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refactor(crypto): introduce bignum512
This commit is contained in:
Ondřej Vejpustek
parent
3a2bdf16dd
commit
2b00c72094
@ -525,8 +525,7 @@ void bn_mod(bignum256 *x, const bignum256 *prime) {
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// res = k * x
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// Assumes k and x are normalized
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// Guarantees res is normalized 18 digit little endian number in base 2**29
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void bn_multiply_long(const bignum256 *k, const bignum256 *x,
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uint32_t res[2 * BN_LIMBS]) {
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void bn_multiply_long(const bignum256 *k, const bignum256 *x, bignum512 *res) {
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// Uses long multiplication in base 2**29, see
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// https://en.wikipedia.org/wiki/Multiplication_algorithm#Long_multiplication
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@ -545,7 +544,7 @@ void bn_multiply_long(const bignum256 *k, const bignum256 *x,
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// <= 2**35 + 9 * 2**58 < 2**64
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}
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res[i] = acc & BN_LIMB_MASK;
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res->val[i] = acc & BN_LIMB_MASK;
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acc >>= BN_BITS_PER_LIMB;
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// acc <= 2**35 - 1 == 2**(64 - BITS_PER_LIMB) - 1
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}
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@ -563,12 +562,12 @@ void bn_multiply_long(const bignum256 *k, const bignum256 *x,
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// <= 2**35 + 9 * 2**58 < 2**64
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}
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res[i] = acc & (BN_BASE - 1);
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res->val[i] = acc & (BN_BASE - 1);
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acc >>= BN_BITS_PER_LIMB;
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// acc < 2**35 == 2**(64 - BITS_PER_LIMB)
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}
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res[2 * BN_LIMBS - 1] = acc;
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res->val[2 * BN_LIMBS - 1] = acc;
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}
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// Auxiliary function for bn_multiply
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@ -576,7 +575,7 @@ void bn_multiply_long(const bignum256 *k, const bignum256 *x,
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// Assumes res is normalized and res < 2**(256 + 29*d + 31)
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// Guarantess res in normalized and res < 2 * prime * 2**(29*d)
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// Assumes prime is normalized, 2**256 - 2**224 <= prime <= 2**256
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void bn_multiply_reduce_step(uint32_t res[2 * BN_LIMBS], const bignum256 *prime,
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void bn_multiply_reduce_step(bignum512 *res, const bignum256 *prime,
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uint32_t d) {
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// clang-format off
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// Computes res = res - (res // 2**(256 + BITS_PER_LIMB * d)) * prime * 2**(BITS_PER_LIMB * d)
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@ -598,8 +597,9 @@ void bn_multiply_reduce_step(uint32_t res[2 * BN_LIMBS], const bignum256 *prime,
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// clang-format on
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uint32_t coef =
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(res[d + BN_LIMBS - 1] >> (256 - (BN_LIMBS - 1) * BN_BITS_PER_LIMB)) +
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(res[d + BN_LIMBS] << ((BN_LIMBS * BN_BITS_PER_LIMB) - 256));
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(res->val[d + BN_LIMBS - 1] >>
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(256 - (BN_LIMBS - 1) * BN_BITS_PER_LIMB)) +
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(res->val[d + BN_LIMBS] << ((BN_LIMBS * BN_BITS_PER_LIMB) - 256));
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// coef == res // 2**(256 + BITS_PER_LIMB * d)
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@ -613,7 +613,7 @@ void bn_multiply_reduce_step(uint32_t res[2 * BN_LIMBS], const bignum256 *prime,
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uint64_t acc = 1ull << shift;
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for (int i = 0; i < BN_LIMBS; i++) {
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acc += (((uint64_t)(BN_BASE - 1)) << shift) + res[d + i] -
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acc += (((uint64_t)(BN_BASE - 1)) << shift) + res->val[d + i] -
