diff options
Diffstat (limited to 'drivers/builtin_openssl2/crypto/ec/ecp_nistp256.c')
| -rw-r--r-- | drivers/builtin_openssl2/crypto/ec/ecp_nistp256.c | 3866 |
1 files changed, 2032 insertions, 1834 deletions
diff --git a/drivers/builtin_openssl2/crypto/ec/ecp_nistp256.c b/drivers/builtin_openssl2/crypto/ec/ecp_nistp256.c index 4bc0f5dce0..a5887086c6 100644 --- a/drivers/builtin_openssl2/crypto/ec/ecp_nistp256.c +++ b/drivers/builtin_openssl2/crypto/ec/ecp_nistp256.c @@ -29,62 +29,67 @@ #include <openssl/opensslconf.h> #ifndef OPENSSL_NO_EC_NISTP_64_GCC_128 -#ifndef OPENSSL_SYS_VMS -#include <stdint.h> -#else -#include <inttypes.h> -#endif +# ifndef OPENSSL_SYS_VMS +# include <stdint.h> +# else +# include <inttypes.h> +# endif -#include <string.h> -#include <openssl/err.h> -#include "ec_lcl.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 */ - typedef __int128_t int128_t; -#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 */ +typedef __int128_t int128_t; +# else +# error "Need GCC 3.1 or later to define type uint128_t" +# endif typedef uint8_t u8; typedef uint32_t u32; typedef uint64_t u64; typedef int64_t s64; -/* The underlying field. - * - * P256 operates over GF(2^256-2^224+2^192+2^96-1). We can serialise an element - * of this field into 32 bytes. We call this an felem_bytearray. */ +/* + * The underlying field. P256 operates over GF(2^256-2^224+2^192+2^96-1). We + * can serialise an element of this field into 32 bytes. We call this an + * felem_bytearray. + */ typedef u8 felem_bytearray[32]; -/* These are the parameters of P256, taken from FIPS 186-3, page 86. These - * values are big-endian. */ +/* + * These are the parameters of P256, taken from FIPS 186-3, page 86. These + * values are big-endian. + */ static const felem_bytearray nistp256_curve_params[5] = { - {0xff, 0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x01, /* p */ - 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, - 0x00, 0x00, 0x00, 0x00, 0xff, 0xff, 0xff, 0xff, - 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff}, - {0xff, 0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x01, /* a = -3 */ - 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, - 0x00, 0x00, 0x00, 0x00, 0xff, 0xff, 0xff, 0xff, - 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfc}, /* b */ - {0x5a, 0xc6, 0x35, 0xd8, 0xaa, 0x3a, 0x93, 0xe7, - 0xb3, 0xeb, 0xbd, 0x55, 0x76, 0x98, 0x86, 0xbc, - 0x65, 0x1d, 0x06, 0xb0, 0xcc, 0x53, 0xb0, 0xf6, - 0x3b, 0xce, 0x3c, 0x3e, 0x27, 0xd2, 0x60, 0x4b}, - {0x6b, 0x17, 0xd1, 0xf2, 0xe1, 0x2c, 0x42, 0x47, /* x */ - 0xf8, 0xbc, 0xe6, 0xe5, 0x63, 0xa4, 0x40, 0xf2, - 0x77, 0x03, 0x7d, 0x81, 0x2d, 0xeb, 0x33, 0xa0, - 0xf4, 0xa1, 0x39, 0x45, 0xd8, 0x98, 0xc2, 0x96}, - {0x4f, 0xe3, 0x42, 0xe2, 0xfe, 0x1a, 0x7f, 0x9b, /* y */ - 0x8e, 0xe7, 0xeb, 0x4a, 0x7c, 0x0f, 0x9e, 0x16, - 0x2b, 0xce, 0x33, 0x57, 0x6b, 0x31, 0x5e, 0xce, - 0xcb, 0xb6, 0x40, 0x68, 0x37, 0xbf, 0x51, 0xf5} + {0xff, 0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x01, /* p */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff}, + {0xff, 0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x01, /* a = -3 */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfc}, /* b */ + {0x5a, 0xc6, 0x35, 0xd8, 0xaa, 0x3a, 0x93, 0xe7, + 0xb3, 0xeb, 0xbd, 0x55, 0x76, 0x98, 0x86, 0xbc, + 0x65, 0x1d, 0x06, 0xb0, 0xcc, 0x53, 0xb0, 0xf6, + 0x3b, 0xce, 0x3c, 0x3e, 0x27, 0xd2, 0x60, 0x4b}, + {0x6b, 0x17, 0xd1, 0xf2, 0xe1, 0x2c, 0x42, 0x47, /* x */ + 0xf8, 0xbc, 0xe6, 0xe5, 0x63, 0xa4, 0x40, 0xf2, + 0x77, 0x03, 0x7d, 0x81, 0x2d, 0xeb, 0x33, 0xa0, + 0xf4, 0xa1, 0x39, 0x45, 0xd8, 0x98, 0xc2, 0x96}, + {0x4f, 0xe3, 0x42, 0xe2, 0xfe, 0x1a, 0x7f, 0x9b, /* y */ + 0x8e, 0xe7, 0xeb, 0x4a, 0x7c, 0x0f, 0x9e, 0x16, + 0x2b, 0xce, 0x33, 0x57, 0x6b, 0x31, 0x5e, 0xce, + 0xcb, 0xb6, 0x40, 0x68, 0x37, 0xbf, 0x51, 0xf5} }; -/* The representation of field elements. +/*- + * The representation of field elements. * ------------------------------------ * * We represent field elements with either four 128-bit values, eight 128-bit @@ -104,7 +109,7 @@ static const felem_bytearray nistp256_curve_params[5] = { * values are used as intermediate values before multiplication. */ -#define NLIMBS 4 +# define NLIMBS 4 typedef uint128_t limb; typedef limb felem[NLIMBS]; @@ -112,189 +117,199 @@ typedef limb longfelem[NLIMBS * 2]; typedef u64 smallfelem[NLIMBS]; /* This is the value of the prime as four 64-bit words, little-endian. */ -static const u64 kPrime[4] = { 0xfffffffffffffffful, 0xffffffff, 0, 0xffffffff00000001ul }; -static const limb bottom32bits = 0xffffffff; +static const u64 kPrime[4] = + { 0xfffffffffffffffful, 0xffffffff, 0, 0xffffffff00000001ul }; static const u64 bottom63bits = 0x7ffffffffffffffful; -/* bin32_to_felem takes a little-endian byte array and converts it into felem - * form. This assumes that the CPU is little-endian. */ +/* + * bin32_to_felem takes a little-endian byte array and converts it into felem + * form. This assumes that the CPU is little-endian. + */ static void bin32_to_felem(felem out, const u8 in[32]) - { - out[0] = *((u64*) &in[0]); - out[1] = *((u64*) &in[8]); - out[2] = *((u64*) &in[16]); - out[3] = *((u64*) &in[24]); - } - -/* smallfelem_to_bin32 takes a smallfelem and serialises into a little endian, - * 32 byte array. This assumes that the CPU is little-endian. */ +{ + out[0] = *((u64 *)&in[0]); + out[1] = *((u64 *)&in[8]); + out[2] = *((u64 *)&in[16]); + out[3] = *((u64 *)&in[24]); +} + +/* + * smallfelem_to_bin32 takes a smallfelem and serialises into a little + * endian, 32 byte array. This assumes that the CPU is little-endian. + */ static void smallfelem_to_bin32(u8 out[32], const smallfelem in) - { - *((u64*) &out[0]) = in[0]; - *((u64*) &out[8]) = in[1]; - *((u64*) &out[16]) = in[2]; - *((u64*) &out[24]) = in[3]; - } +{ + *((u64 *)&out[0]) = in[0]; + *((u64 *)&out[8]) = in[1]; + *((u64 *)&out[16]) = in[2]; + *((u64 *)&out[24]) = in[3]; +} /* 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]; +} /* BN_to_felem converts an OpenSSL BIGNUM into an felem */ 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); - bin32_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); + bin32_to_felem(out, b_out); + return 1; +} /* felem_to_BN converts an felem into an OpenSSL BIGNUM */ static BIGNUM *smallfelem_to_BN(BIGNUM *out, const smallfelem in) - { - felem_bytearray b_in, b_out; - smallfelem_to_bin32(b_in, in); - flip_endian(b_out, b_in, sizeof b_out); - return BN_bin2bn(b_out, sizeof b_out, out); - } - - -/* Field operations - * ---------------- */ +{ + felem_bytearray b_in, b_out; + smallfelem_to_bin32(b_in, in); + flip_endian(b_out, b_in, sizeof b_out); + return BN_bin2bn(b_out, sizeof b_out, out); +} + +/*- + * Field operations + * ---------------- + */ static void smallfelem_one(smallfelem 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 smallfelem_assign(smallfelem out, const smallfelem 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]; +} 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]; +} /* felem_sum sets out = 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]; +} /* felem_small_sum sets out = out + in. */ static void felem_small_sum(felem out, const smallfelem 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]; +} /* felem_scalar sets out = out * scalar */ static void felem_scalar(felem out, const u64 scalar) - { - out[0] *= scalar; - out[1] *= scalar; - out[2] *= scalar; - out[3] *= scalar; - } +{ + out[0] *= scalar; + out[1] *= scalar; + out[2] *= scalar; + out[3] *= scalar; +} /* longfelem_scalar sets out = out * scalar */ static void longfelem_scalar(longfelem out, const u64 scalar) - { - out[0] *= scalar; - out[1] *= scalar; - out[2] *= scalar; - out[3] *= scalar; - out[4] *= scalar; - out[5] *= scalar; - out[6] *= scalar; - out[7] *= scalar; - } - -#define two105m41m9 (((limb)1) << 105) - (((limb)1) << 41) - (((limb)1) << 9) -#define two105 (((limb)1) << 105) -#define two105m41p9 (((limb)1) << 105) - (((limb)1) << 41) + (((limb)1) << 9) +{ + out[0] *= scalar; + out[1] *= scalar; + out[2] *= scalar; + out[3] *= scalar; + out[4] *= scalar; + out[5] *= scalar; + out[6] *= scalar; + out[7] *= scalar; +} + +# define two105m41m9 (((limb)1) << 105) - (((limb)1) << 41) - (((limb)1) << 9) +# define two105 (((limb)1) << 105) +# define two105m41p9 (((limb)1) << 105) - (((limb)1) << 41) + (((limb)1) << 9) /* zero105 is 0 mod p */ -static const felem zero105 = { two105m41m9, two105, two105m41p9, two105m41p9 }; +static const felem zero105 = + { two105m41m9, two105, two105m41p9, two105m41p9 }; -/* smallfelem_neg sets |out| to |-small| +/*- + * smallfelem_neg sets |out| to |-small| * On exit: * out[i] < out[i] + 2^105 */ static void smallfelem_neg(felem out, const smallfelem small) - { - /* In order to prevent underflow, we subtract from 0 mod p. */ - out[0] = zero105[0] - small[0]; - out[1] = zero105[1] - small[1]; - out[2] = zero105[2] - small[2]; - out[3] = zero105[3] - small[3]; - } - -/* felem_diff subtracts |in| from |out| +{ + /* In order to prevent underflow, we subtract from 0 mod p. */ + out[0] = zero105[0] - small[0]; + out[1] = zero105[1] - small[1]; + out[2] = zero105[2] - small[2]; + out[3] = zero105[3] - small[3]; +} + +/*- + * felem_diff subtracts |in| from |out| * On entry: * in[i] < 2^104 * On exit: * out[i] < out[i] + 2^105 */ static void felem_diff(felem out, const felem in) - { - /* In order to prevent underflow, we add 0 mod p before subtracting. */ - out[0] += zero105[0]; - out[1] += zero105[1]; - out[2] += zero105[2]; - out[3] += zero105[3]; - - out[0] -= in[0]; - out[1] -= in[1]; - out[2] -= in[2]; - out[3] -= in[3]; - } - -#define two107m43m11 (((limb)1) << 107) - (((limb)1) << 43) - (((limb)1) << 11) -#define two107 (((limb)1) << 107) -#define two107m43p11 (((limb)1) << 107) - (((limb)1) << 43) + (((limb)1) << 11) +{ + /* + * In order to prevent underflow, we add 0 mod p before subtracting. + */ + out[0] += zero105[0]; + out[1] += zero105[1]; + out[2] += zero105[2]; + out[3] += zero105[3]; + + out[0] -= in[0]; + out[1] -= in[1]; + out[2] -= in[2]; + out[3] -= in[3]; +} + +# define two107m43m11 (((limb)1) << 107) - (((limb)1) << 43) - (((limb)1) << 11) +# define two107 (((limb)1) << 107) +# define two107m43p11 (((limb)1) << 107) - (((limb)1) << 43) + (((limb)1) << 11) /* zero107 is 0 mod p */ -static const felem zero107 = { two107m43m11, two107, two107m43p11, two107m43p11 }; +static const felem zero107 = + { two107m43m11, two107, two107m43p11, two107m43p11 }; -/* An alternative felem_diff for larger inputs |in| +/*- + * An alternative felem_diff for larger inputs |in| * felem_diff_zero107 subtracts |in| from |out| * On entry: * in[i] < 2^106 @@ -302,63 +317,70 @@ static const felem zero107 = { two107m43m11, two107, two107m43p11, two107m43p11 * out[i] < out[i] + 2^107 */ static void felem_diff_zero107(felem out, const felem in) - { - /* In order to prevent underflow, we add 0 mod p before subtracting. */ - out[0] += zero107[0]; - out[1] += zero107[1]; - out[2] += zero107[2]; - out[3] += zero107[3]; - - out[0] -= in[0]; - out[1] -= in[1]; - out[2] -= in[2]; - out[3] -= in[3]; - } - -/* longfelem_diff subtracts |in| from |out| +{ + /* + * In order to prevent underflow, we add 0 mod p before subtracting. + */ + out[0] += zero107[0]; + out[1] += zero107[1]; + out[2] += zero107[2]; + out[3] += zero107[3]; + + out[0] -= in[0]; + out[1] -= in[1]; + out[2] -= in[2]; + out[3] -= in[3]; +} + +/*- + * longfelem_diff subtracts |in| from |out| * On entry: * in[i] < 7*2^67 * On exit: * out[i] < out[i] + 2^70 + 2^40 */ static void longfelem_diff(longfelem out, const longfelem in) - { - static const limb two70m8p6 = (((limb)1) << 70) - (((limb)1) << 8) + (((limb)1) << 6); - static const limb two70p40 = (((limb)1) << 70) + (((limb)1) << 40); - static const limb two70 = (((limb)1) << 70); - static const limb two70m40m38p6 = (((limb)1) << 70) - (((limb)1) << 40) - (((limb)1) << 38) + (((limb)1) << 6); - static const limb two70m6 = (((limb)1) << 70) - (((limb)1) << 6); - - /* add 0 mod p to avoid underflow */ - out[0] += two70m8p6; - out[1] += two70p40; - out[2] += two70; - out[3] += two70m40m38p6; - out[4] += two70m6; - out[5] += two70m6; - out[6] += two70m6; - out[7] += two70m6; - - /* in[i] < 7*2^67 < 2^70 - 2^40 - 2^38 + 2^6 */ - 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]; - out[7] -= in[7]; - } - -#define two64m0 (((limb)1) << 64) - 1 -#define two110p32m0 (((limb)1) << 110) + (((limb)1) << 32) - 1 -#define two64m46 (((limb)1) << 64) - (((limb)1) << 46) -#define two64m32 (((limb)1) << 64) - (((limb)1) << 32) +{ + static const limb two70m8p6 = + (((limb) 1) << 70) - (((limb) 1) << 8) + (((limb) 1) << 6); + static const limb two70p40 = (((limb) 1) << 70) + (((limb) 1) << 40); + static const limb two70 = (((limb) 1) << 70); + static const limb two70m40m38p6 = + (((limb) 1) << 70) - (((limb) 1) << 40) - (((limb) 1) << 38) + + (((limb) 1) << 6); + static const limb two70m6 = (((limb) 1) << 70) - (((limb) 1) << 6); + + /* add 0 mod p to avoid underflow */ + out[0] += two70m8p6; + out[1] += two70p40; + out[2] += two70; + out[3] += two70m40m38p6; + out[4] += two70m6; + out[5] += two70m6; + out[6] += two70m6; + out[7] += two70m6; + + /* in[i] < 7*2^67 < 2^70 - 2^40 - 2^38 + 2^6 */ + 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]; + out[7] -= in[7]; +} + +# define two64m0 (((limb)1) << 64) - 1 +# define two110p32m0 (((limb)1) << 110) + (((limb)1) << 32) - 1 +# define two64m46 (((limb)1) << 64) - (((limb)1) << 46) +# define two64m32 (((limb)1) << 64) - (((limb)1) << 32) /* zero110 is 0 mod p */ static const felem zero110 = { two64m0, two110p32m0, two64m46, two64m32 }; -/* felem_shrink converts an felem into a smallfelem. The result isn't quite +/*- + * felem_shrink converts an felem into a smallfelem. The result isn't quite * minimal as the value may be greater than p. * * On entry: @@ -367,299 +389,309 @@ static const felem zero110 = { two64m0, two110p32m0, two64m46, two64m32 }; * out[i] < 2^64 */ static void felem_shrink(smallfelem out, const felem in) - { - felem tmp; - u64 a, b, mask; - s64 high, low; - static const u64 kPrime3Test = 0x7fffffff00000001ul; /* 2^63 - 2^32 + 1 */ - - /* Carry 2->3 */ - tmp[3] = zero110[3] + in[3] + ((u64) (in[2] >> 64)); - /* tmp[3] < 2^110 */ - - tmp[2] = zero110[2] + (u64) in[2]; - tmp[0] = zero110[0] + in[0]; - tmp[1] = zero110[1] + in[1]; - /* tmp[0] < 2**110, tmp[1] < 2^111, tmp[2] < 2**65 */ - - /* We perform two partial reductions where we eliminate the - * high-word of tmp[3]. We don't update the other words till the end. - */ - a = tmp[3] >> 64; /* a < 2^46 */ - tmp[3] = (u64) tmp[3]; - tmp[3] -= a; - tmp[3] += ((limb)a) << 32; - /* tmp[3] < 2^79 */ - - b = a; - a = tmp[3] >> 64; /* a < 2^15 */ - b += a; /* b < 2^46 + 2^15 < 2^47 */ - tmp[3] = (u64) tmp[3]; - tmp[3] -= a; - tmp[3] += ((limb)a) << 32; - /* tmp[3] < 2^64 + 2^47 */ - - /* This adjusts the other two words to complete the two partial - * reductions. */ - tmp[0] += b; - tmp[1] -= (((limb)b) << 32); - - /* In order to make space in tmp[3] for the carry from 2 -> 3, we - * conditionally subtract kPrime if tmp[3] is large enough. */ - high = tmp[3] >> 64; - /* As tmp[3] < 2^65, high is either 1 or 0 */ - high <<= 63; - high >>= 63; - /* high is: - * all ones if the high word of tmp[3] is 1 - * all zeros if the high word of tmp[3] if 0 */ - low = tmp[3]; - mask = low >> 63; - /* mask is: - * all ones if the MSB of low is 1 - * all zeros if the MSB of low if 0 */ - low &= bottom63bits; - low -= kPrime3Test; - /* if low was greater than kPrime3Test then the MSB is zero */ - low = ~low; - low >>= 63; - /* low is: - * all ones if low was > kPrime3Test - * all zeros if low was <= kPrime3Test */ - mask = (mask & low) | high; - tmp[0] -= mask & kPrime[0]; - tmp[1] -= mask & kPrime[1]; - /* kPrime[2] is zero, so omitted */ - tmp[3] -= mask & kPrime[3]; - /* tmp[3] < 2**64 - 2**32 + 1 */ - - tmp[1] += ((u64) (tmp[0] >> 64)); tmp[0] = (u64) tmp[0]; - tmp[2] += ((u64) (tmp[1] >> 64)); tmp[1] = (u64) tmp[1]; - tmp[3] += ((u64) (tmp[2] >> 64)); tmp[2] = (u64) tmp[2]; - /* tmp[i] < 2^64 */ - - out[0] = tmp[0]; - out[1] = tmp[1]; - out[2] = tmp[2]; - out[3] = tmp[3]; - } +{ + felem tmp; + u64 a, b, mask; + s64 high, low; + static const u64 kPrime3Test = 0x7fffffff00000001ul; /* 2^63 - 2^32 + 1 */ + + /* Carry 2->3 */ + tmp[3] = zero110[3] + in[3] + ((u64)(in[2] >> 64)); + /* tmp[3] < 2^110 */ + + tmp[2] = zero110[2] + (u64)in[2]; + tmp[0] = zero110[0] + in[0]; + tmp[1] = zero110[1] + in[1]; + /* tmp[0] < 2**110, tmp[1] < 2^111, tmp[2] < 2**65 */ + + /* + * We perform two partial reductions where we eliminate the high-word of + * tmp[3]. We don't update the other words till the end. + */ + a = tmp[3] >> 64; /* a < 2^46 */ + tmp[3] = (u64)tmp[3]; + tmp[3] -= a; + tmp[3] += ((limb) a) << 32; + /* tmp[3] < 2^79 */ + + b = a; + a = tmp[3] >> 64; /* a < 2^15 */ + b += a; /* b < 2^46 + 2^15 < 2^47 */ + tmp[3] = (u64)tmp[3]; + tmp[3] -= a; + tmp[3] += ((limb) a) << 32; + /* tmp[3] < 2^64 + 2^47 */ + + /* + * This adjusts the other two words to complete the two partial + * reductions. + */ + tmp[0] += b; + tmp[1] -= (((limb) b) << 32); + + /* + * In order to make space in tmp[3] for the carry from 2 -> 3, we + * conditionally subtract kPrime if tmp[3] is large enough. + */ + high = tmp[3] >> 64; + /* As tmp[3] < 2^65, high is either 1 or 0 */ + high <<= 63; + high >>= 63; + /*- + * high is: + * all ones if the high word of tmp[3] is 1 + * all zeros if the high word of tmp[3] if 0 */ + low = tmp[3]; + mask = low >> 63; + /*- + * mask is: + * all ones if the MSB of low is 1 + * all zeros if the MSB of low if 0 */ + low &= bottom63bits; + low -= kPrime3Test; + /* if low was greater than kPrime3Test then the MSB is zero */ + low = ~low; + low >>= 63; + /*- + * low is: + * all ones if low was > kPrime3Test + * all zeros if low was <= kPrime3Test */ + mask = (mask & low) | high; + tmp[0] -= mask & kPrime[0]; + tmp[1] -= mask & kPrime[1]; + /* kPrime[2] is zero, so omitted */ + tmp[3] -= mask & kPrime[3]; + /* tmp[3] < 2**64 - 2**32 + 1 */ + + tmp[1] += ((u64)(tmp[0] >> 64)); + tmp[0] = (u64)tmp[0]; + tmp[2] += ((u64)(tmp[1] >> 64)); + tmp[1] = (u64)tmp[1]; + tmp[3] += ((u64)(tmp[2] >> 64)); + tmp[2] = (u64)tmp[2]; + /* tmp[i] < 2^64 */ + + out[0] = tmp[0]; + out[1] = tmp[1]; + out[2] = tmp[2]; + out[3] = tmp[3]; +} /* smallfelem_expand converts a smallfelem to an felem */ static void smallfelem_expand(felem out, const smallfelem in) - { - out[0] = in[0]; - out[1] = in[1]; - out[2] = in[2]; - out[3] = in[3]; - } - -/* smallfelem_square sets |out| = |small|^2 +{ + out[0] = in[0]; + out[1] = in[1]; + out[2] = in[2]; + out[3] = in[3]; +} + +/*- + * smallfelem_square sets |out| = |small|^2 * On entry: * small[i] < 2^64 * On exit: * out[i] < 7 * 2^64 < 2^67 */ static void smallfelem_square(longfelem out, const smallfelem small) - { - limb a; - u64 high, low; - - a = ((uint128_t) small[0]) * small[0]; - low = a; - high = a >> 64; - out[0] = low; - out[1] = high; - - a = ((uint128_t) small[0]) * small[1]; - low = a; - high = a >> 64; - out[1] += low; - out[1] += low; - out[2] = high; - - a = ((uint128_t) small[0]) * small[2]; - low = a; - high = a >> 64; - out[2] += low; - out[2] *= 2; - out[3] = high; - - a = ((uint128_t) small[0]) * small[3]; - low = a; - high = a >> 64; - out[3] += low; - out[4] = high; - - a = ((uint128_t) small[1]) * small[2]; - low = a; - high = a >> 64; - out[3] += low; - out[3] *= 2; - out[4] += high; - - a = ((uint128_t) small[1]) * small[1]; - low = a; - high = a >> 64; - out[2] += low; - out[3] += high; - - a = ((uint128_t) small[1]) * small[3]; - low = a; - high = a >> 64; - out[4] += low; - out[4] *= 2; - out[5] = high; - - a = ((uint128_t) small[2]) * small[3]; - low = a; - high = a >> 64; - out[5] += low; - out[5] *= 2; - out[6] = high; - out[6] += high; - - a = ((uint128_t) small[2]) * small[2]; - low = a; - high = a >> 64; - out[4] += low; - out[5] += high; - - a = ((uint128_t) small[3]) * small[3]; - low = a; - high = a >> 64; - out[6] += low; - out[7] = high; - } - -/* felem_square sets |out| = |in|^2 +{ + limb a; + u64 high, low; + + a = ((uint128_t) small[0]) * small[0]; + low = a; + high = a >> 64; + out[0] = low; + out[1] = high; + + a = ((uint128_t) small[0]) * small[1]; + low = a; + high = a >> 64; + out[1] += low; + out[1] += low; + out[2] = high; + + a = ((uint128_t) small[0]) * small[2]; + low = a; + high = a >> 64; + out[2] += low; + out[2] *= 2; + out[3] = high; + + a = ((uint128_t) small[0]) * small[3]; + low = a; + high = a >> 64; + out[3] += low; + out[4] = high; + + a = ((uint128_t) small[1]) * small[2]; + low = a; + high = a >> 64; + out[3] += low; + out[3] *= 2; + out[4] += high; + + a = ((uint128_t) small[1]) * small[1]; + low = a; + high = a >> 64; + out[2] += low; + out[3] += high; + + a = ((uint128_t) small[1]) * small[3]; + low = a; + high = a >> 64; + out[4] += low; + out[4] *= 2; + out[5] = high; + + a = ((uint128_t) small[2]) * small[3]; + low = a; + high = a >> 64; + out[5] += low; + out[5] *= 2; + out[6] = high; + out[6] += high; + + a = ((uint128_t) small[2]) * small[2]; + low = a; + high = a >> 64; + out[4] += low; + out[5] += high; + + a = ((uint128_t) small[3]) * small[3]; + low = a; + high = a >> 64; + out[6] += low; + out[7] = high; +} + +/*- + * felem_square sets |out| = |in|^2 * On entry: * in[i] < 2^109 * On exit: * out[i] < 7 * 2^64 < 2^67 */ static void felem_square(longfelem out, const felem in) - { - u64 small[4]; - felem_shrink(small, in); - smallfelem_square(out, small); - } - -/* smallfelem_mul sets |out| = |small1| * |small2| +{ + u64 small[4]; + felem_shrink(small, in); + smallfelem_square(out, small); +} + +/*- + * smallfelem_mul sets |out| = |small1| * |small2| * On entry: * small1[i] < 2^64 * small2[i] < 2^64 * On exit: * out[i] < 7 * 2^64 < 2^67 */ -static void smallfelem_mul(longfelem out, const smallfelem small1, const smallfelem small2) - { - limb a; - u64 high, low; - - a = ((uint128_t) small1[0]) * small2[0]; - low = a; - high = a >> 64; - out[0] = low; - out[1] = high; - - - a = ((uint128_t) small1[0]) * small2[1]; - low = a; - high = a >> 64; - out[1] += low; - out[2] = high; - - a = ((uint128_t) small1[1]) * small2[0]; - low = a; - high = a >> 64; - out[1] += low; - out[2] += high; - - - a = ((uint128_t) small1[0]) * small2[2]; - low = a; - high = a >> 64; - out[2] += low; - out[3] = high; - - a = ((uint128_t) small1[1]) * small2[1]; - low = a; - high = a >> 64; - out[2] += low; - out[3] += high; - - a = ((uint128_t) small1[2]) * small2[0]; - low = a; - high = a >> 64; - out[2] += low; - out[3] += high; - - - a = ((uint128_t) small1[0]) * small2[3]; - low = a; - high = a >> 64; - out[3] += low; - out[4] = high; - - a = ((uint128_t) small1[1]) * small2[2]; - low = a; - high = a >> 64; - out[3] += low; - out[4] += high; - - a = ((uint128_t) small1[2]) * small2[1]; - low = a; - high = a >> 64; - out[3] += low; - out[4] += high; - - a = ((uint128_t) small1[3]) * small2[0]; - low = a; - high = a >> 64; - out[3] += low; - out[4] += high; - - - a = ((uint128_t) small1[1]) * small2[3]; - low = a; - high = a >> 64; - out[4] += low; - out[5] = high; - - a = ((uint128_t) small1[2]) * small2[2]; - low = a; - high = a >> 64; - out[4] += low; - out[5] += high; - - a = ((uint128_t) small1[3]) * small2[1]; - low = a; - high = a >> 64; - out[4] += low; - out[5] += high; - - - a = ((uint128_t) small1[2]) * small2[3]; - low = a; - high = a >> 64; - out[5] += low; - out[6] = high; - - a = ((uint128_t) small1[3]) * small2[2]; - low = a; - high = a >> 64; - out[5] += low; - out[6] += high; - - - a = ((uint128_t) small1[3]) * small2[3]; - low = a; - high = a >> 64; - out[6] += low; - out[7] = high; - } - -/* felem_mul sets |out| = |in1| * |in2| +static void smallfelem_mul(longfelem out, const smallfelem small1, + const smallfelem small2) +{ + limb a; + u64 high, low; + + a = ((uint128_t) small1[0]) * small2[0]; + low = a; + high = a >> 64; + out[0] = low; + out[1] = high; + + a = ((uint128_t) small1[0]) * small2[1]; + low = a; + high = a >> 64; + out[1] += low; + out[2] = high; + + a = ((uint128_t) small1[1]) * small2[0]; + low = a; + high = a >> 