p224_felem_mul(tmp, x_in, z1); |
Robert Sloan | c9abfe4 | 2018-11-26 12:19:07 -0800 | [diff] [blame] | 897 | p224_felem_reduce(x_out, tmp); |
Robert Sloan | a51059f | 2018-11-12 13:38:50 -0800 | [diff] [blame] | 898 | p224_felem_to_generic(x, x_out); |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 899 | } |
| 900 | |
Robert Sloan | 0db7f54 | 2018-01-16 15:48:33 -0800 | [diff] [blame] | 901 | if (y != NULL) { |
Robert Sloan | c6ebb28 | 2018-04-30 10:10:26 -0700 | [diff] [blame] | 902 | p224_felem y_in, y_out; |
| 903 | p224_generic_to_felem(y_in, &point->Y); |
Robert Sloan | 0db7f54 | 2018-01-16 15:48:33 -0800 | [diff] [blame] | 904 | p224_felem_mul(tmp, z1, z2); |
| 905 | p224_felem_reduce(z1, tmp); |
| 906 | p224_felem_mul(tmp, y_in, z1); |
Robert Sloan | c9abfe4 | 2018-11-26 12:19:07 -0800 | [diff] [blame] | 907 | p224_felem_reduce(y_out, tmp); |
Robert Sloan | a51059f | 2018-11-12 13:38:50 -0800 | [diff] [blame] | 908 | p224_felem_to_generic(y, y_out); |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 909 | } |
| 910 | |
| 911 | return 1; |
| 912 | } |
| 913 | |
Robert Sloan | a51059f | 2018-11-12 13:38:50 -0800 | [diff] [blame] | 914 | static void ec_GFp_nistp224_add(const EC_GROUP *group, EC_RAW_POINT *r, |
| 915 | const EC_RAW_POINT *a, const EC_RAW_POINT *b) { |
| 916 | p224_felem x1, y1, z1, x2, y2, z2; |
| 917 | p224_generic_to_felem(x1, &a->X); |
| 918 | p224_generic_to_felem(y1, &a->Y); |
| 919 | p224_generic_to_felem(z1, &a->Z); |
| 920 | p224_generic_to_felem(x2, &b->X); |
| 921 | p224_generic_to_felem(y2, &b->Y); |
| 922 | p224_generic_to_felem(z2, &b->Z); |
| 923 | p224_point_add(x1, y1, z1, x1, y1, z1, 0 /* both Jacobian */, x2, y2, z2); |
Robert Sloan | c9abfe4 | 2018-11-26 12:19:07 -0800 | [diff] [blame] | 924 | // The outputs are already reduced, but still need to be contracted. |
Robert Sloan | a51059f | 2018-11-12 13:38:50 -0800 | [diff] [blame] | 925 | p224_felem_to_generic(&r->X, x1); |
| 926 | p224_felem_to_generic(&r->Y, y1); |
| 927 | p224_felem_to_generic(&r->Z, z1); |
| 928 | } |
| 929 | |
| 930 | static void ec_GFp_nistp224_dbl(const EC_GROUP *group, EC_RAW_POINT *r, |
| 931 | const EC_RAW_POINT *a) { |
| 932 | p224_felem x, y, z; |
| 933 | p224_generic_to_felem(x, &a->X); |
| 934 | p224_generic_to_felem(y, &a->Y); |
| 935 | p224_generic_to_felem(z, &a->Z); |
| 936 | p224_point_double(x, y, z, x, y, z); |
Robert Sloan | c9abfe4 | 2018-11-26 12:19:07 -0800 | [diff] [blame] | 937 | // The outputs are already reduced, but still need to be contracted. |
Robert Sloan | a51059f | 2018-11-12 13:38:50 -0800 | [diff] [blame] | 938 | p224_felem_to_generic(&r->X, x); |
| 939 | p224_felem_to_generic(&r->Y, y); |
| 940 | p224_felem_to_generic(&r->Z, z); |
| 941 | } |
| 942 | |
Pete Bentley | 0c61efe | 2019-08-13 09:32:23 +0100 | [diff] [blame^] | 943 | static void ec_GFp_nistp224_make_precomp(p224_felem out[17][3], |
| 944 | const EC_RAW_POINT *p) { |
| 945 | OPENSSL_memset(out[0], 0, sizeof(p224_felem) * 3); |
| 946 | |
| 947 | p224_generic_to_felem(out[1][0], &p->X); |
| 948 | p224_generic_to_felem(out[1][1], &p->Y); |
| 949 | p224_generic_to_felem(out[1][2], &p->Z); |
| 950 | |
| 951 | for (size_t j = 2; j <= 16; ++j) { |