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prime->val[i] * (uint64_t)coef;
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// acc neither overflow 64 bits nor underflow zero
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// Proof:
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@ -633,7 +633,7 @@ void bn_multiply_reduce_step(uint32_t res[2 * BN_LIMBS], const bignum256 *prime,
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// == (2**35 - 1) + (2**31 + 1) * (2**29 - 1)
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// <= 2**35 + 2**60 + 2**29 < 2**64
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res[d + i] = acc & BN_LIMB_MASK;
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res->val[d + i] = acc & BN_LIMB_MASK;
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acc >>= BN_BITS_PER_LIMB;
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// acc <= 2**(64 - BITS_PER_LIMB) - 1 == 2**35 - 1
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@ -664,7 +664,7 @@ void bn_multiply_reduce_step(uint32_t res[2 * BN_LIMBS], const bignum256 *prime,
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// == 1 << shift
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// clang-format on
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res[d + BN_LIMBS] = 0;
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res->val[d + BN_LIMBS] = 0;
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}
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// Auxiliary function for bn_multiply
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@ -672,8 +672,7 @@ void bn_multiply_reduce_step(uint32_t res[2 * BN_LIMBS], const bignum256 *prime,
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// Assumes res in normalized and res < 2**519
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// Guarantees x is normalized and partly reduced modulo prime
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// Assumes prime is normalized, 2**256 - 2**224 <= prime <= 2**256
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void bn_multiply_reduce(bignum256 *x, uint32_t res[2 * BN_LIMBS],
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const bignum256 *prime) {
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void bn_multiply_reduce(bignum256 *x, bignum512 *res, const bignum256 *prime) {
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for (int i = BN_LIMBS - 1; i >= 0; i--) {
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// res < 2**(256 + 29*i + 31)
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// Proof:
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@ -688,7 +687,7 @@ void bn_multiply_reduce(bignum256 *x, uint32_t res[2 * BN_LIMBS],
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}
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for (int i = 0; i < BN_LIMBS; i++) {
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x->val[i] = res[i];
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x->val[i] = res->val[i];
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}
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}
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@ -697,12 +696,12 @@ void bn_multiply_reduce(bignum256 *x, uint32_t res[2 * BN_LIMBS],
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// Guarantees x is normalized and partly reduced modulo prime
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// Assumes prime is normalized, 2**256 - 2**224 <= prime <= 2**256
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void bn_multiply(const bignum256 *k, bignum256 *x, const bignum256 *prime) {
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uint32_t res[2 * BN_LIMBS] = {0};
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bignum512 res = {0};
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bn_multiply_long(k, x, res);
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bn_multiply_reduce(x, res, prime);
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bn_multiply_long(k, x, &res);
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bn_multiply_reduce(x, &res, prime);
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memzero(res, sizeof(res));
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memzero(&res, sizeof(res));
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}
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// Partly reduces x modulo prime
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@ -43,6 +43,11 @@ typedef struct {
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uint32_t val[BN_LIMBS];
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} bignum256;
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// Represents the number sum([val[i] * 2**(29*i) for i in range(18))
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typedef struct {
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uint32_t val[2 * BN_LIMBS];
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} bignum512;
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static inline uint32_t read_be(const uint8_t *data) {
