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| 1 Index: mozilla/security/nss/lib/freebl/ecl/ecl.c |
| 2 =================================================================== |
| 3 RCS file: /cvsroot/mozilla/security/nss/lib/freebl/ecl/ecl.c,v |
| 4 retrieving revision 1.13 |
| 5 diff -p -u -r1.13 ecl.c |
| 6 --- mozilla/security/nss/lib/freebl/ecl/ecl.c 25 Apr 2012 14:49:44 -0000
1.13 |
| 7 +++ mozilla/security/nss/lib/freebl/ecl/ecl.c 25 Jan 2013 00:17:14 -0000 |
| 8 @@ -215,8 +215,8 @@ ecgroup_fromNameAndHex(const ECCurveName |
| 9 |
| 10 /* determine which optimizations (if any) to use */ |
| 11 if (params->field == ECField_GFp) { |
| 12 -#ifdef NSS_ECC_MORE_THAN_SUITE_B |
| 13 switch (name) { |
| 14 +#ifdef NSS_ECC_MORE_THAN_SUITE_B |
| 15 #ifdef ECL_USE_FP |
| 16 case ECCurve_SECG_PRIME_160R1: |
| 17 group = |
| 18 @@ -256,29 +256,29 @@ ecgroup_fromNameAndHex(const ECCurveName |
| 19 MP_CHECKOK(ec_group_set_gfp224(group, name)); |
| 20 #endif |
| 21 break; |
| 22 - case ECCurve_SECG_PRIME_256R1: |
| 23 + case ECCurve_SECG_PRIME_521R1: |
| 24 group = |
| 25 ECGroup_consGFp(&irr, &curvea, &curveb, &genx, &
geny, |
| 26 &order, params->
cofactor); |
| 27 if (group == NULL) { res = MP_UNDEF; goto CLEANUP; } |
| 28 - MP_CHECKOK(ec_group_set_gfp256(group, name)); |
| 29 + MP_CHECKOK(ec_group_set_gfp521(group, name)); |
| 30 break; |
| 31 - case ECCurve_SECG_PRIME_521R1: |
| 32 +#endif /* NSS_ECC_MORE_THAN_SUITE_B */ |
| 33 + case ECCurve_SECG_PRIME_256R1: |
| 34 group = |
| 35 ECGroup_consGFp(&irr, &curvea, &curveb, &genx, &
geny, |
| 36 &order, params->
cofactor); |
| 37 if (group == NULL) { res = MP_UNDEF; goto CLEANUP; } |
| 38 - MP_CHECKOK(ec_group_set_gfp521(group, name)); |
| 39 + MP_CHECKOK(ec_group_set_gfp256(group, name)); |
| 40 break; |
| 41 default: |
| 42 /* use generic arithmetic */ |
| 43 -#endif |
| 44 group = |
| 45 ECGroup_consGFp_mont(&irr, &curvea, &curveb, &ge
nx, &geny, |
| 46 &order,
params->cofactor); |
| 47 if (group == NULL) { res = MP_UNDEF; goto CLEANUP; } |
| 48 -#ifdef NSS_ECC_MORE_THAN_SUITE_B |
| 49 } |
| 50 +#ifdef NSS_ECC_MORE_THAN_SUITE_B |
| 51 } else if (params->field == ECField_GF2m) { |
| 52 group = ECGroup_consGF2m(&irr, NULL, &curvea, &curveb, &genx, &g
eny, &order, params->cofactor); |
| 53 if (group == NULL) { res = MP_UNDEF; goto CLEANUP; } |
| 54 Index: mozilla/security/nss/lib/freebl/ecl/ecp_256.c |
| 55 =================================================================== |
| 56 RCS file: /cvsroot/mozilla/security/nss/lib/freebl/ecl/ecp_256.c,v |
| 57 retrieving revision 1.3 |
| 58 diff -p -u -r1.3 ecp_256.c |
| 59 --- mozilla/security/nss/lib/freebl/ecl/ecp_256.c 25 Apr 2012 14:49:44 -00
00 1.3 |
| 60 +++ mozilla/security/nss/lib/freebl/ecl/ecp_256.c 25 Jan 2013 00:17:14 -00
00 |
| 61 @@ -6,6 +6,7 @@ |
| 62 #include "mpi.h" |
| 63 #include "mplogic.h" |
| 64 #include "mpi-priv.h" |
| 65 +#include "prcpucfg.h" |
| 66 #include <stdlib.h> |
| 67 |
| 68 /* Fast modular reduction for p256 = 2^256 - 2^224 + 2^192+ 2^96 - 1. a can be
r. |
| 69 @@ -381,6 +382,26 @@ ec_GFp_nistp256_mul(const mp_int *a, con |
| 70 return res; |
| 71 } |
| 72 |
| 73 +#ifdef IS_LITTLE_ENDIAN |
| 74 +/* These are defined in ecp_256_32.c */ |
| 75 +extern mp_err ec_GFp_nistp256_base_point_mul( |
| 76 + const mp_int *n, |
| 77 + mp_int *out_x, mp_int *out_y, |
| 78 + const ECGroup *group); |
| 79 + |
| 80 +extern mp_err ec_GFp_nistp256_point_mul( |
| 81 + const mp_int *n, |
| 82 + const mp_int *in_x, const mp_int *in_y, |
| 83 + mp_int *out_x, mp_int *out_y, |
| 84 + const ECGroup *group); |
| 85 + |
| 86 +extern mp_err ec_GFp_nistp256_points_mul_vartime( |
| 87 + const mp_int *n1, const mp_int *n2, |
| 88 + const mp_int *in_x, const mp_int *in_y, |
| 89 + mp_int *out_x, mp_int *out_y, |
| 90 + const ECGroup *group); |
| 91 +#endif |
| 92 + |
| 93 /* Wire in fast field arithmetic and precomputation of base point for |
| 94 * named curves. */ |
| 95 mp_err |
| 96 @@ -390,6 +411,11 @@ ec_group_set_gfp256(ECGroup *group, ECCu |
| 97 group->meth->field_mod = &ec_GFp_nistp256_mod; |
| 98 group->meth->field_mul = &ec_GFp_nistp256_mul; |
| 99 group->meth->field_sqr = &ec_GFp_nistp256_sqr; |
| 100 +#ifdef IS_LITTLE_ENDIAN |
| 101 + group->base_point_mul = &ec_GFp_nistp256_base_point_mul; |
| 102 + group->point_mul = &ec_GFp_nistp256_point_mul; |
| 103 + group->points_mul = &ec_GFp_nistp256_points_mul_vartime; |
| 104 +#endif |
| 105 } |
| 106 return MP_OKAY; |
| 107 } |
| 108 Index: mozilla/security/nss/lib/freebl/ecl/ecp_256_32.c |
| 109 =================================================================== |
| 110 RCS file: mozilla/security/nss/lib/freebl/ecl/ecp_256_32.c |
| 111 diff -N mozilla/security/nss/lib/freebl/ecl/ecp_256_32.c |
| 112 --- /dev/null 1 Jan 1970 00:00:00 -0000 |
| 113 +++ mozilla/security/nss/lib/freebl/ecl/ecp_256_32.c 25 Jan 2013 00:17:14 -00
00 |
| 114 @@ -0,0 +1,1459 @@ |
| 115 +/* This Source Code Form is subject to the terms of the Mozilla Public |
| 116 + * License, v. 2.0. If a copy of the MPL was not distributed with this |
| 117 + * file, You can obtain one at http://mozilla.org/MPL/2.0/. */ |
| 118 + |
| 119 +/* A 32-bit implementation of the NIST P-256 elliptic curve. */ |
| 120 + |
| 121 +#include <string.h> |
| 122 + |
| 123 +#include "prtypes.h" |
| 124 +#include "mpi.h" |
| 125 +#include "mpi-priv.h" |
| 126 +#include "ecp.h" |
| 127 + |
| 128 +typedef PRUint8 u8; |
| 129 +typedef PRUint32 u32; |
| 130 +typedef PRInt32 s32; |
| 131 +typedef PRUint64 u64; |
| 132 + |
| 133 +/* Our field elements are represented as nine, unsigned 32-bit words. Freebl's |
| 134 + * MPI library calls them digits, but here they are called limbs, which is |
| 135 + * GMP's terminology. |
| 136 + * |
| 137 + * The value of an felem (field element) is: |
| 138 + * x[0] + (x[1] * 2**29) + (x[2] * 2**57) + ... + (x[8] * 2**228) |
| 139 + * |
| 140 + * That is, each limb is alternately 29 or 28-bits wide in little-endian |
| 141 + * order. |
| 142 + * |
| 143 + * This means that an felem hits 2**257, rather than 2**256 as we would like. A |
| 144 + * 28, 29, ... pattern would cause us to hit 2**256, but that causes problems |
| 145 + * when multiplying as terms end up one bit short of a limb which would require |
| 146 + * much bit-shifting to correct. |
| 147 + * |
| 148 + * Finally, the values stored in an felem are in Montgomery form. So the value |
| 149 + * |y| is stored as (y*R) mod p, where p is the P-256 prime and R is 2**257. |
| 150 + */ |
| 151 +typedef u32 limb; |
| 152 +#define NLIMBS 9 |
| 153 +typedef limb felem[NLIMBS]; |
| 154 + |
| 155 +static const limb kBottom28Bits = 0xfffffff; |
| 156 +static const limb kBottom29Bits = 0x1fffffff; |
| 157 + |
| 158 +/* kOne is the number 1 as an felem. It's 2**257 mod p split up into 29 and |
| 159 + * 28-bit words. |
| 160 + */ |
| 161 +static const felem kOne = { |
| 162 + 2, 0, 0, 0xffff800, |
| 163 + 0x1fffffff, 0xfffffff, 0x1fbfffff, 0x1ffffff, |
| 164 + 0 |
| 165 +}; |
| 166 +static const felem kZero = {0}; |
| 167 +static const felem kP = { |
| 168 + 0x1fffffff, 0xfffffff, 0x1fffffff, 0x3ff, |
| 169 + 0, 0, 0x200000, 0xf000000, |
| 170 + 0xfffffff |
| 171 +}; |
| 172 +static const felem k2P = { |
| 173 + 0x1ffffffe, 0xfffffff, 0x1fffffff, 0x7ff, |
| 174 + 0, 0, 0x400000, 0xe000000, |
| 175 + 0x1fffffff |
| 176 +}; |
| 177 + |
| 178 +/* kPrecomputed contains precomputed values to aid the calculation of scalar |
| 179 + * multiples of the base point, G. It's actually two, equal length, tables |
| 180 + * concatenated. |
| 181 + * |
| 182 + * The first table contains (x,y) felem pairs for 16 multiples of the base |
| 183 + * point, G. |
| 184 + * |
| 185 + * Index | Index (binary) | Value |
| 186 + * 0 | 0000 | 0G (all zeros, omitted) |
| 187 + * 1 | 0001 | G |
| 188 + * 2 | 0010 | 2**64G |
| 189 + * 3 | 0011 | 2**64G + G |
| 190 + * 4 | 0100 | 2**128G |
| 191 + * 5 | 0101 | 2**128G + G |
| 192 + * 6 | 0110 | 2**128G + 2**64G |
| 193 + * 7 | 0111 | 2**128G + 2**64G + G |
| 194 + * 8 | 1000 | 2**192G |
