diff options
Diffstat (limited to 'lib/libcrypto/ec/ecp_nistp521.c')
| -rw-r--r-- | lib/libcrypto/ec/ecp_nistp521.c | 1607 |
1 files changed, 854 insertions, 753 deletions
diff --git a/lib/libcrypto/ec/ecp_nistp521.c b/lib/libcrypto/ec/ecp_nistp521.c index c34c38b7e83..f5b72a4c0d3 100644 --- a/lib/libcrypto/ec/ecp_nistp521.c +++ b/lib/libcrypto/ec/ecp_nistp521.c @@ -133,46 +133,50 @@ static const limb bottom58bits = 0x3ffffffffffffff; /* bin66_to_felem takes a little-endian byte array and converts it into felem * form. This assumes that the CPU is little-endian. */ -static void bin66_to_felem(felem out, const u8 in[66]) - { - out[0] = (*((limb*) &in[0])) & bottom58bits; - out[1] = (*((limb*) &in[7]) >> 2) & bottom58bits; - out[2] = (*((limb*) &in[14]) >> 4) & bottom58bits; - out[3] = (*((limb*) &in[21]) >> 6) & bottom58bits; - out[4] = (*((limb*) &in[29])) & bottom58bits; - out[5] = (*((limb*) &in[36]) >> 2) & bottom58bits; - out[6] = (*((limb*) &in[43]) >> 4) & bottom58bits; - out[7] = (*((limb*) &in[50]) >> 6) & bottom58bits; - out[8] = (*((limb*) &in[58])) & bottom57bits; - } +static void +bin66_to_felem(felem out, const u8 in[66]) +{ + out[0] = (*((limb *) & in[0])) & bottom58bits; + out[1] = (*((limb *) & in[7]) >> 2) & bottom58bits; + out[2] = (*((limb *) & in[14]) >> 4) & bottom58bits; + out[3] = (*((limb *) & in[21]) >> 6) & bottom58bits; + out[4] = (*((limb *) & in[29])) & bottom58bits; + out[5] = (*((limb *) & in[36]) >> 2) & bottom58bits; + out[6] = (*((limb *) & in[43]) >> 4) & bottom58bits; + out[7] = (*((limb *) & in[50]) >> 6) & bottom58bits; + out[8] = (*((limb *) & in[58])) & bottom57bits; +} /* felem_to_bin66 takes an felem and serialises into a little endian, 66 byte * array. This assumes that the CPU is little-endian. */ -static void felem_to_bin66(u8 out[66], const felem in) - { +static void +felem_to_bin66(u8 out[66], const felem in) +{ memset(out, 0, 66); - (*((limb*) &out[0])) = in[0]; - (*((limb*) &out[7])) |= in[1] << 2; - (*((limb*) &out[14])) |= in[2] << 4; - (*((limb*) &out[21])) |= in[3] << 6; - (*((limb*) &out[29])) = in[4]; - (*((limb*) &out[36])) |= in[5] << 2; - (*((limb*) &out[43])) |= in[6] << 4; - (*((limb*) &out[50])) |= in[7] << 6; - (*((limb*) &out[58])) = in[8]; - } + (*((limb *) & out[0])) = in[0]; + (*((limb *) & out[7])) |= in[1] << 2; + (*((limb *) & out[14])) |= in[2] << 4; + (*((limb *) & out[21])) |= in[3] << 6; + (*((limb *) & out[29])) = in[4]; + (*((limb *) & out[36])) |= in[5] << 2; + (*((limb *) & out[43])) |= in[6] << 4; + (*((limb *) & out[50])) |= in[7] << 6; + (*((limb *) & out[58])) = in[8]; +} /* To preserve endianness when using BN_bn2bin and BN_bin2bn */ -static void flip_endian(u8 *out, const u8 *in, unsigned len) - { +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]; - } + 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) - { +static int +BN_to_felem(felem out, const BIGNUM * bn) +{ felem_bytearray b_in; felem_bytearray b_out; unsigned num_bytes; @@ -180,37 +184,37 @@ static int BN_to_felem(felem out, const BIGNUM *bn) /* BN_bn2bin eats leading zeroes */ memset(b_out, 0, sizeof b_out); num_bytes = BN_num_bytes(bn); - if (num_bytes > sizeof b_out) - { + 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)) - { + } + 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); bin66_to_felem(out, b_out); return 1; - } +} /* felem_to_BN converts an felem into an OpenSSL BIGNUM */ -static BIGNUM *felem_to_BN(BIGNUM *out, const felem in) - { +static BIGNUM * +felem_to_BN(BIGNUM * out, const felem in) +{ felem_bytearray b_in, b_out; felem_to_bin66(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 felem_one(felem out) - { +static void +felem_one(felem out) +{ out[0] = 1; out[1] = 0; out[2] = 0; @@ -220,10 +224,11 @@ static void felem_one(felem out) out[6] = 0; out[7] = 0; out[8] = 0; - } +} -static void felem_assign(felem out, const felem in) - { +static void +felem_assign(felem out, const felem in) +{ out[0] = in[0]; out[1] = in[1]; out[2] = in[2]; @@ -233,11 +238,12 @@ static void felem_assign(felem out, const felem in) out[6] = in[6]; out[7] = in[7]; out[8] = in[8]; - } +} /* felem_sum64 sets out = out + in. */ -static void felem_sum64(felem out, const felem in) - { +static void +felem_sum64(felem out, const felem in) +{ out[0] += in[0]; out[1] += in[1]; out[2] += in[2]; @@ -247,11 +253,12 @@ static void felem_sum64(felem out, const felem in) out[6] += in[6]; out[7] += in[7]; out[8] += in[8]; - } +} /* felem_scalar sets out = in * scalar */ -static void felem_scalar(felem out, const felem in, limb scalar) - { +static void +felem_scalar(felem out, const felem in, limb scalar) +{ out[0] = in[0] * scalar; out[1] = in[1] * scalar; out[2] = in[2] * scalar; @@ -261,11 +268,12 @@ static void felem_scalar(felem out, const felem in, limb scalar) out[6] = in[6] * scalar; out[7] = in[7] * scalar; out[8] = in[8] * scalar; - } +} /* felem_scalar64 sets out = out * scalar */ -static void felem_scalar64(felem out, limb scalar) - { +static void +felem_scalar64(felem out, limb scalar) +{ out[0] *= scalar; out[1] *= scalar; out[2] *= scalar; @@ -275,11 +283,12 @@ static void felem_scalar64(felem out, limb scalar) out[6] *= scalar; out[7] *= scalar; out[8] *= scalar; - } +} /* felem_scalar128 sets out = out * scalar */ -static void felem_scalar128(largefelem out, limb scalar) - { +static void +felem_scalar128(largefelem out, limb scalar) +{ out[0] *= scalar; out[1] *= scalar; out[2] *= scalar; @@ -289,7 +298,7 @@ static void felem_scalar128(largefelem out, limb scalar) out[6] *= scalar; out[7] *= scalar; out[8] *= scalar; - } +} /* felem_neg sets |out| to |-in| * On entry: @@ -297,11 +306,12 @@ static void felem_scalar128(largefelem out, limb scalar) * On exit: * out[i] < 2^62 */ -static void felem_neg(felem out, const felem in) - { +static void +felem_neg(felem out, const felem in) +{ /* In order to prevent underflow, we subtract from 0 mod p. */ - static const limb two62m3 = (((limb)1) << 62) - (((limb)1) << 5); - static const limb two62m2 = (((limb)1) << 62) - (((limb)1) << 4); + static const limb two62m3 = (((limb) 1) << 62) - (((limb) 1) << 5); + static const limb two62m2 = (((limb) 1) << 62) - (((limb) 1) << 4); out[0] = two62m3 - in[0]; out[1] = two62m2 - in[1]; @@ -312,7 +322,7 @@ static void felem_neg(felem out, const felem in) out[6] = two62m2 - in[6]; out[7] = two62m2 - in[7]; out[8] = two62m2 - in[8]; - } +} /* felem_diff64 subtracts |in| from |out| * On entry: @@ -320,11 +330,12 @@ static void felem_neg(felem out, const felem in) * On exit: * out[i] < out[i] + 2^62 */ -static void felem_diff64(felem out, const felem in) - { +static void +felem_diff64(felem out, const felem in) +{ /* In order to prevent underflow, we add 0 mod p before subtracting. */ - static const limb two62m3 = (((limb)1) << 62) - (((limb)1) << 5); - static const limb two62m2 = (((limb)1) << 62) - (((limb)1) << 4); + static const limb two62m3 = (((limb) 1) << 62) - (((limb) 1) << 5); + static const limb two62m2 = (((limb) 1) << 62) - (((limb) 1) << 4); out[0] += two62m3 - in[0]; out[1] += two62m2 - in[1]; @@ -335,7 +346,7 @@ static void felem_diff64(felem out, const felem in) out[6] += two62m2 - in[6]; out[7] += two62m2 - in[7]; out[8] += two62m2 - in[8]; - } +} /* felem_diff_128_64 subtracts |in| from |out| * On entry: @@ -343,11 +354,12 @@ static void felem_diff64(felem out, const felem in) * On exit: * out[i] < out[i] + 2^63 */ -static void felem_diff_128_64(largefelem out, const felem in) - { +static void +felem_diff_128_64(largefelem out, const felem in) +{ /* In order to prevent underflow, we add 0 mod p before subtracting. */ - static const limb two63m6 = (((limb)1) << 62) - (((limb)1) << 5); - static const limb two63m5 = (((limb)1) << 62) - (((limb)1) << 4); + static const limb two63m6 = (((limb) 1) << 62) - (((limb) 1) << 5); + static const limb two63m5 = (((limb) 1) << 62) - (((limb) 1) << 4); out[0] += two63m6 - in[0]; out[1] += two63m5 - in[1]; @@ -358,7 +370,7 @@ static void felem_diff_128_64(largefelem out, const felem in) out[6] += two63m5 - in[6]; out[7] += two63m5 - in[7]; out[8] += two63m5 - in[8]; - } +} /* felem_diff_128_64 subtracts |in| from |out| * On entry: @@ -366,11 +378,12 @@ static void felem_diff_128_64(largefelem out, const felem in) * On exit: * out[i] < out[i] + 2^127 - 2^69 */ -static void felem_diff128(largefelem out, const largefelem in) - { +static void +felem_diff128(largefelem out, const largefelem in) +{ /* In order to prevent underflow, we add 0 mod p before subtracting. */ - static const uint128_t two127m70 = (((uint128_t)1) << 127) - (((uint128_t)1) << 70); - static const uint128_t two127m69 = (((uint128_t)1) << 127) - (((uint128_t)1) << 69); + static const uint128_t two127m70 = (((uint128_t) 1) << 127) - (((uint128_t) 1) << 70); + static const uint128_t two127m69 = (((uint128_t) 1) << 127) - (((uint128_t) 1) << 69); out[0] += (two127m70 - in[0]); out[1] += (two127m69 - in[1]); @@ -381,7 +394,7 @@ static void felem_diff128(largefelem out, const largefelem in) out[6] += (two127m69 - in[6]); out[7] += (two127m69 - in[7]); out[8] += (two127m69 - in[8]); - } +} /* felem_square sets |out| = |in|^2 * On entry: @@ -389,90 +402,92 @@ static void felem_diff128(largefelem out, const largefelem in) * On exit: * out[i] < 17 * max(in[i]) * max(in[i]) */ -static void felem_square(largefelem out, const felem in) - { +static void +felem_square(largefelem out, const felem in) +{ felem