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return (((uint32_t)data[0]) << 24) | (((uint32_t)data[1]) << 16) |
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(((uint32_t)data[2]) << 8) | (((uint32_t)data[3]));
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@ -69,15 +69,23 @@ def uint32_p():
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limb_type = c_uint32
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def bignum(limbs_number=limbs_number):
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def bignum(limbs_number):
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return (limbs_number * limb_type)()
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def bignum256():
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return bignum(limbs_number)
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def bignum512():
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return bignum(2 * limbs_number)
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def limbs_to_bignum(limbs):
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return (limbs_number * limb_type)(*limbs)
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def int_to_bignum(number, limbs_number=limbs_number):
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def int_to_bignum(number, limbs_number):
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assert number >= 0
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assert number.bit_length() <= limbs_number * bits_per_limb
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@ -89,7 +97,15 @@ def int_to_bignum(number, limbs_number=limbs_number):
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return bn
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def bignum_to_int(bignum, limbs_number=limbs_number):
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def int_to_bignum256(number):
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return int_to_bignum(number, limbs_number)
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def int_to_bignum512(number):
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return int_to_bignum(number, 2 * limbs_number)
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def bignum_to_int(bignum, limbs_number):
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number = 0
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for i in reversed(range(limbs_number)):
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@ -99,16 +115,40 @@ def bignum_to_int(bignum, limbs_number=limbs_number):
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return number
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def raw_number():
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return (32 * c_uint8)()
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def bignum256_to_int(bignum):
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return bignum_to_int(bignum, limbs_number)
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def bignum512_to_int(bignum):
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return bignum_to_int(bignum, 2 * limbs_number)
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def raw_number(byte_size):
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return (byte_size * c_uint8)()
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def raw_number256():
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return raw_number(32)
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def raw_number512():
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return raw_number(64)
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def raw_number_to_integer(raw_number, endianess):
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return int.from_bytes(raw_number, endianess)
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def integer_to_raw_number(number, endianess):
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return (32 * c_uint8)(*number.to_bytes(32, endianess))
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def integer_to_raw_number(number, endianess, byte_size):
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return (byte_size * c_uint8)(*number.to_bytes(byte_size, endianess))
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def integer_to_raw_number256(number, endianess):
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return integer_to_raw_number(number, endianess, 32)
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def integer_to_raw_number512(number, endianess):
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return integer_to_raw_number(number, endianess, 64)
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def bignum_is_normalised(bignum):
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@ -133,6 +173,9 @@ class Random(random.Random):
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def rand_int_256(self):
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return self.randrange(0, 2**256)
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def rand_int_512(self):
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return self.randrange(0, 2**512)
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def rand_int_reduced(self, p):