| 195 + * 9 | 1001 | 2**192G + G |
| 196 + * 10 | 1010 | 2**192G + 2**64G |
| 197 + * 11 | 1011 | 2**192G + 2**64G + G |
| 198 + * 12 | 1100 | 2**192G + 2**128G |
| 199 + * 13 | 1101 | 2**192G + 2**128G + G |
| 200 + * 14 | 1110 | 2**192G + 2**128G + 2**64G |
| 201 + * 15 | 1111 | 2**192G + 2**128G + 2**64G + G |
| 202 + * |
| 203 + * The second table follows the same style, but the terms are 2**32G, |
| 204 + * 2**96G, 2**160G, 2**224G. |
| 205 + * |
| 206 + * This is ~2KB of data. |
| 207 + */ |
| 208 +static const limb kPrecomputed[NLIMBS * 2 * 15 * 2] = { |
| 209 + 0x11522878, 0xe730d41, 0xdb60179, 0x4afe2ff, 0x12883add, 0xcaddd88, 0x119e7
edc, 0xd4a6eab, 0x3120bee, |
| 210 + 0x1d2aac15, 0xf25357c, 0x19e45cdd, 0x5c721d0, 0x1992c5a5, 0xa237487, 0x154b
a21, 0x14b10bb, 0xae3fe3, |
| 211 + 0xd41a576, 0x922fc51, 0x234994f, 0x60b60d3, 0x164586ae, 0xce95f18, 0x1fe490
73, 0x3fa36cc, 0x5ebcd2c, |
| 212 + 0xb402f2f, 0x15c70bf, 0x1561925c, 0x5a26704, 0xda91e90, 0xcdc1c7f, 0x1ea124
46, 0xe1ade1e, 0xec91f22, |
| 213 + 0x26f7778, 0x566847e, 0xa0bec9e, 0x234f453, 0x1a31f21a, 0xd85e75c, 0x56c710
9, 0xa267a00, 0xb57c050, |
| 214 + 0x98fb57, 0xaa837cc, 0x60c0792, 0xcfa5e19, 0x61bab9e, 0x589e39b, 0xa324c5,
0x7d6dee7, 0x2976e4b, |
| 215 + 0x1fc4124a, 0xa8c244b, 0x1ce86762, 0xcd61c7e, 0x1831c8e0, 0x75774e1, 0x1d96
a5a9, 0x843a649, 0xc3ab0fa, |
| 216 + 0x6e2e7d5, 0x7673a2a, 0x178b65e8, 0x4003e9b, 0x1a1f11c2, 0x7816ea, 0xf643e1
1, 0x58c43df, 0xf423fc2, |
| 217 + 0x19633ffa, 0x891f2b2, 0x123c231c, 0x46add8c, 0x54700dd, 0x59e2b17, 0x172db
40f, 0x83e277d, 0xb0dd609, |
| 218 + 0xfd1da12, 0x35c6e52, 0x19ede20c, 0xd19e0c0, 0x97d0f40, 0xb015b19, 0x449e3f
5, 0xe10c9e, 0x33ab581, |
| 219 + 0x56a67ab, 0x577734d, 0x1dddc062, 0xc57b10d, 0x149b39d, 0x26a9e7b, 0xc35df9
f, 0x48764cd, 0x76dbcca, |
| 220 + 0xca4b366, 0xe9303ab, 0x1a7480e7, 0x57e9e81, 0x1e13eb50, 0xf466cf3, 0x6f16b
20, 0x4ba3173, 0xc168c33, |
| 221 + 0x15cb5439, 0x6a38e11, 0x73658bd, 0xb29564f, 0x3f6dc5b, 0x53b97e, 0x1322c4c
0, 0x65dd7ff, 0x3a1e4f6, |
| 222 + 0x14e614aa, 0x9246317, 0x1bc83aca, 0xad97eed, 0xd38ce4a, 0xf82b006, 0x341f0
77, 0xa6add89, 0x4894acd, |
| 223 + 0x9f162d5, 0xf8410ef, 0x1b266a56, 0xd7f223, 0x3e0cb92, 0xe39b672, 0x6a2901a
, 0x69a8556, 0x7e7c0, |
| 224 + 0x9b7d8d3, 0x309a80, 0x1ad05f7f, 0xc2fb5dd, 0xcbfd41d, 0x9ceb638, 0x1051825
c, 0xda0cf5b, 0x812e881, |
| 225 + 0x6f35669, 0x6a56f2c, 0x1df8d184, 0x345820, 0x1477d477, 0x1645db1, 0xbe80c5
1, 0xc22be3e, 0xe35e65a, |
| 226 + 0x1aeb7aa0, 0xc375315, 0xf67bc99, 0x7fdd7b9, 0x191fc1be, 0x61235d, 0x2c184e
9, 0x1c5a839, 0x47a1e26, |
| 227 + 0xb7cb456, 0x93e225d, 0x14f3c6ed, 0xccc1ac9, 0x17fe37f3, 0x4988989, 0x1a90c
502, 0x2f32042, 0xa17769b, |
| 228 + 0xafd8c7c, 0x8191c6e, 0x1dcdb237, 0x16200c0, 0x107b32a1, 0x66c08db, 0x10d06
a02, 0x3fc93, 0x5620023, |
| 229 + 0x16722b27, 0x68b5c59, 0x270fcfc, 0xfad0ecc, 0xe5de1c2, 0xeab466b, 0x2fc513
c, 0x407f75c, 0xbaab133, |
| 230 + 0x9705fe9, 0xb88b8e7, 0x734c993, 0x1e1ff8f, 0x19156970, 0xabd0f00, 0x10469e
a7, 0x3293ac0, 0xcdc98aa, |
| 231 + 0x1d843fd, 0xe14bfe8, 0x15be825f, 0x8b5212, 0xeb3fb67, 0x81cbd29, 0xbc62f16
, 0x2b6fcc7, 0xf5a4e29, |
| 232 + 0x13560b66, 0xc0b6ac2, 0x51ae690, 0xd41e271, 0xf3e9bd4, 0x1d70aab, 0x1029f7
2, 0x73e1c35, 0xee70fbc, |
| 233 + 0xad81baf, 0x9ecc49a, 0x86c741e, 0xfe6be30, 0x176752e7, 0x23d416, 0x1f83de8
5, 0x27de188, 0x66f70b8, |
| 234 + 0x181cd51f, 0x96b6e4c, 0x188f2335, 0xa5df759, 0x17a77eb6, 0xfeb0e73, 0x154a
e914, 0x2f3ec51, 0x3826b59, |
| 235 + 0xb91f17d, 0x1c72949, 0x1362bf0a, 0xe23fddf, 0xa5614b0, 0xf7d8f, 0x79061, 0
x823d9d2, 0x8213f39, |
| 236 + 0x1128ae0b, 0xd095d05, 0xb85c0c2, 0x1ecb2ef, 0x24ddc84, 0xe35e901, 0x18411a
4a, 0xf5ddc3d, 0x3786689, |
| 237 + 0x52260e8, 0x5ae3564, 0x542b10d, 0x8d93a45, 0x19952aa4, 0x996cc41, 0x1051a7
29, 0x4be3499, 0x52b23aa, |
| 238 + 0x109f307e, 0x6f5b6bb, 0x1f84e1e7, 0x77a0cfa, 0x10c4df3f, 0x25a02ea, 0xb048
035, 0xe31de66, 0xc6ecaa3, |
| 239 + 0x28ea335, 0x2886024, 0x1372f020, 0xf55d35, 0x15e4684c, 0xf2a9e17, 0x1a4a75
29, 0xcb7beb1, 0xb2a78a1, |
| 240 + 0x1ab21f1f, 0x6361ccf, 0x6c9179d, 0xb135627, 0x1267b974, 0x4408bad, 0x1cbff
658, 0xe3d6511, 0xc7d76f, |
| 241 + 0x1cc7a69, 0xe7ee31b, 0x54fab4f, 0x2b914f, 0x1ad27a30, 0xcd3579e, 0xc50124c
, 0x50daa90, 0xb13f72, |
| 242 + 0xb06aa75, 0x70f5cc6, 0x1649e5aa, 0x84a5312, 0x329043c, 0x41c4011, 0x13d324
11, 0xb04a838, 0xd760d2d, |
| 243 + 0x1713b532, 0xbaa0c03, 0x84022ab, 0x6bcf5c1, 0x2f45379, 0x18ae070, 0x18c9e1
1e, 0x20bca9a, 0x66f496b, |
| 244 + 0x3eef294, 0x67500d2, 0xd7f613c, 0x2dbbeb, 0xb741038, 0xe04133f, 0x1582968d
, 0xbe985f7, 0x1acbc1a, |
| 245 + 0x1a6a939f, 0x33e50f6, 0xd665ed4, 0xb4b7bd6, 0x1e5a3799, 0x6b33847, 0x17fa5
6ff, 0x65ef930, 0x21dc4a, |
| 246 + 0x2b37659, 0x450fe17, 0xb357b65, 0xdf5efac, 0x15397bef, 0x9d35a7f, 0x112ac1
5f, 0x624e62e, 0xa90ae2f, |
| 247 + 0x107eecd2, 0x1f69bbe, 0x77d6bce, 0x5741394, 0x13c684fc, 0x950c910, 0x72552
2b, 0xdc78583, 0x40eeabb, |
| 248 + 0x1fde328a, 0xbd61d96, 0xd28c387, 0x9e77d89, 0x12550c40, 0x759cb7d, 0x367ef
34, 0xae2a960, 0x91b8bdc, |
| 249 + 0x93462a9, 0xf469ef, 0xb2e9aef, 0xd2ca771, 0x54e1f42, 0x7aaa49, 0x6316abb,
0x2413c8e, 0x5425bf9, |
| 250 + 0x1bed3e3a, 0xf272274, 0x1f5e7326, 0x6416517, 0xea27072, 0x9cedea7, 0x6e763
3, 0x7c91952, 0xd806dce, |
| 251 + 0x8e2a7e1, 0xe421e1a, 0x418c9e1, 0x1dbc890, 0x1b395c36, 0xa1dc175, 0x1dc4ef
73, 0x8956f34, 0xe4b5cf2, |
| 252 + 0x1b0d3a18, 0x3194a36, 0x6c2641f, 0xe44124c, 0xa2f4eaa, 0xa8c25ba, 0xf927ed
7, 0x627b614, 0x7371cca, |
| 253 + 0xba16694, 0x417bc03, 0x7c0a7e3, 0x9c35c19, 0x1168a205, 0x8b6b00d, 0x10e3ed
c9, 0x9c19bf2, 0x5882229, |
| 254 + 0x1b2b4162, 0xa5cef1a, 0x1543622b, 0x9bd433e, 0x364e04d, 0x7480792, 0x5c9b5
b3, 0xe85ff25, 0x408ef57, |
| 255 + 0x1814cfa4, 0x121b41b, 0xd248a0f, 0x3b05222, 0x39bb16a, 0xc75966d, 0xa03811
3, 0xa4a1769, 0x11fbc6c, |
| 256 + 0x917e50e, 0xeec3da8, 0x169d6eac, 0x10c1699, 0xa416153, 0xf724912, 0x15cd60
b7, 0x4acbad9, 0x5efc5fa, |
| 257 + 0xf150ed7, 0x122b51, 0x1104b40a, 0xcb7f442, 0xfbb28ff, 0x6ac53ca, 0x196142c
c, 0x7bf0fa9, 0x957651, |
| 258 + 0x4e0f215, 0xed439f8, 0x3f46bd5, 0x5ace82f, 0x110916b6, 0x6db078, 0xffd7d57
, 0xf2ecaac, 0xca86dec, |
| 259 + 0x15d6b2da, 0x965ecc9, 0x1c92b4c2, 0x1f3811, 0x1cb080f5, 0x2d8b804, 0x19d1c
12d, 0xf20bd46, 0x1951fa7, |
| 260 + 0xa3656c3, 0x523a425, 0xfcd0692, 0xd44ddc8, 0x131f0f5b, 0xaf80e4a, 0xcd9fc7
4, 0x99bb618, 0x2db944c, |
| 261 + 0xa673090, 0x1c210e1, 0x178c8d23, 0x1474383, 0x10b8743d, 0x985a55b, 0x2e747
79, 0x576138, 0x9587927, |
| 262 + 0x133130fa, 0xbe05516, 0x9f4d619, 0xbb62570, 0x99ec591, 0xd9468fe, 0x1d0778
2d, 0xfc72e0b, 0x701b298, |
| 263 + 0x1863863b, 0x85954b8, 0x121a0c36, 0x9e7fedf, 0xf64b429, 0x9b9d71e, 0x14e2f
5d8, 0xf858d3a, 0x942eea8, |
| 264 + 0xda5b765, 0x6edafff, 0xa9d18cc, 0xc65e4ba, 0x1c747e86, 0xe4ea915, 0x1981d7
a1, 0x8395659, 0x52ed4e2, |
| 265 + 0x87d43b7, 0x37ab11b, 0x19d292ce, 0xf8d4692, 0x18c3053f, 0x8863e13, 0x4c146
c0, 0x6bdf55a, 0x4e4457d, |
| 266 + 0x16152289, 0xac78ec2, 0x1a59c5a2, 0x2028b97, 0x71c2d01, 0x295851f, 0x40474
7b, 0x878558d, 0x7d29aa4, |
| 267 + 0x13d8341f, 0x8daefd7, 0x139c972d, 0x6b7ea75, 0xd4a9dde, 0xff163d8, 0x81d55
d7, 0xa5bef68, 0xb7b30d8, |
| 268 + 0xbe73d6f, 0xaa88141, 0xd976c81, 0x7e7a9cc, 0x18beb771, 0xd773cbd, 0x13f519
51, 0x9d0c177, 0x1c49a78, |
| 269 +}; |
| 270 + |
| 271 +/* Field element operations: |
| 272 + */ |
| 273 + |
| 274 +/* NON_ZERO_TO_ALL_ONES returns: |
| 275 + * 0xffffffff for 0 < x <= 2**31 |
| 276 + * 0 for x == 0 or x > 2**31. |
| 277 + * |
| 278 + * This macro assumes that right-shifting a signed number shifts in the MSB on |
| 279 + * the left. This is not ensured by the C standard, but is true on the CPUs |
| 280 + * that we're targetting with this code (x86 and ARM). |
| 281 + */ |
| 282 +#define NON_ZERO_TO_ALL_ONES(x) (~((u32) (((s32) ((x)-1)) >> 31))) |
| 283 + |
| 284 +/* felem_reduce_carry adds a multiple of p in order to cancel |carry|, |
| 285 + * which is a term at 2**257. |
| 286 + * |
| 287 + * On entry: carry < 2**3, inout[0,2,...] < 2**29, inout[1,3,...] < 2**28. |