64; + out[1] += low; + out[2] += high; + + a = ((uint128_t) small1[0]) * small2[2]; + low = a; + high = a >> 64; + out[2] += low; + out[3] = high; + + a = ((uint128_t) small1[1]) * small2[1]; + low = a; + high = a >> 64; + out[2] += low; + out[3] += high; + + a = ((uint128_t) small1[2]) * small2[0]; + low = a; + high = a >> 64; + out[2] += low; + out[3] += high; + + a = ((uint128_t) small1[0]) * small2[3]; + low = a; + high = a >> 64; + out[3] += low; + out[4] = high; + + a = ((uint128_t) small1[1]) * small2[2]; + low = a; + high = a >> 64; + out[3] += low; + out[4] += high; + + a = ((uint128_t) small1[2]) * small2[1]; + low = a; + high = a >> 64; + out[3] += low; + out[4] += high; + + a = ((uint128_t) small1[3]) * small2[0]; + low = a; + high = a >> 64; + out[3] += low; + out[4] += high; + + a = ((uint128_t) small1[1]) * small2[3]; + low = a; + high = a >> 64; + out[4] += low; + out[5] = high; + + a = ((uint128_t) small1[2]) * small2[2]; + low = a; + high = a >> 64; + out[4] += low; + out[5] += high; + + a = ((uint128_t) small1[3]) * small2[1]; + low = a; + high = a >> 64; + out[4] += low; + out[5] += high; + + a = ((uint128_t) small1[2]) * small2[3]; + low = a; + high = a >> 64; + out[5] += low; + out[6] = high; + + a = ((uint128_t) small1[3]) * small2[2]; + low = a; + high = a >> 64; + out[5] += low; + out[6] += high; + + a = ((uint128_t) small1[3]) * small2[3]; + low = a; + high = a >> 64; + out[6] += low; + out[7] = high; +} + +/*- + * felem_mul sets |out| = |in1| * |in2| * On entry: * in1[i] < 2^109 * in2[i] < 2^109 @@ -667,37 +699,41 @@ static void smallfelem_mul(longfelem out, const smallfelem small1, const smallfe * out[i] < 7 * 2^64 < 2^67 */ static void felem_mul(longfelem out, const felem in1, const felem in2) - { - smallfelem small1, small2; - felem_shrink(small1, in1); - felem_shrink(small2, in2); - smallfelem_mul(out, small1, small2); - } - -/* felem_small_mul sets |out| = |small1| * |in2| +{ + smallfelem small1, small2; + felem_shrink(small1, in1); + felem_shrink(small2, in2); + smallfelem_mul(out, small1, small2); +} + +/*- + * felem_small_mul sets |out| = |small1| * |in2| * On entry: * small1[i] < 2^64 * in2[i] < 2^109 * On exit: * out[i] < 7 * 2^64 < 2^67 */ -static void felem_small_mul(longfelem out, const smallfelem small1, const felem in2) - { - smallfelem small2; - felem_shrink(small2, in2); - smallfelem_mul(out, small1, small2); - } - -#define two100m36m4 (((limb)1) << 100) - (((limb)1) << 36) - (((limb)1) << 4) -#define two100 (((limb)1) << 100) -#define two100m36p4 (((limb)1) << 100) - (((limb)1) << 36) + (((limb)1) << 4) +static void felem_small_mul(longfelem out, const smallfelem small1, + const felem in2) +{ + smallfelem small2; + felem_shrink(small2, in2); + smallfelem_mul(out, small1, small2); +} + +# define two100m36m4 (((limb)1) << 100) - (((limb)1) << 36) - (((limb)1) << 4) +# define two100 (((limb)1) << 100) +# define two100m36p4 (((limb)1) << 100) - (((limb)1) << 36) + (((limb)1) << 4) /* zero100 is 0 mod p */ -static const felem zero100 = { two100m36m4, two100, two100m36p4, two100m36p4 }; +static const felem zero100 = + { two100m36m4, two100, two100m36p4, two100m36p4 }; -/* Internal function for the different flavours of felem_reduce. +/*- + * Internal function for the different flavours of felem_reduce. * felem_reduce_ reduces the higher coefficients in[4]-in[7]. * On entry: - * out[0] >= in[6] + 2^32*in[6] + in[7] + 2^32*in[7] + * out[0] >= in[6] + 2^32*in[6] + in[7] + 2^32*in[7] * out[1] >= in[7] + 2^32*in[4] * out[2] >= in[5] + 2^32*in[5] * out[3] >= in[4] + 2^32*in[5] + 2^32*in[6] @@ -708,40 +744,41 @@ static const felem zero100 = { two100m36m4, two100, two100m36p4, two100m36p4 }; * out[3] <= out[3] + 2^32*in[4] + 3*in[7] */ static void felem_reduce_(felem out, const longfelem in) - { - int128_t c; - /* combine common terms from below */ - c = in[4] + (in[5] << 32); - out[0] += c; - out[3] -= c; - - c = in[5] - in[7]; - out[1] += c; - out[2] -= c; - - /* the remaining terms */ - /* 256: [(0,1),(96,-1),(192,-1),(224,1)] */ - out[1] -= (in[4] << 32); - out[3] += (in[4] << 32); - - /* 320: [(32,1),(64,1),(128,-1),(160,-1),(224,-1)] */ - out[2] -= (in[5] << 32); - - /* 384: [(0,-1),(32,-1),(96,2),(128,2),(224,-1)] */ - out[0] -= in[6]; - out[0] -= (in[6] << 32); - out[1] += (in[6] << 33); - out[2] += (in[6] * 2); - out[3] -= (in[6] << 32); - - /* 448: [(0,-1),(32,-1),(64,-1),(128,1),(160,2),(192,3)] */ - out[0] -= in[7]; - out[0] -= (in[7] << 32); - out[2] += (in[7] << 33); - out[3] += (in[7] * 3); - } - -/* felem_reduce converts a longfelem into an felem. +{ + int128_t c; + /* combine common terms from below */ + c = in[4] + (in[5] << 32); + out[0] += c; + out[3] -= c; + + c = in[5] - in[7]; + out[1] += c; + out[2] -= c; + + /* the remaining terms */ + /* 256: [(0,1),(96,-1),(192,-1),(224,1)] */ + out[1] -= (in[4] << 32); + out[3] += (in[4] << 32); + + /* 320: [(32,1),(64,1),(128,-1),(160,-1),(224,-1)] */ + out[2] -= (in[5] << 32); + + /* 384: [(0,-1),(32,-1),(96,2),(128,2),(224,-1)] */ + out[0] -= in[6]; + out[0] -= (in[6] << 32); + out[1] += (in[6] << 33); + out[2] += (in[6] * 2); + out[3] -= (in[6] << 32); + + /* 448: [(0,-1),(32,-1),(64,-1),(128,1),(160,2),(192,3)] */ + out[0] -= in[7]; + out[0] -= (in[7] << 32); + out[2] += (in[7] << 33); + out[3] += (in[7] * 3); +} + +/*- + * felem_reduce converts a longfelem into an felem. * To be called directly after felem_square or felem_mul. * On entry: * in[0] < 2^64, in[1] < 3*2^64, in[2] < 5*2^64, in[3] < 7*2^64 @@ -750,189 +787,203 @@ static void felem_reduce_(felem out, const longfelem in) * out[i] < 2^101 */ static void felem_reduce(felem out, const longfelem in) - { - out[0] = zero100[0] + in[0]; - out[1] = zero100[1] + in[1]; - out[2] = zero100[2] + in[2]; - out[3] = zero100[3] + in[3]; - - felem_reduce_(out, in); - - /* out[0] > 2^100 - 2^36 - 2^4 - 3*2^64 - 3*2^96 - 2^64 - 2^96 > 0 - * out[1] > 2^100 - 2^64 - 7*2^96 > 0 - * out[2] > 2^100 - 2^36 + 2^4 - 5*2^64 - 5*2^96 > 0 - * out[3] > 2^100 - 2^36 + 2^4 - 7*2^64 - 5*2^96 - 3*2^96 > 0 - * - * out[0] < 2^100 + 2^64 + 7*2^64 + 5*2^96 < 2^101 - * out[1] < 2^100 + 3*2^64 + 5*2^64 + 3*2^97 < 2^101 - * out[2] < 2^100 + 5*2^64 + 2^64 + 3*2^65 + 2^97 < 2^101 - * out[3] < 2^100 + 7*2^64 + 7*2^96 + 3*2^64 < 2^101 - */ - } - -/* felem_reduce_zero105 converts a larger longfelem into an felem. +{ + out[0] = zero100[0] + in[0]; + out[1] = zero100[1] + in[1]; + out[2] = zero100[2] + in[2]; + out[3] = zero100[3] + in[3]; + + felem_reduce_(out, in); + + /*- + * out[0] > 2^100 - 2^36 - 2^4 - 3*2^64 - 3*2^96 - 2^64 - 2^96 > 0 + * out[1] > 2^100 - 2^64 - 7*2^96 > 0 + * out[2] > 2^100 - 2^36 + 2^4 - 5*2^64 - 5*2^96 > 0 + * out[3] > 2^100 - 2^36 + 2^4 - 7*2^64 - 5*2^96 - 3*2^96 > 0 + * + * out[0] < 2^100 + 2^64 + 7*2^64 + 5*2^96 < 2^101 + * out[1] < 2^100 + 3*2^64 + 5*2^64 + 3*2^97 < 2^101 + * out[2] < 2^100 + 5*2^64 + 2^64 + 3*2^65 + 2^97 < 2^101 + * out[3] < 2^100 + 7*2^64 + 7*2^96 + 3*2^64 < 2^101 + */ +} + +/*- + * felem_reduce_zero105 converts a larger longfelem into an felem. * On entry: * in[0] < 2^71 * On exit: * out[i] < 2^106 */ static void felem_reduce_zero105(felem out, const longfelem in) - { - out[0] = zero105[0] + in[0]; - out[1] = zero105[1] + in[1]; - out[2] = zero105[2] + in[2]; - out[3] = zero105[3] + in[3]; - - felem_reduce_(out, in); - - /* out[0] > 2^105 - 2^41 - 2^9 - 2^71 - 2^103 - 2^71 - 2^103 > 0 - * out[1] > 2^105 - 2^71 - 2^103 > 0 - * out[2] > 2^105 - 2^41 + 2^9 - 2^71 - 2^103 > 0 - * out[3] > 2^105 - 2^41 + 2^9 - 2^71 - 2^103 - 2^103 > 0 - * - * out[0] < 2^105 + 2^71 + 2^71 + 2^103 < 2^106 - * out[1] < 2^105 + 2^71 + 2^71 + 2^103 < 2^106 - * out[2] < 2^105 + 2^71 + 2^71 + 2^71 + 2^103 < 2^106 - * out[3] < 2^105 + 2^71 + 2^103 + 2^71 < 2^106 - */ - } - -/* subtract_u64 sets *result = *result - v and *carry to one if the subtraction - * underflowed. */ -static void subtract_u64(u64* result, u64* carry, u64 v) - { - uint128_t r = *result; - r -= v; - *carry = (r >> 64) & 1; - *result = (u64) r; - } - -/* felem_contract converts |in| to its unique, minimal representation. - * On entry: - * in[i] < 2^109 +{ + out[0] = zero105[0] + in[0]; + out[1] = zero105[1] + in[1]; + out[2] = zero105[2] + in[2]; + out[3] = zero105[3] + in[3]; + + felem_reduce_(out, in); + + /*- + * out[0] > 2^105 - 2^41 - 2^9 - 2^71 - 2^103 - 2^71 - 2^103 > 0 + * out[1] > 2^105 - 2^71 - 2^103 > 0 + * out[2] > 2^105 - 2^41 + 2^9 - 2^71 - 2^103 > 0 + * out[3] > 2^105 - 2^41 + 2^9 - 2^71 - 2^103 - 2^103 > 0 + * + * out[0] < 2^105 + 2^71 + 2^71 + 2^103 < 2^106 + * out[1] < 2^105 + 2^71 + 2^71 + 2^103 < 2^106 + * out[2] < 2^105 + 2^71 + 2^71 + 2^71 + 2^103 < 2^106 + * out[3] < 2^105 + 2^71 + 2^103 + 2^71 < 2^106 + */ +} + +/* + * subtract_u64 sets *result = *result - v and *carry to one if the + * subtraction underflowed. + */ +static void subtract_u64(u64 *result, u64 *carry, u64 v) +{ + uint128_t r = *result; + r -= v; + *carry = (r >> 64) & 1; + *result = (u64)r; +} + +/* + * felem_contract converts |in| to its unique, minimal representation. On + * entry: in[i] < 2^109 */ static void felem_contract(smallfelem out, const felem in) - { - unsigned i; - u64 all_equal_so_far = 0, result = 0, carry; - - felem_shrink(out, in); - /* small is minimal except that the value might be > p */ - - all_equal_so_far--; - /* We are doing a constant time test if out >= kPrime. We need to - * compare each u64, from most-significant to least significant. For - * each one, if all words so far have been equal (m is all ones) then a - * non-equal result is the answer. Otherwise we continue. */ - for (i = 3; i < 4; i--) - { - u64 equal; - uint128_t a = ((uint128_t) kPrime[i]) - out[i]; - /* if out[i] > kPrime[i] then a will underflow and the high - * 64-bits will all be set. */ - result |= all_equal_so_far & ((u64) (a >> 64)); - - /* if kPrime[i] == out[i] then |equal| will be all zeros and - * the decrement will make it all ones. */ - equal = kPrime[i] ^ out[i]; - equal--; - equal &= equal << 32; - equal &= equal << 16; - equal &= equal << 8; - equal &= equal << 4; - equal &= equal << 2; - equal &= equal << 1; - equal = ((s64) equal) >> 63; - - all_equal_so_far &= equal; - } - - /* if all_equal_so_far is still all ones then the two values are equal - * and so out >= kPrime is true. */ - result |= all_equal_so_far; - - /* if out >= kPrime then we subtract kPrime. */ - subtract_u64(&out[0], &carry, result & kPrime[0]); - subtract_u64(&out[1], &carry, carry); - subtract_u64(&out[2], &carry, carry); - subtract_u64(&out[3], &carry, carry); - - subtract_u64(&out[1], &carry, result & kPrime[1]); - subtract_u64(&out[2], &carry, carry); - subtract_u64(&out[3], &carry, carry); - - subtract_u64(&out[2], &carry, result & kPrime[2]); - subtract_u64(&out[3], &carry, carry); - - subtract_u64(&out[3], &carry, result & kPrime[3]); - } +{ + unsigned i; + u64 all_equal_so_far = 0, result = 0, carry; + + felem_shrink(out, in); + /* small is minimal except that the value might be > p */ + + all_equal_so_far--; + /* + * We are doing a constant time test if out >= kPrime. We need to compare + * each u64, from most-significant to least significant. For each one, if + * all words so far have been equal (m is all ones) then a non-equal + * result is the answer. Otherwise we continue. + */ + for (i = 3; i < 4; i--) { + u64 equal; + uint128_t a = ((uint128_t) kPrime[i]) - out[i]; + /* + * if out[i] > kPrime[i] then a will underflow and the high 64-bits + * will all be set. + */ + result |= all_equal_so_far & ((u64)(a >> 64)); + + /* + * if kPrime[i] == out[i] then |equal| will be all zeros and the + * decrement will make it all ones. + */ + equal = kPrime[i] ^ out[i]; + equal--; + equal &= equal << 32; + equal &= equal << 16; + equal &= equal << 8; + equal &= equal << 4; + equal &= equal << 2; + equal &= equal << 1; + equal = ((s64) equal) >> 63; + + all_equal_so_far &= equal; + } + + /* + * if all_equal_so_far is still all ones then the two values are equal + * and so out >= kPrime is true. + */ + result |= all_equal_so_far; + + /* if out >= kPrime then we subtract kPrime. */ + subtract_u64(&out[0], &carry, result & kPrime[0]); + subtract_u64(&out[1], &carry, carry); + subtract_u64(&out[2], &carry, carry); + subtract_u64(&out[3], &carry, carry); + + subtract_u64(&out[1], &carry, result & kPrime[1]); + subtract_u64(&out[2], &carry, carry); + subtract_u64(&out[3], &carry, carry); + + subtract_u64(&out[2], &carry, result & kPrime[2]); + subtract_u64(&out[3], &carry, carry); + + subtract_u64(&out[3], &carry, result & kPrime[3]); +} static void smallfelem_square_contract(smallfelem out, const smallfelem in) - { - longfelem longtmp; - felem tmp; - - smallfelem_square(longtmp, in); - felem_reduce(tmp, longtmp); - felem_contract(out, tmp); - } - -static void smallfelem_mul_contract(smallfelem out, const smallfelem in1, const smallfelem in2) - { - longfelem longtmp; - felem tmp; - - smallfelem_mul(longtmp, in1, in2); - felem_reduce(tmp, longtmp); - felem_contract(out, tmp); - } - -/* felem_is_zero returns a limb with all bits set if |in| == 0 (mod p) and 0 +{ + longfelem longtmp; + felem tmp; + + smallfelem_square(longtmp, in); + felem_reduce(tmp, longtmp); + felem_contract(out, tmp); +} + +static void smallfelem_mul_contract(smallfelem out, const smallfelem in1, + const smallfelem in2) +{ + longfelem longtmp; + felem tmp; + + smallfelem_mul(longtmp, in1, in2); + felem_reduce(tmp, longtmp); + felem_contract(out, tmp); +} + +/*- + * felem_is_zero returns a limb with all bits set if |in| == 0 (mod p) and 0 * otherwise. * On entry: * small[i] < 2^64 */ static limb smallfelem_is_zero(const smallfelem small) - { - limb result; - u64 is_p; - - u64 is_zero = small[0] | small[1] | small[2] | small[3]; - is_zero--; - is_zero &= is_zero << 32; - is_zero &= is_zero << 16; - is_zero &= is_zero << 8; - is_zero &= is_zero << 4; - is_zero &= is_zero << 2; - is_zero &= is_zero << 1; - is_zero = ((s64) is_zero) >> 63; - - is_p = (small[0] ^ kPrime[0]) | - (small[1] ^ kPrime[1]) | - (small[2] ^ kPrime[2]) | - (small[3] ^ kPrime[3]); - is_p--; - is_p &= is_p << 32; - is_p &= is_p << 16; - is_p &= is_p << 8; - is_p &= is_p << 4; - is_p &= is_p << 2; - is_p &= is_p << 1; - is_p = ((s64) is_p) >> 63; - - is_zero |= is_p; - - result = is_zero; - result |= ((limb) is_zero) << 64; - return result; - } +{ + limb result; + u64 is_p; + + u64 is_zero = small[0] | small[1] | small[2] | small[3]; + is_zero--; + is_zero &= is_zero << 32; + is_zero &= is_zero << 16; + is_zero &= is_zero << 8; + is_zero &= is_zero << 4; + is_zero &= is_zero << 2; + is_zero &= is_zero << 1; + is_zero = ((s64) is_zero) >> 63; + + is_p = (small[0] ^ kPrime[0]) | + (small[1] ^ kPrime[1]) | + (small[2] ^ kPrime[2]) | (small[3] ^ kPrime[3]); + is_p--; + is_p &= is_p << 32; + is_p &= is_p << 16; + is_p &= is_p << 8; + is_p &= is_p << 4; + is_p &= is_p << 2; + is_p &= is_p << 1; + is_p = ((s64) is_p) >> 63; + + is_zero |= is_p; + + result = is_zero; + result |= ((limb) is_zero) << 64; + return result; +} static int smallfelem_is_zero_int(const smallfelem small) - { - return (int) (smallfelem_is_zero(small) & ((limb)1)); - } +{ + return (int)(smallfelem_is_zero(small) & ((limb) 1)); +} -/* felem_inv calculates |out| = |in|^{-1} +/*- + * felem_inv calculates |out| = |in|^{-1} * * Based on Fermat's Little Theorem: * a^p = a (mod p) @@ -940,213 +991,248 @@ static int smallfelem_is_zero_int(const smallfelem small) * a^{p-2} = a^{-1} (mod p) */ static void felem_inv(felem out, const felem in) - { - felem ftmp, ftmp2; - /* each e_I will hold |in|^{2^I - 1} */ - felem e2, e4, e8, e16, e32, e64; - longfelem tmp; - unsigned i; - - felem_square(tmp, in); felem_reduce(ftmp, tmp); /* 2^1 */ - felem_mul(tmp, in, ftmp); felem_reduce(ftmp, tmp); /* 2^2 - 2^0 */ - felem_assign(e2, ftmp); - felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); /* 2^3 - 2^1 */ - felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); /* 2^4 - 2^2 */ - felem_mul(tmp, ftmp, e2); felem_reduce(ftmp, tmp); /* 2^4 - 2^0 */ - felem_assign(e4, ftmp); - felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); /* 2^5 - 2^1 */ - felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); /* 2^6 - 2^2 */ - felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); /* 2^7 - 2^3 */ - felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); /* 2^8 - 2^4 */ - felem_mul(tmp, ftmp, e4); felem_reduce(ftmp, tmp); /* 2^8 - 2^0 */ - felem_assign(e8, ftmp); - for (i = 0; i < 8; i++) { - felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); - } /* 2^16 - 2^8 */ - felem_mul(tmp, ftmp, e8); felem_reduce(ftmp, tmp); /* 2^16 - 2^0 */ - felem_assign(e16, ftmp); - for (i = 0; i < 16; i++) { - felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); - } /* 2^32 - 2^16 */ - felem_mul(tmp, ftmp, e16); felem_reduce(ftmp, tmp); /* 2^32 - 2^0 */ - felem_assign(e32, ftmp); - for (i = 0; i < 32; i++) { - felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); - } /* 2^64 - 2^32 */ - felem_assign(e64, ftmp); - felem_mul(tmp, ftmp, in); felem_reduce(ftmp, tmp); /* 2^64 - 2^32 + 2^0 */ - for (i = 0; i < 192; i++) { - felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); - } /* 2^256 - 2^224 + 2^192 */ - - felem_mul(tmp, e64, e32); felem_reduce(ftmp2, tmp); /* 2^64 - 2^0 */ - for (i = 0; i < 16; i++) { - felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); - } /* 2^80 - 2^16 */ - felem_mul(tmp, ftmp2, e16); felem_reduce(ftmp2, tmp); /* 2^80 - 2^0 */ - for (i = 0; i < 8; i++) { - felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); - } /* 2^88 - 2^8 */ - felem_mul(tmp, ftmp2, e8); felem_reduce(ftmp2, tmp); /* 2^88 - 2^0 */ - for (i = 0; i < 4; i++) { - felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); - } /* 2^92 - 2^4 */ - felem_mul(tmp, ftmp2, e4); felem_reduce(ftmp2, tmp); /* 2^92 - 2^0 */ - felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); /* 2^93 - 2^1 */ - felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); /* 2^94 - 2^2 */ - felem_mul(tmp, ftmp2, e2); felem_reduce(ftmp2, tmp); /* 2^94 - 2^0 */ - felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); /* 2^95 - 2^1 */ - felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); /* 2^96 - 2^2 */ - felem_mul(tmp, ftmp2, in); felem_reduce(ftmp2, tmp); /* 2^96 - 3 */ - - felem_mul(tmp, ftmp2, ftmp); felem_reduce(out, tmp); /* 2^256 - 2^224 + 2^192 + 2^96 - 3 */ - } +{ + felem ftmp, ftmp2; + /* each e_I will hold |in|^{2^I - 1} */ + felem e2, e4, e8, e16, e32, e64; + longfelem tmp; + unsigned i; + + felem_square(tmp, in); + felem_reduce(ftmp, tmp); /* 2^1 */ + felem_mul(tmp, in, ftmp); + felem_reduce(ftmp, tmp); /* 2^2 - 2^0 */ + felem_assign(e2, ftmp); + felem_square(tmp, ftmp); + felem_reduce(ftmp, tmp); /* 2^3 - 2^1 */ + felem_square(tmp, ftmp); + felem_reduce(ftmp, tmp); /* 2^4 - 2^2 */ + felem_mul(tmp, ftmp, e2); + felem_reduce(ftmp, tmp); /* 2^4 - 2^0 */ + felem_assign(e4, ftmp); + felem_square(tmp, ftmp); + felem_reduce(ftmp, tmp); /* 2^5 - 2^1 */ + felem_square(tmp, ftmp); + felem_reduce(ftmp, tmp); /* 2^6 - 2^2 */ + felem_square(tmp, ftmp); + felem_reduce(ftmp, tmp); /* 2^7 - 2^3 */ + felem_square(tmp, ftmp); + felem_reduce(ftmp, tmp); /* 2^8 - 2^4 */ + felem_mul(tmp, ftmp, e4); + felem_reduce(ftmp, tmp); /* 2^8 - 2^0 */ + felem_assign(e8, ftmp); + for (i = 0; i < 8; i++) { + felem_square(tmp, ftmp); + felem_reduce(ftmp, tmp); + } /* 2^16 - 2^8 */ + felem_mul(tmp, ftmp, e8); + felem_reduce(ftmp, tmp); /* 2^16 - 2^0 */ + felem_assign(e16, ftmp); + for (i = 0; i < 16; i++) { + felem_square(tmp, ftmp); + felem_reduce(ftmp, tmp); + } /* 2^32 - 2^16 */ + felem_mul(tmp, ftmp, e16); + felem_reduce(ftmp, tmp); /* 2^32 - 2^0 */ + felem_assign(e32, ftmp); + for (i = 0; i < 32; i++) { + felem_square(tmp, ftmp); + felem_reduce(ftmp, tmp); + } /* 2^64 - 2^32 */ + felem_assign(e64, ftmp); + felem_mul(tmp, ftmp, in); + felem_reduce(ftmp, tmp); /* 2^64 - 2^32 + 2^0 */ + for (i = 0; i < 192; i++) { + felem_square(tmp, ftmp); + felem_reduce(ftmp, tmp); + } /* 2^256 - 2^224 + 2^192 */ + + felem_mul(tmp, e64, e32); + felem_reduce(ftmp2, tmp); /* 2^64 - 2^0 */ + for (i = 0; i < 16; i++) { + felem_square(tmp, ftmp2); + felem_reduce(ftmp2, tmp); + } /* 2^80 - 2^16 */ + felem_mul(tmp, ftmp2, e16); + felem_reduce(ftmp2, tmp); /* 2^80 - 2^0 */ + for (i = 0; i < 8; i++) { + felem_square(tmp, ftmp2); + felem_reduce(ftmp2, tmp); + } /* 2^88 - 2^8 */ + felem_mul(tmp, ftmp2, e8); + felem_reduce(ftmp2, tmp); /* 2^88 - 2^0 */ + for (i = 0; i < 4; i++) { + felem_square(tmp, ftmp2); + felem_reduce(ftmp2, tmp); + } /* 2^92 - 2^4 */ + felem_mul(tmp, ftmp2, e4); + felem_reduce(ftmp2, tmp); /* 2^92 - 2^0 */ + felem_square(tmp, ftmp2); + felem_reduce(ftmp2, tmp); /* 2^93 - 2^1 */ + felem_square(tmp, ftmp2); + felem_reduce(ftmp2, tmp); /* 2^94 - 2^2 */ + felem_mul(tmp, ftmp2, e2); + felem_reduce(ftmp2, tmp); /* 2^94 - 2^0 */ + felem_square(tmp, ftmp2); + felem_reduce(ftmp2, tmp); /* 2^95 - 2^1 */ + felem_square(tmp, ftmp2); + felem_reduce(ftmp2, tmp); /* 2^96 - 2^2 */ + felem_mul(tmp, ftmp2, in); + felem_reduce(ftmp2, tmp); /* 2^96 - 3 */ + + felem_mul(tmp, ftmp2, ftmp); + felem_reduce(out, tmp); /* 2^256 - 2^224 + 2^192 + 2^96 - 3 */ +} static void smallfelem_inv_contract(smallfelem out, const smallfelem in) - { - felem tmp; +{ + felem tmp; - smallfelem_expand(tmp, in); - felem_inv(tmp, tmp); - felem_contract(out, tmp); - } + smallfelem_expand(tmp, in); + felem_inv(tmp, tmp); + felem_contract(out, tmp); +} -/* Group operations +/*- + * Group operations * ---------------- * * Building on top of the field operations we have the operations on the * elliptic curve group itself. Points on the curve are represented in Jacobian - * coordinates */ + * coordinates + */ -/* point_double calculates 2*(x_in, y_in, z_in) +/*- + * point_double calculates 2*(x_in, y_in, z_in) * * The method is taken from: * http://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#doubling-dbl-2001-b * * 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) - { - longfelem tmp, tmp2; - felem delta, gamma, beta, alpha, ftmp, ftmp2; - smallfelem small1, small2; - - felem_assign(ftmp, x_in); - /* ftmp[i] < 2^106 */ - felem_assign(ftmp2, x_in); - /* ftmp2[i] < 2^106 */ - - /* delta = z^2 */ - felem_square(tmp, z_in); - felem_reduce(delta, tmp); - /* delta[i] < 2^101 */ - - /* gamma = y^2 */ - felem_square(tmp, y_in); - felem_reduce(gamma, tmp); - /* gamma[i] < 2^101 */ - felem_shrink(small1, gamma); - - /* beta = x*gamma */ - felem_small_mul(tmp, small1, x_in); - felem_reduce(beta, tmp); - /* beta[i] < 2^101 */ - - /* alpha = 3*(x-delta)*(x+delta) */ - felem_diff(ftmp, delta); - /* ftmp[i] < 2^105 + 2^106 < 2^107 */ - felem_sum(ftmp2, delta); - /* ftmp2[i] < 2^105 + 2^106 < 2^107 */ - felem_scalar(ftmp2, 3); - /* ftmp2[i] < 3 * 2^107 < 2^109 */ - felem_mul(tmp, ftmp, ftmp2); - felem_reduce(alpha, tmp); - /* alpha[i] < 2^101 */ - felem_shrink(small2, alpha); - - /* x' = alpha^2 - 8*beta */ - smallfelem_square(tmp, small2); - felem_reduce(x_out, tmp); - felem_assign(ftmp, beta); - felem_scalar(ftmp, 8); - /* ftmp[i] < 8 * 2^101 = 2^104 */ - felem_diff(x_out, ftmp); - /* x_out[i] < 2^105 + 2^101 < 2^106 */ - - /* z' = (y + z)^2 - gamma - delta */ - felem_sum(delta, gamma); - /* delta[i] < 2^101 + 2^101 = 2^102 */ - felem_assign(ftmp, y_in); - felem_sum(ftmp, z_in); - /* ftmp[i] < 2^106 + 2^106 = 2^107 */ - felem_square(tmp, ftmp); - felem_reduce(z_out, tmp); - felem_diff(z_out, delta); - /* z_out[i] < 2^105 + 2^101 < 2^106 */ - - /* y' = alpha*(4*beta - x') - 8*gamma^2 */ - felem_scalar(beta, 4); - /* beta[i] < 4 * 2^101 = 2^103 */ - felem_diff_zero107(beta, x_out); - /* beta[i] < 2^107 + 2^103 < 2^108 */ - felem_small_mul(tmp, small2, beta); - /* tmp[i] < 7 * 2^64 < 2^67 */ - smallfelem_square(tmp2, small1); - /* tmp2[i] < 7 * 2^64 */ - longfelem_scalar(tmp2, 8); - /* tmp2[i] < 8 * 7 * 2^64 = 7 * 2^67 */ - longfelem_diff(tmp, tmp2); - /* tmp[i] < 2^67 + 2^70 + 2^40 < 2^71 */ - felem_reduce_zero105(y_out, tmp); - /* y_out[i] < 2^106 */ - } - -/* point_double_small is the same as point_double, except that it operates on - * smallfelems */ + const felem x_in, const felem y_in, const felem z_in) +{ + longfelem tmp, tmp2; + felem