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return self.randrange(0, 2 * p)
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@ -142,35 +185,44 @@ class Random(random.Random):
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def rand_bit_index(self):
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return self.randrange(0, limbs_number * bits_per_limb)
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def rand_bignum(self, limbs_number=limbs_number):
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def rand_bignum(self, limbs_number):
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return (limb_type * limbs_number)(
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*[self.randrange(0, 256**4) for _ in range(limbs_number)]
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)
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def rand_bignum256(self):
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return self.rand_bignum(limbs_number)
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def rand_bignum512(self):
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return self.rand_bignum(2 * limbs_number)
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def assert_bn_read_be(in_number):
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raw_in_number = integer_to_raw_number(in_number, "big")
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bn_out_number = bignum()
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raw_in_number = integer_to_raw_number256(in_number, "big")
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bn_out_number = bignum256()
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lib.bn_read_be(raw_in_number, bn_out_number)
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out_number = bignum_to_int(bn_out_number)
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out_number = bignum256_to_int(bn_out_number)
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assert bignum_is_normalised(bn_out_number)
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assert out_number == in_number
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assert bignum_is_normalised(bn_out_number)
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assert out_number == in_number
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def assert_bn_read_le(in_number):
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raw_in_number = integer_to_raw_number(in_number, "little")
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bn_out_number = bignum()
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raw_in_number = integer_to_raw_number256(in_number, "little")
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bn_out_number = bignum256()
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lib.bn_read_le(raw_in_number, bn_out_number)
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out_number = bignum_to_int(bn_out_number)
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out_number = bignum256_to_int(bn_out_number)
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assert bignum_is_normalised(bn_out_number)
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assert out_number == in_number
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def assert_bn_write_be(in_number):
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bn_in_number = int_to_bignum(in_number)
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raw_out_number = raw_number()
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bn_in_number = int_to_bignum256(in_number)
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raw_out_number = raw_number256()
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lib.bn_write_be(bn_in_number, raw_out_number)
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out_number = raw_number_to_integer(raw_out_number, "big")
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@ -178,8 +230,8 @@ def assert_bn_write_be(in_number):
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def assert_bn_write_le(in_number):
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bn_in_number = int_to_bignum(in_number)
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raw_out_number = raw_number()
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bn_in_number = int_to_bignum256(in_number)
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raw_out_number = raw_number256()
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lib.bn_write_le(bn_in_number, raw_out_number)
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out_number = raw_number_to_integer(raw_out_number, "little")
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@ -187,100 +239,100 @@ def assert_bn_write_le(in_number):
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def assert_bn_read_uint32(x):
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bn_out_number = bignum()
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bn_out_number = bignum256()
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lib.bn_read_uint32(c_uint32(x), bn_out_number)
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out_number = bignum_to_int(bn_out_number)
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out_number = bignum256_to_int(bn_out_number)