| 952 | if (j & 1) { |
| 953 | p224_point_add(out[j][0], out[j][1], out[j][2], out[1][0], out[1][1], |
| 954 | out[1][2], 0, out[j - 1][0], out[j - 1][1], out[j - 1][2]); |
| 955 | } else { |
| 956 | p224_point_double(out[j][0], out[j][1], out[j][2], out[j / 2][0], |
| 957 | out[j / 2][1], out[j / 2][2]); |
| 958 | } |
| 959 | } |
| 960 | } |
| 961 | |
| 962 | static void ec_GFp_nistp224_point_mul(const EC_GROUP *group, EC_RAW_POINT *r, |
| 963 | const EC_RAW_POINT *p, |
| 964 | const EC_SCALAR *scalar) { |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 965 | p224_felem p_pre_comp[17][3]; |
Pete Bentley | 0c61efe | 2019-08-13 09:32:23 +0100 | [diff] [blame^] | 966 | ec_GFp_nistp224_make_precomp(p_pre_comp, p); |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 967 | |
Pete Bentley | 0c61efe | 2019-08-13 09:32:23 +0100 | [diff] [blame^] | 968 | // Set nq to the point at infinity. |
| 969 | p224_felem nq[3], tmp[4]; |
| 970 | OPENSSL_memset(nq, 0, 3 * sizeof(p224_felem)); |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 971 | |
Pete Bentley | 0c61efe | 2019-08-13 09:32:23 +0100 | [diff] [blame^] | 972 | int skip = 1; // Save two point operations in the first round. |
| 973 | for (size_t i = 220; i < 221; i--) { |
| 974 | if (!skip) { |
| 975 | p224_point_double(nq[0], nq[1], nq[2], nq[0], nq[1], nq[2]); |
| 976 | } |
Robert Sloan | 69939df | 2017-01-09 10:53:07 -0800 | [diff] [blame] | 977 | |
Pete Bentley | 0c61efe | 2019-08-13 09:32:23 +0100 | [diff] [blame^] | 978 | // Add every 5 doublings. |
| 979 | if (i % 5 == 0) { |
| 980 | uint64_t bits = p224_get_bit(scalar->bytes, i + 4) << 5; |
| 981 | bits |= p224_get_bit(scalar->bytes, i + 3) << 4; |
| 982 | bits |= p224_get_bit(scalar->bytes, i + 2) << 3; |
| 983 | bits |= p224_get_bit(scalar->bytes, i + 1) << 2; |
| 984 | bits |= p224_get_bit(scalar->bytes, i) << 1; |
| 985 | bits |= p224_get_bit(scalar->bytes, i - 1); |
| 986 | uint8_t sign, digit; |
| 987 | ec_GFp_nistp_recode_scalar_bits(&sign, &digit, bits); |
| 988 | |
| 989 | // Select the point to add or subtract. |
| 990 | p224_select_point(digit, 17, (const p224_felem(*)[3])p_pre_comp, tmp); |
| 991 | p224_felem_neg(tmp[3], tmp[1]); // (X, -Y, Z) is the negative point |
| 992 | p224_copy_conditional(tmp[1], tmp[3], sign); |
| 993 | |
| 994 | if (!skip) { |
| 995 | p224_point_add(nq[0], nq[1], nq[2], nq[0], nq[1], nq[2], 0 /* mixed */, |
| 996 | tmp[0], tmp[1], tmp[2]); |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 997 | } else { |
Pete Bentley | 0c61efe | 2019-08-13 09:32:23 +0100 | [diff] [blame^] | 998 | OPENSSL_memcpy(nq, tmp, 3 * sizeof(p224_felem)); |
| 999 | skip = 0; |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 1000 | } |
| 1001 | } |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 1002 | } |
| 1003 | |
Pete Bentley | 0c61efe | 2019-08-13 09:32:23 +0100 | [diff] [blame^] | 1004 | // Reduce the output to its unique minimal representation. |
| 1005 | p224_felem_to_generic(&r->X, nq[0]); |
| 1006 | p224_felem_to_generic(&r->Y, nq[1]); |
| 1007 | p224_felem_to_generic(&r->Z, nq[2]); |
| 1008 | } |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 1009 | |