delta, gamma, beta, alpha, ftmp, ftmp2; + smallfelem small1, small2; + + felem_assign(ftmp, x_in); + /* ftmp[i] < 2^106 */ + felem_assign(ftmp2, x_in); + /* ftmp2[i] < 2^106 */ + + /* delta = z^2 */ + felem_square(tmp, z_in); + felem_reduce(delta, tmp); + /* delta[i] < 2^101 */ + + /* gamma = y^2 */ + felem_square(tmp, y_in); + felem_reduce(gamma, tmp); + /* gamma[i] < 2^101 */ + felem_shrink(small1, gamma); + + /* beta = x*gamma */ + felem_small_mul(tmp, small1, x_in); + felem_reduce(beta, tmp); + /* beta[i] < 2^101 */ + + /* alpha = 3*(x-delta)*(x+delta) */ + felem_diff(ftmp, delta); + /* ftmp[i] < 2^105 + 2^106 < 2^107 */ + felem_sum(ftmp2, delta); + /* ftmp2[i] < 2^105 + 2^106 < 2^107 */ + felem_scalar(ftmp2, 3); + /* ftmp2[i] < 3 * 2^107 < 2^109 */ + felem_mul(tmp, ftmp, ftmp2); + felem_reduce(alpha, tmp); + /* alpha[i] < 2^101 */ + felem_shrink(small2, alpha); + + /* x' = alpha^2 - 8*beta */ + smallfelem_square(tmp, small2); + felem_reduce(x_out, tmp); + felem_assign(ftmp, beta); + felem_scalar(ftmp, 8); + /* ftmp[i] < 8 * 2^101 = 2^104 */ + felem_diff(x_out, ftmp); + /* x_out[i] < 2^105 + 2^101 < 2^106 */ + + /* z' = (y + z)^2 - gamma - delta */ + felem_sum(delta, gamma); + /* delta[i] < 2^101 + 2^101 = 2^102 */ + felem_assign(ftmp, y_in); + felem_sum(ftmp, z_in); + /* ftmp[i] < 2^106 + 2^106 = 2^107 */ + felem_square(tmp, ftmp); + felem_reduce(z_out, tmp); + felem_diff(z_out, delta); + /* z_out[i] < 2^105 + 2^101 < 2^106 */ + + /* y' = alpha*(4*beta - x') - 8*gamma^2 */ + felem_scalar(beta, 4); + /* beta[i] < 4 * 2^101 = 2^103 */ + felem_diff_zero107(beta, x_out); + /* beta[i] < 2^107 + 2^103 < 2^108 */ + felem_small_mul(tmp, small2, beta); + /* tmp[i] < 7 * 2^64 < 2^67 */ + smallfelem_square(tmp2, small1); + /* tmp2[i] < 7 * 2^64 */ + longfelem_scalar(tmp2, 8); + /* tmp2[i] < 8 * 7 * 2^64 = 7 * 2^67 */ + longfelem_diff(tmp, tmp2); + /* tmp[i] < 2^67 + 2^70 + 2^40 < 2^71 */ + felem_reduce_zero105(y_out, tmp); + /* y_out[i] < 2^106 */ +} + +/* + * point_double_small is the same as point_double, except that it operates on + * smallfelems + */ static void point_double_small(smallfelem x_out, smallfelem y_out, smallfelem z_out, - const smallfelem x_in, const smallfelem y_in, const smallfelem z_in) - { - felem felem_x_out, felem_y_out, felem_z_out; - felem felem_x_in, felem_y_in, felem_z_in; - - smallfelem_expand(felem_x_in, x_in); - smallfelem_expand(felem_y_in, y_in); - smallfelem_expand(felem_z_in, z_in); - point_double(felem_x_out, felem_y_out, felem_z_out, - felem_x_in, felem_y_in, felem_z_in); - felem_shrink(x_out, felem_x_out); - felem_shrink(y_out, felem_y_out); - felem_shrink(z_out, felem_z_out); - } + const smallfelem x_in, const smallfelem y_in, + const smallfelem z_in) +{ + felem felem_x_out, felem_y_out, felem_z_out; + felem felem_x_in, felem_y_in, felem_z_in; + + smallfelem_expand(felem_x_in, x_in); + smallfelem_expand(felem_y_in, y_in); + smallfelem_expand(felem_z_in, z_in); + point_double(felem_x_out, felem_y_out, felem_z_out, + felem_x_in, felem_y_in, felem_z_in); + felem_shrink(x_out, felem_x_out); + felem_shrink(y_out, felem_y_out); + felem_shrink(z_out, felem_z_out); +} /* copy_conditional copies in to out iff mask is all ones. */ -static void -copy_conditional(felem out, const felem in, limb mask) - { - unsigned i; - for (i = 0; i < NLIMBS; ++i) - { - const limb tmp = mask & (in[i] ^ out[i]); - out[i] ^= tmp; - } - } +static void copy_conditional(felem out, const felem in, limb mask) +{ + unsigned i; + for (i = 0; i < NLIMBS; ++i) { + const limb tmp = mask & (in[i] ^ out[i]); + out[i] ^= tmp; + } +} /* copy_small_conditional copies in to out iff mask is all ones. */ -static void -copy_small_conditional(felem out, const smallfelem in, limb mask) - { - unsigned i; - const u64 mask64 = mask; - for (i = 0; i < NLIMBS; ++i) - { - out[i] = ((limb) (in[i] & mask64)) | (out[i] & ~mask); - } - } - -/* point_add calcuates (x1, y1, z1) + (x2, y2, z2) +static void copy_small_conditional(felem out, const smallfelem in, limb mask) +{ + unsigned i; + const u64 mask64 = mask; + for (i = 0; i < NLIMBS; ++i) { + out[i] = ((limb) (in[i] & mask64)) | (out[i] & ~mask); + } +} + +/*- + * point_add calcuates (x1, y1, z1) + (x2, y2, z2) * * The method is taken from: * http://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#addition-add-2007-bl, @@ -1155,187 +1241,191 @@ copy_small_conditional(felem out, const smallfelem in, limb mask) * This function 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. */ + * 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 smallfelem x2, const smallfelem y2, const smallfelem z2) - { - felem ftmp, ftmp2, ftmp3, ftmp4, ftmp5, ftmp6, x_out, y_out, z_out; - longfelem tmp, tmp2; - smallfelem small1, small2, small3, small4, small5; - limb x_equal, y_equal, z1_is_zero, z2_is_zero; - - felem_shrink(small3, z1); - - z1_is_zero = smallfelem_is_zero(small3); - z2_is_zero = smallfelem_is_zero(z2); - - /* ftmp = z1z1 = z1**2 */ - smallfelem_square(tmp, small3); - felem_reduce(ftmp, tmp); - /* ftmp[i] < 2^101 */ - felem_shrink(small1, ftmp); - - if(!mixed) - { - /* ftmp2 = z2z2 = z2**2 */ - smallfelem_square(tmp, z2); - felem_reduce(ftmp2, tmp); - /* ftmp2[i] < 2^101 */ - felem_shrink(small2, ftmp2); - - felem_shrink(small5, x1); - - /* u1 = ftmp3 = x1*z2z2 */ - smallfelem_mul(tmp, small5, small2); - felem_reduce(ftmp3, tmp); - /* ftmp3[i] < 2^101 */ - - /* ftmp5 = z1 + z2 */ - felem_assign(ftmp5, z1); - felem_small_sum(ftmp5, z2); - /* ftmp5[i] < 2^107 */ - - /* ftmp5 = (z1 + z2)**2 - (z1z1 + z2z2) = 2z1z2 */ - felem_square(tmp, ftmp5); - felem_reduce(ftmp5, tmp); - /* ftmp2 = z2z2 + z1z1 */ - felem_sum(ftmp2, ftmp); - /* ftmp2[i] < 2^101 + 2^101 = 2^102 */ - felem_diff(ftmp5, ftmp2); - /* ftmp5[i] < 2^105 + 2^101 < 2^106 */ - - /* ftmp2 = z2 * z2z2 */ - smallfelem_mul(tmp, small2, z2); - felem_reduce(ftmp2, tmp); - - /* s1 = ftmp2 = y1 * z2**3 */ - felem_mul(tmp, y1, ftmp2); - felem_reduce(ftmp6, tmp); - /* ftmp6[i] < 2^101 */ - } - else - { - /* We'll assume z2 = 1 (special case z2 = 0 is handled later) */ - - /* u1 = ftmp3 = x1*z2z2 */ - felem_assign(ftmp3, x1); - /* ftmp3[i] < 2^106 */ - - /* ftmp5 = 2z1z2 */ - felem_assign(ftmp5, z1); - felem_scalar(ftmp5, 2); - /* ftmp5[i] < 2*2^106 = 2^107 */ - - /* s1 = ftmp2 = y1 * z2**3 */ - felem_assign(ftmp6, y1); - /* ftmp6[i] < 2^106 */ - } - - /* u2 = x2*z1z1 */ - smallfelem_mul(tmp, x2, small1); - felem_reduce(ftmp4, tmp); - - /* h = ftmp4 = u2 - u1 */ - felem_diff_zero107(ftmp4, ftmp3); - /* ftmp4[i] < 2^107 + 2^101 < 2^108 */ - felem_shrink(small4, ftmp4); - - x_equal = smallfelem_is_zero(small4); - - /* z_out = ftmp5 * h */ - felem_small_mul(tmp, small4, ftmp5); - felem_reduce(z_out, tmp); - /* z_out[i] < 2^101 */ - - /* ftmp = z1 * z1z1 */ - smallfelem_mul(tmp, small1, small3); - felem_reduce(ftmp, tmp); - - /* s2 = tmp = y2 * z1**3 */ - felem_small_mul(tmp, y2, ftmp); - felem_reduce(ftmp5, tmp); - - /* r = ftmp5 = (s2 - s1)*2 */ - felem_diff_zero107(ftmp5, ftmp6); - /* ftmp5[i] < 2^107 + 2^107 = 2^108*/ - felem_scalar(ftmp5, 2); - /* ftmp5[i] < 2^109 */ - felem_shrink(small1, ftmp5); - y_equal = smallfelem_is_zero(small1); - - if (x_equal && y_equal && !z1_is_zero && !z2_is_zero) - { - point_double(x3, y3, z3, x1, y1, z1); - return; - } - - /* I = ftmp = (2h)**2 */ - felem_assign(ftmp, ftmp4); - felem_scalar(ftmp, 2); - /* ftmp[i] < 2*2^108 = 2^109 */ - felem_square(tmp, ftmp); - felem_reduce(ftmp, tmp); - - /* J = ftmp2 = h * I */ - felem_mul(tmp, ftmp4, ftmp); - felem_reduce(ftmp2, tmp); - - /* V = ftmp4 = U1 * I */ - felem_mul(tmp, ftmp3, ftmp); - felem_reduce(ftmp4, tmp); - - /* x_out = r**2 - J - 2V */ - smallfelem_square(tmp, small1); - felem_reduce(x_out, tmp); - felem_assign(ftmp3, ftmp4); - felem_scalar(ftmp4, 2); - felem_sum(ftmp4, ftmp2); - /* ftmp4[i] < 2*2^101 + 2^101 < 2^103 */ - felem_diff(x_out, ftmp4); - /* x_out[i] < 2^105 + 2^101 */ - - /* y_out = r(V-x_out) - 2 * s1 * J */ - felem_diff_zero107(ftmp3, x_out); - /* ftmp3[i] < 2^107 + 2^101 < 2^108 */ - felem_small_mul(tmp, small1, ftmp3); - felem_mul(tmp2, ftmp6, ftmp2); - longfelem_scalar(tmp2, 2); - /* tmp2[i] < 2*2^67 = 2^68 */ - longfelem_diff(tmp, tmp2); - /* tmp[i] < 2^67 + 2^70 + 2^40 < 2^71 */ - felem_reduce_zero105(y_out, tmp); - /* y_out[i] < 2^106 */ - - copy_small_conditional(x_out, x2, z1_is_zero); - copy_conditional(x_out, x1, z2_is_zero); - copy_small_conditional(y_out, y2, z1_is_zero); - copy_conditional(y_out, y1, z2_is_zero); - copy_small_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); - } - -/* point_add_small is the same as point_add, except that it operates on - * smallfelems */ + const felem x1, const felem y1, const felem z1, + const int mixed, const smallfelem x2, + const smallfelem y2, const smallfelem z2) +{ + felem ftmp, ftmp2, ftmp3, ftmp4, ftmp5, ftmp6, x_out, y_out, z_out; + longfelem tmp, tmp2; + smallfelem small1, small2, small3, small4, small5; + limb x_equal, y_equal, z1_is_zero, z2_is_zero; + + felem_shrink(small3, z1); + + z1_is_zero = smallfelem_is_zero(small3); + z2_is_zero = smallfelem_is_zero(z2); + + /* ftmp = z1z1 = z1**2 */ + smallfelem_square(tmp, small3); + felem_reduce(ftmp, tmp); + /* ftmp[i] < 2^101 */ + felem_shrink(small1, ftmp); + + if (!mixed) { + /* ftmp2 = z2z2 = z2**2 */ + smallfelem_square(tmp, z2); + felem_reduce(ftmp2, tmp); + /* ftmp2[i] < 2^101 */ + felem_shrink(small2, ftmp2); + + felem_shrink(small5, x1); + + /* u1 = ftmp3 = x1*z2z2 */ + smallfelem_mul(tmp, small5, small2); + felem_reduce(ftmp3, tmp); + /* ftmp3[i] < 2^101 */ + + /* ftmp5 = z1 + z2 */ + felem_assign(ftmp5, z1); + felem_small_sum(ftmp5, z2); + /* ftmp5[i] < 2^107 */ + + /* ftmp5 = (z1 + z2)**2 - (z1z1 + z2z2) = 2z1z2 */ + felem_square(tmp, ftmp5); + felem_reduce(ftmp5, tmp); + /* ftmp2 = z2z2 + z1z1 */ + felem_sum(ftmp2, ftmp); + /* ftmp2[i] < 2^101 + 2^101 = 2^102 */ + felem_diff(ftmp5, ftmp2); + /* ftmp5[i] < 2^105 + 2^101 < 2^106 */ + + /* ftmp2 = z2 * z2z2 */ + smallfelem_mul(tmp, small2, z2); + felem_reduce(ftmp2, tmp); + + /* s1 = ftmp2 = y1 * z2**3 */ + felem_mul(tmp, y1, ftmp2); + felem_reduce(ftmp6, tmp); + /* ftmp6[i] < 2^101 */ + } else { + /* + * We'll assume z2 = 1 (special case z2 = 0 is handled later) + */ + + /* u1 = ftmp3 = x1*z2z2 */ + felem_assign(ftmp3, x1); + /* ftmp3[i] < 2^106 */ + + /* ftmp5 = 2z1z2 */ + felem_assign(ftmp5, z1); + felem_scalar(ftmp5, 2); + /* ftmp5[i] < 2*2^106 = 2^107 */ + + /* s1 = ftmp2 = y1 * z2**3 */ + felem_assign(ftmp6, y1); + /* ftmp6[i] < 2^106 */ + } + + /* u2 = x2*z1z1 */ + smallfelem_mul(tmp, x2, small1); + felem_reduce(ftmp4, tmp); + + /* h = ftmp4 = u2 - u1 */ + felem_diff_zero107(ftmp4, ftmp3); + /* ftmp4[i] < 2^107 + 2^101 < 2^108 */ + felem_shrink(small4, ftmp4); + + x_equal = smallfelem_is_zero(small4); + + /* z_out = ftmp5 * h */ + felem_small_mul(tmp, small4, ftmp5); + felem_reduce(z_out, tmp); + /* z_out[i] < 2^101 */ + + /* ftmp = z1 * z1z1 */ + smallfelem_mul(tmp, small1, small3); + felem_reduce(ftmp, tmp); + + /* s2 = tmp = y2 * z1**3 */ + felem_small_mul(tmp, y2, ftmp); + felem_reduce(ftmp5, tmp); + + /* r = ftmp5 = (s2 - s1)*2 */ + felem_diff_zero107(ftmp5, ftmp6); + /* ftmp5[i] < 2^107 + 2^107 = 2^108 */ + felem_scalar(ftmp5, 2); + /* ftmp5[i] < 2^109 */ + felem_shrink(small1, ftmp5); + y_equal = smallfelem_is_zero(small1); + + if (x_equal && y_equal && !z1_is_zero && !z2_is_zero) { + point_double(x3, y3, z3, x1, y1, z1); + return; + } + + /* I = ftmp = (2h)**2 */ + felem_assign(ftmp, ftmp4); + felem_scalar(ftmp, 2); + /* ftmp[i] < 2*2^108 = 2^109 */ + felem_square(tmp, ftmp); + felem_reduce(ftmp, tmp); + + /* J = ftmp2 = h * I */ + felem_mul(tmp, ftmp4, ftmp); + felem_reduce(ftmp2, tmp); + + /* V = ftmp4 = U1 * I */ + felem_mul(tmp, ftmp3, ftmp); + felem_reduce(ftmp4, tmp); + + /* x_out = r**2 - J - 2V */ + smallfelem_square(tmp, small1); + felem_reduce(x_out, tmp); + felem_assign(ftmp3, ftmp4); + felem_scalar(ftmp4, 2); + felem_sum(ftmp4, ftmp2); + /* ftmp4[i] < 2*2^101 + 2^101 < 2^103 */ + felem_diff(x_out, ftmp4); + /* x_out[i] < 2^105 + 2^101 */ + + /* y_out = r(V-x_out) - 2 * s1 * J */ + felem_diff_zero107(ftmp3, x_out); + /* ftmp3[i] < 2^107 + 2^101 < 2^108 */ + felem_small_mul(tmp, small1, ftmp3); + felem_mul(tmp2, ftmp6, ftmp2); + longfelem_scalar(tmp2, 2); + /* tmp2[i] < 2*2^67 = 2^68 */ + longfelem_diff(tmp, tmp2); + /* tmp[i] < 2^67 + 2^70 + 2^40 < 2^71 */ + felem_reduce_zero105(y_out, tmp); + /* y_out[i] < 2^106 */ + + copy_small_conditional(x_out, x2, z1_is_zero); + copy_conditional(x_out, x1, z2_is_zero); + copy_small_conditional(y_out, y2, z1_is_zero); + copy_conditional(y_out, y1, z2_is_zero); + copy_small_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); +} + +/* + * point_add_small is the same as point_add, except that it operates on + * smallfelems + */ static void point_add_small(smallfelem x3, smallfelem y3, smallfelem z3, - smallfelem x1, smallfelem y1, smallfelem z1, - smallfelem x2, smallfelem y2, smallfelem z2) - { - felem felem_x3, felem_y3, felem_z3; - felem felem_x1, felem_y1, felem_z1; - smallfelem_expand(felem_x1, x1); - smallfelem_expand(felem_y1, y1); - smallfelem_expand(felem_z1, z1); - point_add(felem_x3, felem_y3, felem_z3, felem_x1, felem_y1, felem_z1, 0, x2, y2, z2); - felem_shrink(x3, felem_x3); - felem_shrink(y3, felem_y3); - felem_shrink(z3, felem_z3); - } - -/* Base point pre computation + smallfelem x1, smallfelem y1, smallfelem z1, + smallfelem x2, smallfelem y2, smallfelem z2) +{ + felem felem_x3, felem_y3, felem_z3; + felem felem_x1, felem_y1, felem_z1; + smallfelem_expand(felem_x1, x1); + smallfelem_expand(felem_y1, y1); + smallfelem_expand(felem_z1, z1); + point_add(felem_x3, felem_y3, felem_z3, felem_x1, felem_y1, felem_z1, 0, + x2, y2, z2); + felem_shrink(x3, felem_x3); + felem_shrink(y3, felem_y3); + felem_shrink(z3, felem_z3); +} + +/*- + * Base point pre computation * -------------------------- * * Two different sorts of precomputed tables are used in the following code. @@ -1371,801 +1461,909 @@ static void point_add_small(smallfelem x3, smallfelem y3, smallfelem z3, * Tables for other points have table[i] = iG for i in 0 .. 16. */ /* gmul is the table of precomputed base points */ -static const smallfelem gmul[2][16][3] = -{{{{0, 0, 0, 0}, - {0, 0, 0, 0}, - {0, 0, 0, 0}}, - {{0xf4a13945d898c296, 0x77037d812deb33a0, 0xf8bce6e563a440f2, 0x6b17d1f2e12c4247}, - {0xcbb6406837bf51f5, 0x2bce33576b315ece, 0x8ee7eb4a7c0f9e16, 0x4fe342e2fe1a7f9b}, - {1, 0, 0, 0}}, - {{0x90e75cb48e14db63, 0x29493baaad651f7e, 0x8492592e326e25de, 0x0fa822bc2811aaa5}, - {0xe41124545f462ee7, 0x34b1a65050fe82f5, 0x6f4ad4bcb3df188b, 0xbff44ae8f5dba80d}, - {1, 0, 0, 0}}, - {{0x93391ce2097992af, 0xe96c98fd0d35f1fa, 0xb257c0de95e02789, 0x300a4bbc89d6726f}, - {0xaa54a291c08127a0, 0x5bb1eeada9d806a5, 0x7f1ddb25ff1e3c6f, 0x72aac7e0d09b4644}, - {1, 0, 0, 0}}, - {{0x57c84fc9d789bd85, 0xfc35ff7dc297eac3, 0xfb982fd588c6766e, 0x447d739beedb5e67}, - {0x0c7e33c972e25b32, 0x3d349b95a7fae500, 0xe12e9d953a4aaff7, 0x2d4825ab834131ee}, - {1, 0, 0, 0}}, - {{0x13949c932a1d367f, 0xef7fbd2b1a0a11b7, 0xddc6068bb91dfc60, 0xef9519328a9c72ff}, - {0x196035a77376d8a8, 0x23183b0895ca1740, 0xc1ee9807022c219c, 0x611e9fc37dbb2c9b}, - {1, 0, 0, 0}}, - {{0xcae2b1920b57f4bc, 0x2936df5ec6c9bc36, 0x7dea6482e11238bf, 0x550663797b51f5d8}, - {0x44ffe216348a964c, 0x9fb3d576dbdefbe1, 0x0afa40018d9d50e5, 0x157164848aecb851}, - {1, 0, 0, 0}}, - {{0xe48ecafffc5cde01, 0x7ccd84e70d715f26, 0xa2e8f483f43e4391, 0xeb5d7745b21141ea}, - {0xcac917e2731a3479, 0x85f22cfe2844b645, 0x0990e6a158006cee, 0xeafd72ebdbecc17b}, - {1, 0, 0, 0}}, - {{0x6cf20ffb313728be, 0x96439591a3c6b94a, 0x2736ff8344315fc5, 0xa6d39677a7849276}, - {0xf2bab833c357f5f4, 0x824a920c2284059b, 0x66b8babd2d27ecdf, 0x674f84749b0b8816}, - {1, 0, 0, 0}}, - {{0x2df48c04677c8a3e, 0x74e02f080203a56b, 0x31855f7db8c7fedb, 0x4e769e7672c9ddad}, - {0xa4c36165b824bbb0, 0xfb9ae16f3b9122a5, 0x1ec0057206947281, 0x42b99082de830663}, - {1, 0, 0, 0}}, - {{0x6ef95150dda868b9, 0xd1f89e799c0ce131, 0x7fdc1ca008a1c478, 0x78878ef61c6ce04d}, - {0x9c62b9121fe0d976, 0x6ace570ebde08d4f, 0xde53142c12309def, 0xb6cb3f5d7b72c321}, - {1, 0, 0, 0}}, - {{0x7f991ed2c31a3573, 0x5b82dd5bd54fb496, 0x595c5220812ffcae, 0x0c88bc4d716b1287}, - {0x3a57bf635f48aca8, 0x7c8181f4df2564f3, 0x18d1b5b39c04e6aa, 0xdd5ddea3f3901dc6}, - {1, 0, 0, 0}}, - {{0xe96a79fb3e72ad0c, 0x43a0a28c42ba792f, 0xefe0a423083e49f3, 0x68f344af6b317466}, - {0xcdfe17db3fb24d4a, 0x668bfc2271f5c626, 0x604ed93c24d67ff3, 0x31b9c405f8540a20}, - {1, 0, 0, 0}}, - {{0xd36b4789a2582e7f, 0x0d1a10144ec39c28, 0x663c62c3edbad7a0, 0x4052bf4b6f461db9}, - {0x235a27c3188d25eb, 0xe724f33999bfcc5b, 0x862be6bd71d70cc8, 0xfecf4d5190b0fc61}, - {1, 0, 0, 0}}, - {{0x74346c10a1d4cfac, 0xafdf5cc08526a7a4, 0x123202a8f62bff7a, 0x1eddbae2c802e41a}, - {0x8fa0af2dd603f844, 0x36e06b7e4c701917, 0x0c45f45273db33a0, 0x43104d86560ebcfc}, - {1, 0, 0, 0}}, - {{0x9615b5110d1d78e5, 0x66b0de3225c4744b, 0x0a4a46fb6aaf363a, 0xb48e26b484f7a21c}, - {0x06ebb0f621a01b2d, 0xc004e4048b7b0f98, 0x64131bcdfed6f668, 0xfac015404d4d3dab}, - {1, 0, 0, 0}}}, - {{{0, 0, 0, 0}, - {0, 0, 0, 0}, - {0, 0, 0, 0}}, - {{0x3a5a9e22185a5943, 0x1ab919365c65dfb6, 0x21656b32262c71da, 0x7fe36b40af22af89}, - {0xd50d152c699ca101, 0x74b3d5867b8af212, 0x9f09f40407dca6f1, 0xe697d45825b63624}, - {1, 0, 0, 0}}, - {{0xa84aa9397512218e, 0xe9a521b074ca0141, 0x57880b3a18a2e902, 0x4a5b506612a677a6}, - {0x0beada7a4c4f3840, 0x626db15419e26d9d, 0xc42604fbe1627d40, 0xeb13461ceac089f1}, - {1, 0, 0, 0}}, - {{0xf9faed0927a43281, 0x5e52c4144103ecbc, 0xc342967aa815c857, 0x0781b8291c6a220a}, - {0x5a8343ceeac55f80, 0x88f80eeee54a05e3, 0x97b2a14f12916434, 0x690cde8df0151593}, - {1, 0, 0, 0}}, - {{0xaee9c75df7f82f2a, 0x9e4c35874afdf43a, 0xf5622df437371326, 0x8a535f566ec73617}, - {0xc5f9a0ac223094b7, 0xcde533864c8c7669, 0x37e02819085a92bf, 0x0455c08468b08bd7}, - {1, 0, 0, 0}}, - {{0x0c0a6e2c9477b5d9, 0xf9a4bf62876dc444, 0x5050a949b6cdc279, 0x06bada7ab77f8276}, - {0xc8b4aed1ea48dac9, 0xdebd8a4b7ea1070f, 0x427d49101366eb70, 0x5b476dfd0e6cb18a}, - {1, 0, 0, 0}}, - {{0x7c5c3e44278c340a, 0x4d54606812d66f3b, 0x29a751b1ae23c5d8, 0x3e29864e8a2ec908}, - {0x142d2a6626dbb850, 0xad1744c4765bd780, 0x1f150e68e322d1ed, 0x239b90ea3dc31e7e}, - {1, 0, 0, 0}}, - {{0x78c416527a53322a, 0x305dde6709776f8e, 0xdbcab759f8862ed4, 0x820f4dd949f72ff7}, - {0x6cc544a62b5debd4, 0x75be5d937b4e8cc4, 0x1b481b1b215c14d3, 0x140406ec783a05ec}, - {1, 0, 0, 0}}, - {{0x6a703f10e895df07, 0xfd75f3fa01876bd8, 0xeb5b06e70ce08ffe, 0x68f6b8542783dfee}, - {0x90c76f8a78712655, 0xcf5293d2f310bf7f, 0xfbc8044dfda45028, 0xcbe1feba92e40ce6}, - {1, 0, 0, 0}}, - {{0xe998ceea4396e4c1, 0xfc82ef0b6acea274, 0x230f729f2250e927, 0xd0b2f94d2f420109}, - {0x4305adddb38d4966, 0x10b838f8624c3b45, 0x7db2636658954e7a, 0x971459828b0719e5}, - {1, 0, 0, 0}}, - {{0x4bd6b72623369fc9, 0x57f2929e53d0b876, 0xc2d5cba4f2340687, 0x961610004a866aba}, - {0x49997bcd2e407a5e, 0x69ab197d92ddcb24, 0x2cf1f2438fe5131c, 0x7acb9fadcee75e44}, - {1, 0, 0, 0}}, - {{0x254e839423d2d4c0, 0xf57f0c917aea685b, 0xa60d880f6f75aaea, 0x24eb9acca333bf5b}, - {0xe3de4ccb1cda5dea, 0xfeef9341c51a6b4f, 0x743125f88bac4c4d, 0x69f891c5acd079cc}, - {1, 0, 0, 0}}, - {{0xeee44b35702476b5, 0x7ed031a0e45c2258, 0xb422d1e7bd6f8514, 0xe51f547c5972a107}, - {0xa25bcd6fc9cf343d, 0x8ca922ee097c184e, 0xa62f98b3a9fe9a06, 0x1c309a2b25bb1387}, - {1, 0, 0, 0}}, - {{0x9295dbeb1967c459, 0xb00148833472c98e, 0xc504977708011828, 0x20b87b8aa2c4e503}, - {0x3063175de057c277, 0x1bd539338fe582dd, 0x0d11adef5f69a044, 0xf5c6fa49919776be}, - {1, 0, 0, 0}}, - {{0x8c944e760fd59e11, 0x3876cba1102fad5f, 0xa454c3fad83faa56, 0x1ed7d1b9332010b9}, - {0xa1011a270024b889, 0x05e4d0dcac0cd344, 0x52b520f0eb6a2a24, 0x3a2b03f03217257a}, - {1, 0, 0, 0}}, - {{0xf20fc2afdf1d043d, 0xf330240db58d5a62, 0xfc7d229ca0058c3b, 0x15fee545c78dd9f6}, - {0x501e82885bc98cda, 0x41ef80e5d046ac04, 0x557d9f49461210fb, 0x4ab5b6b2b8753f81}, - {1, 0, 0, 0}}}}; - -/* select_point selects the |idx|th point from a precomputation table and - * copies it to out. */ -static void select_point(const u64 idx, unsigned int size, const smallfelem pre_comp[16][3], smallfelem out[3]) - { - unsigned i, j; - u64 *outlimbs = &out[0][0]; - memset(outlimbs, 0, 3 * sizeof(smallfelem)); - - for (i = 0; i < size; i++) - { - const u64 *inlimbs = (u64*) &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 < NLIMBS * 3; j++) - outlimbs[j] |= inlimbs[j] & mask; - } - } +static const smallfelem gmul[2][16][3] = { + {{{0, 0, 0, 0}, + {0, 0, 0, 0}, + {0, 0, 0, 0}}, + {{0xf4a13945d898c296, 0x77037d812deb33a0, 0xf8bce6e563a440f2, + 0x6b17d1f2e12c4247}, + {0xcbb6406837bf51f5, 0x2bce33576b315ece, 0x8ee7eb4a7c0f9e16, + 0x4fe342e2fe1a7f9b}, + {1, 0, 0, 0}}, + {{0x90e75cb48e14db63, 0x29493baaad651f7e, 0x8492592e326e25de, + 0x0fa822bc2811aaa5}, + {0xe41124545f462ee7, 0x34b1a65050fe82f5, 0x6f4ad4bcb3df188b, + 0xbff44ae8f5dba80d}, + {1, 0, 0, 0}}, + {{0x93391ce2097992af, 0xe96c98fd0d35f1fa, 0xb257c0de95e02789, + 0x300a4bbc89d6726f}, + {0xaa54a291c08127a0, 0x5bb1eeada9d806a5, 0x7f1ddb25ff1e3c6f, + 0x72aac7e0d09b4644}, + {1, 0, 0, 0}}, + {{0x57c84fc9d789bd85, 0xfc35ff7dc297eac3, 0xfb982fd588c6766e, + 0x447d739beedb5e67}, + {0x0c7e33c972e25b32, 0x3d349b95a7fae500, 0xe12e9d953a4aaff7, + 0x2d4825ab834131ee}, + {1, 0, 0, 0}}, + {{0x13949c932a1d367f, 0xef7fbd2b1a0a11b7, 0xddc6068bb91dfc60, + 0xef9519328a9c72ff}, + {0x196035a77376d8a8, 0x23183b0895ca1740, 0xc1ee9807022c219c, + 0x611e9fc37dbb2c9b}, + {1, 0, 0, 0}}, + {{0xcae2b1920b57f4bc, 0x2936df5ec6c9bc36, 0x7dea6482e11238bf, + 0x550663797b51f5d8}, + {0x44ffe216348a964c, 0x9fb3d576dbdefbe1, 0x0afa40018d9d50e5, + 0x157164848aecb851}, + {1, 0, 0, 0}}, + {{0xe48ecafffc5cde01, 0x7ccd84e70d715f26, 0xa2e8f483f43e4391, + 0xeb5d7745b21141ea}, + {0xcac917e2731a3479, 0x85f22cfe2844b645, 0x0990e6a158006cee, + 0xeafd72ebdbecc17b}, + {1, 0, 0, 0}}, + {{0x6cf20ffb313728be, 0x96439591a3c6b94a, 0x2736ff8344315fc5, + 0xa6d39677a7849276}, + {0xf2bab833c357f5f4, 0x824a920c2284059b, 0x66b8babd2d27ecdf, + 0x674f84749b0b8816}, + {1, 0, 0, 0}}, + {{0x2df48c04677c8a3e, 0x74e02f080203a56b, 0x31855f7db8c7fedb, + 0x4e769e7672c9ddad}, + {0xa4c36165b824bbb0, 0xfb9ae16f3b9122a5, 0x1ec0057206947281, + 0x42b99082de830663}, + {1, 0, 0, 0}}, + {{0x6ef95150dda868b9, 0xd1f89e799c0ce131, 0x7fdc1ca008a1c478, + 0x78878ef61c6ce04d}, + {0x9c62b9121fe0d976, 0x6ace570ebde08d4f, 0xde53142c12309def, + 0xb6cb3f5d7b72c321}, + {1, 0, 0, 0}}, + {{0x7f991ed2c31a3573, 0x5b82dd5bd54fb496, 0x595c5220812ffcae, + 0x0c88bc4d716b1287}, + {0x3a57bf635f48aca8, 0x7c8181f4df2564f3, 0x18d1b5b39c04e6aa, + 0xdd5ddea3f3901dc6}, + {1, 0, 0, 0}}, + {{0xe96a79fb3e72ad0c, 0x43a0a28c42ba792f, 0xefe0a423083e49f3, + 0x68f344af6b317466}, + {0xcdfe17db3fb24d4a, 0x668bfc2271f5c626, 0x604ed93c24d67ff3, + 0x31b9c405f8540a20}, + {1, 0, 0, 0}}, + {{0xd36b4789a2582e7f, 0x0d1a10144ec39c28, 0x663c62c3edbad7a0, + 0x4052bf4b6f461db9}, + {0x235a27c3188d25eb, 0xe724f33999bfcc5b, 0x862be6bd71d70cc8, + 0xfecf4d5190b0fc61}, + {1, 0, 0, 0}}, + {{0x74346c10a1d4cfac, 0xafdf5cc08526a7a4, 0x123202a8f62bff7a, + 0x1eddbae2c802e41a}, + {0x8fa0af2dd603f844, 0x36e06b7e4c701917, 0x0c45f45273db33a0, + 0x43104d86560ebcfc}, + {1, 0, 0, 0}}, + {{0x9615b5110d1d78e5, 0x66b0de3225c4744b, 0x0a4a46fb6aaf363a, + 0xb48e26b484f7a21c}, + {0x06ebb0f621a01b2d, 0xc004e4048b7b0f98, 0x64131bcdfed6f668, + 0xfac015404d4d3dab}, + {1, 0, 0, 0}}}, + {{{0, 0, 0, 0}, + {0, 0, 0, 0}, + {0, 0, 0, 0}}, + {{0x3a5a9e22185a5943, 0x1ab919365c65dfb6, 0x21656b32262c71da, + 0x7fe36b40af22af89}, + {0xd50d152c699ca101, 0x74b3d5867b8af212, 0x9f09f40407dca6f1, + 0xe697d45825b63624}, + {1, 0, 0, 0}}, + {{0xa84aa9397512218e, 0xe9a521b074ca0141, 0x57880b3a18a2e902, + 0x4a5b506612a677a6}, + {0x0beada7a4c4f3840, 0x626db15419e26d9d, 0xc42604fbe1627d40, + 0xeb13461ceac089f1}, + {1, 0, 0, 0}}, + {{0xf9faed0927a43281, 0x5e52c4144103ecbc, 0xc342967aa815c857, + 0x0781b8291c6a220a}, + {0x5a8343ceeac55f80, 0x88f80eeee54a05e3, 0x97b2a14f12916434, + 0x690cde8df0151593}, + {1, 0, 0, 0}}, + {{0xaee9c75df7f82f2a, 0x9e4c35874afdf43a, 0xf5622df437371326, + 0x8a535f566ec73617}, + {0xc5f9a0ac223094b7, 0xcde533864c8c7669, 0x37e02819085a92bf, + 0x0455c08468b08bd7}, + {1, 0, 0, 0}}, + {{0x0c0a6e2c9477b5d9, 