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assert bignum_is_normalised(bn_out_number)
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assert out_number == x
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def assert_bn_read_uint64(x):
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bn_out_number = bignum()
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bn_out_number = bignum256()
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lib.bn_read_uint64(c_uint64(x), bn_out_number)
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out_number = bignum_to_int(bn_out_number)
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out_number = bignum256_to_int(bn_out_number)
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assert bignum_is_normalised(bn_out_number)
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assert out_number == x
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def assert_bn_bitcount(x):
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bn_x = int_to_bignum(x)
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bn_x = int_to_bignum256(x)
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return_value = lib.bn_bitcount(bn_x)
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assert return_value == x.bit_length()
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def assert_bn_digitcount(x):
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bn_x = int_to_bignum(x)
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bn_x = int_to_bignum256(x)
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return_value = lib.bn_digitcount(bn_x)
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assert return_value == len(str(x))
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def assert_bn_zero():
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bn_x = bignum()
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bn_x = bignum256()
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lib.bn_zero(bn_x)
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x = bignum_to_int(bn_x)
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x = bignum256_to_int(bn_x)
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assert bignum_is_normalised(bn_x)
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assert x == 0
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def assert_bn_one():
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bn_x = bignum()
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bn_x = bignum256()
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lib.bn_one(bn_x)
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x = bignum_to_int(bn_x)
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x = bignum256_to_int(bn_x)
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assert bignum_is_normalised(bn_x)
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assert x == 1
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def assert_bn_is_zero(x):
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bn_x = int_to_bignum(x)
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bn_x = int_to_bignum256(x)
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return_value = lib.bn_is_zero(bn_x)
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assert return_value == (x == 0)
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def assert_bn_is_one(x):
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bn_x = int_to_bignum(x)
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bn_x = int_to_bignum256(x)
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return_value = lib.bn_is_one(bn_x)
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assert return_value == (x == 1)
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def assert_bn_is_less(x, y):
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bn_x = int_to_bignum(x)
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bn_y = int_to_bignum(y)
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bn_x = int_to_bignum256(x)
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bn_y = int_to_bignum256(y)
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return_value = lib.bn_is_less(bn_x, bn_y)
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assert return_value == (x < y)
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def assert_bn_is_equal(x, y):
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bn_x = int_to_bignum(x)
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bn_y = int_to_bignum(y)
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bn_x = int_to_bignum256(x)
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bn_y = int_to_bignum256(y)
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return_value = lib.bn_is_equal(bn_x, bn_y)
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assert return_value == (x == y)
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def assert_bn_cmov(cond, truecase, falsecase):
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bn_res = bignum()
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bn_truecase = int_to_bignum(truecase)
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bn_falsecase = int_to_bignum(falsecase)
