diff options
Diffstat (limited to 'crypto/ec/ecp_nistp224.c')
| -rw-r--r-- | crypto/ec/ecp_nistp224.c | 2921 |
1 files changed, 1507 insertions, 1414 deletions
diff --git a/crypto/ec/ecp_nistp224.c b/crypto/ec/ecp_nistp224.c index d2d225c75e..de7a25b3f0 100644 --- a/crypto/ec/ecp_nistp224.c +++ b/crypto/ec/ecp_nistp224.c @@ -28,23 +28,23 @@ #include <openssl/opensslconf.h> #ifndef OPENSSL_NO_EC_NISTP_64_GCC_128 -#include <stdint.h> -#include <string.h> -#include <openssl/err.h> -#include "ec_lcl.h" +# include <stdint.h> +# include <string.h> +# include <openssl/err.h> +# include "ec_lcl.h" -#if defined(__GNUC__) && (__GNUC__ > 3 || (__GNUC__ == 3 && __GNUC_MINOR__ >= 1)) +# if defined(__GNUC__) && (__GNUC__ > 3 || (__GNUC__ == 3 && __GNUC_MINOR__ >= 1)) /* even with gcc, the typedef won't work for 32-bit platforms */ - typedef __uint128_t uint128_t; /* nonstandard; implemented by gcc on 64-bit platforms */ -#else - #error "Need GCC 3.1 or later to define type uint128_t" -#endif +typedef __uint128_t uint128_t; /* nonstandard; implemented by gcc on 64-bit + * platforms */ +# else +# error "Need GCC 3.1 or later to define type uint128_t" +# endif typedef uint8_t u8; typedef uint64_t u64; typedef int64_t s64; - /******************************************************************************/ /*- * INTERNAL REPRESENTATION OF FIELD ELEMENTS @@ -71,28 +71,29 @@ typedef uint128_t widelimb; typedef limb felem[4]; typedef widelimb widefelem[7]; -/* Field element represented as a byte arrary. - * 28*8 = 224 bits is also the group order size for the elliptic curve, - * and we also use this type for scalars for point multiplication. - */ +/* + * Field element represented as a byte arrary. 28*8 = 224 bits is also the + * group order size for the elliptic curve, and we also use this type for + * scalars for point multiplication. + */ typedef u8 felem_bytearray[28]; static const felem_bytearray nistp224_curve_params[5] = { - {0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* p */ - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x01}, - {0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* a */ - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFE,0xFF,0xFF,0xFF,0xFF, - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFE}, - {0xB4,0x05,0x0A,0x85,0x0C,0x04,0xB3,0xAB,0xF5,0x41, /* b */ - 0x32,0x56,0x50,0x44,0xB0,0xB7,0xD7,0xBF,0xD8,0xBA, - 0x27,0x0B,0x39,0x43,0x23,0x55,0xFF,0xB4}, - {0xB7,0x0E,0x0C,0xBD,0x6B,0xB4,0xBF,0x7F,0x32,0x13, /* x */ - 0x90,0xB9,0x4A,0x03,0xC1,0xD3,0x56,0xC2,0x11,0x22, - 0x34,0x32,0x80,0xD6,0x11,0x5C,0x1D,0x21}, - {0xbd,0x37,0x63,0x88,0xb5,0xf7,0x23,0xfb,0x4c,0x22, /* y */ - 0xdf,0xe6,0xcd,0x43,0x75,0xa0,0x5a,0x07,0x47,0x64, - 0x44,0xd5,0x81,0x99,0x85,0x00,0x7e,0x34} + {0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* p */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01}, + {0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* a */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFE}, + {0xB4, 0x05, 0x0A, 0x85, 0x0C, 0x04, 0xB3, 0xAB, 0xF5, 0x41, /* b */ + 0x32, 0x56, 0x50, 0x44, 0xB0, 0xB7, 0xD7, 0xBF, 0xD8, 0xBA, + 0x27, 0x0B, 0x39, 0x43, 0x23, 0x55, 0xFF, 0xB4}, + {0xB7, 0x0E, 0x0C, 0xBD, 0x6B, 0xB4, 0xBF, 0x7F, 0x32, 0x13, /* x */ + 0x90, 0xB9, 0x4A, 0x03, 0xC1, 0xD3, 0x56, 0xC2, 0x11, 0x22, + 0x34, 0x32, 0x80, 0xD6, 0x11, 0x5C, 0x1D, 0x21}, + {0xbd, 0x37, 0x63, 0x88, 0xb5, 0xf7, 0x23, 0xfb, 0x4c, 0x22, /* y */ + 0xdf, 0xe6, 0xcd, 0x43, 0x75, 0xa0, 0x5a, 0x07, 0x47, 0x64, + 0x44, 0xd5, 0x81, 0x99, 0x85, 0x00, 0x7e, 0x34} }; /*- @@ -126,223 +127,253 @@ static const felem_bytearray nistp224_curve_params[5] = { * locations when doing simple scalar multiplies against the base point, * and then another four locations using the second 16 elements. */ -static const felem gmul[2][16][3] = -{{{{0, 0, 0, 0}, - {0, 0, 0, 0}, - {0, 0, 0, 0}}, - {{0x3280d6115c1d21, 0xc1d356c2112234, 0x7f321390b94a03, 0xb70e0cbd6bb4bf}, - {0xd5819985007e34, 0x75a05a07476444, 0xfb4c22dfe6cd43, 0xbd376388b5f723}, - {1, 0, 0, 0}}, - {{0xfd9675666ebbe9, 0xbca7664d40ce5e, 0x2242df8d8a2a43, 0x1f49bbb0f99bc5}, - {0x29e0b892dc9c43, 0xece8608436e662, 0xdc858f185310d0, 0x9812dd4eb8d321}, - {1, 0, 0, 0}}, - {{0x6d3e678d5d8eb8, 0x559eed1cb362f1, 0x16e9a3bbce8a3f, 0xeedcccd8c2a748}, - {0xf19f90ed50266d, 0xabf2b4bf65f9df, 0x313865468fafec, 0x5cb379ba910a17}, - {1, 0, 0, 0}}, - {{0x0641966cab26e3, 0x91fb2991fab0a0, 0xefec27a4e13a0b, 0x0499aa8a5f8ebe}, - {0x7510407766af5d, 0x84d929610d5450, 0x81d77aae82f706, 0x6916f6d4338c5b}, - {1, 0, 0, 0}}, - {{0xea95ac3b1f15c6, 0x086000905e82d4, 0xdd323ae4d1c8b1, 0x932b56be7685a3}, - {0x9ef93dea25dbbf, 0x41665960f390f0, 0xfdec76dbe2a8a7, 0x523e80f019062a}, - {1, 0, 0, 0}}, - {{0x822fdd26732c73, 0xa01c83531b5d0f, 0x363f37347c1ba4, 0xc391b45c84725c}, - {0xbbd5e1b2d6ad24, 0xddfbcde19dfaec, 0xc393da7e222a7f, 0x1efb7890ede244}, - {1, 0, 0, 0}}, - {{0x4c9e90ca217da1, 0xd11beca79159bb, 0xff8d33c2c98b7c, 0x2610b39409f849}, - {0x44d1352ac64da0, 0xcdbb7b2c46b4fb, 0x966c079b753c89, 0xfe67e4e820b112}, - {1, 0, 0, 0}}, - {{0xe28cae2df5312d, 0xc71b61d16f5c6e, 0x79b7619a3e7c4c, 0x05c73240899b47}, - {0x9f7f6382c73e3a, 0x18615165c56bda, 0x641fab2116fd56, 0x72855882b08394}, - {1, 0, 0, 0}}, - {{0x0469182f161c09, 0x74a98ca8d00fb5, 0xb89da93489a3e0, 0x41c98768fb0c1d}, - {0xe5ea05fb32da81, 0x3dce9ffbca6855, 0x1cfe2d3fbf59e6, 0x0e5e03408738a7}, - {1, 0, 0, 0}}, - {{0xdab22b2333e87f, 0x4430137a5dd2f6, 0xe03ab9f738beb8, 0xcb0c5d0dc34f24}, - {0x764a7df0c8fda5, 0x185ba5c3fa2044, 0x9281d688bcbe50, 0xc40331df893881}, - {1, 0, 0, 0}}, - {{0xb89530796f0f60, 0xade92bd26909a3, 0x1a0c83fb4884da, 0x1765bf22a5a984}, - {0x772a9ee75db09e, 0x23bc6c67cec16f, 0x4c1edba8b14e2f, 0xe2a215d9611369}, - {1, 0, 0, 0}}, - {{0x571e509fb5efb3, 0xade88696410552, 0xc8ae85fada74fe, 0x6c7e4be83bbde3}, - {0xff9f51160f4652, 0xb47ce2495a6539, 0xa2946c53b582f4, 0x286d2db3ee9a60}, - {1, 0, 0, 0}}, - {{0x40bbd5081a44af, 0x0995183b13926c, 0xbcefba6f47f6d0, 0x215619e9cc0057}, - {0x8bc94d3b0df45e, 0xf11c54a3694f6f, 0x8631b93cdfe8b5, 0xe7e3f4b0982db9}, - {1, 0, 0, 0}}, - {{0xb17048ab3e1c7b, 0xac38f36ff8a1d8, 0x1c29819435d2c6, 0xc813132f4c07e9}, - {0x2891425503b11f, 0x08781030579fea, 0xf5426ba5cc9674, 0x1e28ebf18562bc}, - {1, 0, 0, 0}}, - {{0x9f31997cc864eb, 0x06cd91d28b5e4c, 0xff17036691a973, 0xf1aef351497c58}, - {0xdd1f2d600564ff, 0xdead073b1402db, 0x74a684435bd693, 0xeea7471f962558}, - {1, 0, 0, 0}}}, - {{{0, 0, 0, 0}, - {0, 0, 0, 0}, - {0, 0, 0, 0}}, - {{0x9665266dddf554, 0x9613d78b60ef2d, 0xce27a34cdba417, 0xd35ab74d6afc31}, - {0x85ccdd22deb15e, 0x2137e5783a6aab, 0xa141cffd8c93c6, 0x355a1830e90f2d}, - {1, 0, 0, 0}}, - {{0x1a494eadaade65, 0xd6da4da77fe53c, 0xe7992996abec86, 0x65c3553c6090e3}, - {0xfa610b1fb09346, 0xf1c6540b8a4aaf, 0xc51a13ccd3cbab, 0x02995b1b18c28a}, - {1, 0, 0, 0}}, - {{0x7874568e7295ef, 0x86b419fbe38d04, 0xdc0690a7550d9a, 0xd3966a44beac33}, - {0x2b7280ec29132f, 0xbeaa3b6a032df3, 0xdc7dd88ae41200, 0xd25e2513e3a100}, - {1, 0, 0, 0}}, - {{0x924857eb2efafd, 0xac2bce41223190, 0x8edaa1445553fc, 0x825800fd3562d5}, - {0x8d79148ea96621, 0x23a01c3dd9ed8d, 0xaf8b219f9416b5, 0xd8db0cc277daea}, - {1, 0, 0, 0}}, - {{0x76a9c3b1a700f0, 0xe9acd29bc7e691, 0x69212d1a6b0327, 0x6322e97fe154be}, - {0x469fc5465d62aa, 0x8d41ed18883b05, 0x1f8eae66c52b88, 0xe4fcbe9325be51}, - {1, 0, 0, 0}}, - {{0x825fdf583cac16, 0x020b857c7b023a, 0x683c17744b0165, 0x14ffd0a2daf2f1}, - {0x323b36184218f9, 0x4944ec4e3b47d4, 0xc15b3080841acf, 0x0bced4b01a28bb}, - {1, 0, 0, 0}}, - {{0x92ac22230df5c4, 0x52f33b4063eda8, 0xcb3f19870c0c93, 0x40064f2ba65233}, - {0xfe16f0924f8992, 0x012da25af5b517, 0x1a57bb24f723a6, 0x06f8bc76760def}, - {1, 0, 0, 0}}, - {{0x4a7084f7817cb9, 0xbcab0738ee9a78, 0x3ec11e11d9c326, 0xdc0fe90e0f1aae}, - {0xcf639ea5f98390, 0x5c350aa22ffb74, 0x9afae98a4047b7, 0x956ec2d617fc45}, - {1, 0, 0, 0}}, - {{0x4306d648c1be6a, 0x9247cd8bc9a462, 0xf5595e377d2f2e, 0xbd1c3caff1a52e}, - {0x045e14472409d0, 0x29f3e17078f773, 0x745a602b2d4f7d, 0x191837685cdfbb}, - {1, 0, 0, 0}}, - {{0x5b6ee254a8cb79, 0x4953433f5e7026, 0xe21faeb1d1def4, 0xc4c225785c09de}, - {0x307ce7bba1e518, 0x31b125b1036db8, 0x47e91868839e8f, 0xc765866e33b9f3}, - {1, 0, 0, 0}}, - {{0x3bfece24f96906, 0x4794da641e5093, 0xde5df64f95db26, 0x297ecd89714b05}, - {0x701bd3ebb2c3aa, 0x7073b4f53cb1d5, 0x13c5665658af16, 0x9895089d66fe58}, - {1, 0, 0, 0}}, - {{0x0fef05f78c4790, 0x2d773633b05d2e, 0x94229c3a951c94, 0xbbbd70df4911bb}, - {0xb2c6963d2c1168, 0x105f47a72b0d73, 0x9fdf6111614080, 0x7b7e94b39e67b0}, - {1, 0, 0, 0}}, - {{0xad1a7d6efbe2b3, 0xf012482c0da69d, 0x6b3bdf12438345, 0x40d7558d7aa4d9}, - {0x8a09fffb5c6d3d, 0x9a356e5d9ffd38, 0x5973f15f4f9b1c, 0xdcd5f59f63c3ea}, - {1, 0, 0, 0}}, - {{0xacf39f4c5ca7ab, 0x4c8071cc5fd737, 0xc64e3602cd1184, 0x0acd4644c9abba}, - {0x6c011a36d8bf6e, 0xfecd87ba24e32a, 0x19f6f56574fad8, 0x050b204ced9405}, - {1, 0, 0, 0}}, - {{0xed4f1cae7d9a96, 0x5ceef7ad94c40a, 0x778e4a3bf3ef9b, 0x7405783dc3b55e}, - {0x32477c61b6e8c6, 0xb46a97570f018b, 0x91176d0a7e95d1, 0x3df90fbc4c7d0e}, - {1, 0, 0, 0}}}}; +static const felem gmul[2][16][3] = { {{{0, 0, 0, 0}, + {0, 0, 0, 0}, + {0, 0, 0, 0}}, + {{0x3280d6115c1d21, 0xc1d356c2112234, + 0x7f321390b94a03, 0xb70e0cbd6bb4bf}, + {0xd5819985007e34, 0x75a05a07476444, + 0xfb4c22dfe6cd43, 0xbd376388b5f723}, + {1, 0, 0, 0}}, + {{0xfd9675666ebbe9, 0xbca7664d40ce5e, + 0x2242df8d8a2a43, 0x1f49bbb0f99bc5}, + {0x29e0b892dc9c43, 0xece8608436e662, + 0xdc858f185310d0, 0x9812dd4eb8d321}, + {1, 0, 0, 0}}, + {{0x6d3e678d5d8eb8, 0x559eed1cb362f1, + 0x16e9a3bbce8a3f, 0xeedcccd8c2a748}, + {0xf19f90ed50266d, 0xabf2b4bf65f9df, + 0x313865468fafec, 0x5cb379ba910a17}, + {1, 0, 0, 0}}, + {{0x0641966cab26e3, 0x91fb2991fab0a0, + 0xefec27a4e13a0b, 0x0499aa8a5f8ebe}, + {0x7510407766af5d, 0x84d929610d5450, + 0x81d77aae82f706, 0x6916f6d4338c5b}, + {1, 0, 0, 0}}, + {{0xea95ac3b1f15c6, 0x086000905e82d4, + 0xdd323ae4d1c8b1, 0x932b56be7685a3}, + {0x9ef93dea25dbbf, 0x41665960f390f0, + 0xfdec76dbe2a8a7, 0x523e80f019062a}, + {1, 0, 0, 0}}, + {{0x822fdd26732c73, 0xa01c83531b5d0f, + 0x363f37347c1ba4, 0xc391b45c84725c}, + {0xbbd5e1b2d6ad24, 0xddfbcde19dfaec, + 0xc393da7e222a7f, 0x1efb7890ede244}, + {1, 0, 0, 0}}, + {{0x4c9e90ca217da1, 0xd11beca79159bb, + 0xff8d33c2c98b7c, 0x2610b39409f849}, + {0x44d1352ac64da0, 0xcdbb7b2c46b4fb, + 0x966c079b753c89, 0xfe67e4e820b112}, + {1, 0, 0, 0}}, + {{0xe28cae2df5312d, 0xc71b61d16f5c6e, + 0x79b7619a3e7c4c, 0x05c73240899b47}, + {0x9f7f6382c73e3a, 0x18615165c56bda, + 0x641fab2116fd56, 0x72855882b08394}, + {1, 0, 0, 0}}, + {{0x0469182f161c09, 0x74a98ca8d00fb5, + 0xb89da93489a3e0, 0x41c98768fb0c1d}, + {0xe5ea05fb32da81, 0x3dce9ffbca6855, + 0x1cfe2d3fbf59e6, 0x0e5e03408738a7}, + {1, 0, 0, 0}}, + {{0xdab22b2333e87f, 0x4430137a5dd2f6, + 0xe03ab9f738beb8, 0xcb0c5d0dc34f24}, + {0x764a7df0c8fda5, 0x185ba5c3fa2044, + 0x9281d688bcbe50, 0xc40331df893881}, + {1, 0, 0, 0}}, + {{0xb89530796f0f60, 0xade92bd26909a3, + 0x1a0c83fb4884da, 0x1765bf22a5a984}, + {0x772a9ee75db09e, 0x23bc6c67cec16f, + 0x4c1edba8b14e2f, 0xe2a215d9611369}, + {1, 0, 0, 0}}, + {{0x571e509fb5efb3, 0xade88696410552, + 0xc8ae85fada74fe, 0x6c7e4be83bbde3}, + {0xff9f51160f4652, 0xb47ce2495a6539, + 0xa2946c53b582f4, 0x286d2db3ee9a60}, + {1, 0, 0, 0}}, + {{0x40bbd5081a44af, 0x0995183b13926c, + 0xbcefba6f47f6d0, 0x215619e9cc0057}, + {0x8bc94d3b0df45e, 0xf11c54a3694f6f, + 0x8631b93cdfe8b5, 0xe7e3f4b0982db9}, + {1, 0, 0, 0}}, + {{0xb17048ab3e1c7b, 0xac38f36ff8a1d8, + 0x1c29819435d2c6, 0xc813132f4c07e9}, + {0x2891425503b11f, 0x08781030579fea, + 0xf5426ba5cc9674, 0x1e28ebf18562bc}, + {1, 0, 0, 0}}, + {{0x9f31997cc864eb, 0x06cd91d28b5e4c, + 0xff17036691a973, 0xf1aef351497c58}, + {0xdd1f2d600564ff, 0xdead073b1402db, + 0x74a684435bd693, 0xeea7471f962558}, + {1, 0, 0, 0}}}, +{{{0, 0, 0, 0}, + {0, 0, 0, 0}, + {0, 0, 0, 0}}, + {{0x9665266dddf554, 0x9613d78b60ef2d, 0xce27a34cdba417, 0xd35ab74d6afc31}, + {0x85ccdd22deb15e, 0x2137e5783a6aab, 0xa141cffd8c93c6, 0x355a1830e90f2d}, + {1, 