0xf9a4bf62876dc444, 0x5050a949b6cdc279, + 0x06bada7ab77f8276}, + {0xc8b4aed1ea48dac9, 0xdebd8a4b7ea1070f, 0x427d49101366eb70, + 0x5b476dfd0e6cb18a}, + {1, 0, 0, 0}}, + {{0x7c5c3e44278c340a, 0x4d54606812d66f3b, 0x29a751b1ae23c5d8, + 0x3e29864e8a2ec908}, + {0x142d2a6626dbb850, 0xad1744c4765bd780, 0x1f150e68e322d1ed, + 0x239b90ea3dc31e7e}, + {1, 0, 0, 0}}, + {{0x78c416527a53322a, 0x305dde6709776f8e, 0xdbcab759f8862ed4, + 0x820f4dd949f72ff7}, + {0x6cc544a62b5debd4, 0x75be5d937b4e8cc4, 0x1b481b1b215c14d3, + 0x140406ec783a05ec}, + {1, 0, 0, 0}}, + {{0x6a703f10e895df07, 0xfd75f3fa01876bd8, 0xeb5b06e70ce08ffe, + 0x68f6b8542783dfee}, + {0x90c76f8a78712655, 0xcf5293d2f310bf7f, 0xfbc8044dfda45028, + 0xcbe1feba92e40ce6}, + {1, 0, 0, 0}}, + {{0xe998ceea4396e4c1, 0xfc82ef0b6acea274, 0x230f729f2250e927, + 0xd0b2f94d2f420109}, + {0x4305adddb38d4966, 0x10b838f8624c3b45, 0x7db2636658954e7a, + 0x971459828b0719e5}, + {1, 0, 0, 0}}, + {{0x4bd6b72623369fc9, 0x57f2929e53d0b876, 0xc2d5cba4f2340687, + 0x961610004a866aba}, + {0x49997bcd2e407a5e, 0x69ab197d92ddcb24, 0x2cf1f2438fe5131c, + 0x7acb9fadcee75e44}, + {1, 0, 0, 0}}, + {{0x254e839423d2d4c0, 0xf57f0c917aea685b, 0xa60d880f6f75aaea, + 0x24eb9acca333bf5b}, + {0xe3de4ccb1cda5dea, 0xfeef9341c51a6b4f, 0x743125f88bac4c4d, + 0x69f891c5acd079cc}, + {1, 0, 0, 0}}, + {{0xeee44b35702476b5, 0x7ed031a0e45c2258, 0xb422d1e7bd6f8514, + 0xe51f547c5972a107}, + {0xa25bcd6fc9cf343d, 0x8ca922ee097c184e, 0xa62f98b3a9fe9a06, + 0x1c309a2b25bb1387}, + {1, 0, 0, 0}}, + {{0x9295dbeb1967c459, 0xb00148833472c98e, 0xc504977708011828, + 0x20b87b8aa2c4e503}, + {0x3063175de057c277, 0x1bd539338fe582dd, 0x0d11adef5f69a044, + 0xf5c6fa49919776be}, + {1, 0, 0, 0}}, + {{0x8c944e760fd59e11, 0x3876cba1102fad5f, 0xa454c3fad83faa56, + 0x1ed7d1b9332010b9}, + {0xa1011a270024b889, 0x05e4d0dcac0cd344, 0x52b520f0eb6a2a24, + 0x3a2b03f03217257a}, + {1, 0, 0, 0}}, + {{0xf20fc2afdf1d043d, 0xf330240db58d5a62, 0xfc7d229ca0058c3b, + 0x15fee545c78dd9f6}, + {0x501e82885bc98cda, 0x41ef80e5d046ac04, 0x557d9f49461210fb, + 0x4ab5b6b2b8753f81}, + {1, 0, 0, 0}}} +}; + +/* + * select_point selects the |idx|th point from a precomputation table and + * copies it to out. + */ +static void select_point(const u64 idx, unsigned int size, + const smallfelem pre_comp[16][3], smallfelem out[3]) +{ + unsigned i, j; + u64 *outlimbs = &out[0][0]; + memset(outlimbs, 0, 3 * sizeof(smallfelem)); + + for (i = 0; i < size; i++) { + const u64 *inlimbs = (u64 *)&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 < NLIMBS * 3; j++) + outlimbs[j] |= inlimbs[j] & mask; + } +} /* get_bit returns the |i|th bit in |in| */ static char get_bit(const felem_bytearray in, int i) - { - if ((i < 0) || (i >= 256)) - return 0; - return (in[i >> 3] >> (i & 7)) & 1; - } - -/* Interleaved point multiplication using precomputed point multiples: - * The small point multiples 0*P, 1*P, ..., 17*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 < 0) || (i >= 256)) + return 0; + return (in[i >> 3] >> (i & 7)) & 1; +} + +/* + * Interleaved point multiplication using precomputed point multiples: The + * small point multiples 0*P, 1*P, ..., 17*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 smallfelem pre_comp[][17][3], const smallfelem g_pre_comp[2][16][3]) - { - int i, skip; - unsigned num, gen_mul = (g_scalar != NULL); - felem nq[3], ftmp; - smallfelem tmp[3]; - 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 32 rounds) - * and additions of other points multiples (every 5th round). - */ - skip = 1; /* save two point operations in the first round */ - for (i = (num_points ? 255 : 31); 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 <= 31)) - { - /* first, look 32 bits upwards */ - bits = get_bit(g_scalar, i + 224) << 3; - bits |= get_bit(g_scalar, i + 160) << 2; - bits |= get_bit(g_scalar, i + 96) << 1; - bits |= get_bit(g_scalar, i + 32); - /* select the point to add, in constant time */ - select_point(bits, 16, g_pre_comp[1], tmp); - - if (!skip) - { - point_add(nq[0], nq[1], nq[2], - nq[0], nq[1], nq[2], - 1 /* mixed */, tmp[0], tmp[1], tmp[2]); - } - else - { - smallfelem_expand(nq[0], tmp[0]); - smallfelem_expand(nq[1], tmp[1]); - smallfelem_expand(nq[2], tmp[2]); - skip = 0; - } - - /* second, look at the current position */ - bits = get_bit(g_scalar, i + 192) << 3; - bits |= get_bit(g_scalar, i + 128) << 2; - bits |= get_bit(g_scalar, i + 64) << 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, in constant time */ - select_point(digit, 17, pre_comp[num], tmp); - smallfelem_neg(ftmp, tmp[1]); /* (X, -Y, Z) is the negative point */ - copy_small_conditional(ftmp, tmp[1], (((limb) sign) - 1)); - felem_contract(tmp[1], ftmp); - - if (!skip) - { - point_add(nq[0], nq[1], nq[2], - nq[0], nq[1], nq[2], - mixed, tmp[0], tmp[1], tmp[2]); - } - else - { - smallfelem_expand(nq[0], tmp[0]); - smallfelem_expand(nq[1], tmp[1]); - smallfelem_expand(nq[2], tmp[2]); - 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 smallfelem pre_comp[][17][3], + const smallfelem g_pre_comp[2][16][3]) +{ + int i, skip; + unsigned num, gen_mul = (g_scalar != NULL); + felem nq[3], ftmp; + smallfelem tmp[3]; + 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 32 rounds) and additions of + * other points multiples (every 5th round). + */ + skip = 1; /* save two point operations in the first + * round */ + for (i = (num_points ? 255 : 31); 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 <= 31)) { + /* first, look 32 bits upwards */ + bits = get_bit(g_scalar, i + 224) << 3; + bits |= get_bit(g_scalar, i + 160) << 2; + bits |= get_bit(g_scalar, i + 96) << 1; + bits |= get_bit(g_scalar, i + 32); + /* select the point to add, in constant time */ + select_point(bits, 16, g_pre_comp[1], tmp); + + if (!skip) { + /* Arg 1 below is for "mixed" */ + point_add(nq[0], nq[1], nq[2], + nq[0], nq[1], nq[2], 1, tmp[0], tmp[1], tmp[2]); + } else { + smallfelem_expand(nq[0], tmp[0]); + smallfelem_expand(nq[1], tmp[1]); + smallfelem_expand(nq[2], tmp[2]); + skip = 0; + } + + /* second, look at the current position */ + bits = get_bit(g_scalar, i + 192) << 3; + bits |= get_bit(g_scalar, i + 128) << 2; + bits |= get_bit(g_scalar, i + 64) << 1; + bits |= get_bit(g_scalar, i); + /* select the point to add, in constant time */ + select_point(bits, 16, g_pre_comp[0], tmp); + /* Arg 1 below is for "mixed" */ + point_add(nq[0], nq[1], nq[2], + nq[0], nq[1], nq[2], 1, 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, in constant time + */ + select_point(digit, 17, pre_comp[num], tmp); + smallfelem_neg(ftmp, tmp[1]); /* (X, -Y, Z) is the negative + * point */ + copy_small_conditional(ftmp, tmp[1], (((limb) sign) - 1)); + felem_contract(tmp[1], ftmp); + + if (!skip) { + point_add(nq[0], nq[1], nq[2], + nq[0], nq[1], nq[2], + mixed, tmp[0], tmp[1], tmp[2]); + } else { + smallfelem_expand(nq[0], tmp[0]); + smallfelem_expand(nq[1], tmp[1]); + smallfelem_expand(nq[2], tmp[2]); + skip = 0; + } + } + } + } + felem_assign(x_out, nq[0]); + felem_assign(y_out, nq[1]); + felem_assign(z_out, nq[2]); +} /* Precomputation for the group generator. */ typedef struct { - smallfelem g_pre_comp[2][16][3]; - int references; + smallfelem g_pre_comp[2][16][3]; + int references; } NISTP256_PRE_COMP; const EC_METHOD *EC_GFp_nistp256_method(void) - { - static const EC_METHOD ret = { - EC_FLAGS_DEFAULT_OCT, - NID_X9_62_prime_field, - ec_GFp_nistp256_group_init, - ec_GFp_simple_group_finish, - ec_GFp_simple_group_clear_finish, - ec_GFp_nist_group_copy, - ec_GFp_nistp256_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_nistp256_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_nistp256_points_mul, - ec_GFp_nistp256_precompute_mult, - ec_GFp_nistp256_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; - } +{ + static const EC_METHOD ret = { + EC_FLAGS_DEFAULT_OCT, + NID_X9_62_prime_field, + ec_GFp_nistp256_group_init, + ec_GFp_simple_group_finish, + ec_GFp_simple_group_clear_finish, + ec_GFp_nist_group_copy, + ec_GFp_nistp256_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_nistp256_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_nistp256_points_mul, + ec_GFp_nistp256_precompute_mult, + ec_GFp_nistp256_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; +} /******************************************************************************/ -/* FUNCTIONS TO MANAGE PRECOMPUTATION +/* + * FUNCTIONS TO MANAGE PRECOMPUTATION */ static NISTP256_PRE_COMP *nistp256_pre_comp_new() - { - NISTP256_PRE_COMP *ret = NULL; - ret = (NISTP256_PRE_COMP *) OPENSSL_malloc(sizeof *ret); - if (!ret) - { - ECerr(EC_F_NISTP256_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; - } +{ + NISTP256_PRE_COMP *ret = NULL; + ret = (NISTP256_PRE_COMP *) OPENSSL_malloc(sizeof *ret); + if (!ret) { + ECerr(EC_F_NISTP256_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 *nistp256_pre_comp_dup(void *src_) - { - NISTP256_PRE_COMP *src = src_; +{ + NISTP256_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 nistp256_pre_comp_free(void *pre_) - { - int i; - NISTP256_PRE_COMP *pre = pre_; +{ + int i; + NISTP256_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 nistp256_pre_comp_clear_free(void *pre_) - { - int i; - NISTP256_PRE_COMP *pre = pre_; +{ + int i; + NISTP256_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_nistp256_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_nistp256_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(nistp256_curve_params[0], sizeof(felem_bytearray), curve_p); - BN_bin2bn(nistp256_curve_params[1], sizeof(felem_bytearray), curve_a); - BN_bin2bn(nistp256_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_NISTP256_GROUP_SET_CURVE, - EC_R_WRONG_CURVE_PARAMETERS); - goto err; - } - group->field_mod_func = BN_nist_mod_256; - 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(nistp256_curve_params[0], sizeof(felem_bytearray), curve_p); + BN_bin2bn(nistp256_curve_params[1], sizeof(felem_bytearray), curve_a); + BN_bin2bn(nistp256_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_NISTP256_GROUP_SET_CURVE, + EC_R_WRONG_CURVE_PARAMETERS); + goto err; + } + group->field_mod_func = BN_nist_mod_256; + 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_nistp256_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; - smallfelem x_out, y_out; - longfelem tmp; - - if (EC_POINT_is_at_infinity(group, point)) - { - ECerr(EC_F_EC_GFP_NISTP256_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 (!smallfelem_to_BN(x, x_out)) { - ECerr(EC_F_EC_GFP_NISTP256_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 (!smallfelem_to_BN(y, y_out)) - { - ECerr(EC_F_EC_GFP_NISTP256_POINT_GET_AFFINE_COORDINATES, - ERR_R_BN_LIB); - return 0; - } - } - return 1; - } - -static void make_points_affine(size_t num, smallfelem points[/* num */][3], smallfelem tmp_smallfelems[/* 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(smallfelem), - tmp_smallfelems, - (void (*)(void *)) smallfelem_one, - (int (*)(const void *)) smallfelem_is_zero_int, - (void (*)(void *, const void *)) smallfelem_assign, - (void (*)(void *, const void *)) smallfelem_square_contract, - (void (*)(void *, const void *, const void *)) smallfelem_mul_contract, - (void (*)(void *, const void *)) smallfelem_inv_contract, - (void (*)(void *, const void *)) smallfelem_assign /* nothing to 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; + smallfelem x_out, y_out; + longfelem tmp; + + if (EC_POINT_is_at_infinity(group, point)) { + ECerr(EC_F_EC_GFP_NISTP256_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 (!smallfelem_to_BN(x, x_out)) { + ECerr(EC_F_EC_GFP_NISTP256_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 (!smallfelem_to_BN(y, y_out)) { + ECerr(EC_F_EC_GFP_NISTP256_POINT_GET_AFFINE_COORDINATES, + ERR_R_BN_LIB); + return 0; + } + } + return 1; +} + +/* points below is of size |num|, and tmp_smallfelems is of size |num+1| */ +static void make_points_affine(size_t num, smallfelem points[][3], + smallfelem tmp_smallfelems[]) +{ + /* + * 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(smallfelem), + tmp_smallfelems, + (void (*)(void *))smallfelem_one, + (int (*)(const void *)) + smallfelem_is_zero_int, + (void (*)(void *, const void *)) + smallfelem_assign, + (void (*)(void *, const void *)) + smallfelem_square_contract, + (void (*) + (void *, const void *, + const void *)) + smallfelem_mul_contract, + (void (*)(void *, const void *)) + smallfelem_inv_contract, + /* nothing to contract */ + (void (*)(void *, const void *)) + smallfelem_assign); +} + +/* + * 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_nistp256_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; - int mixed = 0; - BN_CTX *new_ctx = NULL; - BIGNUM *x, *y, *z, *tmp_scalar; - felem_bytearray g_secret; - felem_bytearray *secrets = NULL; - smallfelem (*pre_comp)[17][3] = NULL; - smallfelem *tmp_smallfelems = NULL; - felem_bytearray tmp; - unsigned i, num_bytes; - int have_pre_comp = 0; - size_t num_points = num; - smallfelem x_in, y_in, z_in; - felem x_out, y_out, z_out; - NISTP256_PRE_COMP *pre = NULL; - const smallfelem (*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, - nistp256_pre_comp_dup, nistp256_pre_comp_free, - nistp256_pre_comp_clear_free); - if (pre) - /* we have precomputation, try to use it */ - g_pre_comp = (const smallfelem (*)[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 (!smallfelem_to_BN(x, g_pre_comp[0][1][0]) || - !smallfelem_to_BN(y, g_pre_comp[0][1][1]) || - !smallfelem_to_BN(z, g_pre_comp[0][1][2])) - { - ECerr(EC_F_EC_GFP_NISTP256_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++; - } - 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(smallfelem)); - if (mixed) - tmp_smallfelems = OPENSSL_malloc((num_points * 17 + 1) * sizeof(smallfelem)); - if ((secrets == NULL) || (pre_comp == NULL) || (mixed && (tmp_smallfelems == NULL))) - { - ECerr(EC_F_EC_GFP_NISTP256_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(smallfelem)); - for (i = 0; i < num_points; ++i) - { - if (i == num) - /* we didn't have a valid precomputation, so we pick - * 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 < 2^256 */ - if ((BN_num_bits(p_scalar) > 256) || (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_NISTP256_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_shrink(pre_comp[i][1][0], x_out); - felem_shrink(pre_comp[i][1][1], y_out); - felem_shrink(pre_comp[i][1][2], z_out); - for (j = 2; j <= 16; ++j) - { - if (j & 1) - { - point_add_small( - 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], - pre_comp[i][j-1][0], pre_comp[i][j-1][1], pre_comp[i][j-1][2]); - } - else - { - point_double_small( - 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_smallfelems); - } - - /* the scalar for the generator */ - if ((scalar != NULL) && (have_pre_comp)) - { - memset(g_secret, 0, sizeof(g_secret)); - /* reduce scalar to 0 <= scalar < 2^256 */ - if ((BN_num_bits(scalar) > 256) || (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_NISTP256_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 smallfelem (*)[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 smallfelem (*)[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 ((!smallfelem_to_BN(x, x_in)) || (!smallfelem_to_BN(y, y_in)) || - (!smallfelem_to_BN(z, z_in))) - { - ECerr(EC_F_EC_GFP_NISTP256_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_smallfelems != NULL) - OPENSSL_free(tmp_smallfelems); - return ret; - } + const BIGNUM *scalar, size_t num, + const EC_POINT *points[], + const BIGNUM *scalars[], BN_CTX *ctx) +{ + int ret = 0; + int j; + int mixed = 0; + BN_CTX *new_ctx = NULL; + BIGNUM *x, *y, *z, *tmp_scalar; + felem_bytearray g_secret; + felem_bytearray *secrets = NULL; + smallfelem(*pre_comp)[17][3] = NULL; + smallfelem *tmp_smallfelems = NULL; + felem_bytearray tmp; + unsigned i, num_bytes; + int have_pre_comp = 0; + size_t num_points = num; + smallfelem x_in, y_in, z_in; + felem x_out, y_out, z_out; + NISTP256_PRE_COMP *pre = NULL; + const smallfelem(*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, + nistp256_pre_comp_dup, + nistp256_pre_comp_free, + nistp256_pre_comp_clear_free); + if (pre) + /* we have precomputation, try to use it */ + g_pre_comp = (const smallfelem(*)[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 (!smallfelem_to_BN(x, g_pre_comp[0][1][0]) || + !smallfelem_to_BN(y, g_pre_comp[0][1][1]) || + !smallfelem_to_BN(z, g_pre_comp[0][1][2])) { + ECerr(EC_F_EC_GFP_NISTP256_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++; + } + 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(smallfelem)); + if (mixed) + tmp_smallfelems = + OPENSSL_malloc((num_points * 17 + 1) * sizeof(smallfelem)); + if ((secrets == NULL) || (pre_comp == NULL) + || (mixed && (tmp_smallfelems == NULL))) { + ECerr(EC_F_EC_GFP_NISTP256_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(smallfelem)); + for (i = 0; i < num_points; ++i) { + if (i == num) + /* + * we didn't have a valid precomputation, so we pick 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 < 2^256 */ + if ((BN_num_bits(p_scalar) > 256) + || (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_NISTP256_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_shrink(pre_comp[i][1][0], x_out); + felem_shrink(pre_comp[i][1][1], y_out); + felem_shrink(pre_comp[i][1][2], z_out); + for (j = 2; j <= 16; ++j) { + if (j & 1) { + point_add_small(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], + pre_comp[i][j - 1][0], + pre_comp[i][j - 1][1], + pre_comp[i][j - 1][2]); + } else { + point_double_small(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_smallfelems); + } + + /* the scalar for the generator */ + if ((scalar != NULL) && (have_pre_comp)) { + memset(g_secret, 0, sizeof(g_secret)); + /* reduce scalar to 0 <= scalar < 2^256 */ + if ((BN_num_bits(scalar) > 256) || (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_NISTP256_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 smallfelem(*)[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 smallfelem(*)[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 ((!smallfelem_to_BN(x, x_in)) || (!smallfelem_to_BN(y, y_in)) || + (!smallfelem_to_BN(z, z_in))) { + ECerr(EC_F_EC_GFP_NISTP256_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_smallfelems != NULL) + OPENSSL_free(tmp_smallfelems); + return ret; +} int ec_GFp_nistp256_precompute_mult(EC_GROUP *group, BN_CTX *ctx) - { - int ret = 0; - NISTP256_PRE_COMP *pre = NULL; - int i, j; - BN_CTX *new_ctx = NULL; - BIGNUM *x, *y; - EC_POINT *generator = NULL; - smallfelem tmp_smallfelems[32]; - felem x_tmp, y_tmp, z_tmp; - - /* throw away old precomputation */ - EC_EX_DATA_free_data(&group->extra_data, nistp256_pre_comp_dup, - nistp256_pre_comp_free, nistp256_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(nistp256_curve_params[3], sizeof (felem_bytearray), x); - BN_bin2bn(nistp256_curve_params[4], sizeof (felem_bytearray), y); - if (!EC_POINT_set_affine_coordinates_GFp(group, generator, x, y, ctx)) - goto err; - if ((pre = nistp256_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(x_tmp, &group->generator->X)) || - (!BN_to_felem(y_tmp, &group->generator->Y)) || - (!BN_to_felem(z_tmp, &group->generator->Z))) - goto err; - felem_shrink(pre->g_pre_comp[0][1][0], x_tmp); - felem_shrink(pre->g_pre_comp[0][1][1], y_tmp); - felem_shrink(pre->g_pre_comp[0][1][2], z_tmp); - /* compute 2^64*G, 2^128*G, 2^192*G for the first table, - * 2^32*G, 2^96*G, 2^160*G, 2^224*G for the second one - */ - for (i = 1; i <= 8; i <<= 1) - { - point_double_small( - 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 < 31; ++j) - { - point_double_small( - 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_small( - 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 < 31; ++j) - { - point_double_small( - 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 */ - /* 2^64*G + 2^128*G resp. 2^96*G + 2^160*G */ - point_add_small( - 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], - pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1], pre->g_pre_comp[i][2][2]); - /* 2^64*G + 2^192*G resp. 2^96*G + 2^224*G */ - point_add_small( - 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], - pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1], pre->g_pre_comp[i][2][2]); - /* 2^128*G + 2^192*G resp. 2^160*G + 2^224*G */ - point_add_small( - 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], - pre->g_pre_comp[i][4][0], pre->g_pre_comp[i][4][1], pre->g_pre_comp[i][4][2]); - /* 2^64*G + 2^128*G + 2^192*G resp. 2^96*G + 2^160*G + 2^224*G */ - point_add_small( - 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], - 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. 2^32*G */ - point_add_small( - 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], - 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_smallfelems); - - if (!EC_EX_DATA_set_data(&group->extra_data, pre, nistp256_pre_comp_dup, - nistp256_pre_comp_free, nistp256_pre_comp_clear_free)) - goto err; - ret = 1; - pre = NULL; +{ + int ret = 0; + NISTP256_PRE_COMP *pre = NULL; + int i, j; + BN_CTX *new_ctx = NULL; + BIGNUM *x, *y; + EC_POINT *generator = NULL; + smallfelem tmp_smallfelems[32]; + felem x_tmp, y_tmp, z_tmp; + + /* throw away old precomputation */ + EC_EX_DATA_free_data(&group->extra_data, nistp256_pre_comp_dup, + nistp256_pre_comp_free, + nistp256_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(nistp256_curve_params[3], sizeof(felem_bytearray), x); + BN_bin2bn(nistp256_curve_params[4], sizeof(felem_bytearray), y); + if (!EC_POINT_set_affine_coordinates_GFp(group, generator, x, y, ctx)) + goto err; + if ((pre = nistp256_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(x_tmp, &group->generator->X)) || + (!BN_to_felem(y_tmp, &group->generator->Y)) || + (!BN_to_felem(z_tmp, &group->generator->Z))) + goto err; + felem_shrink(pre->g_pre_comp[0][1][0], x_tmp); + felem_shrink(pre->g_pre_comp[0][1][1], y_tmp); + felem_shrink(pre->g_pre_comp[0][1][2], z_tmp); + /* + * compute 2^64*G, 2^128*G, 2^192*G for the first table, 2^32*G, 2^96*G, + * 2^160*G, 2^224*G for the second one + */ + for (i = 1; i <= 8; i <<= 1) { + point_double_small(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 < 31; ++j) { + point_double_small(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_small(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 < 31; ++j) { + point_double_small(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 */ + /* 2^64*G + 2^128*G resp. 2^96*G + 2^160*G */ + point_add_small(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], + pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1], + pre->g_pre_comp[i][2][2]); + /* 2^64*G + 2^192*G resp. 2^96*G + 2^224*G */ + point_add_small(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], + pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1], + pre->g_pre_comp[i][2][2]); + /* 2^128*G + 2^192*G resp. 2^160*G + 2^224*G */ + point_add_small(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], + pre->g_pre_comp[i][4][0], pre->g_pre_comp[i][4][1], + pre->g_pre_comp[i][4][2]); + /* + * 2^64*G + 2^128*G + 2^192*G resp. 2^96*G + 2^160*G + 2^224*G + */ + point_add_small(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], + 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. 2^32*G */ + point_add_small(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], + 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_smallfelems); + + if (!EC_EX_DATA_set_data(&group->extra_data, pre, nistp256_pre_comp_dup, + nistp256_pre_comp_free, + nistp256_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) - nistp256_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) + nistp256_pre_comp_free(pre); + return ret; +} int ec_GFp_nistp256_have_precompute_mult(const EC_GROUP *group) - { - if (EC_EX_DATA_get_data(group->extra_data, nistp256_pre_comp_dup, - nistp256_pre_comp_free, nistp256_pre_comp_clear_free) - != NULL) - return 1; - else - return 0; - } +{ + if (EC_EX_DATA_get_data(group->extra_data, nistp256_pre_comp_dup, + nistp256_pre_comp_free, + nistp256_pre_comp_clear_free) + != NULL) + return 1; + else + return 0; +} #else -static void *dummy=&dummy; +static void *dummy = &dummy; #endif |