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bn_res = bignum256()
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bn_truecase = int_to_bignum256(truecase)
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bn_falsecase = int_to_bignum256(falsecase)
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lib.bn_cmov(bn_res, c_uint32(cond), bn_truecase, bn_falsecase)
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res = bignum_to_int(bn_res)
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res = bignum256_to_int(bn_res)
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assert res == truecase if cond else falsecase
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def assert_bn_cnegate(cond, x_old, prime):
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bn_x = int_to_bignum(x_old)
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bn_prime = int_to_bignum(prime)
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bn_x = int_to_bignum256(x_old)
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bn_prime = int_to_bignum256(prime)
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lib.bn_cnegate(c_uint32(cond), bn_x, bn_prime)
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x_new = bignum_to_int(bn_x)
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x_new = bignum256_to_int(bn_x)
|
||||
|
||||
assert bignum_is_normalised(bn_x)
|
||||
assert number_is_partly_reduced(x_new, prime)
|
||||
@ -288,63 +340,63 @@ def assert_bn_cnegate(cond, x_old, prime):
|
||||
|
||||
|
||||
def assert_bn_lshift(x_old):
|
||||
bn_x = int_to_bignum(x_old)
|
||||
bn_x = int_to_bignum256(x_old)
|
||||
lib.bn_lshift(bn_x)
|
||||
x_new = bignum_to_int(bn_x)
|
||||
x_new = bignum256_to_int(bn_x)
|
||||
|
||||
assert bignum_is_normalised(bn_x)
|
||||
assert x_new == (x_old << 1)
|
||||
|
||||
|
||||
def assert_bn_rshift(x_old):
|
||||
bn_x = int_to_bignum(x_old)
|
||||
bn_x = int_to_bignum256(x_old)
|
||||
lib.bn_rshift(bn_x)
|
||||
x_new = bignum_to_int(bn_x)
|
||||
x_new = bignum256_to_int(bn_x)
|
||||
|
||||
assert bignum_is_normalised(bn_x)
|
||||
assert x_new == (x_old >> 1)
|
||||
|
||||
|
||||
def assert_bn_setbit(x_old, i):
|
||||
bn_x = int_to_bignum(x_old)
|
||||
bn_x = int_to_bignum256(x_old)
|
||||
lib.bn_setbit(bn_x, c_uint16(i))
|
||||
x_new = bignum_to_int(bn_x)
|
||||
x_new = bignum256_to_int(bn_x)
|
||||
|
||||
assert bignum_is_normalised(bn_x)
|
||||
assert x_new == x_old | (1 << i)
|
||||
|
||||
|
||||
def assert_bn_clearbit(x_old, i):
|
||||
bn_x = int_to_bignum(x_old)
|
||||
bn_x = int_to_bignum256(x_old)
|
||||
lib.bn_clearbit(bn_x, c_uint16(i))
|
||||
x_new = bignum_to_int(bn_x)
|
||||
x_new = bignum256_to_int(bn_x)
|
||||
|
||||
assert bignum_is_normalised(bn_x)
|
||||
assert x_new == x_old & ~(1 << i)
|
||||
|
||||
|
||||
def assert_bn_testbit(x_old, i):
|
||||
bn_x = int_to_bignum(x_old)
|
||||
bn_x = int_to_bignum256(x_old)
|
||||
return_value = lib.bn_testbit(bn_x, c_uint16(i))
|
||||
|
||||
assert return_value == x_old >> i & 1
|
||||
|
||||
|
||||
def assert_bn_xor(x, y):
|
||||
bn_res = bignum()
|
||||
bn_x = int_to_bignum(x)
|
||||
bn_y = int_to_bignum(y)
|
||||
bn_res = bignum256()
|
||||
bn_x = int_to_bignum256(x)
|
||||
bn_y = int_to_bignum256(y)
|
||||
lib.bn_xor(bn_res, bn_x, bn_y)
|
||||
res = bignum_to_int(bn_res)
|
||||
res = bignum256_to_int(bn_res)
|
||||
|
||||
assert res == x ^ y
|
||||
|
||||
|
||||
def assert_bn_mult_half(x_old, prime):
|
||||
bn_x = int_to_bignum(x_old)
|
||||
bn_prime = int_to_bignum(prime)
|
||||
bn_x = int_to_bignum256(x_old)
|
||||
bn_prime = int_to_bignum256(prime)
|
||||
lib.bn_mult_half(bn_x, bn_prime)
|
||||
x_new = bignum_to_int(bn_x)
|
||||
x_new = bignum256_to_int(bn_x)
|
||||
|
||||
assert implication(
|
||||
number_is_partly_reduced(x_old, prime), number_is_partly_reduced(x_new, prime)
|
||||
@ -353,10 +405,10 @@ def assert_bn_mult_half(x_old, prime):
|
||||
|
||||
|
||||
def assert_bn_mult_k(x_old, k, prime):
|
||||
bn_x = int_to_bignum(x_old)
|
||||
bn_prime = int_to_bignum(prime)
|
||||
bn_x = int_to_bignum256(x_old)
|
||||
bn_prime = int_to_bignum256(prime)
|
||||
lib.bn_mult_k(bn_x, c_uint8(k), bn_prime)
|
||||
x_new = bignum_to_int(bn_x)
|
||||
x_new = bignum256_to_int(bn_x)
|
||||
|
||||
assert bignum_is_normalised(bn_x)
|
||||
assert number_is_partly_reduced(x_new, prime)
|
||||
@ -364,10 +416,10 @@ def assert_bn_mult_k(x_old, k, prime):
|
||||
|
||||
|
||||
def assert_bn_mod(x_old, prime):
|
||||
bn_x = int_to_bignum(x_old)
|
||||
bn_prime = int_to_bignum(prime)
|
||||
bn_x = int_to_bignum256(x_old)
|
||||
bn_prime = int_to_bignum256(prime)
|
||||
lib.bn_mod(bn_x, bn_prime)
|
||||
x_new = bignum_to_int(bn_x)
|
||||
x_new = bignum256_to_int(bn_x)
|
||||
|
||||
assert bignum_is_normalised(bn_x)
|
||||
assert number_is_fully_reduced(x_new, prime)
|
||||
@ -375,31 +427,31 @@ def assert_bn_mod(x_old, prime):
|
||||
|
||||
|
||||
def assert_bn_multiply_long(k_old, x_old):
|
||||
bn_k = int_to_bignum(k_old)
|
||||
bn_x = int_to_bignum(x_old)
|
||||
bn_res = bignum(2 * limbs_number)
|
||||
bn_k = int_to_bignum256(k_old)
|
||||
bn_x = int_to_bignum256(x_old)
|
||||
bn_res = bignum512()
|
||||