inx2, inx4; felem_scalar(inx2, in, 2); felem_scalar(inx4, in, 4); - /* We have many cases were we want to do - * in[x] * in[y] + - * in[y] * in[x] - * This is obviously just - * 2 * in[x] * in[y] - * However, rather than do the doubling on the 128 bit result, we - * double one of the inputs to the multiplication by reading from - * |inx2| */ + /* + * We have many cases were we want to do in[x] * in[y] + in[y] * + * in[x] This is obviously just 2 * in[x] * in[y] However, rather + * than do the doubling on the 128 bit result, we double one of the + * inputs to the multiplication by reading from |inx2| + */ out[0] = ((uint128_t) in[0]) * in[0]; out[1] = ((uint128_t) in[0]) * inx2[1]; out[2] = ((uint128_t) in[0]) * inx2[2] + - ((uint128_t) in[1]) * in[1]; + ((uint128_t) in[1]) * in[1]; out[3] = ((uint128_t) in[0]) * inx2[3] + - ((uint128_t) in[1]) * inx2[2]; + ((uint128_t) in[1]) * inx2[2]; out[4] = ((uint128_t) in[0]) * inx2[4] + - ((uint128_t) in[1]) * inx2[3] + - ((uint128_t) in[2]) * in[2]; + ((uint128_t) in[1]) * inx2[3] + + ((uint128_t) in[2]) * in[2]; out[5] = ((uint128_t) in[0]) * inx2[5] + - ((uint128_t) in[1]) * inx2[4] + - ((uint128_t) in[2]) * inx2[3]; + ((uint128_t) in[1]) * inx2[4] + + ((uint128_t) in[2]) * inx2[3]; out[6] = ((uint128_t) in[0]) * inx2[6] + - ((uint128_t) in[1]) * inx2[5] + - ((uint128_t) in[2]) * inx2[4] + - ((uint128_t) in[3]) * in[3]; + ((uint128_t) in[1]) * inx2[5] + + ((uint128_t) in[2]) * inx2[4] + + ((uint128_t) in[3]) * in[3]; out[7] = ((uint128_t) in[0]) * inx2[7] + - ((uint128_t) in[1]) * inx2[6] + - ((uint128_t) in[2]) * inx2[5] + - ((uint128_t) in[3]) * inx2[4]; + ((uint128_t) in[1]) * inx2[6] + + ((uint128_t) in[2]) * inx2[5] + + ((uint128_t) in[3]) * inx2[4]; out[8] = ((uint128_t) in[0]) * inx2[8] + - ((uint128_t) in[1]) * inx2[7] + - ((uint128_t) in[2]) * inx2[6] + - ((uint128_t) in[3]) * inx2[5] + - ((uint128_t) in[4]) * in[4]; + ((uint128_t) in[1]) * inx2[7] + + ((uint128_t) in[2]) * inx2[6] + + ((uint128_t) in[3]) * inx2[5] + + ((uint128_t) in[4]) * in[4]; - /* The remaining limbs fall above 2^521, with the first falling at + /* + * The remaining limbs fall above 2^521, with the first falling at * 2^522. They correspond to locations one bit up from the limbs * produced above so we would have to multiply by two to align them. * Again, rather than operate on the 128-bit result, we double one of - * the inputs to the multiplication. If we want to double for both this - * reason, and the reason above, then we end up multiplying by four. */ + * the inputs to the multiplication. If we want to double for both + * this reason, and the reason above, then we end up multiplying by + * four. + */ /* 9 */ out[0] += ((uint128_t) in[1]) * inx4[8] + - ((uint128_t) in[2]) * inx4[7] + - ((uint128_t) in[3]) * inx4[6] + - ((uint128_t) in[4]) * inx4[5]; + ((uint128_t) in[2]) * inx4[7] + + ((uint128_t) in[3]) * inx4[6] + + ((uint128_t) in[4]) * inx4[5]; /* 10 */ out[1] += ((uint128_t) in[2]) * inx4[8] + - ((uint128_t) in[3]) * inx4[7] + - ((uint128_t) in[4]) * inx4[6] + - ((uint128_t) in[5]) * inx2[5]; + ((uint128_t) in[3]) * inx4[7] + + ((uint128_t) in[4]) * inx4[6] + + ((uint128_t) in[5]) * inx2[5]; /* 11 */ out[2] += ((uint128_t) in[3]) * inx4[8] + - ((uint128_t) in[4]) * inx4[7] + - ((uint128_t) in[5]) * inx4[6]; + ((uint128_t) in[4]) * inx4[7] + + ((uint128_t) in[5]) * inx4[6]; /* 12 */ out[3] += ((uint128_t) in[4]) * inx4[8] + - ((uint128_t) in[5]) * inx4[7] + - ((uint128_t) in[6]) * inx2[6]; + ((uint128_t) in[5]) * inx4[7] + + ((uint128_t) in[6]) * inx2[6]; /* 13 */ out[4] += ((uint128_t) in[5]) * inx4[8] + - ((uint128_t) in[6]) * inx4[7]; + ((uint128_t) in[6]) * inx4[7]; /* 14 */ out[5] += ((uint128_t) in[6]) * inx4[8] + - ((uint128_t) in[7]) * inx2[7]; + ((uint128_t) in[7]) * inx2[7]; /* 15 */ out[6] += ((uint128_t) in[7]) * inx4[8]; /* 16 */ out[7] += ((uint128_t) in[8]) * inx2[8]; - } +} /* felem_mul sets |out| = |in1| * |in2| * On entry: @@ -481,111 +496,112 @@ static void felem_square(largefelem out, const felem in) * On exit: * out[i] < 17 * max(in1[i]) * max(in2[i]) */ -static void felem_mul(largefelem out, const felem in1, const felem in2) - { +static void +felem_mul(largefelem out, const felem in1, const felem in2) +{ felem in2x2; felem_scalar(in2x2, in2, 2); out[0] = ((uint128_t) in1[0]) * in2[0]; out[1] = ((uint128_t) in1[0]) * in2[1] + - ((uint128_t) in1[1]) * in2[0]; + ((uint128_t) in1[1]) * in2[0]; out[2] = ((uint128_t) in1[0]) * in2[2] + - ((uint128_t) in1[1]) * in2[1] + - ((uint128_t) in1[2]) * in2[0]; + ((uint128_t) in1[1]) * in2[1] + + ((uint128_t) in1[2]) * in2[0]; out[3] = ((uint128_t) in1[0]) * in2[3] + - ((uint128_t) in1[1]) * in2[2] + - ((uint128_t) in1[2]) * in2[1] + - ((uint128_t) in1[3]) * in2[0]; + ((uint128_t) in1[1]) * in2[2] + + ((uint128_t) in1[2]) * in2[1] + + ((uint128_t) in1[3]) * in2[0]; out[4] = ((uint128_t) in1[0]) * in2[4] + - ((uint128_t) in1[1]) * in2[3] + - ((uint128_t) in1[2]) * in2[2] + - ((uint128_t) in1[3]) * in2[1] + - ((uint128_t) in1[4]) * in2[0]; + ((uint128_t) in1[1]) * in2[3] + + ((uint128_t) in1[2]) * in2[2] + + ((uint128_t) in1[3]) * in2[1] + + ((uint128_t) in1[4]) * in2[0]; out[5] = ((uint128_t) in1[0]) * in2[5] + - ((uint128_t) in1[1]) * in2[4] + - ((uint128_t) in1[2]) * in2[3] + - ((uint128_t) in1[3]) * in2[2] + - ((uint128_t) in1[4]) * in2[1] + - ((uint128_t) in1[5]) * in2[0]; + ((uint128_t) in1[1]) * in2[4] + + ((uint128_t) in1[2]) * in2[3] + + ((uint128_t) in1[3]) * in2[2] + + ((uint128_t) in1[4]) * in2[1] + + ((uint128_t) in1[5]) * in2[0]; out[6] = ((uint128_t) in1[0]) * in2[6] + - ((uint128_t) in1[1]) * in2[5] + - ((uint128_t) in1[2]) * in2[4] + - ((uint128_t) in1[3]) * in2[3] + - ((uint128_t) in1[4]) * in2[2] + - ((uint128_t) in1[5]) * in2[1] + - ((uint128_t) in1[6]) * in2[0]; + ((uint128_t) in1[1]) * in2[5] + + ((uint128_t) in1[2]) * in2[4] + + ((uint128_t) in1[3]) * in2[3] + + ((uint128_t) in1[4]) * in2[2] + + ((uint128_t) in1[5]) * in2[1] + + ((uint128_t) in1[6]) * in2[0]; out[7] = ((uint128_t) in1[0]) * in2[7] + - ((uint128_t) in1[1]) * in2[6] + - ((uint128_t) in1[2]) * in2[5] + - ((uint128_t) in1[3]) * in2[4] + - ((uint128_t) in1[4]) * in2[3] + - ((uint128_t) in1[5]) * in2[2] + - ((uint128_t) in1[6]) * in2[1] + - ((uint128_t) in1[7]) * in2[0]; + ((uint128_t) in1[1]) * in2[6] + + ((uint128_t) in1[2]) * in2[5] + + ((uint128_t) in1[3]) * in2[4] + + ((uint128_t) in1[4]) * in2[3] + + ((uint128_t) in1[5]) * in2[2] + + ((uint128_t) in1[6]) * in2[1] + + ((uint128_t) in1[7]) * in2[0]; out[8] = ((uint128_t) in1[0]) * in2[8] + - ((uint128_t) in1[1]) * in2[7] + - ((uint128_t) in1[2]) * in2[6] + - ((uint128_t) in1[3]) * in2[5] + - ((uint128_t) in1[4]) * in2[4] + - ((uint128_t) in1[5]) * in2[3] + - ((uint128_t) in1[6]) * in2[2] + - ((uint128_t) in1[7]) * in2[1] + - ((uint128_t) in1[8]) * in2[0]; + ((uint128_t) in1[1]) * in2[7] + + ((uint128_t) in1[2]) * in2[6] + + ((uint128_t) in1[3]) * in2[5] + + ((uint128_t) in1[4]) * in2[4] + + ((uint128_t) in1[5]) * in2[3] + + ((uint128_t) in1[6]) * in2[2] + + ((uint128_t) in1[7]) * in2[1] + + ((uint128_t) in1[8]) * in2[0]; /* See comment in felem_square about the use of in2x2 here */ out[0] += ((uint128_t) in1[1]) * in2x2[8] + - ((uint128_t) in1[2]) * in2x2[7] + - ((uint128_t) in1[3]) * in2x2[6] + - ((uint128_t) in1[4]) * in2x2[5] + - ((uint128_t) in1[5]) * in2x2[4] + - ((uint128_t) in1[6]) * in2x2[3] + - ((uint128_t) in1[7]) * in2x2[2] + - ((uint128_t) in1[8]) * in2x2[1]; + ((uint128_t) in1[2]) * in2x2[7] + + ((uint128_t) in1[3]) * in2x2[6] + + ((uint128_t) in1[4]) * in2x2[5] + + ((uint128_t) in1[5]) * in2x2[4] + + ((uint128_t) in1[6]) * in2x2[3] + + ((uint128_t) in1[7]) * in2x2[2] + + ((uint128_t) in1[8]) * in2x2[1]; out[1] += ((uint128_t) in1[2]) * in2x2[8] + - ((uint128_t) in1[3]) * in2x2[7] + - ((uint128_t) in1[4]) * in2x2[6] + - ((uint128_t) in1[5]) * in2x2[5] + - ((uint128_t) in1[6]) * in2x2[4] + - ((uint128_t) in1[7]) * in2x2[3] + - ((uint128_t) in1[8]) * in2x2[2]; + ((uint128_t) in1[3]) * in2x2[7] + + ((uint128_t) in1[4]) * in2x2[6] + + ((uint128_t) in1[5]) * in2x2[5] + + ((uint128_t) in1[6]) * in2x2[4] + + ((uint128_t) in1[7]) * in2x2[3] + + ((uint128_t) in1[8]) * in2x2[2]; out[2] += ((uint128_t) in1[3]) * in2x2[8] + - ((uint128_t) in1[4]) * in2x2[7] + - ((uint128_t) in1[5]) * in2x2[6] + - ((uint128_t) in1[6]) * in2x2[5] + - ((uint128_t) in1[7]) * in2x2[4] + - ((uint128_t) in1[8]) * in2x2[3]; + ((uint128_t) in1[4]) * in2x2[7] + + ((uint128_t) in1[5]) * in2x2[6] + + ((uint128_t) in1[6]) * in2x2[5] + + ((uint128_t) in1[7]) * in2x2[4] + + ((uint128_t) in1[8]) * in2x2[3]; out[3] += ((uint128_t) in1[4]) * in2x2[8] + - ((uint128_t) in1[5]) * in2x2[7] + - ((uint128_t) in1[6]) * in2x2[6] + - ((uint128_t) in1[7]) * in2x2[5] + - ((uint128_t) in1[8]) * in2x2[4]; + ((uint128_t) in1[5]) * in2x2[7] + + ((uint128_t) in1[6]) * in2x2[6] + + ((uint128_t) in1[7]) * in2x2[5] + + ((uint128_t) in1[8]) * in2x2[4]; out[4] += ((uint128_t) in1[5]) * in2x2[8] + - ((uint128_t) in1[6]) * in2x2[7] + - ((uint128_t) in1[7]) * in2x2[6] + - ((uint128_t) in1[8]) * in2x2[5]; + ((uint128_t) in1[6]) * in2x2[7] + + ((uint128_t) in1[7]) * in2x2[6] + + ((uint128_t) in1[8]) * in2x2[5]; out[5] += ((uint128_t) in1[6]) * in2x2[8] + - ((uint128_t) in1[7]) * in2x2[7] + - ((uint128_t) in1[8]) * in2x2[6]; + ((uint128_t) in1[7]) * in2x2[7] + + ((uint128_t) in1[8]) * in2x2[6]; out[6] += ((uint128_t) in1[7]) * in2x2[8] + - ((uint128_t) in1[8]) * in2x2[7]; + ((uint128_t) in1[8]) * in2x2[7]; out[7] += ((uint128_t) in1[8]) * in2x2[8]; - } +} static