| 288 + * On exit: inout[0,2,..] < 2**30, inout[1,3,...] < 2**29. |
| 289 + */ |
| 290 +static void felem_reduce_carry(felem inout, limb carry) |
| 291 +{ |
| 292 + const u32 carry_mask = NON_ZERO_TO_ALL_ONES(carry); |
| 293 + |
| 294 + inout[0] += carry << 1; |
| 295 + inout[3] += 0x10000000 & carry_mask; |
| 296 + /* carry < 2**3 thus (carry << 11) < 2**14 and we added 2**28 in the |
| 297 + * previous line therefore this doesn't underflow. |
| 298 + */ |
| 299 + inout[3] -= carry << 11; |
| 300 + inout[4] += (0x20000000 - 1) & carry_mask; |
| 301 + inout[5] += (0x10000000 - 1) & carry_mask; |
| 302 + inout[6] += (0x20000000 - 1) & carry_mask; |
| 303 + inout[6] -= carry << 22; |
| 304 + /* This may underflow if carry is non-zero but, if so, we'll fix it in the |
| 305 + * next line. |
| 306 + */ |
| 307 + inout[7] -= 1 & carry_mask; |
| 308 + inout[7] += carry << 25; |
| 309 +} |
| 310 + |
| 311 +/* felem_sum sets out = in+in2. |
| 312 + * |
| 313 + * On entry, in[i]+in2[i] must not overflow a 32-bit word. |
| 314 + * On exit: out[0,2,...] < 2**30, out[1,3,...] < 2**29 |
| 315 + */ |
| 316 +static void felem_sum(felem out, const felem in, const felem in2) |
| 317 +{ |
| 318 + limb carry = 0; |
| 319 + unsigned int i; |
| 320 + for (i = 0;; i++) { |
| 321 + out[i] = in[i] + in2[i]; |
| 322 + out[i] += carry; |
| 323 + carry = out[i] >> 29; |
| 324 + out[i] &= kBottom29Bits; |
| 325 + |
| 326 + i++; |
| 327 + if (i == NLIMBS) |
| 328 + break; |
| 329 + |
| 330 + out[i] = in[i] + in2[i]; |
| 331 + out[i] += carry; |
| 332 + carry = out[i] >> 28; |
| 333 + out[i] &= kBottom28Bits; |
| 334 + } |
| 335 + |
| 336 + felem_reduce_carry(out, carry); |
| 337 +} |
| 338 + |
| 339 +#define two31m3 (((limb)1) << 31) - (((limb)1) << 3) |
| 340 +#define two30m2 (((limb)1) << 30) - (((limb)1) << 2) |
| 341 +#define two30p13m2 (((limb)1) << 30) + (((limb)1) << 13) - (((limb)1) << 2) |
| 342 +#define two31m2 (((limb)1) << 31) - (((limb)1) << 2) |
| 343 +#define two31p24m2 (((limb)1) << 31) + (((limb)1) << 24) - (((limb)1) << 2) |
| 344 +#define two30m27m2 (((limb)1) << 30) - (((limb)1) << 27) - (((limb)1) << 2) |
| 345 + |
| 346 +/* zero31 is 0 mod p. |
| 347 + */ |
| 348 +static const felem zero31 = { |
| 349 + two31m3, two30m2, two31m2, two30p13m2, |
| 350 + two31m2, two30m2, two31p24m2, two30m27m2, |
| 351 + two31m2 |
| 352 +}; |
| 353 + |
| 354 +/* felem_diff sets out = in-in2. |
| 355 + * |
| 356 + * On entry: in[0,2,...] < 2**30, in[1,3,...] < 2**29 and |
| 357 + * in2[0,2,...] < 2**30, in2[1,3,...] < 2**29. |
| 358 + * On exit: out[0,2,...] < 2**30, out[1,3,...] < 2**29. |
| 359 + */ |
| 360 +static void felem_diff(felem out, const felem in, const felem in2) |
| 361 +{ |
| 362 + limb carry = 0; |
| 363 + unsigned int i; |
| 364 + |
| 365 + for (i = 0;; i++) { |
| 366 + out[i] = in[i] - in2[i]; |
| 367 + out[i] += zero31[i]; |
| 368 + out[i] += carry; |
| 369 + carry = out[i] >> 29; |
| 370 + out[i] &= kBottom29Bits; |
| 371 + |
| 372 + i++; |
| 373 + if (i == NLIMBS) |
| 374 + break; |
| 375 + |
| 376 + out[i] = in[i] - in2[i]; |
| 377 + out[i] += zero31[i]; |
| 378 + out[i] += carry; |
| 379 + carry = out[i] >> 28; |
| 380 + out[i] &= kBottom28Bits; |
| 381 + } |
| 382 + |
| 383 + felem_reduce_carry(out, carry); |
| 384 +} |
| 385 + |
| 386 +/* felem_reduce_degree sets out = tmp/R mod p where tmp contains 64-bit words |
| 387 + * with the same 29,28,... bit positions as an felem. |
| 388 + * |
| 389 + * The values in felems are in Montgomery form: x*R mod p where R = 2**257. |
| 390 + * Since we just multiplied two Montgomery values together, the result is |
| 391 + * x*y*R*R mod p. We wish to divide by R in order for the result also to be |
| 392 + * in Montgomery form. |
| 393 + * |
| 394 + * On entry: tmp[i] < 2**64 |
| 395 + * On exit: out[0,2,...] < 2**30, out[1,3,...] < 2**29 |
| 396 + */ |
| 397 +static void felem_reduce_degree(felem out, u64 tmp[17]) |
| 398 +{ |
| 399 + /* The following table may be helpful when reading this code: |
| 400 + * |
| 401 + * Limb number: 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10... |
| 402 + * Width (bits): 29| 28| 29| 28| 29| 28| 29| 28| 29| 28| 29 |
| 403 + * Start bit: 0 | 29| 57| 86|114|143|171|200|228|257|285 |
| 404 + * (odd phase): 0 | 28| 57| 85|114|142|171|199|228|256|285 |
| 405 + */ |
| 406 + limb tmp2[18], carry, x, xMask; |
| 407 + unsigned int i; |
| 408 + |
| 409 + /* tmp contains 64-bit words with the same 29,28,29-bit positions as an |
| 410 + * felem. So the top of an element of tmp might overlap with another |
| 411 + * element two positions down. The following loop eliminates this |
| 412 + * overlap. |
| 413 + */ |
| 414 + tmp2[0] = tmp[0] & kBottom29Bits; |
| 415 + |
| 416 + /* In the following we use "(limb) tmp[x]" and "(limb) (tmp[x]>>32)" to try |
| 417 + * and hint to the compiler that it can do a single-word shift by selecting |
| 418 + * the right register rather than doing a double-word shift and truncating |
| 419 + * afterwards. |
| 420 + */ |
| 421 + tmp2[1] = ((limb) tmp[0]) >> 29; |
| 422 + tmp2[1] |= (((limb) (tmp[0] >> 32)) << 3) & kBottom28Bits; |
| 423 + tmp2[1] += ((limb) tmp[1]) & kBottom28Bits; |
| 424 + carry = tmp2[1] >> 28; |
| 425 + tmp2[1] &= kBottom28Bits; |
| 426 + |
| 427 + for (i = 2; i < 17; i++) { |
| 428 + tmp2[i] = ((limb) (tmp[i - 2] >> 32)) >> 25; |
| 429 + tmp2[i] += ((limb) (tmp[i - 1])) >> 28; |
| 430 + tmp2[i] += (((limb) (tmp[i - 1] >> 32)) << 4) & kBottom29Bits; |
| 431 + tmp2[i] += ((limb) tmp[i]) & kBottom29Bits; |
| 432 + tmp2[i] += carry; |
| 433 + carry = tmp2[i] >> 29; |
| 434 + tmp2[i] &= kBottom29Bits; |
| 435 + |
| 436 + i++; |
| 437 + if (i == 17) |
| 438 + break; |
| 439 + tmp2[i] = ((limb) (tmp[i - 2] >> 32)) >> 25; |
| 440 + tmp2[i] += ((limb) (tmp[i - 1])) >> 29; |
| 441 + tmp2[i] += (((limb) (tmp[i - 1] >> 32)) << 3) & kBottom28Bits; |
| 442 + tmp2[i] += ((limb) tmp[i]) & kBottom28Bits; |
| 443 + tmp2[i] += carry; |
| 444 + carry = tmp2[i] >> 28; |
| 445 + tmp2[i] &= kBottom28Bits; |
| 446 + } |
| 447 + |
| 448 + tmp2[17] = ((limb) (tmp[15] >> 32)) >> 25; |
| 449 + tmp2[17] += ((limb) (tmp[16])) >> 29; |
| 450 + tmp2[17] += (((limb) (tmp[16] >> 32)) << 3); |
| 451 + tmp2[17] += carry; |
| 452 + |
| 453 + /* Montgomery elimination of terms: |
| 454 + * |
| 455 + * Since R is 2**257, we can divide by R with a bitwise shift if we can |
| 456 + * ensure that the right-most 257 bits are all zero. We can make that true |
| 457 + * by adding multiplies of p without affecting the value. |
| 458 + * |
| 459 + * So we eliminate limbs from right to left. Since the bottom 29 bits of p |
| 460 + * are all ones, then by adding tmp2[0]*p to tmp2 we'll make tmp2[0] == 0. |
| 461 + * We can do that for 8 further limbs and then right shift to eliminate the |
| 462 + * extra factor of R. |
| 463 + */ |
| 464 + for (i = 0;; i += 2) { |
| 465 + tmp2[i + 1] += tmp2[i] >> 29; |
| 466 + x = tmp2[i] & kBottom29Bits; |
| 467 + xMask = NON_ZERO_TO_ALL_ONES(x); |
| 468 + tmp2[i] = 0; |
| 469 + |
| 470 + /* The bounds calculations for this loop are tricky. Each iteration of |
| 471 + * the loop eliminates two words by adding values to words to their |
| 472 + * right. |
| 473 + * |
| 474 + * The following table contains the amounts added to each word (as an |
| 475 + * offset from the value of i at the top of the loop). The amounts are |
| 476 + * accounted for from the first and second half of the loop separately |
| 477 + * and are written as, for example, 28 to mean a value <2**28. |
| 478 + * |
| 479 + * Word: 3 4 5 6 7 8 9 10 |
| 480 + * Added in top half: 28 11 29 21 29 28 |
| 481 + * 28 29 |
| 482 + * 29 |
| 483 + * Added in bottom half: 29 10 28 21 28 28 |
| 484 + * 29 |
| 485 + * |
| 486 + * The value that is currently offset 7 will be offset 5 for the next |
| 487 + * iteration and then offset 3 for the iteration after that. Therefore |
| 488 + * the total value added will be the values added at 7, 5 and 3. |
| 489 + * |
| 490 + * The following table accumulates these values. The sums at the bottom |