0, 0, 0}}, + {{0x1a494eadaade65, 0xd6da4da77fe53c, 0xe7992996abec86, 0x65c3553c6090e3}, + {0xfa610b1fb09346, 0xf1c6540b8a4aaf, 0xc51a13ccd3cbab, 0x02995b1b18c28a}, + {1, 0, 0, 0}}, + {{0x7874568e7295ef, 0x86b419fbe38d04, 0xdc0690a7550d9a, 0xd3966a44beac33}, + {0x2b7280ec29132f, 0xbeaa3b6a032df3, 0xdc7dd88ae41200, 0xd25e2513e3a100}, + {1, 0, 0, 0}}, + {{0x924857eb2efafd, 0xac2bce41223190, 0x8edaa1445553fc, 0x825800fd3562d5}, + {0x8d79148ea96621, 0x23a01c3dd9ed8d, 0xaf8b219f9416b5, 0xd8db0cc277daea}, + {1, 0, 0, 0}}, + {{0x76a9c3b1a700f0, 0xe9acd29bc7e691, 0x69212d1a6b0327, 0x6322e97fe154be}, + {0x469fc5465d62aa, 0x8d41ed18883b05, 0x1f8eae66c52b88, 0xe4fcbe9325be51}, + {1, 0, 0, 0}}, + {{0x825fdf583cac16, 0x020b857c7b023a, 0x683c17744b0165, 0x14ffd0a2daf2f1}, + {0x323b36184218f9, 0x4944ec4e3b47d4, 0xc15b3080841acf, 0x0bced4b01a28bb}, + {1, 0, 0, 0}}, + {{0x92ac22230df5c4, 0x52f33b4063eda8, 0xcb3f19870c0c93, 0x40064f2ba65233}, + {0xfe16f0924f8992, 0x012da25af5b517, 0x1a57bb24f723a6, 0x06f8bc76760def}, + {1, 0, 0, 0}}, + {{0x4a7084f7817cb9, 0xbcab0738ee9a78, 0x3ec11e11d9c326, 0xdc0fe90e0f1aae}, + {0xcf639ea5f98390, 0x5c350aa22ffb74, 0x9afae98a4047b7, 0x956ec2d617fc45}, + {1, 0, 0, 0}}, + {{0x4306d648c1be6a, 0x9247cd8bc9a462, 0xf5595e377d2f2e, 0xbd1c3caff1a52e}, + {0x045e14472409d0, 0x29f3e17078f773, 0x745a602b2d4f7d, 0x191837685cdfbb}, + {1, 0, 0, 0}}, + {{0x5b6ee254a8cb79, 0x4953433f5e7026, 0xe21faeb1d1def4, 0xc4c225785c09de}, + {0x307ce7bba1e518, 0x31b125b1036db8, 0x47e91868839e8f, 0xc765866e33b9f3}, + {1, 0, 0, 0}}, + {{0x3bfece24f96906, 0x4794da641e5093, 0xde5df64f95db26, 0x297ecd89714b05}, + {0x701bd3ebb2c3aa, 0x7073b4f53cb1d5, 0x13c5665658af16, 0x9895089d66fe58}, + {1, 0, 0, 0}}, + {{0x0fef05f78c4790, 0x2d773633b05d2e, 0x94229c3a951c94, 0xbbbd70df4911bb}, + {0xb2c6963d2c1168, 0x105f47a72b0d73, 0x9fdf6111614080, 0x7b7e94b39e67b0}, + {1, 0, 0, 0}}, + {{0xad1a7d6efbe2b3, 0xf012482c0da69d, 0x6b3bdf12438345, 0x40d7558d7aa4d9}, + {0x8a09fffb5c6d3d, 0x9a356e5d9ffd38, 0x5973f15f4f9b1c, 0xdcd5f59f63c3ea}, + {1, 0, 0, 0}}, + {{0xacf39f4c5ca7ab, 0x4c8071cc5fd737, 0xc64e3602cd1184, 0x0acd4644c9abba}, + {0x6c011a36d8bf6e, 0xfecd87ba24e32a, 0x19f6f56574fad8, 0x050b204ced9405}, + {1, 0, 0, 0}}, + {{0xed4f1cae7d9a96, 0x5ceef7ad94c40a, 0x778e4a3bf3ef9b, 0x7405783dc3b55e}, + {0x32477c61b6e8c6, 0xb46a97570f018b, 0x91176d0a7e95d1, 0x3df90fbc4c7d0e}, + {1, 0, 0, 0}}} +}; /* Precomputation for the group generator. */ typedef struct { - felem g_pre_comp[2][16][3]; - int references; + felem g_pre_comp[2][16][3]; + int references; } NISTP224_PRE_COMP; const EC_METHOD *EC_GFp_nistp224_method(void) - { - static const EC_METHOD ret = { - EC_FLAGS_DEFAULT_OCT, - NID_X9_62_prime_field, - ec_GFp_nistp224_group_init, - ec_GFp_simple_group_finish, - ec_GFp_simple_group_clear_finish, - ec_GFp_nist_group_copy, - ec_GFp_nistp224_group_set_curve, - ec_GFp_simple_group_get_curve, - ec_GFp_simple_group_get_degree, - ec_GFp_simple_group_check_discriminant, - ec_GFp_simple_point_init, - ec_GFp_simple_point_finish, - ec_GFp_simple_point_clear_finish, - ec_GFp_simple_point_copy, - ec_GFp_simple_point_set_to_infinity, - ec_GFp_simple_set_Jprojective_coordinates_GFp, - ec_GFp_simple_get_Jprojective_coordinates_GFp, - ec_GFp_simple_point_set_affine_coordinates, - ec_GFp_nistp224_point_get_affine_coordinates, - 0 /* point_set_compressed_coordinates */, - 0 /* point2oct */, - 0 /* oct2point */, - ec_GFp_simple_add, - ec_GFp_simple_dbl, - ec_GFp_simple_invert, - ec_GFp_simple_is_at_infinity, - ec_GFp_simple_is_on_curve, - ec_GFp_simple_cmp, - ec_GFp_simple_make_affine, - ec_GFp_simple_points_make_affine, - ec_GFp_nistp224_points_mul, - ec_GFp_nistp224_precompute_mult, - ec_GFp_nistp224_have_precompute_mult, - ec_GFp_nist_field_mul, - ec_GFp_nist_field_sqr, - 0 /* field_div */, - 0 /* field_encode */, - 0 /* field_decode */, - 0 /* field_set_to_one */ }; - - return &ret; - } - -/* Helper functions to convert field elements to/from internal representation */ +{ + static const EC_METHOD ret = { + EC_FLAGS_DEFAULT_OCT, + NID_X9_62_prime_field, + ec_GFp_nistp224_group_init, + ec_GFp_simple_group_finish, + ec_GFp_simple_group_clear_finish, + ec_GFp_nist_group_copy, + ec_GFp_nistp224_group_set_curve, + ec_GFp_simple_group_get_curve, + ec_GFp_simple_group_get_degree, + ec_GFp_simple_group_check_discriminant, + ec_GFp_simple_point_init, + ec_GFp_simple_point_finish, + ec_GFp_simple_point_clear_finish, + ec_GFp_simple_point_copy, + ec_GFp_simple_point_set_to_infinity, + ec_GFp_simple_set_Jprojective_coordinates_GFp, + ec_GFp_simple_get_Jprojective_coordinates_GFp, + ec_GFp_simple_point_set_affine_coordinates, + ec_GFp_nistp224_point_get_affine_coordinates, + 0 /* point_set_compressed_coordinates */ , + 0 /* point2oct */ , + 0 /* oct2point */ , + ec_GFp_simple_add, + ec_GFp_simple_dbl, + ec_GFp_simple_invert, + ec_GFp_simple_is_at_infinity, + ec_GFp_simple_is_on_curve, + ec_GFp_simple_cmp, + ec_GFp_simple_make_affine, + ec_GFp_simple_points_make_affine, + ec_GFp_nistp224_points_mul, + ec_GFp_nistp224_precompute_mult, + ec_GFp_nistp224_have_precompute_mult, + ec_GFp_nist_field_mul, + ec_GFp_nist_field_sqr, + 0 /* field_div */ , + 0 /* field_encode */ , + 0 /* field_decode */ , + 0 /* field_set_to_one */ + }; + + return &ret; +} + +/* + * Helper functions to convert field elements to/from internal representation + */ static void bin28_to_felem(felem out, const u8 in[28]) - { - out[0] = *((const uint64_t *)(in)) & 0x00ffffffffffffff; - out[1] = (*((const uint64_t *)(in+7))) & 0x00ffffffffffffff; - out[2] = (*((const uint64_t *)(in+14))) & 0x00ffffffffffffff; - out[3] = (*((const uint64_t *)(in+21))) & 0x00ffffffffffffff; - } +{ + out[0] = *((const uint64_t *)(in)) & 0x00ffffffffffffff; + out[1] = (*((const uint64_t *)(in + 7))) & 0x00ffffffffffffff; + out[2] = (*((const uint64_t *)(in + 14))) & 0x00ffffffffffffff; + out[3] = (*((const uint64_t *)(in + 21))) & 0x00ffffffffffffff; +} static void felem_to_bin28(u8 out[28], const felem in) - { - unsigned i; - for (i = 0; i < 7; ++i) - { - out[i] = in[0]>>(8*i); - out[i+7] = in[1]>>(8*i); - out[i+14] = in[2]>>(8*i); - out[i+21] = in[3]>>(8*i); - } - } +{ + unsigned i; + for (i = 0; i < 7; ++i) { + out[i] = in[0] >> (8 * i); + out[i + 7] = in[1] >> (8 * i); + out[i + 14] = in[2] >> (8 * i); + out[i + 21] = in[3] >> (8 * i); + } +} /* To preserve endianness when using BN_bn2bin and BN_bin2bn */ static void flip_endian(u8 *out, const u8 *in, unsigned len) - { - unsigned i; - for (i = 0; i < len; ++i) - out[i] = in[len-1-i]; - } +{ + unsigned i; + for (i = 0; i < len; ++i) + out[i] = in[len - 1 - i]; +} /* From OpenSSL BIGNUM to internal representation */ static int BN_to_felem(felem out, const BIGNUM *bn) - { - felem_bytearray b_in; - felem_bytearray b_out; - unsigned num_bytes; - - /* BN_bn2bin eats leading zeroes */ - memset(b_out, 0, sizeof b_out); - num_bytes = BN_num_bytes(bn); - if (num_bytes > sizeof b_out) - { - ECerr(EC_F_BN_TO_FELEM, EC_R_BIGNUM_OUT_OF_RANGE); - return 0; - } - if (BN_is_negative(bn)) - { - ECerr(EC_F_BN_TO_FELEM, EC_R_BIGNUM_OUT_OF_RANGE); - return 0; - } - num_bytes = BN_bn2bin(bn, b_in); - flip_endian(b_out, b_in, num_bytes); - bin28_to_felem(out, b_out); - return 1; - } +{ + felem_bytearray b_in; + felem_bytearray b_out; + unsigned num_bytes; + + /* BN_bn2bin eats leading zeroes */ + memset(b_out, 0, sizeof b_out); + num_bytes = BN_num_bytes(bn); + if (num_bytes > sizeof b_out) { + ECerr(EC_F_BN_TO_FELEM, EC_R_BIGNUM_OUT_OF_RANGE); + return 0; + } + if (BN_is_negative(bn)) { + ECerr(EC_F_BN_TO_FELEM, EC_R_BIGNUM_OUT_OF_RANGE); + return 0; + } + num_bytes = BN_bn2bin(bn, b_in); + flip_endian(b_out, b_in, num_bytes); + bin28_to_felem(out, b_out); + return 1; +} /* From internal representation to OpenSSL BIGNUM */ static BIGNUM *felem_to_BN(BIGNUM *out, const felem in) - { - felem_bytearray b_in, b_out; - felem_to_bin28(b_in, in); - flip_endian(b_out, b_in, sizeof b_out); - return BN_bin2bn(b_out, sizeof b_out, out); - } +{ + felem_bytearray b_in, b_out; + felem_to_bin28(b_in, in); + flip_endian(b_out, b_in, sizeof b_out); + return BN_bin2bn(b_out, sizeof b_out, out); +} /******************************************************************************/ /*- - * FIELD OPERATIONS + * FIELD OPERATIONS * * Field operations, using the internal representation of field elements. * NB! These operations are specific to our point multiplication and cannot be @@ -352,406 +383,441 @@ static BIGNUM *felem_to_BN(BIGNUM *out, const felem in) */ static void felem_one(felem out) - { - out[0] = 1; - out[1] = 0; - out[2] = 0; - out[3] = 0; - } +{ + out[0] = 1; + out[1] = 0; + out[2] = 0; + out[3] = 0; +} static void felem_assign(felem out, const felem in) - { - out[0] = in[0]; - out[1] = in[1]; - out[2] = in[2]; - out[3] = in[3]; - } +{ + out[0] = in[0]; + out[1] = in[1]; + out[2] = in[2]; + out[3] = in[3]; +} /* Sum two field elements: out += in */ static void felem_sum(felem out, const felem in) - { - out[0] += in[0]; - out[1] += in[1]; - out[2] += in[2]; - out[3] += in[3]; - } +{ + out[0] += in[0]; + out[1] += in[1]; + out[2] += in[2]; + out[3] += in[3]; +} /* Get negative value: out = -in */ /* Assumes in[i] < 2^57 */ static void felem_neg(felem out, const felem in) - { - static const limb two58p2 = (((limb) 1) << 58) + (((limb) 1) << 2); - static const limb two58m2 = (((limb) 1) << 58) - (((limb) 1) << 2); - static const limb two58m42m2 = (((limb) 1) << 58) - - (((limb) 1) << 42) - (((limb) 1) << 2); - - /* Set to 0 mod 2^224-2^96+1 to ensure out > in */ - out[0] = two58p2 - in[0]; - out[1] = two58m42m2 - in[1]; - out[2] = two58m2 - in[2]; - out[3] = two58m2 - in[3]; - } +{ + static const limb two58p2 = (((limb) 1) << 58) + (((limb) 1) << 2); + static const limb two58m2 = (((limb) 1) << 58) - (((limb) 1) << 2); + static const limb two58m42m2 = (((limb) 1) << 58) - + (((limb) 1) << 42) - (((limb) 1) << 2); + + /* Set to 0 mod 2^224-2^96+1 to ensure out > in */ + out[0] = two58p2 - in[0]; + out[1] = two58m42m2 - in[1]; + out[2] = two58m2 - in[2]; + out[3] = two58m2 - in[3]; +} /* Subtract field elements: out -= in */ /* Assumes in[i] < 2^57 */ static void felem_diff(felem out, const felem in) - { - static const limb two58p2 = (((limb) 1) << 58) + (((limb) 1) << 2); - static const limb two58m2 = (((limb) 1) << 58) - (((limb) 1) << 2); - static const limb two58m42m2 = (((limb) 1) << 58) - - (((limb) 1) << 42) - (((limb) 1) << 2); - - /* Add 0 mod 2^224-2^96+1 to ensure out > in */ - out[0] += two58p2; - out[1] += two58m42m2; - out[2] += two58m2; - out[3] += two58m2; - - out[0] -= in[0]; - out[1] -= in[1]; - out[2] -= in[2]; - out[3] -= in[3]; - } +{ + static const limb two58p2 = (((limb) 1) << 58) + (((limb) 1) << 2); + static const limb two58m2 = (((limb) 1) << 58) - (((limb) 1) << 2); + static const limb two58m42m2 = (((limb) 1) << 58) - + (((limb) 1) << 42) - (((limb) 1) << 2); + + /* Add 0 mod 2^224-2^96+1 to ensure out > in */ + out[0] += two58p2; + out[1] += two58m42m2; + out[2] += two58m2; + out[3] += two58m2; + + out[0] -= in[0]; + out[1] -= in[1]; + out[2] -= in[2]; + out[3] -= in[3]; +} /* Subtract in unreduced 128-bit mode: out -= in */ /* Assumes in[i] < 2^119 */ static void widefelem_diff(widefelem out, const widefelem in) - { - static const widelimb two120 = ((widelimb) 1) << 120; - static const widelimb two120m64 = (((widelimb) 1) << 120) - - (((widelimb) 1) << 64); - static const widelimb two120m104m64 = (((widelimb) 1) << 120) - - (((widelimb) 1) << 104) - (((widelimb) 1) << 64); - - /* Add 0 mod 2^224-2^96+1 to ensure out > in */ - out[0] += two120; - out[1] += two120m64; - out[2] += two120m64; - out[3] += two120; - out[4] += two120m104m64; - out[5] += two120m64; - out[6] += two120m64; - - out[0] -= in[0]; - out[1] -= in[1]; - out[2] -= in[2]; - out[3] -= in[3]; - out[4] -= in[4]; - out[5] -= in[5]; - out[6] -= in[6]; - } +{ + static const widelimb two120 = ((widelimb) 