const limb bottom52bits = 0xfffffffffffff; @@ -595,8 +611,9 @@ static const limb bottom52bits = 0xfffffffffffff; * On exit: * out[i] < 2^59 + 2^14 */ -static void felem_reduce(felem out, const largefelem in) - { +static void +felem_reduce(felem out, const largefelem in) +{ u64 overflow1, overflow2; out[0] = ((limb) in[0]) & bottom58bits; @@ -613,8 +630,9 @@ static void felem_reduce(felem out, const largefelem in) out[1] += ((limb) in[0]) >> 58; out[1] += (((limb) (in[0] >> 64)) & bottom52bits) << 6; - /* out[1] < 2^58 + 2^6 + 2^58 - * = 2^59 + 2^6 */ + /* + * out[1] < 2^58 + 2^6 + 2^58 = 2^59 + 2^6 + */ out[2] += ((limb) (in[0] >> 64)) >> 52; out[2] += ((limb) in[1]) >> 58; @@ -643,39 +661,43 @@ static void felem_reduce(felem out, const largefelem in) out[8] += ((limb) in[7]) >> 58; out[8] += (((limb) (in[7] >> 64)) & bottom52bits) << 6; - /* out[x > 1] < 2^58 + 2^6 + 2^58 + 2^12 - * < 2^59 + 2^13 */ + /* + * out[x > 1] < 2^58 + 2^6 + 2^58 + 2^12 < 2^59 + 2^13 + */ overflow1 = ((limb) (in[7] >> 64)) >> 52; overflow1 += ((limb) in[8]) >> 58; overflow1 += (((limb) (in[8] >> 64)) & bottom52bits) << 6; overflow2 = ((limb) (in[8] >> 64)) >> 52; - overflow1 <<= 1; /* overflow1 < 2^13 + 2^7 + 2^59 */ - overflow2 <<= 1; /* overflow2 < 2^13 */ + overflow1 <<= 1; /* overflow1 < 2^13 + 2^7 + 2^59 */ + overflow2 <<= 1; /* overflow2 < 2^13 */ - out[0] += overflow1; /* out[0] < 2^60 */ - out[1] += overflow2; /* out[1] < 2^59 + 2^6 + 2^13 */ + out[0] += overflow1; /* out[0] < 2^60 */ + out[1] += overflow2; /* out[1] < 2^59 + 2^6 + 2^13 */ - out[1] += out[0] >> 58; out[0] &= bottom58bits; - /* out[0] < 2^58 - * out[1] < 2^59 + 2^6 + 2^13 + 2^2 - * < 2^59 + 2^14 */ - } + out[1] += out[0] >> 58; + out[0] &= bottom58bits; + /* + * out[0] < 2^58 out[1] < 2^59 + 2^6 + 2^13 + 2^2 < 2^59 + 2^14 + */ +} -static void felem_square_reduce(felem out, const felem in) - { +static void +felem_square_reduce(felem out, const felem in) +{ largefelem tmp; felem_square(tmp, in); felem_reduce(out, tmp); - } +} -static void felem_mul_reduce(felem out, const felem in1, const felem in2) - { +static void +felem_mul_reduce(felem out, const felem in1, const felem in2) +{ largefelem tmp; felem_mul(tmp, in1, in2); felem_reduce(out, tmp); - } +} /* felem_inv calculates |out| = |in|^{-1} * @@ -684,117 +706,153 @@ static void felem_mul_reduce(felem out, const felem in1, const felem in2) * a^{p-1} = 1 (mod p) * a^{p-2} = a^{-1} (mod p) */ -static void felem_inv(felem out, const felem in) - { +static void +felem_inv(felem out, const felem in) +{ felem ftmp, ftmp2, ftmp3, ftmp4; largefelem 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_square(tmp, in); + felem_reduce(ftmp, tmp);/* 2^1 */ + felem_mul(tmp, in, ftmp); + felem_reduce(ftmp, tmp);/* 2^2 - 2^0 */ felem_assign(ftmp2, ftmp); - felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); /* 2^3 - 2^1 */ - felem_mul(tmp, in, ftmp); felem_reduce(ftmp, tmp); /* 2^3 - 2^0 */ - felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); /* 2^4 - 2^1 */ + felem_square(tmp, ftmp); + felem_reduce(ftmp, tmp);/* 2^3 - 2^1 */ + felem_mul(tmp, in, ftmp); + felem_reduce(ftmp, tmp);/* 2^3 - 2^0 */ + felem_square(tmp, ftmp); + felem_reduce(ftmp, tmp);/* 2^4 - 2^1 */ - felem_square(tmp, ftmp2); felem_reduce(ftmp3, tmp); /* 2^3 - 2^1 */ - felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp); /* 2^4 - 2^2 */ - felem_mul(tmp, ftmp3, ftmp2); felem_reduce(ftmp3, tmp); /* 2^4 - 2^0 */ + felem_square(tmp, ftmp2); + felem_reduce(ftmp3, tmp); /* 2^3 - 2^1 */ + felem_square(tmp, ftmp3); + felem_reduce(ftmp3, tmp); /* 2^4 - 2^2 */ + felem_mul(tmp, ftmp3, ftmp2); + felem_reduce(ftmp3, tmp); /* 2^4 - 2^0 */ felem_assign(ftmp2, ftmp3); - felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp); /* 2^5 - 2^1 */ - felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp); /* 2^6 - 2^2 */ - felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp); /* 2^7 - 2^3 */ - felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp); /* 2^8 - 2^4 */ + felem_square(tmp, ftmp3); + felem_reduce(ftmp3, tmp); /* 2^5 - 2^1 */ + felem_square(tmp, ftmp3); + felem_reduce(ftmp3, tmp); /* 2^6 - 2^2 */ + felem_square(tmp, ftmp3); + felem_reduce(ftmp3, tmp); /* 2^7 - 2^3 */ + felem_square(tmp, ftmp3); + felem_reduce(ftmp3, tmp); /* 2^8 - 2^4 */ felem_assign(ftmp4, ftmp3); - felem_mul(tmp, ftmp3, ftmp); felem_reduce(ftmp4, tmp); /* 2^8 - 2^1 */ - felem_square(tmp, ftmp4); felem_reduce(ftmp4, tmp); /* 2^9 - 2^2 */ - felem_mul(tmp, ftmp3, ftmp2); felem_reduce(ftmp3, tmp); /* 2^8 - 2^0 */ + felem_mul(tmp, ftmp3, ftmp); + felem_reduce(ftmp4, tmp); /* 2^8 - 2^1 */ + felem_square(tmp, ftmp4); + felem_reduce(ftmp4, tmp); /* 2^9 - 2^2 */ + felem_mul(tmp, ftmp3, ftmp2); + felem_reduce(ftmp3, tmp); /* 2^8 - 2^0 */ felem_assign(ftmp2, ftmp3); - for (i = 0; i < 8; i++) - { - felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp); /* 2^16 - 2^8 */ - } - felem_mul(tmp, ftmp3, ftmp2); felem_reduce(ftmp3, tmp); /* 2^16 - 2^0 */ + for (i = 0; i < 8; i++) { + felem_square(tmp, ftmp3); + felem_reduce(ftmp3, tmp); /* 2^16 - 2^8 */ + } + felem_mul(tmp, ftmp3, ftmp2); + felem_reduce(ftmp3, tmp); /* 2^16 - 2^0 */ felem_assign(ftmp2, ftmp3); - for (i = 0; i < 16; i++) - { - felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp); /* 2^32 - 2^16 */ - } - felem_mul(tmp, ftmp3, ftmp2); felem_reduce(ftmp3, tmp); /* 2^32 - 2^0 */ + for (i = 0; i < 16; i++) { + felem_square(tmp, ftmp3); + felem_reduce(ftmp3, tmp); /* 2^32 - 2^16 */ + } + felem_mul(tmp, ftmp3, ftmp2); + felem_reduce(ftmp3, tmp); /* 2^32 - 2^0 */ felem_assign(ftmp2, ftmp3); - for (i = 0; i < 32; i++) - { - felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp); /* 2^64 - 2^32 */ - } - felem_mul(tmp, ftmp3, ftmp2); felem_reduce(ftmp3, tmp); /* 2^64 - 2^0 */ + for (i = 0; i < 32; i++) { + felem_square(tmp, ftmp3); + felem_reduce(ftmp3, tmp); /* 2^64 - 2^32 */ + } + felem_mul(tmp, ftmp3, ftmp2); + felem_reduce(ftmp3, tmp); /* 2^64 - 2^0 */ felem_assign(ftmp2, ftmp3); - for (i = 0; i < 64; i++) - { - felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp); /* 2^128 - 2^64 */ - } - felem_mul(tmp, ftmp3, ftmp2); felem_reduce(ftmp3, tmp); /* 2^128 - 2^0 */ + for (i = 0; i < 64; i++) { + felem_square(tmp, ftmp3); + felem_reduce(ftmp3, tmp); /* 2^128 - 2^64 */ + } + felem_mul(tmp, ftmp3, ftmp2); + felem_reduce(ftmp3, tmp); /* 2^128 - 2^0 */ felem_assign(ftmp2, ftmp3); - for (i = 0; i < 128; i++) - { - felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp); /* 2^256 - 2^128 */ - } - felem_mul(tmp, ftmp3, ftmp2); felem_reduce(ftmp3, tmp); /* 2^256 - 2^0 */ + for (i = 0; i < 128; i++) { + felem_square(tmp, ftmp3); + felem_reduce(ftmp3, tmp); /* 2^256 - 2^128 */ + } + felem_mul(tmp, ftmp3, ftmp2); + felem_reduce(ftmp3, tmp); /* 2^256 - 2^0 */ felem_assign(ftmp2, ftmp3); - for (i = 0; i < 256; i++) - { - felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp); /* 2^512 - 2^256 */ - } - felem_mul(tmp, ftmp3, ftmp2); felem_reduce(ftmp3, tmp); /* 2^512 - 2^0 */ + for (i = 0; i < 256; i++) { + felem_square(tmp, ftmp3); + felem_reduce(ftmp3, tmp); /* 2^512 - 2^256 */ + } + felem_mul(tmp, ftmp3, ftmp2); + felem_reduce(ftmp3, tmp); /* 2^512 - 2^0 */ - for (i = 0; i < 9; i++) - { - felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp); /* 2^521 - 2^9 */ - } - felem_mul(tmp, ftmp3, ftmp4); felem_reduce(ftmp3, tmp); /* 2^512 - 2^2 */ - felem_mul(tmp, ftmp3, in); felem_reduce(out, tmp); /* 2^512 - 3 */ + for (i = 0; i < 9; i++) { + felem_square(tmp, ftmp3); + felem_reduce(ftmp3, tmp); /* 2^521 - 2^9 */ + } + felem_mul(tmp, ftmp3, ftmp4); + felem_reduce(ftmp3, tmp); /* 2^512 - 2^2 */ + felem_mul(tmp, ftmp3, in); + felem_reduce(out, tmp); /* 2^512 - 3 */ } /* This is 2^521-1, expressed as an felem */ static const felem kPrime = - { +{ 0x03ffffffffffffff, 0x03ffffffffffffff, 0x03ffffffffffffff, 0x03ffffffffffffff, 0x03ffffffffffffff, 0x03ffffffffffffff, 0x03ffffffffffffff, 0x03ffffffffffffff, 0x01ffffffffffffff - }; +}; /* felem_is_zero returns a limb with all bits set if |in| == 0 (mod p) and 0 * otherwise. * On entry: * in[i] < 2^59 + 2^14 */ -static limb felem_is_zero(const felem in) - { +static limb +felem_is_zero(const felem in) +{ felem ftmp; limb is_zero, is_p; felem_assign(ftmp, in); - ftmp[0] += ftmp[8] >> 57; ftmp[8] &= bottom57bits; + ftmp[0] += ftmp[8] >> 57; + ftmp[8] &= bottom57bits; /* ftmp[8] < 2^57 */ - ftmp[1] += ftmp[0] >> 58; ftmp[0] &= bottom58bits; - ftmp[2] += ftmp[1] >> 58; ftmp[1] &= bottom58bits; - ftmp[3] += ftmp[2] >> 58; ftmp[2] &= bottom58bits; - ftmp[4] += ftmp[3] >> 58; ftmp[3] &= bottom58bits; - ftmp[5] += ftmp[4] >> 58; ftmp[4] &= bottom58bits; - ftmp[6] += ftmp[5] >> 58; ftmp[5] &= bottom58bits; - ftmp[7] += ftmp[6] >> 58; ftmp[6] &= bottom58bits; - ftmp[8] += ftmp[7] >> 58; ftmp[7] &= bottom58bits; + ftmp[1] += ftmp[0] >> 58; + ftmp[0] &= bottom58bits; + ftmp[2] += ftmp[1] >> 58; + ftmp[1] &= bottom58bits; + ftmp[3] += ftmp[2] >> 58; + ftmp[2] &= bottom58bits; + ftmp[4] += ftmp[3] >> 58; + ftmp[3] &= bottom58bits; + ftmp[5] += ftmp[4] >> 58; + ftmp[4] &= bottom58bits; + ftmp[6] += ftmp[5] >> 58; + ftmp[5] &= bottom58bits; + ftmp[7] += ftmp[6] >> 58; + ftmp[6] &= bottom58bits; + ftmp[8] += ftmp[7] >> 58; + ftmp[7] &= bottom58bits; /* ftmp[8] < 2^57 + 4 */ - /* The ninth limb of 2*(2^521-1) is 0x03ffffffffffffff, which is - * greater than our bound for