| 491 + * are written as, for example, 29+28, to mean a value < 2**29+2**28. |
| 492 + * |
| 493 + * Word: 3 4 5 6 7 8 9 10 11 12 13 |
| 494 + * 28 11 10 29 21 29 28 28 28 28 28 |
| 495 + * 29 28 11 28 29 28 29 28 29 28 |
| 496 + * 29 28 21 21 29 21 29 21 |
| 497 + * 10 29 28 21 28 21 28 |
| 498 + * 28 29 28 29 28 29 28 |
| 499 + * 11 10 29 10 29 10 |
| 500 + * 29 28 11 28 11 |
| 501 + * 29 29 |
| 502 + * -------------------------------------------- |
| 503 + * 30+ 31+ 30+ 31+ 30+ |
| 504 + * 28+ 29+ 28+ 29+ 21+ |
| 505 + * 21+ 28+ 21+ 28+ 10 |
| 506 + * 10 21+ 10 21+ |
| 507 + * 11 11 |
| 508 + * |
| 509 + * So the greatest amount is added to tmp2[10] and tmp2[12]. If |
| 510 + * tmp2[10/12] has an initial value of <2**29, then the maximum value |
| 511 + * will be < 2**31 + 2**30 + 2**28 + 2**21 + 2**11, which is < 2**32, |
| 512 + * as required. |
| 513 + */ |
| 514 + tmp2[i + 3] += (x << 10) & kBottom28Bits; |
| 515 + tmp2[i + 4] += (x >> 18); |
| 516 + |
| 517 + tmp2[i + 6] += (x << 21) & kBottom29Bits; |
| 518 + tmp2[i + 7] += x >> 8; |
| 519 + |
| 520 + /* At position 200, which is the starting bit position for word 7, we |
| 521 + * have a factor of 0xf000000 = 2**28 - 2**24. |
| 522 + */ |
| 523 + tmp2[i + 7] += 0x10000000 & xMask; |
| 524 + /* Word 7 is 28 bits wide, so the 2**28 term exactly hits word 8. */ |
| 525 + tmp2[i + 8] += (x - 1) & xMask; |
| 526 + tmp2[i + 7] -= (x << 24) & kBottom28Bits; |
| 527 + tmp2[i + 8] -= x >> 4; |
| 528 + |
| 529 + tmp2[i + 8] += 0x20000000 & xMask; |
| 530 + tmp2[i + 8] -= x; |
| 531 + tmp2[i + 8] += (x << 28) & kBottom29Bits; |
| 532 + tmp2[i + 9] += ((x >> 1) - 1) & xMask; |
| 533 + |
| 534 + if (i+1 == NLIMBS) |
| 535 + break; |
| 536 + tmp2[i + 2] += tmp2[i + 1] >> 28; |
| 537 + x = tmp2[i + 1] & kBottom28Bits; |
| 538 + xMask = NON_ZERO_TO_ALL_ONES(x); |
| 539 + tmp2[i + 1] = 0; |
| 540 + |
| 541 + tmp2[i + 4] += (x << 11) & kBottom29Bits; |
| 542 + tmp2[i + 5] += (x >> 18); |
| 543 + |
| 544 + tmp2[i + 7] += (x << 21) & kBottom28Bits; |
| 545 + tmp2[i + 8] += x >> 7; |
| 546 + |
| 547 + /* At position 199, which is the starting bit of the 8th word when |
| 548 + * dealing with a context starting on an odd word, we have a factor of |
| 549 + * 0x1e000000 = 2**29 - 2**25. Since we have not updated i, the 8th |
| 550 + * word from i+1 is i+8. |
| 551 + */ |
| 552 + tmp2[i + 8] += 0x20000000 & xMask; |
| 553 + tmp2[i + 9] += (x - 1) & xMask; |
| 554 + tmp2[i + 8] -= (x << 25) & kBottom29Bits; |
| 555 + tmp2[i + 9] -= x >> 4; |
| 556 + |
| 557 + tmp2[i + 9] += 0x10000000 & xMask; |
| 558 + tmp2[i + 9] -= x; |
| 559 + tmp2[i + 10] += (x - 1) & xMask; |
| 560 + } |
| 561 + |
| 562 + /* We merge the right shift with a carry chain. The words above 2**257 have |
| 563 + * widths of 28,29,... which we need to correct when copying them down. |
| 564 + */ |
| 565 + carry = 0; |
| 566 + for (i = 0; i < 8; i++) { |
| 567 + /* The maximum value of tmp2[i + 9] occurs on the first iteration and |
| 568 + * is < 2**30+2**29+2**28. Adding 2**29 (from tmp2[i + 10]) is |
| 569 + * therefore safe. |
| 570 + */ |
| 571 + out[i] = tmp2[i + 9]; |
| 572 + out[i] += carry; |
| 573 + out[i] += (tmp2[i + 10] << 28) & kBottom29Bits; |
| 574 + carry = out[i] >> 29; |
| 575 + out[i] &= kBottom29Bits; |
| 576 + |
| 577 + i++; |
| 578 + out[i] = tmp2[i + 9] >> 1; |
| 579 + out[i] += carry; |
| 580 + carry = out[i] >> 28; |
| 581 + out[i] &= kBottom28Bits; |
| 582 + } |
| 583 + |
| 584 + out[8] = tmp2[17]; |
| 585 + out[8] += carry; |
| 586 + carry = out[8] >> 29; |
| 587 + out[8] &= kBottom29Bits; |
| 588 + |
| 589 + felem_reduce_carry(out, carry); |
| 590 +} |
| 591 + |
| 592 +/* felem_square sets out=in*in. |
| 593 + * |
| 594 + * On entry: in[0,2,...] < 2**30, in[1,3,...] < 2**29. |
| 595 + * On exit: out[0,2,...] < 2**30, out[1,3,...] < 2**29. |
| 596 + */ |
| 597 +static void felem_square(felem out, const felem in) |
| 598 +{ |
| 599 + u64 tmp[17]; |
| 600 + |
| 601 + tmp[0] = ((u64) in[0]) * in[0]; |
| 602 + tmp[1] = ((u64) in[0]) * (in[1] << 1); |
| 603 + tmp[2] = ((u64) in[0]) * (in[2] << 1) + |
| 604 + ((u64) in[1]) * (in[1] << 1); |
| 605 + tmp[3] = ((u64) in[0]) * (in[3] << 1) + |
| 606 + ((u64) in[1]) * (in[2] << 1); |
| 607 + tmp[4] = ((u64) in[0]) * (in[4] << 1) + |
| 608 + ((u64) in[1]) * (in[3] << 2) + |
| 609 + ((u64) in[2]) * in[2]; |
| 610 + tmp[5] = ((u64) in[0]) * (in[5] << 1) + |
| 611 + ((u64) in[1]) * (in[4] << 1) + |
| 612 + ((u64) in[2]) * (in[3] << 1); |
| 613 + tmp[6] = ((u64) in[0]) * (in[6] << 1) + |
| 614 + ((u64) in[1]) * (in[5] << 2) + |
| 615 + ((u64) in[2]) * (in[4] << 1) + |
| 616 + ((u64) in[3]) * (in[3] << 1); |
| 617 + tmp[7] = ((u64) in[0]) * (in[7] << 1) + |
| 618 + ((u64) in[1]) * (in[6] << 1) + |
| 619 + ((u64) in[2]) * (in[5] << 1) + |
| 620 + ((u64) in[3]) * (in[4] << 1); |
| 621 + /* tmp[8] has the greatest value of 2**61 + 2**60 + 2**61 + 2**60 + 2**60, |
| 622 + * which is < 2**64 as required. |
| 623 + */ |
| 624 + tmp[8] = ((u64) in[0]) * (in[8] << 1) + |
| 625 + ((u64) in[1]) * (in[7] << 2) + |
| 626 + ((u64) in[2]) * (in[6] << 1) + |
| 627 + ((u64) in[3]) * (in[5] << 2) + |
| 628 + ((u64) in[4]) * in[4]; |
| 629 + tmp[9] = ((u64) in[1]) * (in[8] << 1) + |
| 630 + ((u64) in[2]) * (in[7] << 1) + |
| 631 + ((u64) in[3]) * (in[6] << 1) + |
| 632 + ((u64) in[4]) * (in[5] << 1); |
| 633 + tmp[10] = ((u64) in[2]) * (in[8] << 1) + |
| 634 + ((u64) in[3]) * (in[7] << 2) + |
| 635 + ((u64) in[4]) * (in[6] << 1) + |
| 636 + ((u64) in[5]) * (in[5] << 1); |
| 637 + tmp[11] = ((u64) in[3]) * (in[8] << 1) + |
| 638 + ((u64) in[4]) * (in[7] << 1) + |
| 639 + ((u64) in[5]) * (in[6] << 1); |
| 640 + tmp[12] = ((u64) in[4]) * (in[8] << 1) + |
| 641 + ((u64) in[5]) * (in[7] << 2) + |
| 642 + ((u64) in[6]) * in[6]; |
| 643 + tmp[13] = ((u64) in[5]) * (in[8] << 1) + |
| 644 + ((u64) in[6]) * (in[7] << 1); |
| 645 + tmp[14] = ((u64) in[6]) * (in[8] << 1) + |
| 646 + ((u64) in[7]) * (in[7] << 1); |
| 647 + tmp[15] = ((u64) in[7]) * (in[8] << 1); |
| 648 + tmp[16] = ((u64) in[8]) * in[8]; |
| 649 + |
| 650 + felem_reduce_degree(out, tmp); |
| 651 +} |
| 652 + |
| 653 +/* felem_mul sets out=in*in2. |
| 654 + * |
| 655 + * On entry: in[0,2,...] < 2**30, in[1,3,...] < 2**29 and |
| 656 + * in2[0,2,...] < 2**30, in2[1,3,...] < 2**29. |
| 657 + * On exit: out[0,2,...] < 2**30, out[1,3,...] < 2**29. |
| 658 + */ |
| 659 +static void felem_mul(felem out, const felem in, const felem in2) |
| 660 +{ |
| 661 + u64 tmp[17]; |
| 662 + |
| 663 + tmp[0] = ((u64) in[0]) * in2[0]; |
| 664 + tmp[1] = ((u64) in[0]) * (in2[1] << 0) + |
| 665 + ((u64) in[1]) * (in2[0] << 0); |
| 666 + tmp[2] = ((u64) in[0]) * (in2[2] << 0) + |
| 667 + ((u64) in[1]) * (in2[1] << 1) + |
| 668 + ((u64) in[2]) * (in2[0] << 0); |
| 669 + tmp[3] = ((u64) in[0]) * (in2[3] << 0) + |
| 670 + ((u64) in[1]) * (in2[2] << 0) + |
| 671 + ((u64) in[2]) * (in2[1] << 0) + |
| 672 + ((u64) in[3]) * (in2[0] << 0); |
| 673 + tmp[4] = ((u64) in[0]) * (in2[4] << 0) + |
| 674 + ((u64) in[1]) * (in2[3] << 1) + |
| 675 + ((u64) in[2]) * (in2[2] << 0) + |
| 676 + ((u64) in[3]) * (in2[1] << 1) + |
| 677 + ((u64) in[4]) * (in2[0] << 0); |
| 678 + tmp[5] = ((u64) in[0]) * (in2[5] << 0) + |
| 679 + ((u64) in[1]) * (in2[4] << 0) + |
| 680 + ((u64) in[2]) * (in2[3] << 0) + |
| 681 + ((u64) in[3]) * (in2[2] << 0) + |
| 682 + ((u64) in[4]) * (in2[1] << 0) + |
| 683 + ((u64) in[5]) * (in2[0] << 0); |
| 684 + tmp[6] = ((u64) in[0]) * (in2[6] << 0) + |
| 685 + ((u64) in[1]) * (in2[5] << 1) + |
| 686 + ((u64) in[2]) * (in2[4] << 0) + |
| 687 + ((u64) in[3]) * (in2[3] << 1) + |
| 688 + ((u64) in[4]) * (in2[2] << 0) + |
| 689 + ((u64) in[5]) * (in2[1] << 1) + |
| 690 + ((u64) in[6]) * (in2[0] << 0); |
| 691 + tmp[7] = ((u64) in[0]) * (in2[7] << 0) + |
| 692 + ((u64) in[1]) * (in2[6] << 0) + |
| 693 + ((u64) in[2]) * (in2[5] << 0) + |
| 694 + ((u64) in[3]) * (in2[4] << 0) + |
| 695 + ((u64) in[4]) * (in2[3] << 0) + |
| 696 + ((u64) in[5]) * (in2[2] << 0) + |
| 697 + ((u64) in[6]) * (in2[1] << 0) + |