Pete Bentley | 0c61efe | 2019-08-13 09:32:23 +0100 | [diff] [blame^] | 1010 | static void ec_GFp_nistp224_point_mul_base(const EC_GROUP *group, |
| 1011 | EC_RAW_POINT *r, |
| 1012 | const EC_SCALAR *scalar) { |
| 1013 | // Set nq to the point at infinity. |
| 1014 | p224_felem nq[3], tmp[3]; |
| 1015 | OPENSSL_memset(nq, 0, 3 * sizeof(p224_felem)); |
| 1016 | |
| 1017 | int skip = 1; // Save two point operations in the first round. |
| 1018 | for (size_t i = 27; i < 28; i--) { |
| 1019 | // double |
| 1020 | if (!skip) { |
| 1021 | p224_point_double(nq[0], nq[1], nq[2], nq[0], nq[1], nq[2]); |
| 1022 | } |
| 1023 | |
| 1024 | // First, look 28 bits upwards. |
| 1025 | uint64_t bits = p224_get_bit(scalar->bytes, i + 196) << 3; |
| 1026 | bits |= p224_get_bit(scalar->bytes, i + 140) << 2; |
| 1027 | bits |= p224_get_bit(scalar->bytes, i + 84) << 1; |
| 1028 | bits |= p224_get_bit(scalar->bytes, i + 28); |
| 1029 | // Select the point to add, in constant time. |
| 1030 | p224_select_point(bits, 16, g_p224_pre_comp[1], tmp); |
| 1031 | |
| 1032 | if (!skip) { |
| 1033 | p224_point_add(nq[0], nq[1], nq[2], nq[0], nq[1], nq[2], 1 /* mixed */, |
| 1034 | tmp[0], tmp[1], tmp[2]); |
| 1035 | } else { |
| 1036 | OPENSSL_memcpy(nq, tmp, 3 * sizeof(p224_felem)); |
| 1037 | skip = 0; |
| 1038 | } |
| 1039 | |
| 1040 | // Second, look at the current position/ |
| 1041 | bits = p224_get_bit(scalar->bytes, i + 168) << 3; |
| 1042 | bits |= p224_get_bit(scalar->bytes, i + 112) << 2; |
| 1043 | bits |= p224_get_bit(scalar->bytes, i + 56) << 1; |
| 1044 | bits |= p224_get_bit(scalar->bytes, i); |
| 1045 | // Select the point to add, in constant time. |
| 1046 | p224_select_point(bits, 16, g_p224_pre_comp[0], tmp); |
| 1047 | p224_point_add(nq[0], nq[1], nq[2], nq[0], nq[1], nq[2], 1 /* mixed */, |
| 1048 | tmp[0], tmp[1], tmp[2]); |
| 1049 | } |
| 1050 | |
| 1051 | // Reduce the output to its unique minimal representation. |
| 1052 | p224_felem_to_generic(&r->X, nq[0]); |
| 1053 | p224_felem_to_generic(&r->Y, nq[1]); |
| 1054 | p224_felem_to_generic(&r->Z, nq[2]); |
| 1055 | } |
| 1056 | |
| 1057 | static void ec_GFp_nistp224_point_mul_public(const EC_GROUP *group, |
| 1058 | EC_RAW_POINT *r, |
| 1059 | const EC_SCALAR *g_scalar, |
| 1060 | const EC_RAW_POINT *p, |
| 1061 | const EC_SCALAR *p_scalar) { |
| 1062 | // TODO(davidben): If P-224 ECDSA verify performance ever matters, using |
| 1063 | // |ec_compute_wNAF| for |p_scalar| would likely be an easy improvement. |
| 1064 | p224_felem p_pre_comp[17][3]; |
| 1065 | ec_GFp_nistp224_make_precomp(p_pre_comp, p); |
| 1066 | |
| 1067 | // Set nq to the point at infinity. |
| 1068 | p224_felem nq[3], tmp[3]; |
| 1069 | OPENSSL_memset(nq, 0, 3 * sizeof(p224_felem)); |
| 1070 | |
| 1071 | // Loop over both scalars msb-to-lsb, interleaving additions of multiples of |
| 1072 | // the generator (two in each of the last 28 rounds) and additions of p (every |
| 1073 | // 5th round). |
| 1074 | int skip = 1; // Save two point operations in the first round. |
| 1075 | for (size_t i = 220; i < 221; i--) { |
| 1076 | if (!skip) { |
| 1077 | p224_point_double(nq[0], nq[1], nq[2], nq[0], nq[1], nq[2]); |
| 1078 | } |
| 1079 | |