1) << 120; + static const widelimb two120m64 = (((widelimb) 1) << 120) - + (((widelimb) 1) << 64); + static const widelimb two120m104m64 = (((widelimb) 1) << 120) - + (((widelimb) 1) << 104) - (((widelimb) 1) << 64); + + /* Add 0 mod 2^224-2^96+1 to ensure out > in */ + out[0] += two120; + out[1] += two120m64; + out[2] += two120m64; + out[3] += two120; + out[4] += two120m104m64; + out[5] += two120m64; + out[6] += two120m64; + + out[0] -= in[0]; + out[1] -= in[1]; + out[2] -= in[2]; + out[3] -= in[3]; + out[4] -= in[4]; + out[5] -= in[5]; + out[6] -= in[6]; +} /* Subtract in mixed mode: out128 -= in64 */ /* in[i] < 2^63 */ static void felem_diff_128_64(widefelem out, const felem in) - { - static const widelimb two64p8 = (((widelimb) 1) << 64) + - (((widelimb) 1) << 8); - static const widelimb two64m8 = (((widelimb) 1) << 64) - - (((widelimb) 1) << 8); - static const widelimb two64m48m8 = (((widelimb) 1) << 64) - - (((widelimb) 1) << 48) - (((widelimb) 1) << 8); - - /* Add 0 mod 2^224-2^96+1 to ensure out > in */ - out[0] += two64p8; - out[1] += two64m48m8; - out[2] += two64m8; - out[3] += two64m8; - - out[0] -= in[0]; - out[1] -= in[1]; - out[2] -= in[2]; - out[3] -= in[3]; - } - -/* Multiply a field element by a scalar: out = out * scalar - * The scalars we actually use are small, so results fit without overflow */ +{ + static const widelimb two64p8 = (((widelimb) 1) << 64) + + (((widelimb) 1) << 8); + static const widelimb two64m8 = (((widelimb) 1) << 64) - + (((widelimb) 1) << 8); + static const widelimb two64m48m8 = (((widelimb) 1) << 64) - + (((widelimb) 1) << 48) - (((widelimb) 1) << 8); + + /* Add 0 mod 2^224-2^96+1 to ensure out > in */ + out[0] += two64p8; + out[1] += two64m48m8; + out[2] += two64m8; + out[3] += two64m8; + + out[0] -= in[0]; + out[1] -= in[1]; + out[2] -= in[2]; + out[3] -= in[3]; +} + +/* + * Multiply a field element by a scalar: out = out * scalar The scalars we + * actually use are small, so results fit without overflow + */ static void felem_scalar(felem out, const limb scalar) - { - out[0] *= scalar; - out[1] *= scalar; - out[2] *= scalar; - out[3] *= scalar; - } - -/* Multiply an unreduced field element by a scalar: out = out * scalar - * The scalars we actually use are small, so results fit without overflow */ +{ + out[0] *= scalar; + out[1] *= scalar; + out[2] *= scalar; + out[3] *= scalar; +} + +/* + * Multiply an unreduced field element by a scalar: out = out * scalar The + * scalars we actually use are small, so results fit without overflow + */ static void widefelem_scalar(widefelem out, const widelimb scalar) - { - out[0] *= scalar; - out[1] *= scalar; - out[2] *= scalar; - out[3] *= scalar; - out[4] *= scalar; - out[5] *= scalar; - out[6] *= scalar; - } +{ + out[0] *= scalar; + out[1] *= scalar; + out[2] *= scalar; + out[3] *= scalar; + out[4] *= scalar; + out[5] *= scalar; + out[6] *= scalar; +} /* Square a field element: out = in^2 */ static void felem_square(widefelem out, const felem in) - { - limb tmp0, tmp1, tmp2; - tmp0 = 2 * in[0]; tmp1 = 2 * in[1]; tmp2 = 2 * in[2]; - out[0] = ((widelimb) in[0]) * in[0]; - out[1] = ((widelimb) in[0]) * tmp1; - out[2] = ((widelimb) in[0]) * tmp2 + ((widelimb) in[1]) * in[1]; - out[3] = ((widelimb) in[3]) * tmp0 + - ((widelimb) in[1]) * tmp2; - out[4] = ((widelimb) in[3]) * tmp1 + ((widelimb) in[2]) * in[2]; - out[5] = ((widelimb) in[3]) * tmp2; - out[6] = ((widelimb) in[3]) * in[3]; - } +{ + limb tmp0, tmp1, tmp2; + tmp0 = 2 * in[0]; + tmp1 = 2 * in[1]; + tmp2 = 2 * in[2]; + out[0] = ((widelimb) in[0]) * in[0]; + out[1] = ((widelimb) in[0]) * tmp1; + out[2] = ((widelimb) in[0]) * tmp2 + ((widelimb) in[1]) * in[1]; + out[3] = ((widelimb) in[3]) * tmp0 + ((widelimb) in[1]) * tmp2; + out[4] = ((widelimb) in[3]) * tmp1 + ((widelimb) in[2]) * in[2]; + out[5] = ((widelimb) in[3]) * tmp2; + out[6] = ((widelimb) in[3]) * in[3]; +} /* Multiply two field elements: out = in1 * in2 */ static void felem_mul(widefelem out, const felem in1, const felem in2) - { - out[0] = ((widelimb) in1[0]) * in2[0]; - out[1] = ((widelimb) in1[0]) * in2[1] + ((widelimb) in1[1]) * in2[0]; - out[2] = ((widelimb) in1[0]) * in2[2] + ((widelimb) in1[1]) * in2[1] + - ((widelimb) in1[2]) * in2[0]; - out[3] = ((widelimb) in1[0]) * in2[3] + ((widelimb) in1[1]) * in2[2] + - ((widelimb) in1[2]) * in2[1] + ((widelimb) in1[3]) * in2[0]; - out[4] = ((widelimb) in1[1]) * in2[3] + ((widelimb) in1[2]) * in2[2] + - ((widelimb) in1[3]) * in2[1]; - out[5] = ((widelimb) in1[2]) * in2[3] + ((widelimb) in1[3]) * in2[2]; - out[6] = ((widelimb) in1[3]) * in2[3]; - } +{ + out[0] = ((widelimb) in1[0]) * in2[0]; + out[1] = ((widelimb) in1[0]) * in2[1] + ((widelimb) in1[1]) * in2[0]; + out[2] = ((widelimb) in1[0]) * in2[2] + ((widelimb) in1[1]) * in2[1] + + ((widelimb) in1[2]) * in2[0]; + out[3] = ((widelimb) in1[0]) * in2[3] + ((widelimb) in1[1]) * in2[2] + + ((widelimb) in1[2]) * in2[1] + ((widelimb) in1[3]) * in2[0]; + out[4] = ((widelimb) in1[1]) * in2[3] + ((widelimb) in1[2]) * in2[2] + + ((widelimb) in1[3]) * in2[1]; + out[5] = ((widelimb) in1[2]) * in2[3] + ((widelimb) in1[3]) * in2[2]; + out[6] = ((widelimb) in1[3]) * in2[3]; +} /*- * Reduce seven 128-bit coefficients to four 64-bit coefficients. * Requires in[i] < 2^126, * ensures out[0] < 2^56, out[1] < 2^56, out[2] < 2^56, out[3] <= 2^56 + 2^16 */ static void felem_reduce(felem out, const widefelem in) - { - static const widelimb two127p15 = (((widelimb) 1) << 127) + - (((widelimb) 1) << 15); - static const widelimb two127m71 = (((widelimb) 1) << 127) - - (((widelimb) 1) << 71); - static const widelimb two127m71m55 = (((widelimb) 1) << 127) - - (((widelimb) 1) << 71) - (((widelimb) 1) << 55); - widelimb output[5]; - - /* Add 0 mod 2^224-2^96+1 to ensure all differences are positive */ - output[0] = in[0] + two127p15; - output[1] = in[1] + two127m71m55; - output[2] = in[2] + two127m71; - output[3] = in[3]; - output[4] = in[4]; - - /* Eliminate in[4], in[5], in[6] */ - output[4] += in[6] >> 16; - output[3] += (in[6] & 0xffff) << 40; - output[2] -= in[6]; - - output[3] += in[5] >> 16; - output[2] += (in[5] & 0xffff) << 40; - output[1] -= in[5]; - - output[2] += output[4] >> 16; - output[1] += (output[4] & 0xffff) << 40; - output[0] -= output[4]; - - /* Carry 2 -> 3 -> 4 */ - output[3] += output[2] >> 56; - output[2] &= 0x00ffffffffffffff; - - output[4] = output[3] >> 56; - output[3] &= 0x00ffffffffffffff; - - /* Now output[2] < 2^56, output[3] < 2^56, output[4] < 2^72 */ - - /* Eliminate output[4] */ - output[2] += output[4] >> 16; - /* output[2] < 2^56 + 2^56 = 2^57 */ - output[1] += (output[4] & 0xffff) << 40; - output[0] -= output[4]; - - /* Carry 0 -> 1 -> 2 -> 3 */ - output[1] += output[0] >> 56; - out[0] = output[0] & 0x00ffffffffffffff; - - output[2] += output[1] >> 56; - /* output[2] < 2^57 + 2^72 */ - out[1] = output[1] & 0x00ffffffffffffff; - output[3] += output[2] >> 56; - /* output[3] <= 2^56 + 2^16 */ - out[2] = output[2] & 0x00ffffffffffffff; - - /*- - * out[0] < 2^56, out[1] < 2^56, out[2] < 2^56, - * out[3] <= 2^56 + 2^16 (due to final carry), - * so out < 2*p - */ - out[3] = output[3]; - } +{ + static const widelimb two127p15 = (((widelimb) 1) << 127) + + (((widelimb) 1) << 15); + static const widelimb two127m71 = (((widelimb) 1) << 127) - + (((widelimb) 1) << 71); + static const widelimb two127m71m55 = (((widelimb) 1) << 127) - + (((widelimb) 1) << 71) - (((widelimb) 1) << 55); + widelimb output[5]; + + /* Add 0 mod 2^224-2^96+1 to ensure all differences are positive */ + output[0] = in[0] + two127p15; + output[1] = in[1] + two127m71m55; + output[2] = in[2] + two127m71; + output[3] = in[3]; + output[4] = in[4]; + + /* Eliminate in[4], in[5], in[6] */ + output[4] += in[6] >> 16; + output[3] += (in[6] & 0xffff) << 40; + output[2] -= in[6]; + + output[3] += in[5] >> 16; + output[2] += (in[5] & 0xffff) << 40; + output[1] -= in[5]; + + output[2] += output[4] >> 16; + output[1] += (output[4] & 0xffff) << 40; + output[0] -= output[4]; + + /* Carry 2 -> 3 -> 4 */ + output[3] += output[2] >> 56; + output[2] &= 0x00ffffffffffffff; + + output[4] = output[3] >> 56; + output[3] &= 0x00ffffffffffffff; + + /* Now output[2] < 2^56, output[3] < 2^56, output[4] < 2^72 */ + + /* Eliminate output[4] */ + output[2] += output[4] >> 16; + /* output[2] < 2^56 + 2^56 = 2^57 */ + output[1] += (output[4] & 0xffff) << 40; + output[0] -= output[4]; + + /* Carry 0 -> 1 -> 2 -> 3 */ + output[1] += output[0] >> 56; + out[0] = output[0] & 0x00ffffffffffffff; + + output[2] += output[1] >> 56; + /* output[2] < 2^57 + 2^72 */ + out[1] = output[1] & 0x00ffffffffffffff; + output[3] += output[2] >> 56; + /* output[3] <= 2^56 + 2^16 */ + out[2] = output[2] & 0x00ffffffffffffff; + + /*- + * out[0] < 2^56, out[1] < 2^56, out[2] < 2^56, + * out[3] <= 2^56 + 2^16 (due to final carry), + * so out < 2*p + */ + out[3] = output[3]; +} static void felem_square_reduce(felem out, const felem in) - { - widefelem tmp; - felem_square(tmp, in); - felem_reduce(out, tmp); - } +{ + widefelem tmp; + felem_square(tmp, in); + felem_reduce(out, tmp); +} static void felem_mul_reduce(felem out, const felem in1, const felem in2) - { - widefelem tmp; - felem_mul(tmp, in1, in2); - felem_reduce(out, tmp); - } - -/* Reduce to unique minimal representation. - * Requires 0 <= in < 2*p (always call felem_reduce first) */ +{ + widefelem tmp; + felem_mul(tmp, in1, in2); + felem_reduce(out, tmp); +} + +/* + * Reduce to unique minimal representation. Requires 0 <= in < 2*p (always + * call felem_reduce first) + */ static void felem_contract(felem out, const felem in) - { - static const int64_t two56 = ((limb) 1) << 56; - /* 0 <= in < 2*p, p = 2^224 - 2^96 + 1 */ - /* if in > p , reduce in = in - 2^224 + 2^96 - 1 */ - int64_t tmp[4], a; - tmp[0] = in[0]; - tmp[1] = in[1]; - tmp[2] = in[2]; - tmp[3] = in[3]; - /* Case 1: a = 1 iff in >= 2^224 */ - a = (in[3] >> 56); - tmp[0] -= a; - tmp[1] += a << 40; - tmp[3] &= 0x00ffffffffffffff; - /* Case 2: a = 0 iff p <= in < 2^224, i.e., - * the high 128 bits are all 1 and the lower part is non-zero */ - a = ((in[3] & in[2] & (in[1] | 0x000000ffffffffff)) + 1) | - (((int64_t)(in[0] + (in[1] & 0x000000ffffffffff)) - 1) >> 63); - a &= 0x00ffffffffffffff; - /* turn a into an all-one mask (if a = 0) or an all-zero mask */ - a = (a - 1) >> 63; - /* subtract 2^224 - 2^96 + 1 if a is all-one*/ - tmp[3] &= a ^ 0xffffffffffffffff; - tmp[2] &= a ^ 0xffffffffffffffff; - tmp[1] &= (a ^ 0xffffffffffffffff) | 0x000000ffffffffff; - tmp[0] -= 1 & a; - - /* eliminate negative coefficients: if tmp[0] is negative, tmp[1] must - * be non-zero, so we only need one step */ - a = tmp[0] >> 63; - tmp[0] += two56 & a; - tmp[1] -= 1 & a; - - /* carry 1 -> 2 -> 3 */ - tmp[2] += tmp[1] >> 56; - tmp[1] &= 0x00ffffffffffffff; - - tmp[3] += tmp[2] >> 56; - tmp[2] &= 0x00ffffffffffffff; - - /* Now 0 <= out < p */ - out[0] = tmp[0]; - out[1] = tmp[1]; - out[2] = tmp[2]; - out[3] = tmp[3]; - } - -/* Zero-check: returns 1 if input is 0, and 0 otherwise. - * We know that field elements are reduced to in < 2^225, - * so we only need to check three cases: 0, 2^224 - 2^96 + 1, - * and 2^225 - 2^97 + 2 */ +{ + static const int64_t two56 = ((limb) 1) << 56; + /* 0 <= in < 2*p, p = 2^224 - 2^96 + 1 */ + /* if in > p , reduce in = in - 2^224 + 2^96 - 1 */ + int64_t tmp[4], a; + tmp[0] = in[0]; + tmp[1] = in[1]; + tmp[2] = in[2]; + tmp[3] = in[3]; + /* Case 1: a = 1 iff in >= 2^224 */ + a = (in[3] >> 56); + tmp[0] -= a; + tmp[1] += a << 40; + tmp[3] &= 0x00ffffffffffffff; + /* + * Case 2: a = 0 iff p <= in < 2^224, i.e., the high 128 bits are all 1 + * and the lower part is non-zero + */ + a = ((in[3] & in[2] & (in[1] | 0x000000ffffffffff)) + 1) | + (((int64_t) (in[0] + (in[1] & 0x000000ffffffffff)) - 1) >> 63); + a &= 0x00ffffffffffffff; + /* turn a into an all-one mask (if a = 0) or an all-zero mask */ + a = (a - 1) >> 63; + /* subtract 2^224 - 2^96 + 