| 698 + ((u64) in[7]) * (in2[0] << 0); |
| 699 + /* tmp[8] has the greatest value but doesn't overflow. See logic in |
| 700 + * felem_square. |
| 701 + */ |
| 702 + tmp[8] = ((u64) in[0]) * (in2[8] << 0) + |
| 703 + ((u64) in[1]) * (in2[7] << 1) + |
| 704 + ((u64) in[2]) * (in2[6] << 0) + |
| 705 + ((u64) in[3]) * (in2[5] << 1) + |
| 706 + ((u64) in[4]) * (in2[4] << 0) + |
| 707 + ((u64) in[5]) * (in2[3] << 1) + |
| 708 + ((u64) in[6]) * (in2[2] << 0) + |
| 709 + ((u64) in[7]) * (in2[1] << 1) + |
| 710 + ((u64) in[8]) * (in2[0] << 0); |
| 711 + tmp[9] = ((u64) in[1]) * (in2[8] << 0) + |
| 712 + ((u64) in[2]) * (in2[7] << 0) + |
| 713 + ((u64) in[3]) * (in2[6] << 0) + |
| 714 + ((u64) in[4]) * (in2[5] << 0) + |
| 715 + ((u64) in[5]) * (in2[4] << 0) + |
| 716 + ((u64) in[6]) * (in2[3] << 0) + |
| 717 + ((u64) in[7]) * (in2[2] << 0) + |
| 718 + ((u64) in[8]) * (in2[1] << 0); |
| 719 + tmp[10] = ((u64) in[2]) * (in2[8] << 0) + |
| 720 + ((u64) in[3]) * (in2[7] << 1) + |
| 721 + ((u64) in[4]) * (in2[6] << 0) + |
| 722 + ((u64) in[5]) * (in2[5] << 1) + |
| 723 + ((u64) in[6]) * (in2[4] << 0) + |
| 724 + ((u64) in[7]) * (in2[3] << 1) + |
| 725 + ((u64) in[8]) * (in2[2] << 0); |
| 726 + tmp[11] = ((u64) in[3]) * (in2[8] << 0) + |
| 727 + ((u64) in[4]) * (in2[7] << 0) + |
| 728 + ((u64) in[5]) * (in2[6] << 0) + |
| 729 + ((u64) in[6]) * (in2[5] << 0) + |
| 730 + ((u64) in[7]) * (in2[4] << 0) + |
| 731 + ((u64) in[8]) * (in2[3] << 0); |
| 732 + tmp[12] = ((u64) in[4]) * (in2[8] << 0) + |
| 733 + ((u64) in[5]) * (in2[7] << 1) + |
| 734 + ((u64) in[6]) * (in2[6] << 0) + |
| 735 + ((u64) in[7]) * (in2[5] << 1) + |
| 736 + ((u64) in[8]) * (in2[4] << 0); |
| 737 + tmp[13] = ((u64) in[5]) * (in2[8] << 0) + |
| 738 + ((u64) in[6]) * (in2[7] << 0) + |
| 739 + ((u64) in[7]) * (in2[6] << 0) + |
| 740 + ((u64) in[8]) * (in2[5] << 0); |
| 741 + tmp[14] = ((u64) in[6]) * (in2[8] << 0) + |
| 742 + ((u64) in[7]) * (in2[7] << 1) + |
| 743 + ((u64) in[8]) * (in2[6] << 0); |
| 744 + tmp[15] = ((u64) in[7]) * (in2[8] << 0) + |
| 745 + ((u64) in[8]) * (in2[7] << 0); |
| 746 + tmp[16] = ((u64) in[8]) * (in2[8] << 0); |
| 747 + |
| 748 + felem_reduce_degree(out, tmp); |
| 749 +} |
| 750 + |
| 751 +static void felem_assign(felem out, const felem in) |
| 752 +{ |
| 753 + memcpy(out, in, sizeof(felem)); |
| 754 +} |
| 755 + |
| 756 +/* felem_inv calculates |out| = |in|^{-1} |
| 757 + * |
| 758 + * Based on Fermat's Little Theorem: |
| 759 + * a^p = a (mod p) |
| 760 + * a^{p-1} = 1 (mod p) |
| 761 + * a^{p-2} = a^{-1} (mod p) |
| 762 + */ |
| 763 +static void felem_inv(felem out, const felem in) |
| 764 +{ |
| 765 + felem ftmp, ftmp2; |
| 766 + /* each e_I will hold |in|^{2^I - 1} */ |
| 767 + felem e2, e4, e8, e16, e32, e64; |
| 768 + unsigned int i; |
| 769 + |
| 770 + felem_square(ftmp, in); /* 2^1 */ |
| 771 + felem_mul(ftmp, in, ftmp); /* 2^2 - 2^0 */ |
| 772 + felem_assign(e2, ftmp); |
| 773 + felem_square(ftmp, ftmp); /* 2^3 - 2^1 */ |
| 774 + felem_square(ftmp, ftmp); /* 2^4 - 2^2 */ |
| 775 + felem_mul(ftmp, ftmp, e2); /* 2^4 - 2^0 */ |
| 776 + felem_assign(e4, ftmp); |
| 777 + felem_square(ftmp, ftmp); /* 2^5 - 2^1 */ |
| 778 + felem_square(ftmp, ftmp); /* 2^6 - 2^2 */ |
| 779 + felem_square(ftmp, ftmp); /* 2^7 - 2^3 */ |
| 780 + felem_square(ftmp, ftmp); /* 2^8 - 2^4 */ |
| 781 + felem_mul(ftmp, ftmp, e4); /* 2^8 - 2^0 */ |
| 782 + felem_assign(e8, ftmp); |
| 783 + for (i = 0; i < 8; i++) { |
| 784 + felem_square(ftmp, ftmp); |
| 785 + } /* 2^16 - 2^8 */ |
| 786 + felem_mul(ftmp, ftmp, e8); /* 2^16 - 2^0 */ |
| 787 + felem_assign(e16, ftmp); |
| 788 + for (i = 0; i < 16; i++) { |
| 789 + felem_square(ftmp, ftmp); |
| 790 + } /* 2^32 - 2^16 */ |
| 791 + felem_mul(ftmp, ftmp, e16); /* 2^32 - 2^0 */ |
| 792 + felem_assign(e32, ftmp); |
| 793 + for (i = 0; i < 32; i++) { |
| 794 + felem_square(ftmp, ftmp); |
| 795 + } /* 2^64 - 2^32 */ |
| 796 + felem_assign(e64, ftmp); |
| 797 + felem_mul(ftmp, ftmp, in); /* 2^64 - 2^32 + 2^0 */ |
| 798 + for (i = 0; i < 192; i++) { |
| 799 + felem_square(ftmp, ftmp); |
| 800 + } /* 2^256 - 2^224 + 2^192 */ |
| 801 + |
| 802 + felem_mul(ftmp2, e64, e32); /* 2^64 - 2^0 */ |
| 803 + for (i = 0; i < 16; i++) { |
| 804 + felem_square(ftmp2, ftmp2); |
| 805 + } /* 2^80 - 2^16 */ |
| 806 + felem_mul(ftmp2, ftmp2, e16); /* 2^80 - 2^0 */ |
| 807 + for (i = 0; i < 8; i++) { |
| 808 + felem_square(ftmp2, ftmp2); |
| 809 + } /* 2^88 - 2^8 */ |
| 810 + felem_mul(ftmp2, ftmp2, e8); /* 2^88 - 2^0 */ |
| 811 + for (i = 0; i < 4; i++) { |
| 812 + felem_square(ftmp2, ftmp2); |
| 813 + } /* 2^92 - 2^4 */ |
| 814 + felem_mul(ftmp2, ftmp2, e4); /* 2^92 - 2^0 */ |
| 815 + felem_square(ftmp2, ftmp2); /* 2^93 - 2^1 */ |
| 816 + felem_square(ftmp2, ftmp2); /* 2^94 - 2^2 */ |
| 817 + felem_mul(ftmp2, ftmp2, e2); /* 2^94 - 2^0 */ |
| 818 + felem_square(ftmp2, ftmp2); /* 2^95 - 2^1 */ |
| 819 + felem_square(ftmp2, ftmp2); /* 2^96 - 2^2 */ |
| 820 + felem_mul(ftmp2, ftmp2, in); /* 2^96 - 3 */ |
| 821 + |
| 822 + felem_mul(out, ftmp2, ftmp); /* 2^256 - 2^224 + 2^192 + 2^96 - 3 */ |
| 823 +} |
| 824 + |
| 825 +/* felem_scalar_3 sets out=3*out. |
| 826 + * |
| 827 + * On entry: out[0,2,...] < 2**30, out[1,3,...] < 2**29. |
| 828 + * On exit: out[0,2,...] < 2**30, out[1,3,...] < 2**29. |
| 829 + */ |
| 830 +static void felem_scalar_3(felem out) |
| 831 +{ |
| 832 + limb carry = 0; |
| 833 + unsigned int i; |
| 834 + |
| 835 + for (i = 0;; i++) { |
| 836 + out[i] *= 3; |
| 837 + out[i] += carry; |
| 838 + carry = out[i] >> 29; |
| 839 + out[i] &= kBottom29Bits; |
| 840 + |
| 841 + i++; |
| 842 + if (i == NLIMBS) |
| 843 + break; |
| 844 + |
| 845 + out[i] *= 3; |
| 846 + out[i] += carry; |
| 847 + carry = out[i] >> 28; |
| 848 + out[i] &= kBottom28Bits; |
| 849 + } |
| 850 + |
| 851 + felem_reduce_carry(out, carry); |
| 852 +} |
| 853 + |
| 854 +/* felem_scalar_4 sets out=4*out. |
| 855 + * |
| 856 + * On entry: out[0,2,...] < 2**30, out[1,3,...] < 2**29. |
| 857 + * On exit: out[0,2,...] < 2**30, out[1,3,...] < 2**29. |
| 858 + */ |
| 859 +static void felem_scalar_4(felem out) |
| 860 +{ |
| 861 + limb carry = 0, next_carry; |
| 862 + unsigned int i; |
| 863 + |
| 864 + for (i = 0;; i++) { |
| 865 + next_carry = out[i] >> 27; |
| 866 + out[i] <<= 2; |
| 867 + out[i] &= kBottom29Bits; |
| 868 + out[i] += carry; |
| 869 + carry = next_carry + (out[i] >> 29); |
| 870 + out[i] &= kBottom29Bits; |
| 871 + |
| 872 + i++; |
| 873 + if (i == NLIMBS) |
| 874 + break; |
| 875 + next_carry = out[i] >> 26; |
| 876 + out[i] <<= 2; |
| 877 + out[i] &= kBottom28Bits; |
| 878 + out[i] += carry; |
| 879 + carry = next_carry + (out[i] >> 28); |
| 880 + out[i] &= kBottom28Bits; |
| 881 + } |
| 882 + |
| 883 + felem_reduce_carry(out, carry); |
| 884 +} |
| 885 + |
| 886 +/* felem_scalar_8 sets out=8*out. |
| 887 + * |
| 888 + * On entry: out[0,2,...] < 2**30, out[1,3,...] < 2**29. |
| 889 + * On exit: out[0,2,...] < 2**30, out[1,3,...] < 2**29. |
| 890 + */ |
| 891 +static void felem_scalar_8(felem out) |
| 892 +{ |
| 893 + limb carry = 0, next_carry; |
| 894 + unsigned int i; |
| 895 + |
| 896 + for (i = 0;; i++) { |
| 897 + next_carry = out[i] >> 26; |
| 898 + out[i] <<= 3; |
| 899 + out[i] &= kBottom29Bits; |
| 900 + out[i] += carry; |
| 901 + carry = next_carry + (out[i] >> 29); |
| 902 + out[i] &= kBottom29Bits; |
| 903 + |
| 904 + i++; |
| 905 + if (i == NLIMBS) |
| 906 + break; |
| 907 + next_carry = out[i] >> 25; |
| 908 + out[i] <<= 3; |
| 909 + out[i] &= kBottom28Bits; |
| 910 + out[i] += carry; |
| 911 + carry = next_carry + (out[i] >> 28); |
| 912 + out[i] &= kBottom28Bits; |
| 913 + } |
| 914 + |
| 915 + felem_reduce_carry(out, carry); |
| 916 +} |
| 917 + |
| 918 +/* felem_is_zero_vartime returns 1 iff |in| == 0. It takes a variable amount of |
| 919 + * time depending on the value of |in|. |
| 920 + */ |
| 921 +static char felem_is_zero_vartime(const felem in) |
| 922 +{ |
| 923 + limb carry; |
| 924 + int i; |
| 925 + limb tmp[NLIMBS]; |
| 926 + felem_assign(tmp, in); |
| 927 + |
| 928 + /* First, reduce tmp to a minimal form. |