ftmp[8]. Therefore we only have to check - * if the zero is zero or 2^521-1. */ + /* + * The ninth limb of 2*(2^521-1) is 0x03ffffffffffffff, which is + * greater than our bound for ftmp[8]. Therefore we only have to + * check if the zero is zero or 2^521-1. + */ is_zero = 0; is_zero |= ftmp[0]; @@ -808,8 +866,10 @@ static limb felem_is_zero(const felem in) is_zero |= ftmp[8]; is_zero--; - /* We know that ftmp[i] < 2^63, therefore the only way that the top bit - * can be set is if is_zero was 0 before the decrement. */ + /* + * We know that ftmp[i] < 2^63, therefore the only way that the top + * bit can be set is if is_zero was 0 before the decrement. + */ is_zero = ((s64) is_zero) >> 63; is_p = ftmp[0] ^ kPrime[0]; @@ -827,41 +887,57 @@ static limb felem_is_zero(const felem in) is_zero |= is_p; return is_zero; - } +} -static int felem_is_zero_int(const felem in) - { - return (int) (felem_is_zero(in) & ((limb)1)); - } +static int +felem_is_zero_int(const felem in) +{ + return (int) (felem_is_zero(in) & ((limb) 1)); +} /* felem_contract converts |in| to its unique, minimal representation. * On entry: * in[i] < 2^59 + 2^14 */ -static void felem_contract(felem out, const felem in) - { +static void +felem_contract(felem out, const felem in) +{ limb is_p, is_greater, sign; - static const limb two58 = ((limb)1) << 58; + static const limb two58 = ((limb) 1) << 58; felem_assign(out, in); - out[0] += out[8] >> 57; out[8] &= bottom57bits; + out[0] += out[8] >> 57; + out[8] &= bottom57bits; /* out[8] < 2^57 */ - out[1] += out[0] >> 58; out[0] &= bottom58bits; - out[2] += out[1] >> 58; out[1] &= bottom58bits; - out[3] += out[2] >> 58; out[2] &= bottom58bits; - out[4] += out[3] >> 58; out[3] &= bottom58bits; - out[5] += out[4] >> 58; out[4] &= bottom58bits; - out[6] += out[5] >> 58; out[5] &= bottom58bits; - out[7] += out[6] >> 58; out[6] &= bottom58bits; - out[8] += out[7] >> 58; out[7] &= bottom58bits; + out[1] += out[0] >> 58; + out[0] &= bottom58bits; + out[2] += out[1] >> 58; + out[1] &= bottom58bits; + out[3] += out[2] >> 58; + out[2] &= bottom58bits; + out[4] += out[3] >> 58; + out[3] &= bottom58bits; + out[5] += out[4] >> 58; + out[4] &= bottom58bits; + out[6] += out[5] >> 58; + out[5] &= bottom58bits; + out[7] += out[6] >> 58; + out[6] &= bottom58bits; + out[8] += out[7] >> 58; + out[7] &= bottom58bits; /* out[8] < 2^57 + 4 */ - /* If the value is greater than 2^521-1 then we have to subtract + /* + * If the value is greater than 2^521-1 then we have to subtract * 2^521-1 out. See the comments in felem_is_zero regarding why we - * don't test for other multiples of the prime. */ + * don't test for other multiples of the prime. + */ - /* First, if |out| is equal to 2^521-1, we subtract it out to get zero. */ + /* + * First, if |out| is equal to 2^521-1, we subtract it out to get + * zero. + */ is_p = out[0] ^ kPrime[0]; is_p |= out[1] ^ kPrime[1]; @@ -895,8 +971,10 @@ static void felem_contract(felem out, const felem in) out[7] &= is_p; out[8] &= is_p; - /* In order to test that |out| >= 2^521-1 we need only test if out[8] - * >> 57 is greater than zero as (2^521-1) + x >= 2^522 */ + /* + * In order to test that |out| >= 2^521-1 we need only test if out[8] + * >> 57 is greater than zero as (2^521-1) + x >= 2^522 + */ is_greater = out[8] >> 57; is_greater |= is_greater << 32; is_greater |= is_greater << 16; @@ -917,18 +995,40 @@ static void felem_contract(felem out, const felem in) out[8] -= kPrime[8] & is_greater; /* Eliminate negative coefficients */ - sign = -(out[0] >> 63); out[0] += (two58 & sign); out[1] -= (1 & sign); - sign = -(out[1] >> 63); out[1] += (two58 & sign); out[2] -= (1 & sign); - sign = -(out[2] >> 63); out[2] += (two58 & sign); out[3] -= (1 & sign); - sign = -(out[3] >> 63); out[3] += (two58 & sign); out[4] -= (1 & sign); - sign = -(out[4] >> 63); out[4] += (two58 & sign); out[5] -= (1 & sign); - sign = -(out[0] >> 63); out[5] += (two58 & sign); out[6] -= (1 & sign); - sign = -(out[6] >> 63); out[6] += (two58 & sign); out[7] -= (1 & sign); - sign = -(out[7] >> 63); out[7] += (two58 & sign); out[8] -= (1 & sign); - sign = -(out[5] >> 63); out[5] += (two58 & sign); out[6] -= (1 & sign); - sign = -(out[6] >> 63); out[6] += (two58 & sign); out[7] -= (1 & sign); - sign = -(out[7] >> 63); out[7] += (two58 & sign); out[8] -= (1 & sign); - } + sign = -(out[0] >> 63); + out[0] += (two58 & sign); + out[1] -= (1 & sign); + sign = -(out[1] >> 63); + out[1] += (two58 & sign); + out[2] -= (1 & sign); + sign = -(out[2] >> 63); + out[2] += (two58 & sign); + out[3] -= (1 & sign); + sign = -(out[3] >> 63); + out[3] += (two58 & sign); + out[4] -= (1 & sign); + sign = -(out[4] >> 63); + out[4] += (two58 & sign); + out[5] -= (1 & sign); + sign = -(out[0] >> 63); + out[5] += (two58 & sign); + out[6] -= (1 & sign); + sign = -(out[6] >> 63); + out[6] += (two58 & sign); + out[7] -= (1 & sign); + sign = -(out[7] >> 63); + out[7] += (two58 & sign); + out[8] -= (1 & sign); + sign = -(out[5] >> 63); + out[5] += (two58 & sign); + out[6] -= (1 & sign); + sign = -(out[6] >> 63); + out[6] += (two58 & sign); + out[7] -= (1 & sign); + sign = -(out[7] >> 63); + out[7] += (two58 & sign); + out[8] -= (1 & sign); +} /* Group operations * ---------------- @@ -946,8 +1046,8 @@ static void felem_contract(felem out, const felem in) * 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) - { + const felem x_in, const felem y_in, const felem z_in) +{ largefelem tmp, tmp2; felem delta, gamma, beta, alpha, ftmp, ftmp2; @@ -956,15 +1056,15 @@ point_double(felem x_out, felem y_out, felem z_out, /* delta = z^2 */ felem_square(tmp, z_in); - felem_reduce(delta, tmp); /* delta[i] < 2^59 + 2^14 */ + felem_reduce(delta, tmp); /* delta[i] < 2^59 + 2^14 */ /* gamma = y^2 */ felem_square(tmp, y_in); - felem_reduce(gamma, tmp); /* gamma[i] < 2^59 + 2^14 */ + felem_reduce(gamma, tmp); /* gamma[i] < 2^59 + 2^14 */ /* beta = x*gamma */ felem_mul(tmp, x_in, gamma); - felem_reduce(beta, tmp); /* beta[i] < 2^59 + 2^14 */ + felem_reduce(beta, tmp);/* beta[i] < 2^59 + 2^14 */ /* alpha = 3*(x-delta)*(x+delta) */ felem_diff64(ftmp, delta); @@ -974,17 +1074,17 @@ point_double(felem x_out, felem y_out, felem z_out, felem_scalar64(ftmp2, 3); /* ftmp2[i] < 3*2^60 + 3*2^15 */ felem_mul(tmp, ftmp, ftmp2); - /* tmp[i] < 17(3*2^121 + 3*2^76) - * = 61*2^121 + 61*2^76 - * < 64*2^121 + 64*2^76 - * = 2^127 + 2^82 - * < 2^128 */ + /* + * tmp[i] < 17(3*2^121 + 3*2^76) = 61*2^121 + 61*2^76 < 64*2^121 + + * 64*2^76 = 2^127 + 2^82 < 2^128 + */ felem_reduce(alpha, tmp); /* x' = alpha^2 - 8*beta */ felem_square(tmp, alpha); - /* tmp[i] < 17*2^120 - * < 2^125 */ + /* + * tmp[i] < 17*2^120 < 2^125 + */ felem_assign(ftmp, beta); felem_scalar64(ftmp, 8); /* ftmp[i] < 2^62 + 2^17 */ @@ -999,8 +1099,9 @@ point_double(felem x_out, felem y_out, felem z_out, felem_sum64(ftmp, z_in); /* ftmp[i] < 2^60 + 2^15 */ felem_square(tmp, ftmp); - /* tmp[i] < 17(2^122) - * < 2^127 */ + /* + * tmp[i] < 17(2^122) < 2^127 + */ felem_diff_128_64(tmp, delta); /* tmp[i] < 2^127 + 2^63 */ felem_reduce(z_out, tmp); @@ -1011,36 +1112,39 @@ point_double(felem x_out, felem y_out, felem z_out, felem_diff64(beta, x_out); /* beta[i] < 2^61 + 2^60 + 2^16 */ felem_mul(tmp, alpha, beta); - /* tmp[i] < 17*((2^59 + 2^14)(2^61 + 2^60 + 2^16)) - * = 17*(2^120 + 2^75 + 2^119 + 2^74 + 2^75 + 2^30) - * = 17*(2^120 + 2^119 + 2^76 + 2^74 + 2^30) - * < 2^128 */ + /* + * tmp[i] < 17*((2^59 + 2^14)(2^61 + 2^60 + 2^16)) = 17*(2^120 + 2^75 + * + 2^119 + 2^74 + 2^75 + 2^30) = 17*(2^120 + 2^119 + 2^76 + 2^74 + + * 2^30) < 2^128 + */ felem_square(tmp2, gamma); - /* tmp2[i] < 17*(2^59 + 2^14)^2 - * = 17*(2^118 + 2^74 + 2^28) */ + /* + * tmp2[i] < 17*(2^59 + 2^14)^2 = 17*(2^118 + 2^74 + 2^28) + */ felem_scalar128(tmp2, 8); - /* tmp2[i] < 8*17*(2^118 + 2^74 + 2^28) - * = 2^125 + 2^121 + 2^81 + 2^77 + 2^35 + 2^31 - * < 2^126 */ + /* + * tmp2[i] < 8*17*(2^118 + 2^74 + 2^28) = 2^125 + 2^121 + 2^81 + 2^77 + * + 2^35 + 2^31 < 2^126 + */ felem_diff128(tmp, tmp2); - /* tmp[i] < 2^127 - 2^69 + 17(2^120 + 2^119 + 2^76 + 2^74 + 2^30) - * = 2^127 + 2^124 + 2^122 + 2^120 + 2^118 + 2^80 + 2^78 + 2^76 + - * 2^74 + 2^69 + 2^34 + 2^30 - * < 2^128 */ + /* + * tmp[i] < 2^127 - 2^69 + 17(2^120 + 2^119 + 2^76 + 2^74 + 2^30) = + * 2^127 + 2^124 + 2^122 + 2^120 + 2^118 + 2^80 + 2^78 + 2^76 + 2^74 + * + 2^69 + 2^34 + 2^30 < 2^128 + */ felem_reduce(y_out, tmp); - } +} /* 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) - { + for (i = 0; i < NLIMBS; ++i) { const limb tmp = mask & (in[i] ^ out[i]); out[i] ^= tmp; - } } +} /* point_add calcuates (x1, y1, z1) + (x2, y2, z2) * @@ -1052,10 +1156,11 @@ copy_conditional(felem out, const felem in, limb mask) * are equal (while not equal to the point at infinity). This case never * happens during single point multiplication, so there is no timing leak for * ECDH or ECDSA signing. */ -static void point_add(felem x3, felem y3, felem z3, - const felem x1, const felem y1, const felem z1, - const int mixed, const felem x2, const felem y2, const felem z2) - { +static void +point_add(felem x3, felem y3, felem z3, + const felem x1, const felem y1, const felem z1, + const int mixed, const felem x2, const felem y2, const felem z2) +{ felem ftmp, ftmp2, ftmp3, ftmp4, ftmp5, ftmp6, x_out, y_out, z_out; largefelem tmp, tmp2; limb x_equal, y_equal, z1_is_zero, z2_is_zero; @@ -1067,8 +1172,7 @@ static void point_add(felem x3, felem y3, felem z3, felem_square(tmp, z1); felem_reduce(ftmp, tmp); - if (!mixed) - { + if (!mixed) { /* ftmp2 = z2z2 = z2**2 */ felem_square(tmp, z2); felem_reduce(ftmp2, tmp); @@ -1098,9 +1202,7 @@ static void point_add(felem x3, felem y3, felem z3, /* s1 = ftmp6 = y1 * z2**3 */ felem_mul(tmp, y1, ftmp2); felem_reduce(ftmp6, tmp); - } - else - { + } else { /* We'll assume z2 = 1 (special case z2 = 0 is handled later) */ /* u1 = ftmp3 = x1*z2z2 */ @@ -1111,7 +1213,7 @@ static void point_add(felem x3, felem y3, felem z3, /* s1 = ftmp6 = y1 * z2**3 */ felem_assign(ftmp6, y1); - } + } /* u2 = x2*z1z1 */ felem_mul(tmp, x2, ftmp); @@ -1144,12 +1246,10 @@ static void point_add(felem x3, felem y3, felem z3, felem_scalar64(ftmp5, 2); /* ftmp5[i] < 2^61 */ - if (x_equal && y_equal && !z1_is_zero && !z2_is_zero) - { + 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_scalar64(ftmp, 2); @@ -1180,8 +1280,9 @@ static void point_add(felem x3, felem y3, felem z3, /* y_out = r(V-x_out) - 2 * s1 * J */ felem_diff64(ftmp3, x_out); - /* ftmp3[i] < 2^60 + 2^60 - * = 2^61 */ + /* + * ftmp3[i] < 2^60 + 2^60 = 2^61 + */ felem_mul(tmp, ftmp5, ftmp3); /* tmp[i] < 17*2^122 */ felem_mul(tmp2, ftmp6, ftmp2); @@ -1189,9 +1290,10 @@ static void point_add(felem x3, felem y3, felem z3, felem_scalar128(tmp2, 2); /* tmp2[i] < 17*2^121 */ felem_diff128(tmp, tmp2); - /* tmp[i] < 2^127 - 2^69 + 17*2^122 - * = 2^126 - 2^122 - 2^6 - 2^2 - 1 - * < 2^127 */ + /* + * tmp[i] < 2^127 - 2^69 + 17*2^122 = 2^126 - 2^122 - 2^6 - 2^2 - 1 < + * 2^127 + */ felem_reduce(y_out, tmp); copy_conditional(x_out, x2, z1_is_zero); @@ -1203,7 +1305,7 @@ static void point_add(felem x3, felem y3, felem z3, felem_assign(x3, x_out); felem_assign(y3, y_out); felem_assign(z3, z_out); - } +} /* Base point pre computation * -------------------------- @@ -1240,126 +1342,126 @@ static void point_add(felem x3, felem y3, felem z3, /* gmul is the table of precomputed base points */ static const felem gmul[16][3] = - {{{0, 0, 0, 0, 0, 0, 0, 0, 0}, - {0, 0, 0, 0, 0, 0, 0, 0, 0}, - {0, 0, 0, 0, 0, 0, 0, 0, 0}}, - {{0x017e7e31c2e5bd66, 0x022cf0615a90a6fe, 0x00127a2ffa8de334, - 0x01dfbf9d64a3f877, 0x006b4d3dbaa14b5e, 0x014fed487e0a2bd8, - 0x015b4429c6481390, 0x03a73678fb2d988e, 0x00c6858e06b70404}, - {0x00be94769fd16650, 0x031c21a89cb09022, 0x039013fad0761353, - 0x02657bd099031542, 0x03273e662c97ee72, 0x01e6d11a05ebef45, - 0x03d1bd998f544495, 0x03001172297ed0b1, 0x011839296a789a3b}, - {1, 0, 0, 0, 0, 0, 0, 0, 0}}, - {{0x0373faacbc875bae, 0x00f325023721c671, 0x00f666fd3dbde5ad, - 0x01a6932363f88ea7, 0x01fc6d9e13f9c47b, 0x03bcbffc2bbf734e, - 0x013ee3c3647f3a92, 0x029409fefe75d07d, 0x00ef9199963d85e5}, - {0x011173743ad5b178, 0x02499c7c21bf7d46, 0x035beaeabb8b1a58, - 0x00f989c4752ea0a3, 0x0101e1de48a9c1a3, 0x01a20076be28ba6c, - 0x02f8052e5eb2de95, 0x01bfe8f82dea117c, 0x0160074d3c36ddb7}, - {1, 0, 0, 0, 0, 0, 0, 0, 0}}, - {{0x012f3fc373393b3b, 0x03d3d6172f1419fa, 0x02adc943c0b86873, - 0x00d475584177952b, 0x012a4d1673750ee2, 0x00512517a0f13b0c, - 0x02b184671a7b1734, 0x0315b84236f1a50a, 0x00a4afc472edbdb9}, - {0x00152a7077f385c4, 0x03044007d8d1c2ee, 0x0065829d61d52b52, - 0x00494ff6b6631d0d, 0x00a11d94d5f06bcf, 0x02d2f89474d9282e, - 0x0241c5727c06eeb9, 0x0386928710fbdb9d, 0x01f883f727b0dfbe}, - {1, 0, 0, 0, 0, 0, 0, 0, 0}}, - {{0x019b0c3c9185544d, 0x006243a37c9d97db, 0x02ee3cbe030a2ad2, - 0x00cfdd946bb51e0d, 0x0271c00932606b91, 0x03f817d1ec68c561, - 0x03f37009806a369c, 0x03c1f30baf184fd5, 0x01091022d6d2f065}, - {0x0292c583514c45ed, 0x0316fca51f9a286c, 0x00300af507c1489a, - 0x0295f69008298cf1, 0x02c0ed8274943d7b, 0x016509b9b47a431e, - 0x02bc9de9634868ce, 0x005b34929bffcb09, 0x000c1a0121681524}, - {1, 0, 0, 0, 0, 0, 0, 0, 0}}, - {{0x0286abc0292fb9f2, 0x02665eee9805b3f7, 0x01ed7455f17f26d6, - 0x0346355b83175d13, 0x006284944cd0a097, 0x0191895bcdec5e51, - 0x02e288370afda7d9, 0x03b22312bfefa67a, 0x01d104d3fc0613fe}, - {0x0092421a12f7e47f, 0x0077a83fa373c501, 0x03bd25c5f696bd0d, - 0x035c41e4d5459761, 0x01ca0d1742b24f53, 0x00aaab27863a509c, - 0x018b6de47df73917, 0x025c0b771705cd01, 0x01fd51d566d760a7}, - {1, 0, 0, 0, 0, 0, 0, 0, 0}}, - {{0x01dd92ff6b0d1dbd, 0x039c5e2e8f8afa69, 0x0261ed13242c3b27, - 0x0382c6e67026e6a0, 0x01d60b10be2089f9, 0x03c15f3dce86723f, - 0x03c764a32d2a062d, 0x017307eac0fad056, 0x018207c0b96c5256}, - {0x0196a16d60e13154, 0x03e6ce74c0267030, 0x00ddbf2b4e52a5aa, - 0x012738241bbf31c8, 0x00ebe8dc04685a28, 0x024c2ad6d380d4a2, - 0x035ee062a6e62d0e, 0x0029ed74af7d3a0f, 0x00eef32aec142ebd}, - {1, 0, 0, 0, 0, 0, 0, 0, 0}}, - {{0x00c31ec398993b39, 0x03a9f45bcda68253, 0x00ac733c24c70890, - 0x00872b111401ff01, 0x01d178c23195eafb, 0x03bca2c816b87f74, - 0x0261a9af46fbad7a, 0x0324b2a8dd3d28f9, 0x00918121d8f24e23}, - {0x032bc8c1ca983cd7, 0x00d869dfb08fc8c6, 0x01693cb61fce1516, - 0x012a5ea68f4e88a8, 0x010869cab88d7ae3, 0x009081ad277ceee1, - 0x033a77166d064cdc, 0x03955235a1fb3a95, 0x01251a4a9b25b65e}, - {1, 0, 0, 0, 0, 0, 0, 0, 0}}, - {{0x00148a3a1b27f40b, 0x0123186df1b31fdc, 0x00026e7beaad34ce, - 0x01db446ac1d3dbba, 0x0299c1a33437eaec, 0x024540610183cbb7, - 0x0173bb0e9ce92e46, 0x02b937e43921214b, 0x01ab0436a9bf01b5}, - {0x0383381640d46948, 0x008dacbf0e7f330f, 0x03602122bcc3f318, - 0x01ee596b200620d6, 0x03bd0585fda430b3, 0x014aed77fd123a83, - 0x005ace749e52f742, 0x0390fe041da2b842, 0x0189a8ceb3299242}, - {1, 0, 0, 0, 0, 0, 0, 0, 0}}, - {{0x012a19d6b3282473, 0x00c0915918b423ce, 0x023a954eb94405ae, - 0x00529f692be26158, 0x0289fa1b6fa4b2aa, 0x0198ae4ceea346ef, - 0x0047d8cdfbdedd49, 0x00cc8c8953f0f6b8, 0x001424abbff49203}, - {0x0256732a1115a03a, 0x0351bc38665c6733, 0x03f7b950fb4a6447, - 0x000afffa94c22155, 0x025763d0a4dab540, 0x000511e92d4fc283, - 0x030a7e9eda0ee96c, 0x004c3cd93a28bf0a, 0x017edb3a8719217f}, - {1, 0, 0, 0, 0, 0, 0, 0, 0}}, - {{0x011de5675a88e673, 0x031d7d0f5e567fbe, 0x0016b2062c970ae5, - 0x03f4a2be49d90aa7, 0x03cef0bd13822866, 0x03f0923dcf774a6c, - 0x0284bebc4f322f72, 0x016ab2645302bb2c, 0x01793f95dace0e2a}, - {0x010646e13527a28f, 0x01ca1babd59dc5e7, 0x01afedfd9a5595df, - 0x01f15785212ea6b1, 0x0324e5d64f6ae3f4, 0x02d680f526d00645, - 0x0127920fadf627a7, 0x03b383f75df4f684, 0x0089e0057e783b0a}, - {1, 0, 0, 0, 0, 0, 0, 0, 0}}, - {{0x00f334b9eb3c26c6, 0x0298fdaa98568dce, 0x01c2d24843a82292, - 0x020bcb24fa1b0711, 0x02cbdb3d2b1875e6, 0x0014907598f89422, - 0x03abe3aa43b26664, 0x02cbf47f720bc168, 0x0133b5e73014b79b}, - {0x034aab5dab05779d, 0x00cdc5d71fee9abb, 0x0399f16bd4bd9d30, - 0x03582fa592d82647, 0x02be1cdfb775b0e9, 0x0034f7cea32e94cb, - 0x0335a7f08f56f286, 0x03b707e9565d1c8b, 0x0015c946ea5b614f}, - {1, 0, 0, 0, 0, 0, 0, 0, 0}}, - {{0x024676f6cff72255, 0x00d14625cac96378, 0x00532b6008bc3767, - 0x01fc16721b985322, 0x023355ea1b091668, 0x029de7afdc0317c3, - 0x02fc8a7ca2da037c, 0x02de1217d74a6f30, 0x013f7173175b73bf}, - {0x0344913f441490b5, 0x0200f9e272b61eca, 0x0258a246b1dd55d2, - 0x03753db9ea496f36, 0x025e02937a09c5ef, 0x030cbd3d14012692, - 0x01793a67e70dc72a, 0x03ec1d37048a662e, 0x006550f700c32a8d}, - {1, 0, 0, 0, 0, 0, 0, 0, 0}}, - {{0x00d3f48a347eba27, 0x008e636649b61bd8, 0x00d3b93716778fb3, - 0x004d1915757bd209, 0x019d5311a3da44e0, 0x016d1afcbbe6aade, - 0x0241bf5f73265616, 0x0384672e5d50d39b, 0x005009fee522b684}, - {0x029b4fab064435fe, 0x018868ee095bbb07, 0x01ea3d6936cc92b8, - 0x000608b00f78a2f3, 0x02db911073d1c20f, 0x018205938470100a, - 0x01f1e4964cbe6ff2, 0x021a19a29eed4663, 0x01414485f42afa81}, - {1, 0, 0, 0, 0, 0, 0, 0, 0}}, - {{0x01612b3a17f63e34, 0x03813992885428e6, 0x022b3c215b5a9608, - 0x029b4057e19f2fcb, 0x0384059a587af7e6, 0x02d6400ace6fe610, - 0x029354d896e8e331, 0x00c047ee6dfba65e, 0x0037720542e9d49d}, - {0x02ce9eed7c5e9278, 0x0374ed703e79643b, 0x01316c54c4072006, - 0x005aaa09054b2ee8, 0x002824000c840d57, 0x03d4eba24771ed86, - 0x0189c50aabc3bdae, 0x0338c01541e15510, 0x00466d56e38eed42}, - {1, 0, 0, 0, 0, 0, 0, 0, 0}}, - {{0x007efd8330ad8bd6, 0x02465ed48047710b, 0x0034c6606b215e0c, - 0x016ae30c53cbf839, 0x01fa17bd37161216, 0x018ead4e61ce8ab9, - 0x005482ed5f5dee46, 0x037543755bba1d7f, 0x005e5ac7e70a9d0f}, - {0x0117e1bb2fdcb2a2, 0x03deea36249f40c4, 0x028d09b4a6246cb7, - 0x03524b8855bcf756, 0x023d7d109d5ceb58, 0x0178e43e3223ef9c, - 0x0154536a0c6e966a, 0x037964d1286ee9fe, 0x0199bcd90e125055}, - {1, 0, 0, 0, 0, 0, 0, 0, 0}}}; +{{{0, 0, 0, 0, 0, 0, 0, 0, 0}, +{0, 0, 0, 0, 0, 0, 0, 0, 0}, +{0, 0, 0, 0, 0, 0, 0, 0, 0}}, +{{0x017e7e31c2e5bd66, 0x022cf0615a90a6fe, 0x00127a2ffa8de334, + 0x01dfbf9d64a3f877, 0x006b4d3dbaa14b5e, 0x014fed487e0a2bd8, +0x015b4429c6481390, 0x03a73678fb2d988e, 0x00c6858e06b70404}, +{0x00be94769fd16650, 0x031c21a89cb09022, 0x039013fad0761353, + 0x02657bd099031542, 0x03273e662c97ee72, 0x01e6d11a05ebef45, +0x03d1bd998f544495, 0x03001172297ed0b1, 0x011839296a789a3b}, +{1, 0, 0, 0, 0, 0, 0, 0, 0}}, +{{0x0373faacbc875bae, 0x00f325023721c671, 0x00f666fd3dbde5ad, + 0x01a6932363f88ea7, 0x01fc6d9e13f9c47b, 0x03bcbffc2bbf734e, +0x013ee3c3647f3a92, 0x029409fefe75d07d, 0x00ef9199963d85e5}, +{0x011173743ad5b178, 0x02499c7c21bf7d46, 0x035beaeabb8b1a58, + 0x00f989c4752ea0a3, 0x0101e1de48a9c1a3, 0x01a20076be28ba6c, +0x02f8052e5eb2de95, 0x01bfe8f82dea117c, 0x0160074d3c36ddb7}, +{1, 0, 0, 0, 0, 0, 0, 0, 0}}, +{{0x012f3fc373393b3b, 0x03d3d6172f1419fa, 0x02adc943c0b86873, + 0x00d475584177952b, 0x012a4d1673750ee2, 0x00512517a0f13b0c, +0x02b184671a7b1734, 0x0315b84236f1a50a, 0x00a4afc472edbdb9}, +{0x00152a7077f385c4, 0x03044007d8d1c2ee, 0x0065829d61d52b52, + 0x00494ff6b6631d0d, 0x00a11d94d5f06bcf, 0x02d2f89474d9282e, +0x0241c5727c06eeb9, 0x0386928710fbdb9d, 0x01f883f727b0dfbe}, +{1, 