1 if a is all-one */ + tmp[3] &= a ^ 0xffffffffffffffff; + tmp[2] &= a ^ 0xffffffffffffffff; + tmp[1] &= (a ^ 0xffffffffffffffff) | 0x000000ffffffffff; + tmp[0] -= 1 & a; + + /* + * eliminate negative coefficients: if tmp[0] is negative, tmp[1] must be + * non-zero, so we only need one step + */ + a = tmp[0] >> 63; + tmp[0] += two56 & a; + tmp[1] -= 1 & a; + + /* carry 1 -> 2 -> 3 */ + tmp[2] += tmp[1] >> 56; + tmp[1] &= 0x00ffffffffffffff; + + tmp[3] += tmp[2] >> 56; + tmp[2] &= 0x00ffffffffffffff; + + /* Now 0 <= out < p */ + out[0] = tmp[0]; + out[1] = tmp[1]; + out[2] = tmp[2]; + out[3] = tmp[3]; +} + +/* + * Zero-check: returns 1 if input is 0, and 0 otherwise. We know that field + * elements are reduced to in < 2^225, so we only need to check three cases: + * 0, 2^224 - 2^96 + 1, and 2^225 - 2^97 + 2 + */ static limb felem_is_zero(const felem in) - { - limb zero, two224m96p1, two225m97p2; - - zero = in[0] | in[1] | in[2] | in[3]; - zero = (((int64_t)(zero) - 1) >> 63) & 1; - two224m96p1 = (in[0] ^ 1) | (in[1] ^ 0x00ffff0000000000) - | (in[2] ^ 0x00ffffffffffffff) | (in[3] ^ 0x00ffffffffffffff); - two224m96p1 = (((int64_t)(two224m96p1) - 1) >> 63) & 1; - two225m97p2 = (in[0] ^ 2) | (in[1] ^ 0x00fffe0000000000) - | (in[2] ^ 0x00ffffffffffffff) | (in[3] ^ 0x01ffffffffffffff); - two225m97p2 = (((int64_t)(two225m97p2) - 1) >> 63) & 1; - return (zero | two224m96p1 | two225m97p2); - } +{ + limb zero, two224m96p1, two225m97p2; + + zero = in[0] | in[1] | in[2] | in[3]; + zero = (((int64_t) (zero) - 1) >> 63) & 1; + two224m96p1 = (in[0] ^ 1) | (in[1] ^ 0x00ffff0000000000) + | (in[2] ^ 0x00ffffffffffffff) | (in[3] ^ 0x00ffffffffffffff); + two224m96p1 = (((int64_t) (two224m96p1) - 1) >> 63) & 1; + two225m97p2 = (in[0] ^ 2) | (in[1] ^ 0x00fffe0000000000) + | (in[2] ^ 0x00ffffffffffffff) | (in[3] ^ 0x01ffffffffffffff); + two225m97p2 = (((int64_t) (two225m97p2) - 1) >> 63) & 1; + return (zero | two224m96p1 | two225m97p2); +} static limb felem_is_zero_int(const felem in) - { - return (int) (felem_is_zero(in) & ((limb)1)); - } +{ + return (int)(felem_is_zero(in) & ((limb) 1)); +} /* Invert a field element */ /* Computation chain copied from djb's code */ static void felem_inv(felem out, const felem in) - { - felem ftmp, ftmp2, ftmp3, ftmp4; - widefelem tmp; - unsigned i; - - felem_square(tmp, in); felem_reduce(ftmp, tmp); /* 2 */ - felem_mul(tmp, in, ftmp); felem_reduce(ftmp, tmp); /* 2^2 - 1 */ - felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); /* 2^3 - 2 */ - felem_mul(tmp, in, ftmp); felem_reduce(ftmp, tmp); /* 2^3 - 1 */ - felem_square(tmp, ftmp); felem_reduce(ftmp2, tmp); /* 2^4 - 2 */ - felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); /* 2^5 - 4 */ - felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); /* 2^6 - 8 */ - felem_mul(tmp, ftmp2, ftmp); felem_reduce(ftmp, tmp); /* 2^6 - 1 */ - felem_square(tmp, ftmp); felem_reduce(ftmp2, tmp); /* 2^7 - 2 */ - for (i = 0; i < 5; ++i) /* 2^12 - 2^6 */ - { - felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); - } - felem_mul(tmp, ftmp2, ftmp); felem_reduce(ftmp2, tmp); /* 2^12 - 1 */ - felem_square(tmp, ftmp2); felem_reduce(ftmp3, tmp); /* 2^13 - 2 */ - for (i = 0; i < 11; ++i) /* 2^24 - 2^12 */ - { - felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp); - } - felem_mul(tmp, ftmp3, ftmp2); felem_reduce(ftmp2, tmp); /* 2^24 - 1 */ - felem_square(tmp, ftmp2); felem_reduce(ftmp3, tmp); /* 2^25 - 2 */ - for (i = 0; i < 23; ++i) /* 2^48 - 2^24 */ - { - felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp); - } - felem_mul(tmp, ftmp3, ftmp2); felem_reduce(ftmp3, tmp); /* 2^48 - 1 */ - felem_square(tmp, ftmp3); felem_reduce(ftmp4, tmp); /* 2^49 - 2 */ - for (i = 0; i < 47; ++i) /* 2^96 - 2^48 */ - { - felem_square(tmp, ftmp4); felem_reduce(ftmp4, tmp); - } - felem_mul(tmp, ftmp3, ftmp4); felem_reduce(ftmp3, tmp); /* 2^96 - 1 */ - felem_square(tmp, ftmp3); felem_reduce(ftmp4, tmp); /* 2^97 - 2 */ - for (i = 0; i < 23; ++i) /* 2^120 - 2^24 */ - { - felem_square(tmp, ftmp4); felem_reduce(ftmp4, tmp); - } - felem_mul(tmp, ftmp2, ftmp4); felem_reduce(ftmp2, tmp); /* 2^120 - 1 */ - for (i = 0; i < 6; ++i) /* 2^126 - 2^6 */ - { - felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); - } - felem_mul(tmp, ftmp2, ftmp); felem_reduce(ftmp, tmp); /* 2^126 - 1 */ - felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); /* 2^127 - 2 */ - felem_mul(tmp, ftmp, in); felem_reduce(ftmp, tmp); /* 2^127 - 1 */ - for (i = 0; i < 97; ++i) /* 2^224 - 2^97 */ - { - felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); - } - felem_mul(tmp, ftmp, ftmp3); felem_reduce(out, tmp); /* 2^224 - 2^96 - 1 */ - } - -/* Copy in constant time: - * if icopy == 1, copy in to out, - * if icopy == 0, copy out to itself. */ -static void -copy_conditional(felem out, const felem in, limb icopy) - { - unsigned i; - /* icopy is a (64-bit) 0 or 1, so copy is either all-zero or all-one */ - const limb copy = -icopy; - for (i = 0; i < 4; ++i) - { - const limb tmp = copy & (in[i] ^ out[i]); - out[i] ^= tmp; - } - } +{ + felem ftmp, ftmp2, ftmp3, ftmp4; + widefelem tmp; + unsigned i; + + felem_square(tmp, in); + felem_reduce(ftmp, tmp); /* 2 */ + felem_mul(tmp, in, ftmp); + felem_reduce(ftmp, tmp); /* 2^2 - 1 */ + felem_square(tmp, ftmp); + felem_reduce(ftmp, tmp); /* 2^3 - 2 */ + felem_mul(tmp, in, ftmp); + felem_reduce(ftmp, tmp); /* 2^3 - 1 */ + felem_square(tmp, ftmp); + felem_reduce(ftmp2, tmp); /* 2^4 - 2 */ + felem_square(tmp, ftmp2); + felem_reduce(ftmp2, tmp); /* 2^5 - 4 */ + felem_square(tmp, ftmp2); + felem_reduce(ftmp2, tmp); /* 2^6 - 8 */ + felem_mul(tmp, ftmp2, ftmp); + felem_reduce(ftmp, tmp); /* 2^6 - 1 */ + felem_square(tmp, ftmp); + felem_reduce(ftmp2, tmp); /* 2^7 - 2 */ + for (i = 0; i < 5; ++i) { /* 2^12 - 2^6 */ + felem_square(tmp, ftmp2); + felem_reduce(ftmp2, tmp); + } + felem_mul(tmp, ftmp2, ftmp); + felem_reduce(ftmp2, tmp); /* 2^12 - 1 */ + felem_square(tmp, ftmp2); + felem_reduce(ftmp3, tmp); /* 2^13 - 2 */ + for (i = 0; i < 11; ++i) { /* 2^24 - 2^12 */ + felem_square(tmp, ftmp3); + felem_reduce(ftmp3, tmp); + } + felem_mul(tmp, ftmp3, ftmp2); + felem_reduce(ftmp2, tmp); /* 2^24 - 1 */ + felem_square(tmp, ftmp2); + felem_reduce(ftmp3, tmp); /* 2^25 - 2 */ + for (i = 0; i < 23; ++i) { /* 2^48 - 2^24 */ + felem_square(tmp, ftmp3); + felem_reduce(ftmp3, tmp); + } + felem_mul(tmp, ftmp3, ftmp2); + felem_reduce(ftmp3, tmp); /* 2^48 - 1 */ + felem_square(tmp, ftmp3); + felem_reduce(ftmp4, tmp); /* 2^49 - 2 */ + for (i = 0; i < 47; ++i) { /* 2^96 - 2^48 */ + felem_square(tmp, ftmp4); + felem_reduce(ftmp4, tmp); + } + felem_mul(tmp, ftmp3, ftmp4); + felem_reduce(ftmp3, tmp); /* 2^96 - 1 */ + felem_square(tmp, ftmp3); + felem_reduce(ftmp4, tmp); /* 2^97 - 2 */ + for (i = 0; i < 23; ++i) { /* 2^120 - 2^24 */ + felem_square(tmp, ftmp4); + felem_reduce(ftmp4, tmp); + } + felem_mul(tmp, ftmp2, ftmp4); + felem_reduce(ftmp2, tmp); /* 2^120 - 1 */ + for (i = 0; i < 6; ++i) { /* 2^126 - 2^6 */ + felem_square(tmp, ftmp2); + felem_reduce(ftmp2, tmp); + } + felem_mul(tmp, ftmp2, ftmp); + felem_reduce(ftmp, tmp); /* 2^126 - 1 */ + felem_square(tmp, ftmp); + felem_reduce(ftmp, tmp); /* 2^127 - 2 */ + felem_mul(tmp, ftmp, in); + felem_reduce(ftmp, tmp); /* 2^127 - 1 */ + for (i = 0; i < 97; ++i) { /* 2^224 - 2^97 */ + felem_square(tmp, ftmp); + felem_reduce(ftmp, tmp); + } + felem_mul(tmp, ftmp, ftmp3); + felem_reduce(out, tmp); /* 2^224 - 2^96 - 1 */ +} + +/* + * Copy in constant time: if icopy == 1, copy in to out, if icopy == 0, copy + * out to itself. + */ +static void copy_conditional(felem out, const felem in, limb icopy) +{ + unsigned i; + /* + * icopy is a (64-bit) 0 or 1, so copy is either all-zero or all-one + */ + const limb copy = -icopy; + for (i = 0; i < 4; ++i) { + const limb tmp = copy & (in[i] ^ out[i]); + out[i] ^= tmp; + } +} /******************************************************************************/ /*- - * ELLIPTIC CURVE POINT OPERATIONS + * ELLIPTIC CURVE POINT OPERATIONS * * Points are represented in Jacobian projective coordinates: * (X, Y, Z) corresponds to the affine point (X/Z^2, Y/Z^3), @@ -766,78 +832,78 @@ copy_conditional(felem out, const felem in, limb icopy) * Y' = 3 * (X - Z^2) * (X + Z^2) * (4 * X * Y^2 - X') - 8 * Y^2 * Z' = (Y + Z)^2 - Y^2 - Z^2 = 2 * Y * Z * Outputs can equal corresponding inputs, i.e., x_out == x_in is allowed, - * while x_out == y_in is not (maybe this works, but it's not tested). + * while x_out == y_in is not (maybe this works, but it's not tested). */ static void point_double(felem x_out, felem y_out, felem z_out, const felem x_in, const felem y_in, const felem z_in) - { - widefelem tmp, tmp2; - felem delta, gamma, beta, alpha, ftmp, ftmp2; - - felem_assign(ftmp, x_in); - felem_assign(ftmp2, x_in); - - /* delta = z^2 */ - felem_square(tmp, z_in); - felem_reduce(delta, tmp); - - /* gamma = y^2 */ - felem_square(tmp, y_in); - felem_reduce(gamma, tmp); - - /* beta = x*gamma */ - felem_mul(tmp, x_in, gamma); - felem_reduce(beta, tmp); - - /* alpha = 3*(x-delta)*(x+delta) */ - felem_diff(ftmp, delta); - /* ftmp[i] < 2^57 + 2^58 + 2 < 2^59 */ - felem_sum(ftmp2, delta); - /* ftmp2[i] < 2^57 + 2^57 = 2^58 */ - felem_scalar(ftmp2, 3); - /* ftmp2[i] < 3 * 2^58 < 2^60 */ - felem_mul(tmp, ftmp, ftmp2); - /* tmp[i] < 2^60 * 2^59 * 4 = 2^121 */ - felem_reduce(alpha, tmp); - - /* x' = alpha^2 - 8*beta */ - felem_square(tmp, alpha); - /* tmp[i] < 4 * 2^57 * 2^57 = 2^116 */ - felem_assign(ftmp, beta); - felem_scalar(ftmp, 8); - /* ftmp[i] < 8 * 2^57 = 2^60 */ - felem_diff_128_64(tmp, ftmp); - /* tmp[i] < 2^116 + 2^64 + 8 < 2^117 */ - felem_reduce(x_out, tmp); - - /* z' = (y + z)^2 - gamma - delta */ - felem_sum(delta, gamma); - /* delta[i] < 2^57 + 2^57 = 2^58 */ - felem_assign(ftmp, y_in); - felem_sum(ftmp, z_in); - /* ftmp[i] < 2^57 + 2^57 = 2^58 */ - felem_square(tmp, ftmp); - /* tmp[i] < 4 * 2^58 * 2^58 = 2^118 */ - felem_diff_128_64(tmp, delta); - /* tmp[i] < 2^118 + 2^64 + 8 < 2^119 */ - felem_reduce(z_out, tmp); - - /* y' = alpha*(4*beta - x') - 8*gamma^2 */ - felem_scalar(beta, 4); - /* beta[i] < 4 * 2^57 = 2^59 */ - felem_diff(beta, x_out); - /* beta[i] < 2^59 + 2^58 + 2 < 2^60 */ - felem_mul(tmp, alpha, beta); - /* tmp[i] < 4 * 2^57 * 2^60 = 2^119 */ - felem_square(tmp2, gamma); - /* tmp2[i] < 4 * 2^57 * 2^57 = 2^116 */ - widefelem_scalar(tmp2, 8); - /* tmp2[i] < 8 * 2^116 = 2^119 */ - widefelem_diff(tmp, tmp2); - /* tmp[i] < 2^119 + 2^120 < 2^121 */ - felem_reduce(y_out, tmp); - } +{ + widefelem tmp, tmp2; + felem delta, gamma, beta, alpha, ftmp, ftmp2; + + felem_assign(ftmp, x_in); + felem_assign(ftmp2, x_in); + + /* delta = z^2 */ + felem_square(tmp, z_in); + felem_reduce(delta, tmp); + + /* gamma = y^2 */ + felem_square(tmp, y_in); + felem_reduce(gamma, tmp); + + /* beta = x*gamma */ + felem_mul(tmp, x_in, gamma); + felem_reduce(beta, tmp); + + /* alpha = 3*(x-delta)*(x+delta) */ + felem_diff(ftmp, delta); + /* ftmp[i] < 2^57 + 2^58 + 2 < 2^59 */ + felem_sum(ftmp2, delta); + /* ftmp2[i] < 2^57 + 2^57 = 2^58 */ + felem_scalar(ftmp2, 3); + /* ftmp2[i] < 3 * 2^58 < 2^60 */ + felem_mul(tmp, ftmp, ftmp2); + /* tmp[i] < 2^60 * 2^59 * 4 = 2^121 */ + felem_reduce(alpha, tmp); + + /* x' = alpha^2 - 8*beta */ + felem_square(tmp, alpha); + /* tmp[i] < 4 * 2^57 * 2^57 = 2^116 */ + felem_assign(ftmp, beta); + felem_scalar(ftmp, 8); + /* ftmp[i] < 8 * 2^57 = 2^60 */ + felem_diff_128_64(tmp, ftmp); + /* tmp[i] < 2^116 + 2^64 + 8 < 2^117 */ + felem_reduce(x_out, tmp); + + /* z' = (y + z)^2 - gamma - delta */ + felem_sum(delta, gamma); + /* delta[i] < 2^57 + 2^57 = 2^58 */ + felem_assign(ftmp, y_in); + felem_sum(ftmp, z_in); + /* ftmp[i] < 2^57 + 2^57 = 2^58 */ + felem_square(tmp, ftmp); + /* tmp[i] < 4 * 2^58 * 2^58 = 2^118 */ + felem_diff_128_64(tmp, delta); + /* tmp[i] < 2^118 + 2^64 + 8 < 2^119 */ + felem_reduce(z_out, tmp); + + /* y' = alpha*(4*beta - x') - 8*gamma^2 */ + felem_scalar(beta, 