| 1080 | // Add multiples of the generator. |
| 1081 | if (i <= 27) { |
| 1082 | // First, look 28 bits upwards. |
| 1083 | uint64_t bits = p224_get_bit(g_scalar->bytes, i + 196) << 3; |
| 1084 | bits |= p224_get_bit(g_scalar->bytes, i + 140) << 2; |
| 1085 | bits |= p224_get_bit(g_scalar->bytes, i + 84) << 1; |
| 1086 | bits |= p224_get_bit(g_scalar->bytes, i + 28); |
| 1087 | |
| 1088 | p224_point_add(nq[0], nq[1], nq[2], nq[0], nq[1], nq[2], 1 /* mixed */, |
| 1089 | g_p224_pre_comp[1][bits][0], g_p224_pre_comp[1][bits][1], |
| 1090 | g_p224_pre_comp[1][bits][2]); |
| 1091 | assert(!skip); |
| 1092 | |
| 1093 | // Second, look at the current position. |
| 1094 | bits = p224_get_bit(g_scalar->bytes, i + 168) << 3; |
| 1095 | bits |= p224_get_bit(g_scalar->bytes, i + 112) << 2; |
| 1096 | bits |= p224_get_bit(g_scalar->bytes, i + 56) << 1; |
| 1097 | bits |= p224_get_bit(g_scalar->bytes, i); |
| 1098 | p224_point_add(nq[0], nq[1], nq[2], nq[0], nq[1], nq[2], 1 /* mixed */, |
| 1099 | g_p224_pre_comp[0][bits][0], g_p224_pre_comp[0][bits][1], |
| 1100 | g_p224_pre_comp[0][bits][2]); |
| 1101 | } |
| 1102 | |
| 1103 | // Incorporate |p_scalar| every 5 doublings. |
| 1104 | if (i % 5 == 0) { |
| 1105 | uint64_t bits = p224_get_bit(p_scalar->bytes, i + 4) << 5; |
| 1106 | bits |= p224_get_bit(p_scalar->bytes, i + 3) << 4; |
| 1107 | bits |= p224_get_bit(p_scalar->bytes, i + 2) << 3; |
| 1108 | bits |= p224_get_bit(p_scalar->bytes, i + 1) << 2; |
| 1109 | bits |= p224_get_bit(p_scalar->bytes, i) << 1; |
| 1110 | bits |= p224_get_bit(p_scalar->bytes, i - 1); |
| 1111 | uint8_t sign, digit; |
| 1112 | ec_GFp_nistp_recode_scalar_bits(&sign, &digit, bits); |
| 1113 | |
| 1114 | // Select the point to add or subtract. |
| 1115 | OPENSSL_memcpy(tmp, p_pre_comp[digit], 3 * sizeof(p224_felem)); |
| 1116 | if (sign) { |
| 1117 | p224_felem_neg(tmp[1], tmp[1]); // (X, -Y, Z) is the negative point |
| 1118 | } |
| 1119 | |
| 1120 | if (!skip) { |
| 1121 | p224_point_add(nq[0], nq[1], nq[2], nq[0], nq[1], nq[2], 0 /* mixed */, |
| 1122 | tmp[0], tmp[1], tmp[2]); |
| 1123 | } else { |
| 1124 | OPENSSL_memcpy(nq, tmp, 3 * sizeof(p224_felem)); |
| 1125 | skip = 0; |
| 1126 | } |
| 1127 | } |
| 1128 | } |
| 1129 | |
| 1130 | // Reduce the output to its unique minimal representation. |
| 1131 | p224_felem_to_generic(&r->X, nq[0]); |
| 1132 | p224_felem_to_generic(&r->Y, nq[1]); |
| 1133 | p224_felem_to_generic(&r->Z, nq[2]); |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 1134 | } |
| 1135 | |
Robert Sloan | c6ebb28 | 2018-04-30 10:10:26 -0700 | [diff] [blame] | 1136 | static void ec_GFp_nistp224_felem_mul(const EC_GROUP *group, EC_FELEM *r, |
| 1137 | const EC_FELEM *a, const EC_FELEM *b) { |
Robert Sloan | 49d063b | 2018-04-03 11:30:38 -0700 | [diff] [blame] | 1138 | p224_felem felem1, felem2; |
| 1139 | p224_widefelem wide; |
Robert Sloan | c6ebb28 | 2018-04-30 10:10:26 -0700 | [diff] [blame] | 1140 | p224_generic_to_felem(felem1, a); |
| 1141 | p224_generic_to_felem(felem2, b); |
Robert Sloan | 49d063b | 2018-04-03 11:30:38 -0700 | [diff] [blame] | 1142 | p224_felem_mul(wide, felem1, felem2); |
| 1143 | p224_felem_reduce(felem1, wide); |