| 929 + */ |
| 930 + do { |
| 931 + carry = 0; |
| 932 + for (i = 0;; i++) { |
| 933 + tmp[i] += carry; |
| 934 + carry = tmp[i] >> 29; |
| 935 + tmp[i] &= kBottom29Bits; |
| 936 + |
| 937 + i++; |
| 938 + if (i == NLIMBS) |
| 939 + break; |
| 940 + |
| 941 + tmp[i] += carry; |
| 942 + carry = tmp[i] >> 28; |
| 943 + tmp[i] &= kBottom28Bits; |
| 944 + } |
| 945 + |
| 946 + felem_reduce_carry(tmp, carry); |
| 947 + } while (carry); |
| 948 + |
| 949 + /* tmp < 2**257, so the only possible zero values are 0, p and 2p. |
| 950 + */ |
| 951 + return memcmp(tmp, kZero, sizeof(tmp)) == 0 || |
| 952 + memcmp(tmp, kP, sizeof(tmp)) == 0 || |
| 953 + memcmp(tmp, k2P, sizeof(tmp)) == 0; |
| 954 +} |
| 955 + |
| 956 +/* Group operations: |
| 957 + * |
| 958 + * Elements of the elliptic curve group are represented in Jacobian |
| 959 + * coordinates: (x, y, z). An affine point (x', y') is x'=x/z**2, y'=y/z**3 in |
| 960 + * Jacobian form. |
| 961 + */ |
| 962 + |
| 963 +/* point_double sets {x_out,y_out,z_out} = 2*{x,y,z}. |
| 964 + * |
| 965 + * See http://www.hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-0.html#doublin
g-dbl-2009-l |
| 966 + */ |
| 967 +static void point_double(felem x_out, felem y_out, felem z_out, |
| 968 + const felem x, const felem y, const felem z) |
| 969 +{ |
| 970 + felem delta, gamma, alpha, beta, tmp, tmp2; |
| 971 + |
| 972 + felem_square(delta, z); |
| 973 + felem_square(gamma, y); |
| 974 + felem_mul(beta, x, gamma); |
| 975 + |
| 976 + felem_sum(tmp, x, delta); |
| 977 + felem_diff(tmp2, x, delta); |
| 978 + felem_mul(alpha, tmp, tmp2); |
| 979 + felem_scalar_3(alpha); |
| 980 + |
| 981 + felem_sum(tmp, y, z); |
| 982 + felem_square(tmp, tmp); |
| 983 + felem_diff(tmp, tmp, gamma); |
| 984 + felem_diff(z_out, tmp, delta); |
| 985 + |
| 986 + felem_scalar_4(beta); |
| 987 + felem_square(x_out, alpha); |
| 988 + felem_diff(x_out, x_out, beta); |
| 989 + felem_diff(x_out, x_out, beta); |
| 990 + |
| 991 + felem_diff(tmp, beta, x_out); |
| 992 + felem_mul(tmp, alpha, tmp); |
| 993 + felem_square(tmp2, gamma); |
| 994 + felem_scalar_8(tmp2); |
| 995 + felem_diff(y_out, tmp, tmp2); |
| 996 +} |
| 997 + |
| 998 +/* point_add_mixed sets {x_out,y_out,z_out} = {x1,y1,z1} + {x2,y2,1}. |
| 999 + * (i.e. the second point is affine.) |
| 1000 + * |
| 1001 + * See http://www.hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-0.html#additio
n-add-2007-bl |
| 1002 + * |
| 1003 + * Note that this function does not handle P+P, infinity+P nor P+infinity |
| 1004 + * correctly. |
| 1005 + */ |
| 1006 +static void point_add_mixed(felem x_out, felem y_out, felem z_out, |
| 1007 + const felem x1, const felem y1, const felem z1, |
| 1008 + const felem x2, const felem y2) |
| 1009 +{ |
| 1010 + felem z1z1, z1z1z1, s2, u2, h, i, j, r, rr, v, tmp; |
| 1011 + |
| 1012 + felem_square(z1z1, z1); |
| 1013 + felem_sum(tmp, z1, z1); |
| 1014 + |
| 1015 + felem_mul(u2, x2, z1z1); |
| 1016 + felem_mul(z1z1z1, z1, z1z1); |
| 1017 + felem_mul(s2, y2, z1z1z1); |
| 1018 + felem_diff(h, u2, x1); |
| 1019 + felem_sum(i, h, h); |
| 1020 + felem_square(i, i); |
| 1021 + felem_mul(j, h, i); |
| 1022 + felem_diff(r, s2, y1); |
| 1023 + felem_sum(r, r, r); |
| 1024 + felem_mul(v, x1, i); |
| 1025 + |
| 1026 + felem_mul(z_out, tmp, h); |
| 1027 + felem_square(rr, r); |
| 1028 + felem_diff(x_out, rr, j); |
| 1029 + felem_diff(x_out, x_out, v); |
| 1030 + felem_diff(x_out, x_out, v); |
| 1031 + |
| 1032 + felem_diff(tmp, v, x_out); |
| 1033 + felem_mul(y_out, tmp, r); |
| 1034 + felem_mul(tmp, y1, j); |
| 1035 + felem_diff(y_out, y_out, tmp); |
| 1036 + felem_diff(y_out, y_out, tmp); |
| 1037 +} |
| 1038 + |
| 1039 +/* point_add sets {x_out,y_out,z_out} = {x1,y1,z1} + {x2,y2,z2}. |
| 1040 + * |
| 1041 + * See http://www.hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-0.html#additio
n-add-2007-bl |
| 1042 + * |
| 1043 + * Note that this function does not handle P+P, infinity+P nor P+infinity |
| 1044 + * correctly. |
| 1045 + */ |
| 1046 +static void point_add(felem x_out, felem y_out, felem z_out, |
| 1047 + const felem x1, const felem y1, const felem z1, |
| 1048 + const felem x2, const felem y2, const felem z2) |
| 1049 +{ |
| 1050 + felem z1z1, z1z1z1, z2z2, z2z2z2, s1, s2, u1, u2, h, i, j, r, rr, v, tmp; |
| 1051 + |
| 1052 + felem_square(z1z1, z1); |
| 1053 + felem_square(z2z2, z2); |
| 1054 + felem_mul(u1, x1, z2z2); |
| 1055 + |
| 1056 + felem_sum(tmp, z1, z2); |
| 1057 + felem_square(tmp, tmp); |
| 1058 + felem_diff(tmp, tmp, z1z1); |
| 1059 + felem_diff(tmp, tmp, z2z2); |
| 1060 + |
| 1061 + felem_mul(z2z2z2, z2, z2z2); |
| 1062 + felem_mul(s1, y1, z2z2z2); |
| 1063 + |
| 1064 + felem_mul(u2, x2, z1z1); |
| 1065 + felem_mul(z1z1z1, z1, z1z1); |
| 1066 + felem_mul(s2, y2, z1z1z1); |
| 1067 + felem_diff(h, u2, u1); |
| 1068 + felem_sum(i, h, h); |
| 1069 + felem_square(i, i); |
| 1070 + felem_mul(j, h, i); |
| 1071 + felem_diff(r, s2, s1); |
| 1072 + felem_sum(r, r, r); |
| 1073 + felem_mul(v, u1, i); |
| 1074 + |
| 1075 + felem_mul(z_out, tmp, h); |
| 1076 + felem_square(rr, r); |
| 1077 + felem_diff(x_out, rr, j); |
| 1078 + felem_diff(x_out, x_out, v); |
| 1079 + felem_diff(x_out, x_out, v); |
| 1080 + |
| 1081 + felem_diff(tmp, v, x_out); |
| 1082 + felem_mul(y_out, tmp, r); |
| 1083 + felem_mul(tmp, s1, j); |
| 1084 + felem_diff(y_out, y_out, tmp); |
| 1085 + felem_diff(y_out, y_out, tmp); |
| 1086 +} |
| 1087 + |
| 1088 +/* point_add_or_double_vartime sets {x_out,y_out,z_out} = {x1,y1,z1} + |
| 1089 + * {x2,y2,z2}. |
| 1090 + * |
| 1091 + * See http://www.hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-0.html#additio
n-add-2007-bl |
| 1092 + * |
| 1093 + * This function handles the case where {x1,y1,z1}={x2,y2,z2}. |
| 1094 + */ |
| 1095 +static void point_add_or_double_vartime( |
| 1096 + felem x_out, felem y_out, felem z_out, |
| 1097 + const felem x1, const felem y1, const felem z1, |
| 1098 + const felem x2, const felem y2, const felem z2) |
| 1099 +{ |
| 1100 + felem z1z1, z1z1z1, z2z2, z2z2z2, s1, s2, u1, u2, h, i, j, r, rr, v, tmp; |
| 1101 + char x_equal, y_equal; |
| 1102 + |
| 1103 + felem_square(z1z1, z1); |
| 1104 + felem_square(z2z2, z2); |
| 1105 + felem_mul(u1, x1, z2z2); |
| 1106 + |
| 1107 + felem_sum(tmp, z1, z2); |
| 1108 + felem_square(tmp, tmp); |
| 1109 + felem_diff(tmp, tmp, z1z1); |
| 1110 + felem_diff(tmp, tmp, z2z2); |
| 1111 + |
| 1112 + felem_mul(z2z2z2, z2, z2z2); |
| 1113 + felem_mul(s1, y1, z2z2z2); |
| 1114 + |
| 1115 + felem_mul(u2, x2, z1z1); |
| 1116 + felem_mul(z1z1z1, z1, z1z1); |
| 1117 + felem_mul(s2, y2, z1z1z1); |
| 1118 + felem_diff(h, u2, u1); |
| 1119 + x_equal = felem_is_zero_vartime(h); |
| 1120 + felem_sum(i, h, h); |
| 1121 + felem_square(i, i); |
| 1122 + felem_mul(j, h, i); |
| 1123 + felem_diff(r, s2, s1); |
| 1124 + y_equal = felem_is_zero_vartime(r); |
| 1125 + if (x_equal && y_equal) { |
| 1126 + point_double(x_out, y_out, z_out, x1, y1, z1); |
| 1127 + return; |
| 1128 + } |
| 1129 + felem_sum(r, r, r); |
| 1130 + felem_mul(v, u1, i); |
| 1131 + |
| 1132 + felem_mul(z_out, tmp, h); |
| 1133 + felem_square(rr, r); |
| 1134 + felem_diff(x_out, rr, j); |
| 1135 + felem_diff(x_out, x_out, v); |
| 1136 + felem_diff(x_out, x_out, v); |
| 1137 + |
| 1138 + felem_diff(tmp, v, x_out); |
| 1139 + felem_mul(y_out, tmp, r); |
| 1140 + felem_mul(tmp, s1, j); |
| 1141 + felem_diff(y_out, y_out, tmp); |
| 1142 + felem_diff(y_out, y_out, tmp); |
| 1143 +} |
| 1144 + |
| 1145 +/* copy_conditional sets out=in if mask = 0xffffffff in constant time. |
| 1146 + * |
| 1147 + * On entry: mask is either 0 or 0xffffffff. |
| 1148 + */ |
| 1149 +static void copy_conditional(felem out, const felem in, limb mask) |
| 1150 +{ |
| 1151 + int i; |
| 1152 + |
| 1153 + for (i = 0; i < NLIMBS; i++) { |
| 1154 + const limb tmp = mask & (in[i] ^ out[i]); |
| 1155 + out[i] ^= tmp; |
| 1156 + } |
| 1157 +} |
| 1158 + |
| 1159 +/* select_affine_point sets {out_x,out_y} to the index'th entry of table. |
| 1160 + * On entry: index < 16, table[0] must be zero. |