4); + /* beta[i] < 4 * 2^57 = 2^59 */ + felem_diff(beta, x_out); + /* beta[i] < 2^59 + 2^58 + 2 < 2^60 */ + felem_mul(tmp, alpha, beta); + /* tmp[i] < 4 * 2^57 * 2^60 = 2^119 */ + felem_square(tmp2, gamma); + /* tmp2[i] < 4 * 2^57 * 2^57 = 2^116 */ + widefelem_scalar(tmp2, 8); + /* tmp2[i] < 8 * 2^116 = 2^119 */ + widefelem_diff(tmp, tmp2); + /* tmp[i] < 2^119 + 2^120 < 2^121 */ + felem_reduce(y_out, tmp); +} /*- * Add two elliptic curve points: @@ -851,821 +917,848 @@ point_double(felem x_out, felem y_out, felem z_out, * This runs faster if 'mixed' is set, which requires Z_2 = 1 or Z_2 = 0. */ -/* This function is not entirely constant-time: - * it includes a branch for checking whether the two input points are equal, - * (while not equal to the point at infinity). - * This case never happens during single point multiplication, - * so there is no timing leak for ECDH or ECDSA signing. */ +/* + * This function is not entirely constant-time: it includes a branch for + * checking whether the two input points are equal, (while not equal to the + * point at infinity). This case never happens during single point + * multiplication, so there is no timing leak for ECDH or ECDSA signing. + */ static void point_add(felem x3, felem y3, felem z3, - const felem x1, const felem y1, const felem z1, - const int mixed, const felem x2, const felem y2, const felem z2) - { - felem ftmp, ftmp2, ftmp3, ftmp4, ftmp5, x_out, y_out, z_out; - widefelem tmp, tmp2; - limb z1_is_zero, z2_is_zero, x_equal, y_equal; - - if (!mixed) - { - /* ftmp2 = z2^2 */ - felem_square(tmp, z2); - felem_reduce(ftmp2, tmp); - - /* ftmp4 = z2^3 */ - felem_mul(tmp, ftmp2, z2); - felem_reduce(ftmp4, tmp); - - /* ftmp4 = z2^3*y1 */ - felem_mul(tmp2, ftmp4, y1); - felem_reduce(ftmp4, tmp2); - - /* ftmp2 = z2^2*x1 */ - felem_mul(tmp2, ftmp2, x1); - felem_reduce(ftmp2, tmp2); - } - else - { - /* We'll assume z2 = 1 (special case z2 = 0 is handled later) */ - - /* ftmp4 = z2^3*y1 */ - felem_assign(ftmp4, y1); - - /* ftmp2 = z2^2*x1 */ - felem_assign(ftmp2, x1); - } - - /* ftmp = z1^2 */ - felem_square(tmp, z1); - felem_reduce(ftmp, tmp); - - /* ftmp3 = z1^3 */ - felem_mul(tmp, ftmp, z1); - felem_reduce(ftmp3, tmp); - - /* tmp = z1^3*y2 */ - felem_mul(tmp, ftmp3, y2); - /* tmp[i] < 4 * 2^57 * 2^57 = 2^116 */ - - /* ftmp3 = z1^3*y2 - z2^3*y1 */ - felem_diff_128_64(tmp, ftmp4); - /* tmp[i] < 2^116 + 2^64 + 8 < 2^117 */ - felem_reduce(ftmp3, tmp); - - /* tmp = z1^2*x2 */ - felem_mul(tmp, ftmp, x2); - /* tmp[i] < 4 * 2^57 * 2^57 = 2^116 */ - - /* ftmp = z1^2*x2 - z2^2*x1 */ - felem_diff_128_64(tmp, ftmp2); - /* tmp[i] < 2^116 + 2^64 + 8 < 2^117 */ - felem_reduce(ftmp, tmp); - - /* the formulae are incorrect if the points are equal - * so we check for this and do doubling if this happens */ - x_equal = felem_is_zero(ftmp); - y_equal = felem_is_zero(ftmp3); - z1_is_zero = felem_is_zero(z1); - z2_is_zero = felem_is_zero(z2); - /* In affine coordinates, (X_1, Y_1) == (X_2, Y_2) */ - if (x_equal && y_equal && !z1_is_zero && !z2_is_zero) - { - point_double(x3, y3, z3, x1, y1, z1); - return; - } - - /* ftmp5 = z1*z2 */ - if (!mixed) - { - felem_mul(tmp, z1, z2); - felem_reduce(ftmp5, tmp); - } - else - { - /* special case z2 = 0 is handled later */ - felem_assign(ftmp5, z1); - } - - /* z_out = (z1^2*x2 - z2^2*x1)*(z1*z2) */ - felem_mul(tmp, ftmp, ftmp5); - felem_reduce(z_out, tmp); - - /* ftmp = (z1^2*x2 - z2^2*x1)^2 */ - felem_assign(ftmp5, ftmp); - felem_square(tmp, ftmp); - felem_reduce(ftmp, tmp); - - /* ftmp5 = (z1^2*x2 - z2^2*x1)^3 */ - felem_mul(tmp, ftmp, ftmp5); - felem_reduce(ftmp5, tmp); - - /* ftmp2 = z2^2*x1*(z1^2*x2 - z2^2*x1)^2 */ - felem_mul(tmp, ftmp2, ftmp); - felem_reduce(ftmp2, tmp); - - /* tmp = z2^3*y1*(z1^2*x2 - z2^2*x1)^3 */ - felem_mul(tmp, ftmp4, ftmp5); - /* tmp[i] < 4 * 2^57 * 2^57 = 2^116 */ - - /* tmp2 = (z1^3*y2 - z2^3*y1)^2 */ - felem_square(tmp2, ftmp3); - /* tmp2[i] < 4 * 2^57 * 2^57 < 2^116 */ - - /* tmp2 = (z1^3*y2 - z2^3*y1)^2 - (z1^2*x2 - z2^2*x1)^3 */ - felem_diff_128_64(tmp2, ftmp5); - /* tmp2[i] < 2^116 + 2^64 + 8 < 2^117 */ - - /* ftmp5 = 2*z2^2*x1*(z1^2*x2 - z2^2*x1)^2 */ - felem_assign(ftmp5, ftmp2); - felem_scalar(ftmp5, 2); - /* ftmp5[i] < 2 * 2^57 = 2^58 */ - - /*- - * x_out = (z1^3*y2 - z2^3*y1)^2 - (z1^2*x2 - z2^2*x1)^3 - - * 2*z2^2*x1*(z1^2*x2 - z2^2*x1)^2 - */ - felem_diff_128_64(tmp2, ftmp5); - /* tmp2[i] < 2^117 + 2^64 + 8 < 2^118 */ - felem_reduce(x_out, tmp2); - - /* ftmp2 = z2^2*x1*(z1^2*x2 - z2^2*x1)^2 - x_out */ - felem_diff(ftmp2, x_out); - /* ftmp2[i] < 2^57 + 2^58 + 2 < 2^59 */ - - /* tmp2 = (z1^3*y2 - z2^3*y1)*(z2^2*x1*(z1^2*x2 - z2^2*x1)^2 - x_out) */ - felem_mul(tmp2, ftmp3, ftmp2); - /* tmp2[i] < 4 * 2^57 * 2^59 = 2^118 */ - - /*- - * y_out = (z1^3*y2 - z2^3*y1)*(z2^2*x1*(z1^2*x2 - z2^2*x1)^2 - x_out) - - * z2^3*y1*(z1^2*x2 - z2^2*x1)^3 - */ - widefelem_diff(tmp2, tmp); - /* tmp2[i] < 2^118 + 2^120 < 2^121 */ - felem_reduce(y_out, tmp2); - - /* the result (x_out, y_out, z_out) is incorrect if one of the inputs is - * the point at infinity, so we need to check for this separately */ - - /* if point 1 is at infinity, copy point 2 to output, and vice versa */ - copy_conditional(x_out, x2, z1_is_zero); - copy_conditional(x_out, x1, z2_is_zero); - copy_conditional(y_out, y2, z1_is_zero); - copy_conditional(y_out, y1, z2_is_zero); - copy_conditional(z_out, z2, z1_is_zero); - copy_conditional(z_out, z1, z2_is_zero); - felem_assign(x3, x_out); - felem_assign(y3, y_out); - felem_assign(z3, z_out); - } + const felem x1, const felem y1, const felem z1, + const int mixed, const felem x2, const felem y2, + const felem z2) +{ + felem ftmp, ftmp2, ftmp3, ftmp4, ftmp5, x_out, y_out, z_out; + widefelem tmp, tmp2; + limb z1_is_zero, z2_is_zero, x_equal, y_equal; + + if (!mixed) { + /* ftmp2 = z2^2 */ + felem_square(tmp, z2); + felem_reduce(ftmp2, tmp); + + /* ftmp4 = z2^3 */ + felem_mul(tmp, ftmp2, z2); + felem_reduce(ftmp4, tmp); + + /* ftmp4 = z2^3*y1 */ + felem_mul(tmp2, ftmp4, y1); + felem_reduce(ftmp4, tmp2); + + /* ftmp2 = z2^2*x1 */ + felem_mul(tmp2, ftmp2, x1); + felem_reduce(ftmp2, tmp2); + } else { + /* + * We'll assume z2 = 1 (special case z2 = 0 is handled later) + */ + + /* ftmp4 = z2^3*y1 */ + felem_assign(ftmp4, y1); + + /* ftmp2 = z2^2*x1 */ + felem_assign(ftmp2, x1); + } + + /* ftmp = z1^2 */ + felem_square(tmp, z1); + felem_reduce(ftmp, tmp); + + /* ftmp3 = z1^3 */ + felem_mul(tmp, ftmp, z1); + felem_reduce(ftmp3, tmp); + + /* tmp = z1^3*y2 */ + felem_mul(tmp, ftmp3, y2); + /* tmp[i] < 4 * 2^57 * 2^57 = 2^116 */ + + /* ftmp3 = z1^3*y2 - z2^3*y1 */ + felem_diff_128_64(tmp, ftmp4); + /* tmp[i] < 2^116 + 2^64 + 8 < 2^117 */ + felem_reduce(ftmp3, tmp); + + /* tmp = z1^2*x2 */ + felem_mul(tmp, ftmp, x2); + /* tmp[i] < 4 * 2^57 * 2^57 = 2^116 */ + + /* ftmp = z1^2*x2 - z2^2*x1 */ + felem_diff_128_64(tmp, ftmp2); + /* tmp[i] < 2^116 + 2^64 + 8 < 2^117 */ + felem_reduce(ftmp, tmp); + + /* + * the formulae are incorrect if the points are equal so we check for + * this and do doubling if this happens + */ + x_equal = felem_is_zero(ftmp); + y_equal = felem_is_zero(ftmp3); + z1_is_zero = felem_is_zero(z1); + z2_is_zero = felem_is_zero(z2); + /* In affine coordinates, (X_1, Y_1) == (X_2, Y_2) */ + if (x_equal && y_equal && !z1_is_zero && !z2_is_zero) { + point_double(x3, y3, z3, x1, y1, z1); + return; + } + + /* ftmp5 = z1*z2 */ + if (!mixed) { + felem_mul(tmp, z1, z2); + felem_reduce(ftmp5, tmp); + } else { + /* special case z2 = 0 is handled later */ + felem_assign(ftmp5, z1); + } + + /* z_out = (z1^2*x2 - z2^2*x1)*(z1*z2) */ + felem_mul(tmp, ftmp, ftmp5); + felem_reduce(z_out, tmp); + + /* ftmp = (z1^2*x2 - z2^2*x1)^2 */ + felem_assign(ftmp5, ftmp); + felem_square(tmp, ftmp); + felem_reduce(ftmp, tmp); + + /* ftmp5 = (z1^2*x2 - z2^2*x1)^3 */ + felem_mul(tmp, ftmp, ftmp5); + felem_reduce(ftmp5, tmp); + + /* ftmp2 = z2^2*x1*(z1^2*x2 - z2^2*x1)^2 */ + felem_mul(tmp, ftmp2, ftmp); + felem_reduce(ftmp2, tmp); + + /* tmp = z2^3*y1*(z1^2*x2 - z2^2*x1)^3 */ + felem_mul(tmp, ftmp4, ftmp5); + /* tmp[i] < 4 * 2^57 * 2^57 = 2^116 */ + + /* tmp2 = (z1^3*y2 - z2^3*y1)^2 */ + felem_square(tmp2, ftmp3); + /* tmp2[i] < 4 * 2^57 * 2^57 < 2^116 */ + + /* tmp2 = (z1^3*y2 - z2^3*y1)^2 - (z1^2*x2 - z2^2*x1)^3 */ + felem_diff_128_64(tmp2, ftmp5); + /* tmp2[i] < 2^116 + 2^64 + 8 < 2^117 */ + + /* ftmp5 = 2*z2^2*x1*(z1^2*x2 - z2^2*x1)^2 */ + felem_assign(ftmp5, ftmp2); + felem_scalar(ftmp5, 2); + /* ftmp5[i] < 2 * 2^57 = 2^58 */ + + /*- + * x_out = (z1^3*y2 - z2^3*y1)^2 - (z1^2*x2 - z2^2*x1)^3 - + * 2*z2^2*x1*(z1^2*x2 - z2^2*x1)^2 + */ + felem_diff_128_64(tmp2, ftmp5); + /* tmp2[i] < 2^117 + 2^64 + 8 < 2^118 */ + felem_reduce(x_out, tmp2); + + /* ftmp2 = z2^2*x1*(z1^2*x2 - z2^2*x1)^2 - x_out */ + felem_diff(ftmp2, x_out); + /* ftmp2[i] < 2^57 + 2^58 + 2 < 2^59 */ + + /* + * tmp2 = (z1^3*y2 - z2^3*y1)*(z2^2*x1*(z1^2*x2 - z2^2*x1)^2 - x_out) + */ + felem_mul(tmp2, ftmp3, ftmp2); + /* tmp2[i] < 4 * 2^57 * 2^59 = 2^118 */ + + /*- + * y_out = (z1^3*y2 - z2^3*y1)*(z2^2*x1*(z1^2*x2 - z2^2*x1)^2 - x_out) - + * z2^3*y1*(z1^2*x2 - z2^2*x1)^3 + */ + widefelem_diff(tmp2, tmp); + /* tmp2[i] < 2^118 + 2^120 < 2^121 */ + felem_reduce(y_out, tmp2); + + /* + * the result (x_out, y_out, z_out) is incorrect if one of the inputs is + * the point at infinity, so we need to check for this separately + */ + + /* + * if point 1 is at infinity, copy point 2 to output, and vice versa + */ + copy_conditional(x_out, x2, z1_is_zero); + copy_conditional(x_out, x1, z2_is_zero); + copy_conditional(y_out, y2, z1_is_zero); + copy_conditional(y_out, y1, z2_is_zero); + copy_conditional(z_out, z2, z1_is_zero); + copy_conditional(z_out, z1, z2_is_zero); + felem_assign(x3, x_out); + felem_assign(y3, y_out); + felem_assign(z3, z_out); +} /* * select_point selects the |idx|th point from a precomputation table and * copies it to out. * The pre_comp array argument should be size of |size| argument */ -static void select_point(const u64 idx, unsigned int size, const felem pre_comp[][3], felem out[3]) - { - unsigned i, j; - limb *outlimbs = &out[0][0]; - memset(outlimbs, 0, 3 * sizeof(felem)); - - for (i = 0; i < size; i++) - { - const limb *inlimbs = &pre_comp[i][0][0]; - u64 mask = i ^ idx; - mask |= mask >> 4; - mask |= mask >> 2; - mask |= mask >> 1; - mask &= 1; - mask--; - for (j = 0; j < 4 * 3; j++) - outlimbs[j] |= inlimbs[j] & mask; - } - } +static void select_point(const u64 idx, unsigned int size, + const felem pre_comp[][3], felem out[3]) +{ + unsigned i, j; + limb *outlimbs = &out[0][0]; + memset(outlimbs, 0, 3 * sizeof(felem)); + + for (i = 0; i < size; i++) { + const limb *inlimbs = &pre_comp[i][0][0]; + u64 mask = i ^ idx; + mask |= mask >> 4; + mask |= mask >> 2; + mask |= mask >> 1; + mask &= 1; + mask--; + for (j = 0; j < 4 * 3; j++) + outlimbs[j] |= inlimbs[j] & mask; + } +} /* get_bit returns the |i|th bit in |in| */ static char get_bit(const felem_bytearray in, unsigned i) - { - if (i >= 224) - return 0; - return (in[i >> 3] >> (i & 7)) & 1; - } - -/* Interleaved point multiplication using precomputed point multiples: - * The small point multiples 0*P, 1*P, ..., 16*P are in pre_comp[], - * the scalars in scalars[]. If g_scalar is non-NULL, we also add this multiple - * of the generator, using certain (large) precomputed multiples in g_pre_comp. - * Output point (X, Y, Z) is stored in x_out, y_out, z_out */ +{ + if (i >= 224) + return 0; + return (in[i >> 3] >> (i & 7)) & 1; +} + +/* + * Interleaved point multiplication using precomputed point multiples: The + * small point multiples 0*P, 1*P, ..., 16*P are in pre_comp[], the scalars + * in scalars[]. If g_scalar is non-NULL, we also add this multiple of the + * generator, using certain (large) precomputed multiples in g_pre_comp. + * Output point (X, Y, Z) is stored in x_out, y_out, z_out + */ static void batch_mul(felem x_out, felem y_out, felem z_out, - const felem_bytearray scalars[], const unsigned num_points, const u8 *g_scalar, - const int mixed, const felem pre_comp[][17][3], const felem g_pre_comp[2][16][3]) - { - int i, skip; - unsigned num; - unsigned gen_mul = (g_scalar != NULL); - felem nq[3], tmp[4]; - u64 bits; - u8 sign, digit; - - /* set nq to the point at infinity */ - memset(nq, 0, 3 * sizeof(felem)); - - /* Loop over all scalars msb-to-lsb, interleaving additions - * of multiples of the generator (two in each of the last 28 rounds) - * and additions of other points multiples (every 5th round). - */ - skip = 1; /* save two point operations in the first round */ - for (i = (num_points ? 