Robert Sloan | c6ebb28 | 2018-04-30 10:10:26 -0700 | [diff] [blame] | 1144 | p224_felem_to_generic(r, felem1); |
Robert Sloan | 49d063b | 2018-04-03 11:30:38 -0700 | [diff] [blame] | 1145 | } |
| 1146 | |
Robert Sloan | c6ebb28 | 2018-04-30 10:10:26 -0700 | [diff] [blame] | 1147 | static void ec_GFp_nistp224_felem_sqr(const EC_GROUP *group, EC_FELEM *r, |
| 1148 | const EC_FELEM *a) { |
Robert Sloan | 49d063b | 2018-04-03 11:30:38 -0700 | [diff] [blame] | 1149 | p224_felem felem; |
Robert Sloan | c6ebb28 | 2018-04-30 10:10:26 -0700 | [diff] [blame] | 1150 | p224_generic_to_felem(felem, a); |
Robert Sloan | 49d063b | 2018-04-03 11:30:38 -0700 | [diff] [blame] | 1151 | p224_widefelem wide; |
| 1152 | p224_felem_square(wide, felem); |
| 1153 | p224_felem_reduce(felem, wide); |
Robert Sloan | c6ebb28 | 2018-04-30 10:10:26 -0700 | [diff] [blame] | 1154 | p224_felem_to_generic(r, felem); |
| 1155 | } |
| 1156 | |
| 1157 | static int ec_GFp_nistp224_bignum_to_felem(const EC_GROUP *group, EC_FELEM *out, |
| 1158 | const BIGNUM *in) { |
| 1159 | return bn_copy_words(out->words, group->field.width, in); |
| 1160 | } |
| 1161 | |
| 1162 | static int ec_GFp_nistp224_felem_to_bignum(const EC_GROUP *group, BIGNUM *out, |
| 1163 | const EC_FELEM *in) { |
| 1164 | return bn_set_words(out, in->words, group->field.width); |
Robert Sloan | 49d063b | 2018-04-03 11:30:38 -0700 | [diff] [blame] | 1165 | } |
| 1166 | |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 1167 | DEFINE_METHOD_FUNCTION(EC_METHOD, EC_GFp_nistp224_method) { |
| 1168 | out->group_init = ec_GFp_simple_group_init; |
| 1169 | out->group_finish = ec_GFp_simple_group_finish; |
Robert Sloan | 8ff0355 | 2017-06-14 12:40:58 -0700 | [diff] [blame] | 1170 | out->group_set_curve = ec_GFp_simple_group_set_curve; |
| 1171 | out->point_get_affine_coordinates = |
| 1172 | ec_GFp_nistp224_point_get_affine_coordinates; |
Robert Sloan | a51059f | 2018-11-12 13:38:50 -0800 | [diff] [blame] | 1173 | out->add = ec_GFp_nistp224_add; |
| 1174 | out->dbl = ec_GFp_nistp224_dbl; |
Pete Bentley | 0c61efe | 2019-08-13 09:32:23 +0100 | [diff] [blame^] | 1175 | out->mul = ec_GFp_nistp224_point_mul; |
| 1176 | out->mul_base = ec_GFp_nistp224_point_mul_base; |
| 1177 | out->mul_public = ec_GFp_nistp224_point_mul_public; |
Robert Sloan | c6ebb28 | 2018-04-30 10:10:26 -0700 | [diff] [blame] | 1178 | out->felem_mul = ec_GFp_nistp224_felem_mul; |
| 1179 | out->felem_sqr = ec_GFp_nistp224_felem_sqr; |
| 1180 | out->bignum_to_felem = ec_GFp_nistp224_bignum_to_felem; |
| 1181 | out->felem_to_bignum = ec_GFp_nistp224_felem_to_bignum; |
Robert Sloan | 5cbb5c8 | 2018-04-24 11:35:46 -0700 | [diff] [blame] | 1182 | out->scalar_inv_montgomery = ec_simple_scalar_inv_montgomery; |
Robert Sloan | a51059f | 2018-11-12 13:38:50 -0800 | [diff] [blame] | 1183 | out->scalar_inv_montgomery_vartime = ec_GFp_simple_mont_inv_mod_ord_vartime; |
| 1184 | out->cmp_x_coordinate = ec_GFp_simple_cmp_x_coordinate; |
Robert Sloan | 4c22c5f | 2019-03-01 15:53:37 -0800 | [diff] [blame] | 1185 | } |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 1186 | |
Robert Sloan | 5581810 | 2017-12-18 11:26:17 -0800 | [diff] [blame] | 1187 | #endif // BORINGSSL_HAS_UINT128 && !SMALL |