| 1161 + */ |
| 1162 +static void select_affine_point(felem out_x, felem out_y, |
| 1163 + const limb *table, limb index) |
| 1164 +{ |
| 1165 + limb i, j; |
| 1166 + |
| 1167 + memset(out_x, 0, sizeof(felem)); |
| 1168 + memset(out_y, 0, sizeof(felem)); |
| 1169 + |
| 1170 + for (i = 1; i < 16; i++) { |
| 1171 + limb mask = i ^ index; |
| 1172 + mask |= mask >> 2; |
| 1173 + mask |= mask >> 1; |
| 1174 + mask &= 1; |
| 1175 + mask--; |
| 1176 + for (j = 0; j < NLIMBS; j++, table++) { |
| 1177 + out_x[j] |= *table & mask; |
| 1178 + } |
| 1179 + for (j = 0; j < NLIMBS; j++, table++) { |
| 1180 + out_y[j] |= *table & mask; |
| 1181 + } |
| 1182 + } |
| 1183 +} |
| 1184 + |
| 1185 +/* select_jacobian_point sets {out_x,out_y,out_z} to the index'th entry of |
| 1186 + * table. On entry: index < 16, table[0] must be zero. |
| 1187 + */ |
| 1188 +static void select_jacobian_point(felem out_x, felem out_y, felem out_z, |
| 1189 + const limb *table, limb index) |
| 1190 +{ |
| 1191 + limb i, j; |
| 1192 + |
| 1193 + memset(out_x, 0, sizeof(felem)); |
| 1194 + memset(out_y, 0, sizeof(felem)); |
| 1195 + memset(out_z, 0, sizeof(felem)); |
| 1196 + |
| 1197 + /* The implicit value at index 0 is all zero. We don't need to perform that |
| 1198 + * iteration of the loop because we already set out_* to zero. |
| 1199 + */ |
| 1200 + table += 3*NLIMBS; |
| 1201 + |
| 1202 + for (i = 1; i < 16; i++) { |
| 1203 + limb mask = i ^ index; |
| 1204 + mask |= mask >> 2; |
| 1205 + mask |= mask >> 1; |
| 1206 + mask &= 1; |
| 1207 + mask--; |
| 1208 + for (j = 0; j < NLIMBS; j++, table++) { |
| 1209 + out_x[j] |= *table & mask; |
| 1210 + } |
| 1211 + for (j = 0; j < NLIMBS; j++, table++) { |
| 1212 + out_y[j] |= *table & mask; |
| 1213 + } |
| 1214 + for (j = 0; j < NLIMBS; j++, table++) { |
| 1215 + out_z[j] |= *table & mask; |
| 1216 + } |
| 1217 + } |
| 1218 +} |
| 1219 + |
| 1220 +/* get_bit returns the bit'th bit of scalar. */ |
| 1221 +static char get_bit(const u8 scalar[32], int bit) |
| 1222 +{ |
| 1223 + return ((scalar[bit >> 3]) >> (bit & 7)) & 1; |
| 1224 +} |
| 1225 + |
| 1226 +/* scalar_base_mult sets {nx,ny,nz} = scalar*G where scalar is a little-endian |
| 1227 + * number. Note that the value of scalar must be less than the order of the |
| 1228 + * group. |
| 1229 + */ |
| 1230 +static void scalar_base_mult(felem nx, felem ny, felem nz, const u8 scalar[32]) |
| 1231 +{ |
| 1232 + int i, j; |
| 1233 + limb n_is_infinity_mask = -1, p_is_noninfinite_mask, mask; |
| 1234 + u32 table_offset; |
| 1235 + |
| 1236 + felem px, py; |
| 1237 + felem tx, ty, tz; |
| 1238 + |
| 1239 + memset(nx, 0, sizeof(felem)); |
| 1240 + memset(ny, 0, sizeof(felem)); |
| 1241 + memset(nz, 0, sizeof(felem)); |
| 1242 + |
| 1243 + /* The loop adds bits at positions 0, 64, 128 and 192, followed by |
| 1244 + * positions 32,96,160 and 224 and does this 32 times. |
| 1245 + */ |
| 1246 + for (i = 0; i < 32; i++) { |
| 1247 + if (i) { |
| 1248 + point_double(nx, ny, nz, nx, ny, nz); |
| 1249 + } |
| 1250 + for (j = 0; j <= 32; j += 32) { |
| 1251 + char bit0 = get_bit(scalar, 31 - i + j); |
| 1252 + char bit1 = get_bit(scalar, 95 - i + j); |
| 1253 + char bit2 = get_bit(scalar, 159 - i + j); |
| 1254 + char bit3 = get_bit(scalar, 223 - i + j); |
| 1255 + limb index = bit0 | (bit1 << 1) | (bit2 << 2) | (bit3 << 3); |
| 1256 + |
| 1257 + table_offset = ((((s32)j) << (32-6)) >> 31) & (30*NLIMBS); |
| 1258 + select_affine_point(px, py, kPrecomputed + table_offset, index); |
| 1259 + |
| 1260 + /* Since scalar is less than the order of the group, we know that |
| 1261 + * {nx,ny,nz} != {px,py,1}, unless both are zero, which we handle |
| 1262 + * below. |
| 1263 + */ |
| 1264 + point_add_mixed(tx, ty, tz, nx, ny, nz, px, py); |
| 1265 + /* The result of point_add_mixed is incorrect if {nx,ny,nz} is zero |
| 1266 + * (a.k.a. the point at infinity). We handle that situation by |
| 1267 + * copying the point from the table. |
| 1268 + */ |
| 1269 + copy_conditional(nx, px, n_is_infinity_mask); |
| 1270 + copy_conditional(ny, py, n_is_infinity_mask); |
| 1271 + copy_conditional(nz, kOne, n_is_infinity_mask); |
| 1272 + |
| 1273 + /* Equally, the result is also wrong if the point from the table is |
| 1274 + * zero, which happens when the index is zero. We handle that by |
| 1275 + * only copying from {tx,ty,tz} to {nx,ny,nz} if index != 0. |
| 1276 + */ |
| 1277 + p_is_noninfinite_mask = NON_ZERO_TO_ALL_ONES(index); |
| 1278 + mask = p_is_noninfinite_mask & ~n_is_infinity_mask; |
| 1279 + copy_conditional(nx, tx, mask); |
| 1280 + copy_conditional(ny, ty, mask); |
| 1281 + copy_conditional(nz, tz, mask); |
| 1282 + /* If p was not zero, then n is now non-zero. */ |
| 1283 + n_is_infinity_mask &= ~p_is_noninfinite_mask; |
| 1284 + } |
| 1285 + } |
| 1286 +} |
| 1287 + |
| 1288 +/* point_to_affine converts a Jacobian point to an affine point. If the input |
| 1289 + * is the point at infinity then it returns (0, 0) in constant time. |
| 1290 + */ |
| 1291 +static void point_to_affine(felem x_out, felem y_out, |
| 1292 + const felem nx, const felem ny, const felem nz) { |
| 1293 + felem z_inv, z_inv_sq; |
| 1294 + felem_inv(z_inv, nz); |
| 1295 + felem_square(z_inv_sq, z_inv); |
| 1296 + felem_mul(x_out, nx, z_inv_sq); |
| 1297 + felem_mul(z_inv, z_inv, z_inv_sq); |
| 1298 + felem_mul(y_out, ny, z_inv); |
| 1299 +} |
| 1300 + |
| 1301 +/* scalar_mult sets {nx,ny,nz} = scalar*{x,y}. */ |
| 1302 +static void scalar_mult(felem nx, felem ny, felem nz, |
| 1303 + const felem x, const felem y, const u8 scalar[32]) |
| 1304 +{ |
| 1305 + int i; |
| 1306 + felem px, py, pz, tx, ty, tz; |
| 1307 + felem precomp[16][3]; |
| 1308 + limb n_is_infinity_mask, index, p_is_noninfinite_mask, mask; |
| 1309 + |
| 1310 + /* We precompute 0,1,2,... times {x,y}. */ |
| 1311 + memset(precomp, 0, sizeof(felem) * 3); |
| 1312 + memcpy(&precomp[1][0], x, sizeof(felem)); |
| 1313 + memcpy(&precomp[1][1], y, sizeof(felem)); |
| 1314 + memcpy(&precomp[1][2], kOne, sizeof(felem)); |
| 1315 + |
| 1316 + for (i = 2; i < 16; i += 2) { |
| 1317 + point_double(precomp[i][0], precomp[i][1], precomp[i][2], |
| 1318 + precomp[i / 2][0], precomp[i / 2][1], precomp[i / 2][2]); |
| 1319 + |
| 1320 + point_add_mixed(precomp[i + 1][0], precomp[i + 1][1], precomp[i + 1][2], |
| 1321 + precomp[i][0], precomp[i][1], precomp[i][2], x, y); |
| 1322 + } |
| 1323 + |
| 1324 + memset(nx, 0, sizeof(felem)); |
| 1325 + memset(ny, 0, sizeof(felem)); |
| 1326 + memset(nz, 0, sizeof(felem)); |
| 1327 + n_is_infinity_mask = -1; |
| 1328 + |
| 1329 + /* We add in a window of four bits each iteration and do this 64 times. */ |
| 1330 + for (i = 0; i < 64; i++) { |
| 1331 + if (i) { |
| 1332 + point_double(nx, ny, nz, nx, ny, nz); |
| 1333 + point_double(nx, ny, nz, nx, ny, nz); |
| 1334 + point_double(nx, ny, nz, nx, ny, nz); |
| 1335 + point_double(nx, ny, nz, nx, ny, nz); |
| 1336 + } |
| 1337 + |
| 1338 + index = scalar[31 - i / 2]; |
| 1339 + if ((i & 1) == 1) { |
| 1340 + index &= 15; |
| 1341 + } else { |
| 1342 + index >>= 4; |
| 1343 + } |
| 1344 + |
| 1345 + /* See the comments in scalar_base_mult about handling infinities. */ |
| 1346 + select_jacobian_point(px, py, pz, (limb *) precomp, index); |
| 1347 + point_add(tx, ty, tz, nx, ny, nz, px, py, pz); |
| 1348 + copy_conditional(nx, px, n_is_infinity_mask); |
| 1349 + copy_conditional(ny, py, n_is_infinity_mask); |
| 1350 + copy_conditional(nz, pz, n_is_infinity_mask); |
| 1351 + |
| 1352 + p_is_noninfinite_mask = ((s32) ~ (index - 1)) >> 31; |
| 1353 + mask = p_is_noninfinite_mask & ~n_is_infinity_mask; |
| 1354 + copy_conditional(nx, tx, mask); |
| 1355 + copy_conditional(ny, ty, mask); |
| 1356 + copy_conditional(nz, tz, mask); |
| 1357 + n_is_infinity_mask &= ~p_is_noninfinite_mask; |
| 1358 + } |
| 1359 +} |
| 1360 + |
| 1361 +/* Interface with Freebl: */ |
| 1362 + |
| 1363 +#ifdef IS_BIG_ENDIAN |
| 1364 +#error "This code needs a little-endian processor" |
| 1365 +#endif |
| 1366 + |