220 : 27); i >= 0; --i) - { - /* double */ - if (!skip) - point_double(nq[0], nq[1], nq[2], nq[0], nq[1], nq[2]); - - /* add multiples of the generator */ - if (gen_mul && (i <= 27)) - { - /* first, look 28 bits upwards */ - bits = get_bit(g_scalar, i + 196) << 3; - bits |= get_bit(g_scalar, i + 140) << 2; - bits |= get_bit(g_scalar, i + 84) << 1; - bits |= get_bit(g_scalar, i + 28); - /* select the point to add, in constant time */ - select_point(bits, 16, g_pre_comp[1], tmp); - - if (!skip) - { - /* value 1 below is argument for "mixed" */ - point_add(nq[0], nq[1], nq[2], - nq[0], nq[1], nq[2], - 1, tmp[0], tmp[1], tmp[2]); - } - else - { - memcpy(nq, tmp, 3 * sizeof(felem)); - skip = 0; - } - - /* second, look at the current position */ - bits = get_bit(g_scalar, i + 168) << 3; - bits |= get_bit(g_scalar, i + 112) << 2; - bits |= get_bit(g_scalar, i + 56) << 1; - bits |= get_bit(g_scalar, i); - /* select the point to add, in constant time */ - select_point(bits, 16, g_pre_comp[0], tmp); - point_add(nq[0], nq[1], nq[2], - nq[0], nq[1], nq[2], - 1 /* mixed */, tmp[0], tmp[1], tmp[2]); - } - - /* do other additions every 5 doublings */ - if (num_points && (i % 5 == 0)) - { - /* loop over all scalars */ - for (num = 0; num < num_points; ++num) - { - bits = get_bit(scalars[num], i + 4) << 5; - bits |= get_bit(scalars[num], i + 3) << 4; - bits |= get_bit(scalars[num], i + 2) << 3; - bits |= get_bit(scalars[num], i + 1) << 2; - bits |= get_bit(scalars[num], i) << 1; - bits |= get_bit(scalars[num], i - 1); - ec_GFp_nistp_recode_scalar_bits(&sign, &digit, bits); - - /* select the point to add or subtract */ - select_point(digit, 17, pre_comp[num], tmp); - felem_neg(tmp[3], tmp[1]); /* (X, -Y, Z) is the negative point */ - copy_conditional(tmp[1], tmp[3], sign); - - if (!skip) - { - point_add(nq[0], nq[1], nq[2], - nq[0], nq[1], nq[2], - mixed, tmp[0], tmp[1], tmp[2]); - } - else - { - memcpy(nq, tmp, 3 * sizeof(felem)); - skip = 0; - } - } - } - } - felem_assign(x_out, nq[0]); - felem_assign(y_out, nq[1]); - felem_assign(z_out, nq[2]); - } + const felem_bytearray scalars[], + const unsigned num_points, const u8 *g_scalar, + const int mixed, const felem pre_comp[][17][3], + const felem g_pre_comp[2][16][3]) +{ + int i, skip; + unsigned num; + unsigned gen_mul = (g_scalar != NULL); + felem nq[3], tmp[4]; + u64 bits; + u8 sign, digit; + + /* set nq to the point at infinity */ + memset(nq, 0, 3 * sizeof(felem)); + + /* + * Loop over all scalars msb-to-lsb, interleaving additions of multiples + * of the generator (two in each of the last 28 rounds) and additions of + * other points multiples (every 5th round). + */ + skip = 1; /* save two point operations in the first + * round */ + for (i = (num_points ? 220 : 27); i >= 0; --i) { + /* double */ + if (!skip) + point_double(nq[0], nq[1], nq[2], nq[0], nq[1], nq[2]); + + /* add multiples of the generator */ + if (gen_mul && (i <= 27)) { + /* first, look 28 bits upwards */ + bits = get_bit(g_scalar, i + 196) << 3; + bits |= get_bit(g_scalar, i + 140) << 2; + bits |= get_bit(g_scalar, i + 84) << 1; + bits |= get_bit(g_scalar, i + 28); + /* select the point to add, in constant time */ + select_point(bits, 16, g_pre_comp[1], tmp); + + if (!skip) { + /* value 1 below is argument for "mixed" */ + point_add(nq[0], nq[1], nq[2], + nq[0], nq[1], nq[2], 1, tmp[0], tmp[1], tmp[2]); + } else { + memcpy(nq, tmp, 3 * sizeof(felem)); + skip = 0; + } + + /* second, look at the current position */ + bits = get_bit(g_scalar, i + 168) << 3; + bits |= get_bit(g_scalar, i + 112) << 2; + bits |= get_bit(g_scalar, i + 56) << 1; + bits |= get_bit(g_scalar, i); + /* select the point to add, in constant time */ + select_point(bits, 16, g_pre_comp[0], tmp); + point_add(nq[0], nq[1], nq[2], + nq[0], nq[1], nq[2], + 1 /* mixed */ , tmp[0], tmp[1], tmp[2]); + } + + /* do other additions every 5 doublings */ + if (num_points && (i % 5 == 0)) { + /* loop over all scalars */ + for (num = 0; num < num_points; ++num) { + bits = get_bit(scalars[num], i + 4) << 5; + bits |= get_bit(scalars[num], i + 3) << 4; + bits |= get_bit(scalars[num], i + 2) << 3; + bits |= get_bit(scalars[num], i + 1) << 2; + bits |= get_bit(scalars[num], i) << 1; + bits |= get_bit(scalars[num], i - 1); + ec_GFp_nistp_recode_scalar_bits(&sign, &digit, bits); + + /* select the point to add or subtract */ + select_point(digit, 17, pre_comp[num], tmp); + felem_neg(tmp[3], tmp[1]); /* (X, -Y, Z) is the negative + * point */ + copy_conditional(tmp[1], tmp[3], sign); + + if (!skip) { + point_add(nq[0], nq[1], nq[2], + nq[0], nq[1], nq[2], + mixed, tmp[0], tmp[1], tmp[2]); + } else { + memcpy(nq, tmp, 3 * sizeof(felem)); + skip = 0; + } + } + } + } + felem_assign(x_out, nq[0]); + felem_assign(y_out, nq[1]); + felem_assign(z_out, nq[2]); +} /******************************************************************************/ -/* FUNCTIONS TO MANAGE PRECOMPUTATION +/* + * FUNCTIONS TO MANAGE PRECOMPUTATION */ static NISTP224_PRE_COMP *nistp224_pre_comp_new() - { - NISTP224_PRE_COMP *ret = NULL; - ret = (NISTP224_PRE_COMP *) OPENSSL_malloc(sizeof *ret); - if (!ret) - { - ECerr(EC_F_NISTP224_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE); - return ret; - } - memset(ret->g_pre_comp, 0, sizeof(ret->g_pre_comp)); - ret->references = 1; - return ret; - } +{ + NISTP224_PRE_COMP *ret = NULL; + ret = (NISTP224_PRE_COMP *) OPENSSL_malloc(sizeof *ret); + if (!ret) { + ECerr(EC_F_NISTP224_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE); + return ret; + } + memset(ret->g_pre_comp, 0, sizeof(ret->g_pre_comp)); + ret->references = 1; + return ret; +} static void *nistp224_pre_comp_dup(void *src_) - { - NISTP224_PRE_COMP *src = src_; +{ + NISTP224_PRE_COMP *src = src_; - /* no need to actually copy, these objects never change! */ - CRYPTO_add(&src->references, 1, CRYPTO_LOCK_EC_PRE_COMP); + /* no need to actually copy, these objects never change! */ + CRYPTO_add(&src->references, 1, CRYPTO_LOCK_EC_PRE_COMP); - return src_; - } + return src_; +} static void nistp224_pre_comp_free(void *pre_) - { - int i; - NISTP224_PRE_COMP *pre = pre_; +{ + int i; + NISTP224_PRE_COMP *pre = pre_; - if (!pre) - return; + if (!pre) + return; - i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP); - if (i > 0) - return; + i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP); + if (i > 0) + return; - OPENSSL_free(pre); - } + OPENSSL_free(pre); +} static void nistp224_pre_comp_clear_free(void *pre_) - { - int i; - NISTP224_PRE_COMP *pre = pre_; +{ + int i; + NISTP224_PRE_COMP *pre = pre_; - if (!pre) - return; + if (!pre) + return; - i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP); - if (i > 0) - return; + i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP); + if (i > 0) + return; - OPENSSL_cleanse(pre, sizeof *pre); - OPENSSL_free(pre); - } + OPENSSL_cleanse(pre, sizeof *pre); + OPENSSL_free(pre); +} /******************************************************************************/ -/* OPENSSL EC_METHOD FUNCTIONS +/* + * OPENSSL EC_METHOD FUNCTIONS */ int ec_GFp_nistp224_group_init(EC_GROUP *group) - { - int ret; - ret = ec_GFp_simple_group_init(group); - group->a_is_minus3 = 1; - return ret; - } +{ + int ret; + ret = ec_GFp_simple_group_init(group); + group->a_is_minus3 = 1; + return ret; +} int ec_GFp_nistp224_group_set_curve(EC_GROUP *group, const BIGNUM *p, - const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) - { - int ret = 0; - BN_CTX *new_ctx = NULL; - BIGNUM *curve_p, *curve_a, *curve_b; - - if (ctx == NULL) - if ((ctx = new_ctx = BN_CTX_new()) == NULL) return 0; - BN_CTX_start(ctx); - if (((curve_p = BN_CTX_get(ctx)) == NULL) || - ((curve_a = BN_CTX_get(ctx)) == NULL) || - ((curve_b = BN_CTX_get(ctx)) == NULL)) goto err; - BN_bin2bn(nistp224_curve_params[0], sizeof(felem_bytearray), curve_p); - BN_bin2bn(nistp224_curve_params[1], sizeof(felem_bytearray), curve_a); - BN_bin2bn(nistp224_curve_params[2], sizeof(felem_bytearray), curve_b); - if ((BN_cmp(curve_p, p)) || (BN_cmp(curve_a, a)) || - (BN_cmp(curve_b, b))) - { - ECerr(EC_F_EC_GFP_NISTP224_GROUP_SET_CURVE, - EC_R_WRONG_CURVE_PARAMETERS); - goto err; - } - group->field_mod_func = BN_nist_mod_224; - ret = ec_GFp_simple_group_set_curve(group, p, a, b, ctx); -err: - BN_CTX_end(ctx); - if (new_ctx != NULL) - BN_CTX_free(new_ctx); - return ret; - } - -/* Takes the Jacobian coordinates (X, Y, Z) of a point and returns - * (X', Y') = (X/Z^2, Y/Z^3) */ + const BIGNUM *a, const BIGNUM *b, + BN_CTX *ctx) +{ + int ret = 0; + BN_CTX *new_ctx = NULL; + BIGNUM *curve_p, *curve_a, *curve_b; + + if (ctx == NULL) + if ((ctx = new_ctx = BN_CTX_new()) == NULL) + return 0; + BN_CTX_start(ctx); + if (((curve_p = BN_CTX_get(ctx)) == NULL) || + ((curve_a = BN_CTX_get(ctx)) == NULL) || + ((curve_b = BN_CTX_get(ctx)) == NULL)) + goto err; + BN_bin2bn(nistp224_curve_params[0], sizeof(felem_bytearray), curve_p); + BN_bin2bn(nistp224_curve_params[1], sizeof(felem_bytearray), curve_a); + BN_bin2bn(nistp224_curve_params[2], sizeof(felem_bytearray), curve_b); + if ((BN_cmp(curve_p, p)) || (BN_cmp(curve_a, a)) || (BN_cmp(curve_b, b))) { + ECerr(EC_F_EC_GFP_NISTP224_GROUP_SET_CURVE, + EC_R_WRONG_CURVE_PARAMETERS); + goto err; + } + group->field_mod_func = BN_nist_mod_224; + ret = ec_GFp_simple_group_set_curve(group, p, a, b, ctx); + err: + BN_CTX_end(ctx); + if (new_ctx != NULL) + BN_CTX_free(new_ctx); + return ret; +} + +/* + * Takes the Jacobian coordinates (X, Y, Z) of a point and returns (X', Y') = + * (X/Z^2, Y/Z^3) + */ int ec_GFp_nistp224_point_get_affine_coordinates(const EC_GROUP *group, - const EC_POINT *point, BIGNUM *x, BIGNUM *y, BN_CTX *ctx) - { - felem z1, z2, x_in, y_in, x_out, y_out; - widefelem tmp; - - if (EC_POINT_is_at_infinity(group, point)) - { - ECerr(EC_F_EC_GFP_NISTP224_POINT_GET_AFFINE_COORDINATES, - EC_R_POINT_AT_INFINITY); - return 0; - } - if ((!BN_to_felem(x_in, &point->X)) || (!BN_to_felem(y_in, &point->Y)) || - (!BN_to_felem(z1, &point->Z))) return 0; - felem_inv(z2, z1); - felem_square(tmp, z2); felem_reduce(z1, tmp); - felem_mul(tmp, x_in, z1); felem_reduce(x_in, tmp); - felem_contract(x_out, x_in); - if (x != NULL) - { - if (!felem_to_BN(x, x_out)) { - ECerr(EC_F_EC_GFP_NISTP224_POINT_GET_AFFINE_COORDINATES, - ERR_R_BN_LIB); - return 0; - } - } - felem_mul(tmp, z1, z2); felem_reduce(z1, tmp); - felem_mul(tmp, y_in, z1); felem_reduce(y_in, tmp); - felem_contract(y_out, y_in); - if (y != NULL) - { - if (!felem_to_BN(y, y_out)) { - ECerr(EC_F_EC_GFP_NISTP224_POINT_GET_AFFINE_COORDINATES, - ERR_R_BN_LIB); - return 0; - } - } - return 1; - } - -static void make_points_affine(size_t num, felem points[/*num*/][3], felem tmp_felems[/*num+1*/]) - { - /* Runs in constant time, unless an input is the point at infinity - * (which normally shouldn't happen). */ - ec_GFp_nistp_points_make_affine_internal( - num, - points, - sizeof(felem), - tmp_felems, - (void (*)(void *)) felem_one, - (int (*)(const void *)) felem_is_zero_int, - (void (*)(void *, const void *)) felem_assign, - (void (*)(void *, const void *)) felem_square_reduce, - (void (*)(void *, const void *, const void *)) felem_mul_reduce, - (void (*)(void *, const void *)) felem_inv, - (void (*)(void *, const void *)) felem_contract); - } - -/* Computes scalar*generator + \sum