lib.bn_multiply_long(bn_k, bn_x, bn_res)
|
||||
res = bignum_to_int(bn_res, 2 * limbs_number)
|
||||
res = bignum512_to_int(bn_res)
|
||||
|
||||
assert res == k_old * x_old
|
||||
|
||||
|
||||
def assert_bn_multiply_reduce_step(res_old, prime, d):
|
||||
bn_res = int_to_bignum(res_old, 2 * limbs_number)
|
||||
bn_prime = int_to_bignum(prime)
|
||||
bn_res = int_to_bignum512(res_old)
|
||||
bn_prime = int_to_bignum256(prime)
|
||||
lib.bn_multiply_reduce_step(bn_res, bn_prime, d)
|
||||
res_new = bignum_to_int(bn_res, 2 * limbs_number)
|
||||
res_new = bignum512_to_int(bn_res)
|
||||
|
||||
assert bignum_is_normalised(bn_res)
|
||||
assert res_new < 2 * prime * 2 ** (d * bits_per_limb)
|
||||
|
||||
|
||||
def assert_bn_multiply(k, x_old, prime):
|
||||
bn_k = int_to_bignum(k)
|
||||
bn_x = int_to_bignum(x_old)
|
||||
bn_prime = int_to_bignum(prime)
|
||||
bn_k = int_to_bignum256(k)
|
||||
bn_x = int_to_bignum256(x_old)
|
||||
bn_prime = int_to_bignum256(prime)
|
||||
lib.bn_multiply(bn_k, bn_x, bn_prime)
|
||||
x_new = bignum_to_int(bn_x)
|
||||
x_new = bignum256_to_int(bn_x)
|
||||
|
||||
assert bignum_is_normalised(bn_x)
|
||||
assert number_is_partly_reduced(x_new, prime)
|
||||
@ -407,10 +459,10 @@ def assert_bn_multiply(k, x_old, prime):
|
||||
|
||||
|
||||
def assert_bn_fast_mod(x_old, prime):
|
||||
bn_x = int_to_bignum(x_old)
|
||||
bn_prime = int_to_bignum(prime)
|
||||
bn_x = int_to_bignum256(x_old)
|
||||
bn_prime = int_to_bignum256(prime)
|
||||
lib.bn_fast_mod(bn_x, bn_prime)
|
||||
x_new = bignum_to_int(bn_x)
|
||||
x_new = bignum256_to_int(bn_x)
|
||||
|
||||
assert bignum_is_normalised(bn_x)
|
||||
assert number_is_partly_reduced(x_new, prime)
|
||||
@ -419,10 +471,10 @@ def assert_bn_fast_mod(x_old, prime):
|
||||
|
||||
def assert_bn_fast_mod_bn(bn_x, prime):
|
||||
bn_x
|
||||
x_old = bignum_to_int(bn_x)
|
||||
bn_prime = int_to_bignum(prime)
|
||||
x_old = bignum256_to_int(bn_x)
|
||||
bn_prime = int_to_bignum256(prime)
|
||||
lib.bn_fast_mod(bn_x, bn_prime)
|
||||
x_new = bignum_to_int(bn_x)
|
||||
x_new = bignum256_to_int(bn_x)
|
||||
|
||||
assert bignum_is_normalised(bn_x)
|
||||
assert number_is_partly_reduced(x_new, prime)
|
||||
@ -430,12 +482,12 @@ def assert_bn_fast_mod_bn(bn_x, prime):
|
||||
|
||||
|
||||
def assert_bn_power_mod(x, e, prime):
|
||||
bn_x = int_to_bignum(x)
|
||||
bn_e = int_to_bignum(e)
|
||||
bn_prime = int_to_bignum(prime)
|
||||
bn_res_new = bignum()
|
||||
bn_x = int_to_bignum256(x)
|
||||
bn_e = int_to_bignum256(e)
|
||||
bn_prime = int_to_bignum256(prime)
|
||||
bn_res_new = bignum256()
|
||||
lib.bn_power_mod(bn_x, bn_e, bn_prime, bn_res_new)
|
||||
res_new = bignum_to_int(bn_res_new)
|
||||
res_new = bignum256_to_int(bn_res_new)
|
||||
|
||||
assert bignum_is_normalised(bn_res_new)
|
||||
assert number_is_partly_reduced(res_new, prime)
|
||||
@ -443,10 +495,10 @@ def assert_bn_power_mod(x, e, prime):
|
||||
|
||||
|
||||
def assert_bn_sqrt(x_old, prime):
|
||||
bn_x = int_to_bignum(x_old)
|
||||
bn_prime = int_to_bignum(prime)
|
||||
bn_x = int_to_bignum256(x_old)
|
||||
bn_prime = int_to_bignum256(prime)
|
||||
lib.bn_sqrt(bn_x, bn_prime)
|
||||
x_new = bignum_to_int(bn_x)
|
||||
x_new = bignum256_to_int(bn_x)
|
||||
|
||||
assert bignum_is_normalised(bn_x)
|
||||
assert number_is_fully_reduced(x_new, prime)
|
||||
@ -460,10 +512,10 @@ def assert_inverse_mod_power_two(x, m):
|
||||
|
||||
|
||||
def assert_bn_divide_base(x_old, prime):
|
||||
bn_x = int_to_bignum(x_old)
|
||||
bn_prime = int_to_bignum(prime)
|
||||
bn_x = int_to_bignum256(x_old)
|
||||
bn_prime = int_to_bignum256(prime)
|
||||
lib.bn_divide_base(bn_x, bn_prime)
|
||||
x_new = bignum_to_int(bn_x)
|
||||
x_new = bignum256_to_int(bn_x)
|
||||
|
||||
assert implication(
|
||||
number_is_fully_reduced(x_old, prime), number_is_fully_reduced(x_new, prime)
|
||||
@ -475,10 +527,10 @@ def assert_bn_divide_base(x_old, prime):
|
||||
|
||||
|
||||
def assert_bn_inverse(x_old, prime):
|
||||
bn_x = int_to_bignum(x_old)
|
||||
bn_prime = int_to_bignum(prime)
|
||||
bn_x = int_to_bignum256(x_old)
|
||||
bn_prime = int_to_bignum256(prime)
|
||||
lib.bn_inverse(bn_x, bn_prime)
|
||||
x_new = bignum_to_int(bn_x)
|
||||
x_new = bignum256_to_int(bn_x)
|
||||
|
||||
assert bignum_is_normalised(bn_x)
|
||||
assert number_is_fully_reduced(x_new, prime)
|
||||
@ -486,31 +538,31 @@ def assert_bn_inverse(x_old, prime):
|
||||
|
||||
|
||||
def assert_bn_normalize(bn_x):
|
||||
x_old = bignum_to_int(bn_x)
|
||||
x_old = bignum256_to_int(bn_x)
|
||||
lib.bn_normalize(bn_x)
|
||||
x_new = bignum_to_int(bn_x)
|
||||
x_new = bignum256_to_int(bn_x)
|
||||
|
||||
assert x_new == x_old % 2 ** (bits_per_limb * limbs_number)
|
||||
assert bignum_is_normalised(bn_x)
|
||||
|
||||
|
||||
def assert_bn_add(x_old, y):
|
||||
bn_x = int_to_bignum(x_old)
|
||||
bn_y = int_to_bignum(y)
|
||||
bn_x = int_to_bignum256(x_old)
|
||||
bn_y = int_to_bignum256(y)
|
||||
lib.bn_add(bn_x, bn_y)
|
||||
x_new = bignum_to_int(bn_x)
|
||||
y = bignum_to_int(bn_y)
|
||||
x_new = bignum256_to_int(bn_x)
|
||||
y = bignum256_to_int(bn_y)
|
||||
|
||||
assert bignum_is_normalised(bn_x)
|
||||
assert x_new == x_old + y
|
||||
|
||||
|
||||
def assert_bn_addmod(x_old, y, prime):