0, 0, 0, 0, 0, 0, 0, 0}}, +{{0x019b0c3c9185544d, 0x006243a37c9d97db, 0x02ee3cbe030a2ad2, + 0x00cfdd946bb51e0d, 0x0271c00932606b91, 0x03f817d1ec68c561, +0x03f37009806a369c, 0x03c1f30baf184fd5, 0x01091022d6d2f065}, +{0x0292c583514c45ed, 0x0316fca51f9a286c, 0x00300af507c1489a, + 0x0295f69008298cf1, 0x02c0ed8274943d7b, 0x016509b9b47a431e, +0x02bc9de9634868ce, 0x005b34929bffcb09, 0x000c1a0121681524}, +{1, 0, 0, 0, 0, 0, 0, 0, 0}}, +{{0x0286abc0292fb9f2, 0x02665eee9805b3f7, 0x01ed7455f17f26d6, + 0x0346355b83175d13, 0x006284944cd0a097, 0x0191895bcdec5e51, +0x02e288370afda7d9, 0x03b22312bfefa67a, 0x01d104d3fc0613fe}, +{0x0092421a12f7e47f, 0x0077a83fa373c501, 0x03bd25c5f696bd0d, + 0x035c41e4d5459761, 0x01ca0d1742b24f53, 0x00aaab27863a509c, +0x018b6de47df73917, 0x025c0b771705cd01, 0x01fd51d566d760a7}, +{1, 0, 0, 0, 0, 0, 0, 0, 0}}, +{{0x01dd92ff6b0d1dbd, 0x039c5e2e8f8afa69, 0x0261ed13242c3b27, + 0x0382c6e67026e6a0, 0x01d60b10be2089f9, 0x03c15f3dce86723f, +0x03c764a32d2a062d, 0x017307eac0fad056, 0x018207c0b96c5256}, +{0x0196a16d60e13154, 0x03e6ce74c0267030, 0x00ddbf2b4e52a5aa, + 0x012738241bbf31c8, 0x00ebe8dc04685a28, 0x024c2ad6d380d4a2, +0x035ee062a6e62d0e, 0x0029ed74af7d3a0f, 0x00eef32aec142ebd}, +{1, 0, 0, 0, 0, 0, 0, 0, 0}}, +{{0x00c31ec398993b39, 0x03a9f45bcda68253, 0x00ac733c24c70890, + 0x00872b111401ff01, 0x01d178c23195eafb, 0x03bca2c816b87f74, +0x0261a9af46fbad7a, 0x0324b2a8dd3d28f9, 0x00918121d8f24e23}, +{0x032bc8c1ca983cd7, 0x00d869dfb08fc8c6, 0x01693cb61fce1516, + 0x012a5ea68f4e88a8, 0x010869cab88d7ae3, 0x009081ad277ceee1, +0x033a77166d064cdc, 0x03955235a1fb3a95, 0x01251a4a9b25b65e}, +{1, 0, 0, 0, 0, 0, 0, 0, 0}}, +{{0x00148a3a1b27f40b, 0x0123186df1b31fdc, 0x00026e7beaad34ce, + 0x01db446ac1d3dbba, 0x0299c1a33437eaec, 0x024540610183cbb7, +0x0173bb0e9ce92e46, 0x02b937e43921214b, 0x01ab0436a9bf01b5}, +{0x0383381640d46948, 0x008dacbf0e7f330f, 0x03602122bcc3f318, + 0x01ee596b200620d6, 0x03bd0585fda430b3, 0x014aed77fd123a83, +0x005ace749e52f742, 0x0390fe041da2b842, 0x0189a8ceb3299242}, +{1, 0, 0, 0, 0, 0, 0, 0, 0}}, +{{0x012a19d6b3282473, 0x00c0915918b423ce, 0x023a954eb94405ae, + 0x00529f692be26158, 0x0289fa1b6fa4b2aa, 0x0198ae4ceea346ef, +0x0047d8cdfbdedd49, 0x00cc8c8953f0f6b8, 0x001424abbff49203}, +{0x0256732a1115a03a, 0x0351bc38665c6733, 0x03f7b950fb4a6447, + 0x000afffa94c22155, 0x025763d0a4dab540, 0x000511e92d4fc283, +0x030a7e9eda0ee96c, 0x004c3cd93a28bf0a, 0x017edb3a8719217f}, +{1, 0, 0, 0, 0, 0, 0, 0, 0}}, +{{0x011de5675a88e673, 0x031d7d0f5e567fbe, 0x0016b2062c970ae5, + 0x03f4a2be49d90aa7, 0x03cef0bd13822866, 0x03f0923dcf774a6c, +0x0284bebc4f322f72, 0x016ab2645302bb2c, 0x01793f95dace0e2a}, +{0x010646e13527a28f, 0x01ca1babd59dc5e7, 0x01afedfd9a5595df, + 0x01f15785212ea6b1, 0x0324e5d64f6ae3f4, 0x02d680f526d00645, +0x0127920fadf627a7, 0x03b383f75df4f684, 0x0089e0057e783b0a}, +{1, 0, 0, 0, 0, 0, 0, 0, 0}}, +{{0x00f334b9eb3c26c6, 0x0298fdaa98568dce, 0x01c2d24843a82292, + 0x020bcb24fa1b0711, 0x02cbdb3d2b1875e6, 0x0014907598f89422, +0x03abe3aa43b26664, 0x02cbf47f720bc168, 0x0133b5e73014b79b}, +{0x034aab5dab05779d, 0x00cdc5d71fee9abb, 0x0399f16bd4bd9d30, + 0x03582fa592d82647, 0x02be1cdfb775b0e9, 0x0034f7cea32e94cb, +0x0335a7f08f56f286, 0x03b707e9565d1c8b, 0x0015c946ea5b614f}, +{1, 0, 0, 0, 0, 0, 0, 0, 0}}, +{{0x024676f6cff72255, 0x00d14625cac96378, 0x00532b6008bc3767, + 0x01fc16721b985322, 0x023355ea1b091668, 0x029de7afdc0317c3, +0x02fc8a7ca2da037c, 0x02de1217d74a6f30, 0x013f7173175b73bf}, +{0x0344913f441490b5, 0x0200f9e272b61eca, 0x0258a246b1dd55d2, + 0x03753db9ea496f36, 0x025e02937a09c5ef, 0x030cbd3d14012692, +0x01793a67e70dc72a, 0x03ec1d37048a662e, 0x006550f700c32a8d}, +{1, 0, 0, 0, 0, 0, 0, 0, 0}}, +{{0x00d3f48a347eba27, 0x008e636649b61bd8, 0x00d3b93716778fb3, + 0x004d1915757bd209, 0x019d5311a3da44e0, 0x016d1afcbbe6aade, +0x0241bf5f73265616, 0x0384672e5d50d39b, 0x005009fee522b684}, +{0x029b4fab064435fe, 0x018868ee095bbb07, 0x01ea3d6936cc92b8, + 0x000608b00f78a2f3, 0x02db911073d1c20f, 0x018205938470100a, +0x01f1e4964cbe6ff2, 0x021a19a29eed4663, 0x01414485f42afa81}, +{1, 0, 0, 0, 0, 0, 0, 0, 0}}, +{{0x01612b3a17f63e34, 0x03813992885428e6, 0x022b3c215b5a9608, + 0x029b4057e19f2fcb, 0x0384059a587af7e6, 0x02d6400ace6fe610, +0x029354d896e8e331, 0x00c047ee6dfba65e, 0x0037720542e9d49d}, +{0x02ce9eed7c5e9278, 0x0374ed703e79643b, 0x01316c54c4072006, + 0x005aaa09054b2ee8, 0x002824000c840d57, 0x03d4eba24771ed86, +0x0189c50aabc3bdae, 0x0338c01541e15510, 0x00466d56e38eed42}, +{1, 0, 0, 0, 0, 0, 0, 0, 0}}, +{{0x007efd8330ad8bd6, 0x02465ed48047710b, 0x0034c6606b215e0c, + 0x016ae30c53cbf839, 0x01fa17bd37161216, 0x018ead4e61ce8ab9, +0x005482ed5f5dee46, 0x037543755bba1d7f, 0x005e5ac7e70a9d0f}, +{0x0117e1bb2fdcb2a2, 0x03deea36249f40c4, 0x028d09b4a6246cb7, + 0x03524b8855bcf756, 0x023d7d109d5ceb58, 0x0178e43e3223ef9c, +0x0154536a0c6e966a, 0x037964d1286ee9fe, 0x0199bcd90e125055}, +{1, 0, 0, 0, 0, 0, 0, 0, 0}}}; /* select_point selects the |idx|th point from a precomputation table and * copies it to out. */ -static void select_point(const limb idx, unsigned int size, const felem pre_comp[/* size */][3], - felem out[3]) - { +static void +select_point(const limb idx, unsigned int size, const felem pre_comp[ /* size */ ][3], + felem out[3]) +{ unsigned i, j; limb *outlimbs = &out[0][0]; memset(outlimbs, 0, 3 * sizeof(felem)); - for (i = 0; i < size; i++) - { + for (i = 0; i < size; i++) { const limb *inlimbs = &pre_comp[i][0][0]; limb mask = i ^ idx; mask |= mask >> 4; @@ -1369,26 +1471,28 @@ static void select_point(const limb idx, unsigned int size, const felem pre_comp 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) - { +static char +get_bit(const felem_bytearray in, int i) +{ if (i < 0) return 0; return (in[i >> 3] >> (i & 7)) & 1; - } +} /* Interleaved point multiplication using precomputed point multiples: * The small point multiples 0*P, 1*P, ..., 16*P are in pre_comp[], * the scalars in scalars[]. If g_scalar is non-NULL, we also add this multiple * of the generator, using certain (large) precomputed multiples in g_pre_comp. * Output point (X, Y, Z) is stored in x_out, y_out, z_out */ -static void batch_mul(felem x_out, felem y_out, felem z_out, - const felem_bytearray scalars[], const unsigned num_points, const u8 *g_scalar, - const int mixed, const felem pre_comp[][17][3], const felem g_pre_comp[16][3]) - { +static void +batch_mul(felem x_out, felem y_out, felem z_out, + const felem_bytearray scalars[], const unsigned num_points, const u8 * g_scalar, + const int mixed, const felem pre_comp[][17][3], const felem g_pre_comp[16][3]) +{ int i, skip; unsigned num, gen_mul = (g_scalar != NULL); felem nq[3], tmp[4]; @@ -1398,48 +1502,41 @@ static void batch_mul(felem x_out, felem y_out, felem z_out, /* 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 (last quarter of rounds) - * and additions of other points multiples (every 5th round). + /* + * Loop over all scalars msb-to-lsb, interleaving additions of + * multiples of the generator (last quarter of rounds) and additions + * of other points multiples (every 5th round). */ - skip = 1; /* save two point operations in the first round */ - for (i = (num_points ? 520 : 130); i >= 0; --i) - { + skip = 1; /* save two point operations in the first + * round */ + for (i = (num_points ? 520 : 130); 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 <= 130)) - { + if (gen_mul && (i <= 130)) { bits = get_bit(g_scalar, i + 390) << 3; - if (i < 130) - { + if (i < 130) { bits |= get_bit(g_scalar, i + 260) << 2; bits |= get_bit(g_scalar, i + 130) << 1; bits |= get_bit(g_scalar, i); - } + } /* select the point to add, in constant time */ select_point(bits, 16, g_pre_comp, tmp); - if (!skip) - { + 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 - { + nq[0], nq[1], nq[2], + 1 /* mixed */ , tmp[0], tmp[1], tmp[2]); + } else { memcpy(nq, tmp, 3 * sizeof(felem)); skip = 0; - } } - + } /* do other additions every 5 doublings */ - if (num_points && (i % 5 == 0)) - { + if (num_points && (i % 5 == 0)) { /* loop over all scalars */ - for (num = 0; num < num_points; ++num) - { + 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; @@ -1448,29 +1545,30 @@ static void batch_mul(felem x_out, felem y_out, felem z_out, 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 the point to add or subtract, in + * constant time + */ select_point(digit, 17, pre_comp[num], tmp); - felem_neg(tmp[3], tmp[1]); /* (X, -Y, Z) is the negative point */ + felem_neg(tmp[3], tmp[1]); /* (X, -Y, Z) is the + * negative point */ copy_conditional(tmp[1], tmp[3], (-(limb) sign)); - if (!skip) - { + if (!skip) { point_add(nq[0], nq[1], nq[2], - nq[0], nq[1], nq[2], - mixed, tmp[0], tmp[1], tmp[2]); - } - else - { + nq[0], nq[1], nq[2], + mixed, tmp[0], tmp[1], tmp[2]); + } else { memcpy(nq, tmp, 3 * sizeof(felem)); skip = 0; - } } } } + } felem_assign(x_out, nq[0]); felem_assign(y_out, nq[1]); felem_assign(z_out, nq[2]); - } +} /* Precomputation for the group generator. */ @@ -1493,20 +1591,20 @@ EC_GFp_nistp521_method(void) .group_get_curve = ec_GFp_simple_group_get_curve, .group_get_degree = ec_GFp_simple_group_get_degree, .group_check_discriminant = - ec_GFp_simple_group_check_discriminant, + ec_GFp_simple_group_check_discriminant, .point_init = ec_GFp_simple_point_init, .point_finish = ec_GFp_simple_point_finish, .point_clear_finish = ec_GFp_simple_point_clear_finish, .point_copy = ec_GFp_simple_point_copy, .point_set_to_infinity = ec_GFp_simple_point_set_to_infinity, .point_set_Jprojective_coordinates_GFp = - ec_GFp_simple_set_Jprojective_coordinates_GFp, + ec_GFp_simple_set_Jprojective_coordinates_GFp, .point_get_Jprojective_coordinates_GFp = - ec_GFp_simple_get_Jprojective_coordinates_GFp, + ec_GFp_simple_get_Jprojective_coordinates_GFp, .point_set_affine_coordinates = - ec_GFp_simple_point_set_affine_coordinates, + ec_GFp_simple_point_set_affine_coordinates, .point_get_affine_coordinates = - ec_GFp_nistp521_point_get_affine_coordinates, + ec_GFp_nistp521_point_get_affine_coordinates, .add = ec_GFp_simple_add, .dbl = ec_GFp_simple_dbl, .invert = ec_GFp_simple_invert, @@ -1530,32 +1628,34 @@ EC_GFp_nistp521_method(void) /* FUNCTIONS TO MANAGE PRECOMPUTATION */ -static NISTP521_PRE_COMP *nistp521_pre_comp_new() - { +static NISTP521_PRE_COMP * +nistp521_pre_comp_new() +{ NISTP521_PRE_COMP *ret = NULL; - ret = (NISTP521_PRE_COMP *)malloc(sizeof(NISTP521_PRE_COMP)); - if (!ret) - { + ret = (NISTP521_PRE_COMP *) malloc(sizeof(NISTP521_PRE_COMP)); + if (!ret) { ECerr(EC_F_NISTP521_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 *nistp521_pre_comp_dup(void *src_) - { +static void * +nistp521_pre_comp_dup(void *src_) +{ NISTP521_PRE_COMP *src = src_; /* no need to actually copy, these objects never change! */ CRYPTO_add(&src->references, 1, CRYPTO_LOCK_EC_PRE_COMP); return src_; - } +} -static void nistp521_pre_comp_free(void *pre_) - { +static void +nistp521_pre_comp_free(void *pre_) +{ int i; NISTP521_PRE_COMP *pre = pre_; @@ -1567,10 +1667,11 @@ static void nistp521_pre_comp_free(void *pre_) return; free(pre); - } +} -static void nistp521_pre_comp_clear_free(void *pre_) - { +static void +nistp521_pre_comp_clear_free(void *pre_) +{ int i; NISTP521_PRE_COMP *pre = pre_; @@ -1583,43 +1684,46 @@ static void nistp521_pre_comp_clear_free(void *pre_) OPENSSL_cleanse(pre, sizeof(*pre)); free(pre); - } +} /******************************************************************************/ /* OPENSSL EC_METHOD FUNCTIONS */ -int ec_GFp_nistp521_group_init(EC_GROUP *group) - { +int +ec_GFp_nistp521_group_init(EC_GROUP * group) +{ int ret; ret = ec_GFp_simple_group_init(group); group->a_is_minus3 = 1; return ret; - } +} -int ec_GFp_nistp521_group_set_curve(EC_GROUP *group, const BIGNUM *p, - const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) - { +int +ec_GFp_nistp521_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; + 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; + ((curve_a = BN_CTX_get(ctx)) == NULL) || + ((curve_b = BN_CTX_get(ctx)) == NULL)) + goto err; BN_bin2bn(nistp521_curve_params[0], sizeof(felem_bytearray), curve_p); BN_bin2bn(nistp521_curve_params[1], sizeof(felem_bytearray), curve_a); BN_bin2bn(nistp521_curve_params[2], sizeof(felem_bytearray), curve_b); if ((BN_cmp(curve_p, p)) || (BN_cmp(curve_a, a)) || - (BN_cmp(curve_b, b))) - { + (BN_cmp(curve_b, b))) { ECerr(EC_F_EC_GFP_NISTP521_GROUP_SET_CURVE, - EC_R_WRONG_CURVE_PARAMETERS); + EC_R_WRONG_CURVE_PARAMETERS); goto err; - } + } group->field_mod_func = BN_nist_mod_521; ret = ec_GFp_simple_group_set_curve(group, p, a, b, ctx); err: @@ -1627,74 +1731,79 @@ err: 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_nistp521_point_get_affine_coordinates(const EC_GROUP *group, - const EC_POINT *point, BIGNUM *x, BIGNUM *y, BN_CTX *ctx) - { +int +ec_GFp_nistp521_point_get_affine_coordinates(const EC_GROUP * group, + const EC_POINT * point, BIGNUM * x, BIGNUM * y, BN_CTX * ctx) +{ felem z1, z2, x_in, y_in, x_out, y_out; largefelem tmp; - if (EC_POINT_is_at_infinity(group, point)) - { + if (EC_POINT_is_at_infinity(group, point)) { ECerr(EC_F_EC_GFP_NISTP521_POINT_GET_AFFINE_COORDINATES, - EC_R_POINT_AT_INFINITY); + 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; + (!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_square(tmp, z2); + felem_reduce(z1, tmp); + felem_mul(tmp, x_in, z1); + felem_reduce(x_in, tmp); felem_contract(x_out, x_in); - if (x != NULL) - { - if (!felem_to_BN(x, x_out)) - { + if (x != NULL) { + if (!felem_to_BN(x, x_out)) { ECerr(EC_F_EC_GFP_NISTP521_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_mul(tmp, z1, z2); + felem_reduce(z1, tmp); + felem_mul(tmp, y_in, z1); + felem_reduce(y_in, tmp); felem_contract(y_out, y_in); - if (y != NULL) - { - if (!felem_to_BN(y, y_out)) - { + if (y != NULL) { + if (!felem_to_BN(y, y_out)) { ECerr(EC_F_EC_GFP_NISTP521_POINT_GET_AFFINE_COORDINATES, ERR_R_BN_LIB); return 0; - } } - return 1; } + return 1; +} -static void make_points_affine(size_t num, felem points[/* num */][3], felem tmp_felems[/* num+1 */]) - { - /* Runs in constant time, unless an input is the point at infinity - * (which normally shouldn't happen). */ +static void +make_points_affine(size_t num, felem points[ /* num */ ][3], felem tmp_felems[ /* num+1 */ ]) +{ + /* + * Runs in constant time, unless an input is the point at infinity + * (which normally shouldn't happen). + */ ec_GFp_nistp_points_make_affine_internal( - num, - points, - sizeof(felem), - tmp_felems, - (void (*)(void *)) felem_one, - (int (*)(const void *)) felem_is_zero_int, - (void (*)(void *, const void *)) felem_assign, - (void (*)(void *, const void *)) felem_square_reduce, - (void (*)(void *, const void *, const void *)) felem_mul_reduce, - (void (*)(void *, const void *)) felem_inv, - (void (*)(void *, const void *)) felem_contract); - } + num, + points, + sizeof(felem), + tmp_felems, + (void (*) (void *)) felem_one, + (int (*) (const void *)) felem_is_zero_int, + (void (*) (void *, const void *)) felem_assign, + (void (*) (void *, const void *)) felem_square_reduce, + (void (*) (void *, const void *, const void *)) felem_mul_reduce, + (void (*) (void *, const void *)) felem_inv, + (void (*) (void *, const void *)) felem_contract); +} /* Computes scalar*generator + \sum scalars[i]*points[i], ignoring NULL values * Result is stored in r (r can equal one of the inputs). */ -int ec_GFp_nistp521_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 +ec_GFp_nistp521_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; @@ -1702,7 +1811,7 @@ int ec_GFp_nistp521_points_mul(const EC_GROUP *group, EC_POINT *r, BIGNUM *x, *y, *z, *tmp_scalar; felem_bytearray g_secret; felem_bytearray *secrets = NULL; - felem (*pre_comp)[17][3] = NULL; + felem(*pre_comp)[17][3] = NULL; felem *tmp_felems = NULL; felem_bytearray tmp; unsigned i, num_bytes; @@ -1710,178 +1819,170 @@ int ec_GFp_nistp521_points_mul(const EC_GROUP *group, EC_POINT *r, size_t num_points = num; felem x_in, y_in, z_in, x_out, y_out, z_out; NISTP521_PRE_COMP *pre = NULL; - felem (*g_pre_comp)[3] = NULL; + felem(*g_pre_comp)[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; + 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)) + ((y = BN_CTX_get(ctx)) == NULL) || + ((z = BN_CTX_get(ctx)) == NULL) || + ((tmp_scalar = BN_CTX_get(ctx)) == NULL)) goto err; - if (scalar != NULL) - { + if (scalar != NULL) { pre = EC_EX_DATA_get_data(group->extra_data, - nistp521_pre_comp_dup, nistp521_pre_comp_free, - nistp521_pre_comp_clear_free); + nistp521_pre_comp_dup, nistp521_pre_comp_free, + nistp521_pre_comp_clear_free); if (pre) /* we have precomputation, try to use it */ g_pre_comp = &pre->g_pre_comp[0]; else /* try to use the standard precomputation */ - g_pre_comp = (felem (*)[3]) gmul; + g_pre_comp = (felem(*)[3]) gmul; generator = EC_POINT_new(group); if (generator == NULL) goto err; /* get the generator from precomputation */ if (!felem_to_BN(x, g_pre_comp[1][0]) || - !felem_to_BN(y, g_pre_comp[1][1]) || - !felem_to_BN(z, g_pre_comp[1][2])) - { + !felem_to_BN(y, g_pre_comp[1][1]) || + !felem_to_BN(z, g_pre_comp[1][2])) { ECerr(EC_F_EC_GFP_NISTP521_POINTS_MUL, ERR_R_BN_LIB); goto err; - } + } if (!EC_POINT_set_Jprojective_coordinates_GFp(group, - generator, x, y, z, ctx)) + 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 */ + /* + * we don't have valid precomputation: treat the + * generator as a random point + */ num_points++; - } - - if (num_points > 0) - { - if (num_points >= 2) - { - /* unless we precompute multiples for just one point, - * converting those into affine form is time well spent */ + } + if (num_points > 0) { + if (num_points >= 2) { + /* + * unless we precompute multiples for just one point, + * converting those into affine form is time well + * spent + */ mixed = 1; - } + } secrets = malloc(num_points * sizeof(felem_bytearray)); pre_comp = malloc(num_points * 17 * 3 * sizeof(felem)); if (mixed) tmp_felems = malloc((num_points * 17 + 1) * sizeof(felem)); - if ((secrets == NULL) || (pre_comp == NULL) || (mixed && (tmp_felems == NULL))) - { + if ((secrets == NULL) || (pre_comp == NULL) || (mixed && (tmp_felems == NULL))) { ECerr(EC_F_EC_GFP_NISTP521_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 */ + } + /* + * we treat NULL scalars as 0, and NULL points as points at + * infinity, i.e., they contribute nothing to the linear + * combination + */ memset(secrets, 0, num_points * sizeof(felem_bytearray)); memset(pre_comp, 0, num_points * 17 * 3 * sizeof(felem)); - for (i = 0; i < num_points; ++i) - { + for (i = 0; i < num_points; ++i) { if (i == num) - /* we didn't have a valid precomputation, so we pick - * the generator */ - { + /* + * we didn't have a valid precomputation, so + * we pick the generator + */ + { p = EC_GROUP_get0_generator(group); p_scalar = scalar; - } - else + } else /* the i^th point */ - { + { p = points[i]; p_scalar = scalars[i]; - } - if ((p_scalar != NULL) && (p != NULL)) - { + } + if ((p_scalar != NULL) && (p != NULL)) { /* reduce scalar to 0 <= scalar < 2^521 */ - if ((BN_num_bits(p_scalar) > 521) || (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)) - { + if ((BN_num_bits(p_scalar) > 521) || (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_NISTP521_POINTS_MUL, ERR_R_BN_LIB); goto err; - } - num_bytes = BN_bn2bin(tmp_scalar, tmp); } - else + 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; + (!BN_to_felem(y_out, &p->Y)) || + (!BN_to_felem(z_out, &p->Z))) + goto err; memcpy(pre_comp[i][1][0], x_out, sizeof(felem)); memcpy(pre_comp[i][1][1], y_out, sizeof(felem)); memcpy(pre_comp[i][1][2], z_out, sizeof(felem)); - for (j = 2; j <= 16; ++j) - { - if (j & 1) - { + for (j = 2; j <= 16; ++j) { + if (j & 1) { point_add( - pre_comp[i][j][0], pre_comp[i][j][1], pre_comp[i][j][2], - pre_comp[i][1][0], pre_comp[i][1][1], pre_comp[i][1][2], - 0, pre_comp[i][j-1][0], pre_comp[i][j-1][1], pre_comp[i][j-1][2]); - } - else - { + pre_comp[i][j][0], pre_comp[i][j][1], pre_comp[i][j][2], + pre_comp[i][1][0], pre_comp[i][1][1], pre_comp[i][1][2], + 0, pre_comp[i][j - 1][0], pre_comp[i][j - 1][1], pre_comp[i][j - 1][2]); + } else { point_double( - pre_comp[i][j][0], pre_comp[i][j][1], pre_comp[i][j][2], - pre_comp[i][j/2][0], pre_comp[i][j/2][1], pre_comp[i][j/2][2]); - } + pre_comp[i][j][0], pre_comp[i][j][1], pre_comp[i][j][2], + pre_comp[i][j / 2][0], pre_comp[i][j / 2][1], pre_comp[i][j / 2][2]); } } } + } if (mixed) make_points_affine(num_points * 17, pre_comp[0], tmp_felems); - } - + } /* the scalar for the generator */ - if ((scalar != NULL) && (have_pre_comp)) - { + if ((scalar != NULL) && (have_pre_comp)) { memset(g_secret, 0, sizeof(g_secret)); /* reduce scalar to 0 <= scalar < 2^521 */ - if ((BN_num_bits(scalar) > 521) || (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)) - { + if ((BN_num_bits(scalar) > 521) || (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_NISTP521_POINTS_MUL, ERR_R_BN_LIB); goto err; - } - num_bytes = BN_bn2bin(tmp_scalar, tmp); } - else + 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*/ + /* do the multiplication with generator precomputation */ batch_mul(x_out, y_out, z_out, - (const felem_bytearray (*)) secrets, num_points, - g_secret, - mixed, (const felem (*)[17][3]) pre_comp, - (const felem (*)[3]) g_pre_comp); - } - else + (const felem_bytearray(*)) secrets, num_points, + g_secret, + mixed, (const felem(*)[17][3]) pre_comp, + (const felem(*)[3]) g_pre_comp); + } else /* do the multiplication without generator precomputation */ batch_mul(x_out, y_out, z_out, - (const felem_bytearray (*)) secrets, num_points, - NULL, mixed, (const felem (*)[17][3]) pre_comp, NULL); + (const felem_bytearray(*)) secrets, num_points, + NULL, mixed, (const felem(*)[17][3]) pre_comp, NULL); /* reduce the output to its unique minimal representation */ felem_contract(x_in, x_out); felem_contract(y_in, y_out); felem_contract(z_in, z_out); if ((!felem_to_BN(x, x_in)) || (!felem_to_BN(y, y_in)) || - (!felem_to_BN(z, z_in))) - { + (!felem_to_BN(z, z_in))) { ECerr(EC_F_EC_GFP_NISTP521_POINTS_MUL, ERR_R_BN_LIB); goto err; - } + } ret = EC_POINT_set_Jprojective_coordinates_GFp(group, r, x, y, z, ctx); err: @@ -1897,10 +1998,11 @@ err: if (tmp_felems != NULL) free(tmp_felems); return ret; - } +} -int ec_GFp_nistp521_precompute_mult(EC_GROUP *group, BN_CTX *ctx) - { +int +ec_GFp_nistp521_precompute_mult(EC_GROUP * group, BN_CTX * ctx) +{ int ret = 0; NISTP521_PRE_COMP *pre = NULL; int i, j; @@ -1911,95 +2013,93 @@ int ec_GFp_nistp521_precompute_mult(EC_GROUP *group, BN_CTX *ctx) /* throw away old precomputation */ EC_EX_DATA_free_data(&group->extra_data, nistp521_pre_comp_dup, - nistp521_pre_comp_free, nistp521_pre_comp_clear_free); + nistp521_pre_comp_free, nistp521_pre_comp_clear_free); if (ctx == NULL) - if ((ctx = new_ctx = BN_CTX_new()) == NULL) return 0; + 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)) + ((y = BN_CTX_get(ctx)) == NULL)) goto err; /* get the generator */ - if (group->generator == NULL) goto err; + if (group->generator == NULL) + goto err; generator = EC_POINT_new(group); if (generator == NULL) goto err; - BN_bin2bn(nistp521_curve_params[3], sizeof (felem_bytearray), x); - BN_bin2bn(nistp521_curve_params[4], sizeof (felem_bytearray), y); + BN_bin2bn(nistp521_curve_params[3], sizeof(felem_bytearray), x); + BN_bin2bn(nistp521_curve_params[4], sizeof(felem_bytearray), y); if (!EC_POINT_set_affine_coordinates_GFp(group, generator, x, y, ctx)) goto err; if ((pre = nistp521_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)) - { + if (0 == EC_POINT_cmp(group, generator, group->generator, ctx)) { memcpy(pre->g_pre_comp, gmul, sizeof(pre->g_pre_comp)); ret = 1; goto err; - } + } if ((!BN_to_felem(pre->g_pre_comp[1][0], &group->generator->X)) || - (!BN_to_felem(pre->g_pre_comp[1][1], &group->generator->Y)) || - (!BN_to_felem(pre->g_pre_comp[1][2], &group->generator->Z))) + (!BN_to_felem(pre->g_pre_comp[1][1], &group->generator->Y)) || + (!BN_to_felem(pre->g_pre_comp[1][2], &group->generator->Z))) goto err; /* compute 2^130*G, 2^260*G, 2^390*G */ - for (i = 1; i <= 4; i <<= 1) - { - point_double(pre->g_pre_comp[2*i][0], pre->g_pre_comp[2*i][1], - pre->g_pre_comp[2*i][2], pre->g_pre_comp[i][0], - pre->g_pre_comp[i][1], pre->g_pre_comp[i][2]); - for (j = 0; j < 129; ++j) - { - point_double(pre->g_pre_comp[2*i][0], - pre->g_pre_comp[2*i][1], - pre->g_pre_comp[2*i][2], - pre->g_pre_comp[2*i][0], - pre->g_pre_comp[2*i][1], - pre->g_pre_comp[2*i][2]); - } + for (i = 1; i <= 4; i <<= 1) { + point_double(pre->g_pre_comp[2 * i][0], pre->g_pre_comp[2 * i][1], + pre->g_pre_comp[2 * i][2], pre->g_pre_comp[i][0], + pre->g_pre_comp[i][1], pre->g_pre_comp[i][2]); + for (j = 0; j < 129; ++j) { + point_double(pre->g_pre_comp[2 * i][0], + pre->g_pre_comp[2 * i][1], + pre->g_pre_comp[2 * i][2], + pre->g_pre_comp[2 * i][0], + pre->g_pre_comp[2 * i][1], + pre->g_pre_comp[2 * i][2]); } + } /* g_pre_comp[0] is the point at infinity */ memset(pre->g_pre_comp[0], 0, sizeof(pre->g_pre_comp[0])); /* the remaining multiples */ /* 2^130*G + 2^260*G */ point_add(pre->g_pre_comp[6][0], pre->g_pre_comp[6][1], - pre->g_pre_comp[6][2], pre->g_pre_comp[4][0], - pre->g_pre_comp[4][1], pre->g_pre_comp[4][2], - 0, pre->g_pre_comp[2][0], pre->g_pre_comp[2][1], - pre->g_pre_comp[2][2]); + pre->g_pre_comp[6][2], pre->g_pre_comp[4][0], + pre->g_pre_comp[4][1], pre->g_pre_comp[4][2], + 0, pre->g_pre_comp[2][0], pre->g_pre_comp[2][1], + pre->g_pre_comp[2][2]); /* 2^130*G + 2^390*G */ point_add(pre->g_pre_comp[10][0], pre->g_pre_comp[10][1], - pre->g_pre_comp[10][2], pre->g_pre_comp[8][0], - pre->g_pre_comp[8][1], pre->g_pre_comp[8][2], - 0, pre->g_pre_comp[2][0], pre->g_pre_comp[2][1], - pre->g_pre_comp[2][2]); + pre->g_pre_comp[10][2], pre->g_pre_comp[8][0], + pre->g_pre_comp[8][1], pre->g_pre_comp[8][2], + 0, pre->g_pre_comp[2][0], pre->g_pre_comp[2][1], + pre->g_pre_comp[2][2]); /* 2^260*G + 2^390*G */ point_add(pre->g_pre_comp[12][0], pre->g_pre_comp[12][1], - pre->g_pre_comp[12][2], pre->g_pre_comp[8][0], - pre->g_pre_comp[8][1], pre->g_pre_comp[8][2], - 0, pre->g_pre_comp[4][0], pre->g_pre_comp[4][1], - pre->g_pre_comp[4][2]); + pre->g_pre_comp[12][2], pre->g_pre_comp[8][0], + pre->g_pre_comp[8][1], pre->g_pre_comp[8][2], + 0, pre->g_pre_comp[4][0], pre->g_pre_comp[4][1], + pre->g_pre_comp[4][2]); /* 2^130*G + 2^260*G + 2^390*G */ point_add(pre->g_pre_comp[14][0], pre->g_pre_comp[14][1], - pre->g_pre_comp[14][2], pre->g_pre_comp[12][0], - pre->g_pre_comp[12][1], pre->g_pre_comp[12][2], - 0, pre->g_pre_comp[2][0], pre->g_pre_comp[2][1], - pre->g_pre_comp[2][2]); - for (i = 1; i < 8; ++i) - { + pre->g_pre_comp[14][2], pre->g_pre_comp[12][0], + pre->g_pre_comp[12][1], pre->g_pre_comp[12][2], + 0, pre->g_pre_comp[2][0], pre->g_pre_comp[2][1], + pre->g_pre_comp[2][2]); + for (i = 1; i < 8; ++i) { /* odd multiples: add G */ - point_add(pre->g_pre_comp[2*i+1][0], pre->g_pre_comp[2*i+1][1], - pre->g_pre_comp[2*i+1][2], pre->g_pre_comp[2*i][0], - pre->g_pre_comp[2*i][1], pre->g_pre_comp[2*i][2], - 0, pre->g_pre_comp[1][0], pre->g_pre_comp[1][1], - pre->g_pre_comp[1][2]); - } + point_add(pre->g_pre_comp[2 * i + 1][0], pre->g_pre_comp[2 * i + 1][1], + pre->g_pre_comp[2 * i + 1][2], pre->g_pre_comp[2 * i][0], + pre->g_pre_comp[2 * i][1], pre->g_pre_comp[2 * i][2], + 0, pre->g_pre_comp[1][0], pre->g_pre_comp[1][1], + pre->g_pre_comp[1][2]); + } make_points_affine(15, &(pre->g_pre_comp[1]), tmp_felems); if (!EC_EX_DATA_set_data(&group->extra_data, pre, nistp521_pre_comp_dup, - nistp521_pre_comp_free, nistp521_pre_comp_clear_free)) + nistp521_pre_comp_free, nistp521_pre_comp_clear_free)) goto err; ret = 1; pre = NULL; - err: +err: BN_CTX_end(ctx); if (generator != NULL) EC_POINT_free(generator); @@ -2008,18 +2108,19 @@ int ec_GFp_nistp521_precompute_mult(EC_GROUP *group, BN_CTX *ctx) if (pre) nistp521_pre_comp_free(pre); return ret; - } +} -int ec_GFp_nistp521_have_precompute_mult(const EC_GROUP *group) - { +int +ec_GFp_nistp521_have_precompute_mult(const EC_GROUP * group) +{ if (EC_EX_DATA_get_data(group->extra_data, nistp521_pre_comp_dup, - nistp521_pre_comp_free, nistp521_pre_comp_clear_free) - != NULL) + nistp521_pre_comp_free, nistp521_pre_comp_clear_free) + != NULL) return 1; else return 0; - } +} #else -static void *dummy=&dummy; +static void *dummy = &dummy; #endif |