scalars[i]*points[i], ignoring NULL values - * Result is stored in r (r can equal one of the inputs). */ + const EC_POINT *point, + BIGNUM *x, BIGNUM *y, + BN_CTX *ctx) +{ + felem z1, z2, x_in, y_in, x_out, y_out; + widefelem tmp; + + if (EC_POINT_is_at_infinity(group, point)) { + ECerr(EC_F_EC_GFP_NISTP224_POINT_GET_AFFINE_COORDINATES, + EC_R_POINT_AT_INFINITY); + return 0; + } + if ((!BN_to_felem(x_in, &point->X)) || (!BN_to_felem(y_in, &point->Y)) || + (!BN_to_felem(z1, &point->Z))) + return 0; + felem_inv(z2, z1); + felem_square(tmp, z2); + felem_reduce(z1, tmp); + felem_mul(tmp, x_in, z1); + felem_reduce(x_in, tmp); + felem_contract(x_out, x_in); + if (x != NULL) { + if (!felem_to_BN(x, x_out)) { + ECerr(EC_F_EC_GFP_NISTP224_POINT_GET_AFFINE_COORDINATES, + ERR_R_BN_LIB); + return 0; + } + } + felem_mul(tmp, z1, z2); + felem_reduce(z1, tmp); + felem_mul(tmp, y_in, z1); + felem_reduce(y_in, tmp); + felem_contract(y_out, y_in); + if (y != NULL) { + if (!felem_to_BN(y, y_out)) { + ECerr(EC_F_EC_GFP_NISTP224_POINT_GET_AFFINE_COORDINATES, + ERR_R_BN_LIB); + return 0; + } + } + return 1; +} + +static void make_points_affine(size_t num, felem points[ /* num */ ][3], + felem tmp_felems[ /* num+1 */ ]) +{ + /* + * Runs in constant time, unless an input is the point at infinity (which + * normally shouldn't happen). + */ + ec_GFp_nistp_points_make_affine_internal(num, + points, + sizeof(felem), + tmp_felems, + (void (*)(void *))felem_one, + (int (*)(const void *)) + felem_is_zero_int, + (void (*)(void *, const void *)) + felem_assign, + (void (*)(void *, const void *)) + felem_square_reduce, (void (*) + (void *, + const void + *, + const void + *)) + felem_mul_reduce, + (void (*)(void *, const void *)) + felem_inv, + (void (*)(void *, const void *)) + felem_contract); +} + +/* + * Computes scalar*generator + \sum scalars[i]*points[i], ignoring NULL + * values Result is stored in r (r can equal one of the inputs). + */ int ec_GFp_nistp224_points_mul(const EC_GROUP *group, EC_POINT *r, - const BIGNUM *scalar, size_t num, const EC_POINT *points[], - const BIGNUM *scalars[], BN_CTX *ctx) - { - int ret = 0; - int j; - unsigned i; - int mixed = 0; - BN_CTX *new_ctx = NULL; - BIGNUM *x, *y, *z, *tmp_scalar; - felem_bytearray g_secret; - felem_bytearray *secrets = NULL; - felem (*pre_comp)[17][3] = NULL; - felem *tmp_felems = NULL; - felem_bytearray tmp; - unsigned num_bytes; - int have_pre_comp = 0; - size_t num_points = num; - felem x_in, y_in, z_in, x_out, y_out, z_out; - NISTP224_PRE_COMP *pre = NULL; - const felem (*g_pre_comp)[16][3] = NULL; - EC_POINT *generator = NULL; - const EC_POINT *p = NULL; - const BIGNUM *p_scalar = NULL; - - if (ctx == NULL) - if ((ctx = new_ctx = BN_CTX_new()) == NULL) return 0; - BN_CTX_start(ctx); - if (((x = BN_CTX_get(ctx)) == NULL) || - ((y = BN_CTX_get(ctx)) == NULL) || - ((z = BN_CTX_get(ctx)) == NULL) || - ((tmp_scalar = BN_CTX_get(ctx)) == NULL)) - goto err; - - if (scalar != NULL) - { - pre = EC_EX_DATA_get_data(group->extra_data, - nistp224_pre_comp_dup, nistp224_pre_comp_free, - nistp224_pre_comp_clear_free); - if (pre) - /* we have precomputation, try to use it */ - g_pre_comp = (const felem (*)[16][3]) pre->g_pre_comp; - else - /* try to use the standard precomputation */ - g_pre_comp = &gmul[0]; - generator = EC_POINT_new(group); - if (generator == NULL) - goto err; - /* get the generator from precomputation */ - if (!felem_to_BN(x, g_pre_comp[0][1][0]) || - !felem_to_BN(y, g_pre_comp[0][1][1]) || - !felem_to_BN(z, g_pre_comp[0][1][2])) - { - ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_BN_LIB); - goto err; - } - if (!EC_POINT_set_Jprojective_coordinates_GFp(group, - generator, x, y, z, ctx)) - goto err; - if (0 == EC_POINT_cmp(group, generator, group->generator, ctx)) - /* precomputation matches generator */ - have_pre_comp = 1; - else - /* we don't have valid precomputation: - * treat the generator as a random point */ - num_points = num_points + 1; - } - - if (num_points > 0) - { - if (num_points >= 3) - { - /* unless we precompute multiples for just one or two points, - * converting those into affine form is time well spent */ - mixed = 1; - } - secrets = OPENSSL_malloc(num_points * sizeof(felem_bytearray)); - pre_comp = OPENSSL_malloc(num_points * 17 * 3 * sizeof(felem)); - if (mixed) - tmp_felems = OPENSSL_malloc((num_points * 17 + 1) * sizeof(felem)); - if ((secrets == NULL) || (pre_comp == NULL) || (mixed && (tmp_felems == NULL))) - { - ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_MALLOC_FAILURE); - goto err; - } - - /* we treat NULL scalars as 0, and NULL points as points at infinity, - * i.e., they contribute nothing to the linear combination */ - memset(secrets, 0, num_points * sizeof(felem_bytearray)); - memset(pre_comp, 0, num_points * 17 * 3 * sizeof(felem)); - for (i = 0; i < num_points; ++i) - { - if (i == num) - /* the generator */ - { - p = EC_GROUP_get0_generator(group); - p_scalar = scalar; - } - else - /* the i^th point */ - { - p = points[i]; - p_scalar = scalars[i]; - } - if ((p_scalar != NULL) && (p != NULL)) - { - /* reduce scalar to 0 <= scalar < 2^224 */ - if ((BN_num_bits(p_scalar) > 224) || (BN_is_negative(p_scalar))) - { - /* this is an unusual input, and we don't guarantee - * constant-timeness */ - if (!BN_nnmod(tmp_scalar, p_scalar, &group->order, ctx)) - { - ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_BN_LIB); - goto err; - } - num_bytes = BN_bn2bin(tmp_scalar, tmp); - } - else - num_bytes = BN_bn2bin(p_scalar, tmp); - flip_endian(secrets[i], tmp, num_bytes); - /* precompute multiples */ - if ((!BN_to_felem(x_out, &p->X)) || - (!BN_to_felem(y_out, &p->Y)) || - (!BN_to_felem(z_out, &p->Z))) goto err; - felem_assign(pre_comp[i][1][0], x_out); - felem_assign(pre_comp[i][1][1], y_out); - felem_assign(pre_comp[i][1][2], z_out); - for (j = 2; j <= 16; ++j) - { - if (j & 1) - { - point_add( - pre_comp[i][j][0], pre_comp[i][j][1], pre_comp[i][j][2], - pre_comp[i][1][0], pre_comp[i][1][1], pre_comp[i][1][2], - 0, pre_comp[i][j-1][0], pre_comp[i][j-1][1], pre_comp[i][j-1][2]); - } - else - { - point_double( - pre_comp[i][j][0], pre_comp[i][j][1], pre_comp[i][j][2], - pre_comp[i][j/2][0], pre_comp[i][j/2][1], pre_comp[i][j/2][2]); - } - } - } - } - if (mixed) - make_points_affine(num_points * 17, pre_comp[0], tmp_felems); - } - - /* the scalar for the generator */ - if ((scalar != NULL) && (have_pre_comp)) - { - memset(g_secret, 0, sizeof g_secret); - /* reduce scalar to 0 <= scalar < 2^224 */ - if ((BN_num_bits(scalar) > 224) || (BN_is_negative(scalar))) - { - /* this is an unusual input, and we don't guarantee - * constant-timeness */ - if (!BN_nnmod(tmp_scalar, scalar, &group->order, ctx)) - { - ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_BN_LIB); - goto err; - } - num_bytes = BN_bn2bin(tmp_scalar, tmp); - } - else - num_bytes = BN_bn2bin(scalar, tmp); - flip_endian(g_secret, tmp, num_bytes); - /* do the multiplication with generator precomputation*/ - batch_mul(x_out, y_out, z_out, - (const felem_bytearray (*)) secrets, num_points, - g_secret, - mixed, (const felem (*)[17][3]) pre_comp, - g_pre_comp); - } - else - /* do the multiplication without generator precomputation */ - batch_mul(x_out, y_out, z_out, - (const felem_bytearray (*)) secrets, num_points, - NULL, mixed, (const felem (*)[17][3]) pre_comp, NULL); - /* reduce the output to its unique minimal representation */ - felem_contract(x_in, x_out); - felem_contract(y_in, y_out); - felem_contract(z_in, z_out); - if ((!felem_to_BN(x, x_in)) || (!felem_to_BN(y, y_in)) || - (!felem_to_BN(z, z_in))) - { - ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_BN_LIB); - goto err; - } - ret = EC_POINT_set_Jprojective_coordinates_GFp(group, r, x, y, z, ctx); - -err: - BN_CTX_end(ctx); - if (generator != NULL) - EC_POINT_free(generator); - if (new_ctx != NULL) - BN_CTX_free(new_ctx); - if (secrets != NULL) - OPENSSL_free(secrets); - if (pre_comp != NULL) - OPENSSL_free(pre_comp); - if (tmp_felems != NULL) - OPENSSL_free(tmp_felems); - return ret; - } + const BIGNUM *scalar, size_t num, + const EC_POINT *points[], + const BIGNUM *scalars[], BN_CTX *ctx) +{ + int ret = 0; + int j; + unsigned i; + int mixed = 0; + BN_CTX *new_ctx = NULL; + BIGNUM *x, *y, *z, *tmp_scalar; + felem_bytearray g_secret; + felem_bytearray *secrets = NULL; + felem(*pre_comp)[17][3] = NULL; + felem *tmp_felems = NULL; + felem_bytearray tmp; + unsigned num_bytes; + int have_pre_comp = 0; + size_t num_points = num; + felem x_in, y_in, z_in, x_out, y_out, z_out; + NISTP224_PRE_COMP *pre = NULL; + const felem(*g_pre_comp)[16][3] = NULL; + EC_POINT *generator = NULL; + const EC_POINT *p = NULL; + const BIGNUM *p_scalar = NULL; + + if (ctx == NULL) + if ((ctx = new_ctx = BN_CTX_new()) == NULL) + return 0; + BN_CTX_start(ctx); + if (((x = BN_CTX_get(ctx)) == NULL) || + ((y = BN_CTX_get(ctx)) == NULL) || + ((z = BN_CTX_get(ctx)) == NULL) || + ((tmp_scalar = BN_CTX_get(ctx)) == NULL)) + goto err; + + if (scalar != NULL) { + pre = EC_EX_DATA_get_data(group->extra_data, + nistp224_pre_comp_dup, + nistp224_pre_comp_free, + nistp224_pre_comp_clear_free); + if (pre) + /* we have precomputation, try to use it */ + g_pre_comp = (const felem(*)[16][3])pre->g_pre_comp; + else + /* try to use the standard precomputation */ + g_pre_comp = &gmul[0]; + generator = EC_POINT_new(group); + if (generator == NULL) + goto err; + /* get the generator from precomputation */ + if (!felem_to_BN(x, g_pre_comp[0][1][0]) || + !felem_to_BN(y, g_pre_comp[0][1][1]) || + !felem_to_BN(z, g_pre_comp[0][1][2])) { + ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_BN_LIB); + goto err; + } + if (!EC_POINT_set_Jprojective_coordinates_GFp(group, + generator, x, y, z, + ctx)) + goto err; + if (0 == EC_POINT_cmp(group, generator, group->generator, ctx)) + /* precomputation matches generator */ + have_pre_comp = 1; + else + /* + * we don't have valid precomputation: treat the generator as a + * random point + */ + num_points = num_points + 1; + } + + if (num_points > 0) { + if (num_points >= 3) { + /* + * unless we precompute multiples for just one or two points, + * converting those into affine form is time well spent + */ + mixed = 1; + } + secrets = OPENSSL_malloc(num_points * sizeof(felem_bytearray)); + pre_comp = OPENSSL_malloc(num_points * 17 * 3 * sizeof(felem)); + if (mixed) + tmp_felems = + OPENSSL_malloc((num_points * 17 + 1) * sizeof(felem)); + if ((secrets == NULL) || (pre_comp == NULL) + || (mixed && (tmp_felems == NULL))) { + ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_MALLOC_FAILURE); + goto err; + } + + /* + * we treat NULL scalars as 0, and NULL points as points at infinity, + * i.e., they contribute nothing to the linear combination + */ + memset(secrets, 0, num_points * sizeof(felem_bytearray)); + memset(pre_comp, 0, num_points * 17 * 3 * sizeof(felem)); + for (i = 0; i < num_points; ++i) { + if (i == num) + /* the generator */ + { + p = EC_GROUP_get0_generator(group); + p_scalar = scalar; + } else + /* the i^th point */ + { + p = points[i]; + p_scalar = scalars[i]; + } + if ((p_scalar != NULL) && (p != NULL)) { + /* reduce scalar to 0 <= scalar < 2^224 */ + if ((BN_num_bits(p_scalar) > 224) + || (BN_is_negative(p_scalar))) { + /* + * this is an unusual input, and we don't guarantee + * constant-timeness + */ + if (!BN_nnmod(tmp_scalar, p_scalar, &group->order, ctx)) { + ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_BN_LIB); + goto err; + } + num_bytes = BN_bn2bin(tmp_scalar, tmp); + } else + num_bytes = BN_bn2bin(p_scalar, tmp); + flip_endian(secrets[i], tmp, num_bytes); + /* precompute multiples */ + if ((!BN_to_felem(x_out, &p->X)) || + (!BN_to_felem(y_out, &p->Y)) || + (!BN_to_felem(z_out, &p->Z))) + goto err; + felem_assign(pre_comp[i][1][0], x_out); + felem_assign(pre_comp[i][1][1], y_out); + felem_assign(pre_comp[i][1][2], z_out); + for (j = 2; j <= 16; ++j) { + if (j & 1) { + point_add(pre_comp[i][j][0], pre_comp[i][j][1], + pre_comp[i][j][2], pre_comp[i][1][0], + pre_comp[i][1][1], pre_comp[i][1][2], 0, + pre_comp[i][j - 1][0], + pre_comp[i][j - 1][1], + pre_comp[i][j - 1][2]); + } else { + point_double(pre_comp[i][j][0], pre_comp[i][j][1], + pre_comp[i][j][2], pre_comp[i][j / 2][0], + pre_comp[i][j / 2][1], + pre_comp[i][j / 2][2]); + } + } + } + } + if (mixed) + make_points_affine(num_points * 17, pre_comp[0], tmp_felems); + } + + /* the scalar for the generator */ + if ((scalar != NULL) && (have_pre_comp)) { + memset(g_secret, 0, sizeof g_secret); + /* reduce scalar to 0 <= scalar < 2^224 */ + if ((BN_num_bits(scalar) > 224) || (BN_is_negative(scalar))) { + /* + * this is an unusual input, and we don't guarantee + * constant-timeness + */ + if (!BN_nnmod(tmp_scalar, scalar, &group->order, ctx)) { + ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_BN_LIB); + goto err; + } + num_bytes = BN_bn2bin(tmp_scalar, tmp); + } else + num_bytes = BN_bn2bin(scalar, tmp); + flip_endian(g_secret, tmp, num_bytes); + /* do the multiplication with generator precomputation */ + batch_mul(x_out, y_out, z_out, + (const felem_bytearray(*))secrets, num_points, + g_secret, + mixed, (const felem(*)[17][3])pre_comp, g_pre_comp); + } else + /* do the multiplication without generator precomputation */ + batch_mul(x_out, y_out, z_out, + (const felem_bytearray(*))secrets, num_points, + NULL, mixed, (const felem(*)[17][3])pre_comp, NULL); + /* reduce the output to its unique minimal representation */ + felem_contract(x_in, x_out); + felem_contract(y_in, y_out); + felem_contract(z_in, z_out); + if ((!felem_to_BN(x, x_in)) || (!felem_to_BN(y, y_in)) || + (!felem_to_BN(z, z_in))) { + ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_BN_LIB); + goto err; + } + ret = EC_POINT_set_Jprojective_coordinates_GFp(group, r, x, y, z, ctx); + + err: + BN_CTX_end(ctx); + if (generator != NULL) + EC_POINT_free(generator); + if (new_ctx != NULL) + BN_CTX_free(new_ctx); + if (secrets != NULL) + OPENSSL_free(secrets); + if (pre_comp != NULL) + OPENSSL_free(pre_comp); + if (tmp_felems != NULL) + OPENSSL_free(tmp_felems); + return ret; +} int ec_GFp_nistp224_precompute_mult(EC_GROUP *group, BN_CTX *ctx) - { - int ret = 0; - NISTP224_PRE_COMP *pre = NULL; - int i, j; - BN_CTX *new_ctx = NULL; - BIGNUM *x, *y; - EC_POINT *generator = NULL; - felem tmp_felems[32]; - - /* throw away old precomputation */ - EC_EX_DATA_free_data(&group->extra_data, nistp224_pre_comp_dup, - nistp224_pre_comp_free, nistp224_pre_comp_clear_free); - if (ctx == NULL) - if ((ctx = new_ctx = BN_CTX_new()) == NULL) return 0; - BN_CTX_start(ctx); - if (((x = BN_CTX_get(ctx)) == NULL) || - ((y = BN_CTX_get(ctx)) == NULL)) - goto err; - /* get the generator */ - if (group->generator == NULL) goto err; - generator = EC_POINT_new(group); - if (generator == NULL) - goto err; - BN_bin2bn(nistp224_curve_params[3], sizeof (felem_bytearray), x); - BN_bin2bn(nistp224_curve_params[4], sizeof (felem_bytearray), y); - if (!EC_POINT_set_affine_coordinates_GFp(group, generator, x, y, ctx)) - goto err; - if ((pre = nistp224_pre_comp_new()) == NULL) - goto err; - /* if the generator is the standard one, use built-in precomputation */ - if (0 == EC_POINT_cmp(group, generator, group->generator, ctx)) - { - memcpy(pre->g_pre_comp, gmul, sizeof(pre->g_pre_comp)); - ret = 1; - goto err; - } - if ((!BN_to_felem(pre->g_pre_comp[0][1][0], &group->generator->X)) || - (!BN_to_felem(pre->g_pre_comp[0][1][1], &group->generator->Y)) || - (!BN_to_felem(pre->g_pre_comp[0][1][2], &group->generator->Z))) - goto err; - /* compute 2^56*G, 2^112*G, 2^168*G for the first table, - * 2^28*G, 2^84*G, 2^140*G, 2^196*G for the second one - */ - for (i = 1; i <= 8; i <<= 1) - { - point_double( - pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2], - pre->g_pre_comp[0][i][0], pre->g_pre_comp[0][i][1], pre->g_pre_comp[0][i][2]); - for (j = 0; j < 27; ++j) - { - point_double( - pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2], - pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2]); - } - if (i == 8) - break; - point_double( - pre->g_pre_comp[0][2*i][0], pre->g_pre_comp[0][2*i][1], pre->g_pre_comp[0][2*i][2], - pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2]); - for (j = 0; j < 27; ++j) - { - point_double( - pre->g_pre_comp[0][2*i][0], pre->g_pre_comp[0][2*i][1], pre->g_pre_comp[0][2*i][2], - pre->g_pre_comp[0][2*i][0], pre->g_pre_comp[0][2*i][1], pre->g_pre_comp[0][2*i][2]); - } - } - for (i = 0; i < 2; i++) - { - /* g_pre_comp[i][0] is the point at infinity */ - memset(pre->g_pre_comp[i][0], 0, sizeof(pre->g_pre_comp[i][0])); - /* the remaining multiples */ - /* 2^56*G + 2^112*G resp. 2^84*G + 2^140*G */ - point_add( - pre->g_pre_comp[i][6][0], pre->g_pre_comp[i][6][1], - pre->g_pre_comp[i][6][2], pre->g_pre_comp[i][4][0], - pre->g_pre_comp[i][4][1], pre->g_pre_comp[i][4][2], - 0, pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1], - pre->g_pre_comp[i][2][2]); - /* 2^56*G + 2^168*G resp. 2^84*G + 2^196*G */ - point_add( - pre->g_pre_comp[i][10][0], pre->g_pre_comp[i][10][1], - pre->g_pre_comp[i][10][2], pre->g_pre_comp[i][8][0], - pre->g_pre_comp[i][8][1], pre->g_pre_comp[i][8][2], - 0, pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1], - pre->g_pre_comp[i][2][2]); - /* 2^112*G + 2^168*G resp. 2^140*G + 2^196*G */ - point_add( - pre->g_pre_comp[i][12][0], pre->g_pre_comp[i][12][1], - pre->g_pre_comp[i][12][2], pre->g_pre_comp[i][8][0], - pre->g_pre_comp[i][8][1], pre->g_pre_comp[i][8][2], - 0, pre->g_pre_comp[i][4][0], pre->g_pre_comp[i][4][1], - pre->g_pre_comp[i][4][2]); - /* 2^56*G + 2^112*G + 2^168*G resp. 2^84*G + 2^140*G + 2^196*G */ - point_add( - pre->g_pre_comp[i][14][0], pre->g_pre_comp[i][14][1], - pre->g_pre_comp[i][14][2], pre->g_pre_comp[i][12][0], - pre->g_pre_comp[i][12][1], pre->g_pre_comp[i][12][2], - 0, pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1], - pre->g_pre_comp[i][2][2]); - for (j = 1; j < 8; ++j) - { - /* odd multiples: add G resp. 2^28*G */ - point_add( - pre->g_pre_comp[i][2*j+1][0], pre->g_pre_comp[i][2*j+1][1], - pre->g_pre_comp[i][2*j+1][2], pre->g_pre_comp[i][2*j][0], - pre->g_pre_comp[i][2*j][1], pre->g_pre_comp[i][2*j][2], - 0, pre->g_pre_comp[i][1][0], pre->g_pre_comp[i][1][1], - pre->g_pre_comp[i][1][2]); - } - } - make_points_affine(31, &(pre->g_pre_comp[0][1]), tmp_felems); - - if (!EC_EX_DATA_set_data(&group->extra_data, pre, nistp224_pre_comp_dup, - nistp224_pre_comp_free, nistp224_pre_comp_clear_free)) - goto err; - ret = 1; - pre = NULL; +{ + int ret = 0; + NISTP224_PRE_COMP *pre = NULL; + int i, j; + BN_CTX *new_ctx = NULL; + BIGNUM *x, *y; + EC_POINT *generator = NULL; + felem tmp_felems[32]; + + /* throw away old precomputation */ + EC_EX_DATA_free_data(&group->extra_data, nistp224_pre_comp_dup, + nistp224_pre_comp_free, + nistp224_pre_comp_clear_free); + if (ctx == NULL) + if ((ctx = new_ctx = BN_CTX_new()) == NULL) + return 0; + BN_CTX_start(ctx); + if (((x = BN_CTX_get(ctx)) == NULL) || ((y = BN_CTX_get(ctx)) == NULL)) + goto err; + /* get the generator */ + if (group->generator == NULL) + goto err; + generator = EC_POINT_new(group); + if (generator == NULL) + goto err; + BN_bin2bn(nistp224_curve_params[3], sizeof(felem_bytearray), x); + BN_bin2bn(nistp224_curve_params[4], sizeof(felem_bytearray), y); + if (!EC_POINT_set_affine_coordinates_GFp(group, generator, x, y, ctx)) + goto err; + if ((pre = nistp224_pre_comp_new()) == NULL) + goto err; + /* + * if the generator is the standard one, use built-in precomputation + */ + if (0 == EC_POINT_cmp(group, generator, group->generator, ctx)) { + memcpy(pre->g_pre_comp, gmul, sizeof(pre->g_pre_comp)); + ret = 1; + goto err; + } + if ((!BN_to_felem(pre->g_pre_comp[0][1][0], &group->generator->X)) || + (!BN_to_felem(pre->g_pre_comp[0][1][1], &group->generator->Y)) || + (!BN_to_felem(pre->g_pre_comp[0][1][2], &group->generator->Z))) + goto err; + /* + * compute 2^56*G, 2^112*G, 2^168*G for the first table, 2^28*G, 2^84*G, + * 2^140*G, 2^196*G for the second one + */ + for (i = 1; i <= 8; i <<= 1) { + point_double(pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], + pre->g_pre_comp[1][i][2], pre->g_pre_comp[0][i][0], + pre->g_pre_comp[0][i][1], pre->g_pre_comp[0][i][2]); + for (j = 0; j < 27; ++j) { + point_double(pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], + pre->g_pre_comp[1][i][2], pre->g_pre_comp[1][i][0], + pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2]); + } + if (i == 8) + break; + point_double(pre->g_pre_comp[0][2 * i][0], + pre->g_pre_comp[0][2 * i][1], + pre->g_pre_comp[0][2 * i][2], pre->g_pre_comp[1][i][0], + pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2]); + for (j = 0; j < 27; ++j) { + point_double(pre->g_pre_comp[0][2 * i][0], + pre->g_pre_comp[0][2 * i][1], + pre->g_pre_comp[0][2 * i][2], + pre->g_pre_comp[0][2 * i][0], + pre->g_pre_comp[0][2 * i][1], + pre->g_pre_comp[0][2 * i][2]); + } + } + for (i = 0; i < 2; i++) { + /* g_pre_comp[i][0] is the point at infinity */ + memset(pre->g_pre_comp[i][0], 0, sizeof(pre->g_pre_comp[i][0])); + /* the remaining multiples */ + /* 2^56*G + 2^112*G resp. 2^84*G + 2^140*G */ + point_add(pre->g_pre_comp[i][6][0], pre->g_pre_comp[i][6][1], + pre->g_pre_comp[i][6][2], pre->g_pre_comp[i][4][0], + pre->g_pre_comp[i][4][1], pre->g_pre_comp[i][4][2], + 0, pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1], + pre->g_pre_comp[i][2][2]); + /* 2^56*G + 2^168*G resp. 2^84*G + 2^196*G */ + point_add(pre->g_pre_comp[i][10][0], pre->g_pre_comp[i][10][1], + pre->g_pre_comp[i][10][2], pre->g_pre_comp[i][8][0], + pre->g_pre_comp[i][8][1], pre->g_pre_comp[i][8][2], + 0, pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1], + pre->g_pre_comp[i][2][2]); + /* 2^112*G + 2^168*G resp. 2^140*G + 2^196*G */ + point_add(pre->g_pre_comp[i][12][0], pre->g_pre_comp[i][12][1], + pre->g_pre_comp[i][12][2], pre->g_pre_comp[i][8][0], + pre->g_pre_comp[i][8][1], pre->g_pre_comp[i][8][2], + 0, pre->g_pre_comp[i][4][0], pre->g_pre_comp[i][4][1], + pre->g_pre_comp[i][4][2]); + /* + * 2^56*G + 2^112*G + 2^168*G resp. 2^84*G + 2^140*G + 2^196*G + */ + point_add(pre->g_pre_comp[i][14][0], pre->g_pre_comp[i][14][1], + pre->g_pre_comp[i][14][2], pre->g_pre_comp[i][12][0], + pre->g_pre_comp[i][12][1], pre->g_pre_comp[i][12][2], + 0, pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1], + pre->g_pre_comp[i][2][2]); + for (j = 1; j < 8; ++j) { + /* odd multiples: add G resp. 2^28*G */ + point_add(pre->g_pre_comp[i][2 * j + 1][0], + pre->g_pre_comp[i][2 * j + 1][1], + pre->g_pre_comp[i][2 * j + 1][2], + pre->g_pre_comp[i][2 * j][0], + pre->g_pre_comp[i][2 * j][1], + pre->g_pre_comp[i][2 * j][2], 0, + pre->g_pre_comp[i][1][0], pre->g_pre_comp[i][1][1], + pre->g_pre_comp[i][1][2]); + } + } + make_points_affine(31, &(pre->g_pre_comp[0][1]), tmp_felems); + + if (!EC_EX_DATA_set_data(&group->extra_data, pre, nistp224_pre_comp_dup, + nistp224_pre_comp_free, + nistp224_pre_comp_clear_free)) + goto err; + ret = 1; + pre = NULL; err: - BN_CTX_end(ctx); - if (generator != NULL) - EC_POINT_free(generator); - if (new_ctx != NULL) - BN_CTX_free(new_ctx); - if (pre) - nistp224_pre_comp_free(pre); - return ret; - } + BN_CTX_end(ctx); + if (generator != NULL) + EC_POINT_free(generator); + if (new_ctx != NULL) + BN_CTX_free(new_ctx); + if (pre) + nistp224_pre_comp_free(pre); + return ret; +} int ec_GFp_nistp224_have_precompute_mult(const EC_GROUP *group) - { - if (EC_EX_DATA_get_data(group->extra_data, nistp224_pre_comp_dup, - nistp224_pre_comp_free, nistp224_pre_comp_clear_free) - != NULL) - return 1; - else - return 0; - } +{ + if (EC_EX_DATA_get_data(group->extra_data, nistp224_pre_comp_dup, + nistp224_pre_comp_free, + nistp224_pre_comp_clear_free) + != NULL) + return 1; + else + return 0; +} #else -static void *dummy=&dummy; +static void *dummy = &dummy; #endif |