|
||||
bn_x = int_to_bignum(x_old)
|
||||
bn_y = int_to_bignum(y)
|
||||
bn_prime = int_to_bignum(prime)
|
||||
bn_x = int_to_bignum256(x_old)
|
||||
bn_y = int_to_bignum256(y)
|
||||
bn_prime = int_to_bignum256(prime)
|
||||
lib.bn_addmod(bn_x, bn_y, bn_prime)
|
||||
x_new = bignum_to_int(bn_x)
|
||||
x_new = bignum256_to_int(bn_x)
|
||||
|
||||
assert bignum_is_normalised(bn_x)
|
||||
assert number_is_partly_reduced(x_new, prime)
|
||||
@ -518,19 +570,19 @@ def assert_bn_addmod(x_old, y, prime):
|
||||
|
||||
|
||||
def assert_bn_addi(x_old, y):
|
||||
bn_x = int_to_bignum(x_old)
|
||||
bn_x = int_to_bignum256(x_old)
|
||||
lib.bn_addi(bn_x, c_uint32(y))
|
||||
x_new = bignum_to_int(bn_x)
|
||||
x_new = bignum256_to_int(bn_x)
|
||||
|
||||
assert bignum_is_normalised(bn_x)
|
||||
assert x_new == x_old + y
|
||||
|
||||
|
||||
def assert_bn_subi(x_old, y, prime):
|
||||
bn_x = int_to_bignum(x_old)
|
||||
bn_prime = int_to_bignum(prime)
|
||||
bn_x = int_to_bignum256(x_old)
|
||||
bn_prime = int_to_bignum256(prime)
|
||||
lib.bn_subi(bn_x, c_uint32(y), bn_prime)
|
||||
x_new = bignum_to_int(bn_x)
|
||||
x_new = bignum256_to_int(bn_x)
|
||||
|
||||
assert bignum_is_normalised(bn_x)
|
||||
assert implication(
|
||||
@ -540,12 +592,12 @@ def assert_bn_subi(x_old, y, prime):
|
||||
|
||||
|
||||
def assert_bn_subtractmod(x, y, prime):
|
||||
bn_x = int_to_bignum(x)
|
||||
bn_y = int_to_bignum(y)
|
||||
bn_prime = int_to_bignum(prime)
|
||||
bn_res = bignum()
|
||||
bn_x = int_to_bignum256(x)
|
||||
bn_y = int_to_bignum256(y)
|
||||
bn_prime = int_to_bignum256(prime)
|
||||
bn_res = bignum256()
|
||||
lib.bn_subtractmod(bn_x, bn_y, bn_res, bn_prime)
|
||||
res = bignum_to_int(bn_res)
|
||||
res = bignum256_to_int(bn_res)
|
||||
|
||||
assert bignum_is_normalised(bn_x)
|
||||
assert res % prime == (x - y) % prime
|
||||
@ -559,31 +611,31 @@ def legendre(x, prime):
|
||||
|
||||
|
||||
def assert_bn_legendre(x, prime):
|
||||
bn_x = int_to_bignum(x)
|
||||
bn_prime = int_to_bignum(prime)
|
||||
bn_x = int_to_bignum256(x)
|
||||
bn_prime = int_to_bignum256(prime)
|
||||
return_value = lib.bn_legendre(bn_x, bn_prime)
|
||||
|
||||
assert return_value == legendre(x, prime)
|
||||
|
||||
|
||||
def assert_bn_subtract(x, y):
|
||||
bn_x = int_to_bignum(x)
|
||||
bn_y = int_to_bignum(y)
|
||||
bn_res = bignum()
|
||||
bn_x = int_to_bignum256(x)
|
||||
bn_y = int_to_bignum256(y)
|
||||
bn_res = bignum256()
|
||||
lib.bn_subtract(bn_x, bn_y, bn_res)
|
||||
res = bignum_to_int(bn_res)
|
||||
res = bignum256_to_int(bn_res)
|
||||
|
||||
assert bignum_is_normalised(bn_x)
|
||||
assert res == x - y
|
||||
|
||||
|
||||
def assert_bn_long_division(x, d):
|
||||
bn_x = int_to_bignum(x)
|
||||
bn_q = bignum()
|
||||
bn_x = int_to_bignum256(x)
|
||||
bn_q = bignum256()
|
||||
uint32_p_r = uint32_p()
|
||||
lib.bn_long_division(bn_x, d, bn_q, uint32_p_r)
|
||||
r = uint32_p_to_int(uint32_p_r)
|
||||
q = bignum_to_int(bn_q)
|
||||
q = bignum256_to_int(bn_q)
|
||||
|
||||
assert bignum_is_normalised(bn_q)
|
||||
assert q == x // d
|
||||
@ -591,10 +643,10 @@ def assert_bn_long_division(x, d):
|
||||
|
||||
|
||||
def assert_bn_divmod58(x_old):
|
||||
bn_x = int_to_bignum(x_old)
|
||||
bn_x = int_to_bignum256(x_old)
|
||||
uint32_p_r = uint32_p()
|
||||
lib.bn_divmod58(bn_x, uint32_p_r)
|
||||
x_new = bignum_to_int(bn_x)
|
||||
x_new = bignum256_to_int(bn_x)
|
||||
r = uint32_p_to_int(uint32_p_r)
|
||||
|
||||
assert bignum_is_normalised(bn_x)
|
||||
@ -603,10 +655,10 @@ def assert_bn_divmod58(x_old):
|
||||
|
||||
|
||||
def assert_bn_divmod1000(x_old):
|
||||
bn_x = int_to_bignum(x_old)
|
||||
bn_x = int_to_bignum256(x_old)
|
||||
uint32_p_r = uint32_p()
|
||||
lib.bn_divmod1000(bn_x, uint32_p_r)
|
||||
x_new = bignum_to_int(bn_x)
|
||||
x_new = bignum256_to_int(bn_x)
|
||||
r = uint32_p_to_int(uint32_p_r)
|
||||
|
||||
assert bignum_is_normalised(bn_x)
|
||||
@ -615,10 +667,10 @@ def assert_bn_divmod1000(x_old):
|
||||
|
||||
|
||||
def assert_bn_divmod10(x_old):
|
||||
bn_x = int_to_bignum(x_old)
|
||||
bn_x = int_to_bignum256(x_old)
|
||||
uint32_p_r = uint32_p()
|
||||
lib.bn_divmod10(bn_x, uint32_p_r)
|
||||
x_new = bignum_to_int(bn_x)
|
||||
x_new = bignum256_to_int(bn_x)
|
||||
r = uint32_p_to_int(uint32_p_r)
|
||||
|
||||
assert bignum_is_normalised(bn_x)
|
||||
@ -654,7 +706,7 @@ def assert_bn_format(x, prefix, suffix, decimals, exponent, trailing, thousands)
|
||||
def char_p_to_string(pointer):
|
||||
return str(pointer.value, "ascii")
|
||||
|
||||
bn_x = int_to_bignum(x)
|
||||
bn_x = int_to_bignum256(x)
|
||||
output_length = 100
|
||||
output = string_to_char_p("?" * output_length)
|
||||
return_value = lib.bn_format(
|
||||
@ -875,7 +927,7 @@ def test_bn_fast_mod_1(r, prime):
|
||||
|
||||
|
||||
def test_bn_fast_mod_2(r, prime):
|
||||
bn_x = r.rand_bignum()
|
||||
bn_x = r.rand_bignum256()
|
||||
assert_bn_fast_mod_bn(bn_x, prime)
|
||||
|
||||
|
||||
@ -929,7 +981,7 @@ def test_bn_inverse_2(r, prime):
|
||||
|
||||
|
||||
def test_bn_normalize(r):
|
||||
assert_bn_normalize(r.rand_bignum())
|
||||
assert_bn_normalize(r.rand_bignum256())
|
||||
|
||||
|
||||
def test_bn_add_1(r):
|
||||
|
||||
Loading…
Reference in New Issue
Block a user