| 1367 +static const u32 kRInvDigits[8] = { |
| 1368 + 0x80000000, 1, 0xffffffff, 0, |
| 1369 + 0x80000001, 0xfffffffe, 1, 0x7fffffff |
| 1370 +}; |
| 1371 +#define MP_DIGITS_IN_256_BITS (32/sizeof(mp_digit)) |
| 1372 +static const mp_int kRInv = { |
| 1373 + MP_ZPOS, |
| 1374 + MP_DIGITS_IN_256_BITS, |
| 1375 + MP_DIGITS_IN_256_BITS, |
| 1376 + /* Because we are running on a little-endian processor, this cast works for |
| 1377 + * both 32 and 64-bit processors. |
| 1378 + */ |
| 1379 + (mp_digit*) kRInvDigits |
| 1380 +}; |
| 1381 + |
| 1382 +static const limb kTwo28 = 0x10000000; |
| 1383 +static const limb kTwo29 = 0x20000000; |
| 1384 + |
| 1385 +/* to_montgomery sets out = R*in. */ |
| 1386 +static mp_err to_montgomery(felem out, const mp_int *in, const ECGroup *group) |
| 1387 +{ |
| 1388 + /* There are no MPI functions for bitshift operations and we wish to shift |
| 1389 + * in 257 bits left so we move the digits 256-bits left and then multiply |
| 1390 + * by two. |
| 1391 + */ |
| 1392 + mp_int in_shifted; |
| 1393 + int i; |
| 1394 + mp_err res; |
| 1395 + |
| 1396 + mp_init(&in_shifted); |
| 1397 + s_mp_pad(&in_shifted, MP_USED(in) + MP_DIGITS_IN_256_BITS); |
| 1398 + memcpy(&MP_DIGIT(&in_shifted, MP_DIGITS_IN_256_BITS), |
| 1399 + MP_DIGITS(in), |
| 1400 + MP_USED(in)*sizeof(mp_digit)); |
| 1401 + mp_mul_2(&in_shifted, &in_shifted); |
| 1402 + MP_CHECKOK(group->meth->field_mod(&in_shifted, &in_shifted, group->meth)); |
| 1403 + |
| 1404 + for (i = 0;; i++) { |
| 1405 + out[i] = MP_DIGIT(&in_shifted, 0) & kBottom29Bits; |
| 1406 + mp_div_d(&in_shifted, kTwo29, &in_shifted, NULL); |
| 1407 + |
| 1408 + i++; |
| 1409 + if (i == NLIMBS) |
| 1410 + break; |
| 1411 + out[i] = MP_DIGIT(&in_shifted, 0) & kBottom28Bits; |
| 1412 + mp_div_d(&in_shifted, kTwo28, &in_shifted, NULL); |
| 1413 + } |
| 1414 + |
| 1415 +CLEANUP: |
| 1416 + mp_clear(&in_shifted); |
| 1417 + return res; |
| 1418 +} |
| 1419 + |
| 1420 +/* from_montgomery sets out=in/R. */ |
| 1421 +static mp_err from_montgomery(mp_int *out, const felem in, |
| 1422 + const ECGroup *group) |
| 1423 +{ |
| 1424 + mp_int result, tmp; |
| 1425 + mp_err res; |
| 1426 + int i; |
| 1427 + |
| 1428 + mp_init(&result); |
| 1429 + mp_init(&tmp); |
| 1430 + |
| 1431 + MP_CHECKOK(mp_add_d(&tmp, in[NLIMBS-1], &result)); |
| 1432 + for (i = NLIMBS-2; i >= 0; i--) { |
| 1433 + if ((i & 1) == 0) { |
| 1434 + MP_CHECKOK(mp_mul_d(&result, kTwo29, &tmp)); |
| 1435 + } else { |
| 1436 + MP_CHECKOK(mp_mul_d(&result, kTwo28, &tmp)); |
| 1437 + } |
| 1438 + MP_CHECKOK(mp_add_d(&tmp, in[i], &result)); |
| 1439 + } |
| 1440 + |
| 1441 + MP_CHECKOK(mp_mul(&result, &kRInv, out)); |
| 1442 + MP_CHECKOK(group->meth->field_mod(out, out, group->meth)); |
| 1443 + |
| 1444 +CLEANUP: |
| 1445 + mp_clear(&result); |
| 1446 + mp_clear(&tmp); |
| 1447 + return res; |
| 1448 +} |
| 1449 + |
| 1450 +/* scalar_from_mp_int sets out_scalar=n, where n < the group order. */ |
| 1451 +static void scalar_from_mp_int(u8 out_scalar[32], const mp_int *n) |
| 1452 +{ |
| 1453 + /* We require that |n| is less than the order of the group and therefore it |
| 1454 + * will fit into |scalar|. However, these is a timing side-channel here tha
t |
| 1455 + * we cannot avoid: if |n| is sufficiently small it may be one or more word
s |
| 1456 + * too short and we'll copy less data. |
| 1457 + */ |
| 1458 + memset(out_scalar, 0, 32); |
| 1459 + memcpy(out_scalar, MP_DIGITS(n), MP_USED(n) * sizeof(mp_digit)); |
| 1460 +} |
| 1461 + |
| 1462 +/* ec_GFp_nistp256_base_point_mul sets {out_x,out_y} = nG, where n is < the |
| 1463 + * order of the group. |
| 1464 + */ |
| 1465 +mp_err ec_GFp_nistp256_base_point_mul(const mp_int *n, |
| 1466 + mp_int *out_x, mp_int *out_y, |
| 1467 + const ECGroup *group) |
| 1468 +{ |
| 1469 + u8 scalar[32]; |
| 1470 + felem x, y, z, x_affine, y_affine; |
| 1471 + mp_err res; |
| 1472 + |
| 1473 + /* FIXME(agl): test that n < order. */ |
| 1474 + |
| 1475 + scalar_from_mp_int(scalar, n); |
| 1476 + scalar_base_mult(x, y, z, scalar); |
| 1477 + point_to_affine(x_affine, y_affine, x, y, z); |
| 1478 + MP_CHECKOK(from_montgomery(out_x, x_affine, group)); |
| 1479 + MP_CHECKOK(from_montgomery(out_y, y_affine, group)); |
| 1480 + |
| 1481 +CLEANUP: |
| 1482 + return res; |
| 1483 +} |
| 1484 + |
| 1485 +/* ec_GFp_nistp256_point_mul sets {out_x,out_y} = n*{in_x,in_y}, where n is < |
| 1486 + * the order of the group. |
| 1487 + */ |
| 1488 +mp_err ec_GFp_nistp256_point_mul(const mp_int *n, |
| 1489 + const mp_int *in_x, const mp_int *in_y, |
| 1490 + mp_int *out_x, mp_int *out_y, |
| 1491 + const ECGroup *group) |
| 1492 +{ |
| 1493 + u8 scalar[32]; |
| 1494 + felem x, y, z, x_affine, y_affine, px, py; |
| 1495 + mp_err res; |
| 1496 + |
| 1497 + scalar_from_mp_int(scalar, n); |
| 1498 + |
| 1499 + MP_CHECKOK(to_montgomery(px, in_x, group)); |
| 1500 + MP_CHECKOK(to_montgomery(py, in_y, group)); |
| 1501 + |
| 1502 + scalar_mult(x, y, z, px, py, scalar); |
| 1503 + point_to_affine(x_affine, y_affine, x, y, z); |
| 1504 + MP_CHECKOK(from_montgomery(out_x, x_affine, group)); |
| 1505 + MP_CHECKOK(from_montgomery(out_y, y_affine, group)); |
| 1506 + |
| 1507 +CLEANUP: |
| 1508 + return res; |
| 1509 +} |
| 1510 + |
| 1511 +/* ec_GFp_nistp256_point_mul_vartime sets {out_x,out_y} = n1*G + |
| 1512 + * n2*{in_x,in_y}, where n1 and n2 are < the order of the group. |
| 1513 + * |
| 1514 + * As indicated by the name, this function operates in variable time. This |
| 1515 + * is safe because it's used for signature validation which doesn't deal |
| 1516 + * with secrets. |
| 1517 + */ |
| 1518 +mp_err ec_GFp_nistp256_points_mul_vartime( |
| 1519 + const mp_int *n1, const mp_int *n2, |
| 1520 + const mp_int *in_x, const mp_int *in_y, |
| 1521 + mp_int *out_x, mp_int *out_y, |
| 1522 + const ECGroup *group) |
| 1523 +{ |
| 1524 + u8 scalar1[32], scalar2[32]; |
| 1525 + felem x1, y1, z1, x2, y2, z2, x_affine, y_affine, px, py; |
| 1526 + mp_err res = MP_OKAY; |
| 1527 + |
| 1528 + /* If n2 == NULL, this is just a base-point multiplication. */ |
| 1529 + if (n2 == NULL) { |
| 1530 + return ec_GFp_nistp256_base_point_mul(n1, out_x, out_y, group); |
| 1531 + } |
| 1532 + |
| 1533 + /* If n1 == nULL, this is just an arbitary-point multiplication. */ |
| 1534 + if (n1 == NULL) { |
| 1535 + return ec_GFp_nistp256_point_mul(n2, in_x, in_y, out_x, out_y, group); |
| 1536 + } |
| 1537 + |
| 1538 + /* If both scalars are zero, then the result is the point at infinity. */ |
| 1539 + if (mp_cmp_z(n1) == 0 && mp_cmp_z(n2) == 0) { |
| 1540 + mp_zero(out_x); |
| 1541 + mp_zero(out_y); |
| 1542 + return res; |
| 1543 + } |
| 1544 + |
| 1545 + scalar_from_mp_int(scalar1, n1); |
| 1546 + scalar_from_mp_int(scalar2, n2); |
| 1547 + |
| 1548 + MP_CHECKOK(to_montgomery(px, in_x, group)); |
| 1549 + MP_CHECKOK(to_montgomery(py, in_y, group)); |
| 1550 + scalar_base_mult(x1, y1, z1, scalar1); |
| 1551 + scalar_mult(x2, y2, z2, px, py, scalar2); |
| 1552 + |
| 1553 + if (mp_cmp_z(n2) == 0) { |
| 1554 + /* If n2 == 0, then {x2,y2,z2} is zero and the result is just |
| 1555 + * {x1,y1,z1}. */ |
| 1556 + } else if (mp_cmp_z(n1) == 0) { |
| 1557 + /* If n1 == 0, then {x1,y1,z1} is zero and the result is just |
| 1558 + * {x2,y2,z2}. */ |
| 1559 + memcpy(x1, x2, sizeof(x2)); |
| 1560 + memcpy(y1, y2, sizeof(y2)); |
| 1561 + memcpy(z1, z2, sizeof(z2)); |
| 1562 + } else { |
| 1563 + /* This function handles the case where {x1,y1,z1} == {x2,y2,z2}. */ |
| 1564 + point_add_or_double_vartime(x1, y1, z1, x1, y1, z1, x2, y2, z2); |
| 1565 + } |
| 1566 + |
| 1567 + point_to_affine(x_affine, y_affine, x1, y1, z1); |
| 1568 + MP_CHECKOK(from_montgomery(out_x, x_affine, group)); |
| 1569 + MP_CHECKOK(from_montgomery(out_y, y_affine, group)); |
| 1570 + |
| 1571 +CLEANUP: |
| 1572 + return res; |
| 1573 +} |
| OLD | NEW |
|---|
Chromium Code Reviews
Issue 12042100:
Add an optimized 32-bit implementation of the NIST P-256 elliptic curve. (Closed)
Base URL: svn://svn.chromium.org/chrome/trunk/deps/third_party/nss/