/* Public domain by Andrew M. <liquidsun@gmail.com> */ /* Arithmetic modulo the group order n = 2^252 + 27742317777372353535851937790883648493 = 7237005577332262213973186563042994240857116359379907606001950938285454250989 k = 32 b = 1 << 8 = 256 m = 2^252 + 27742317777372353535851937790883648493 = 0x1000000000000000000000000000000014def9dea2f79cd65812631a5cf5d3ed mu = floor( b^(k*2) / m ) = 0xfffffffffffffffffffffffffffffffeb2106215d086329a7ed9ce5a30a2c131b */ #define bignum256modm_bits_per_limb 30 #define bignum256modm_limb_size 9 typedef uint32_t bignum256modm_element_t; typedef bignum256modm_element_t bignum256modm[9]; /* see HAC, Alg. 14.42 Step 4 */ void reduce256_modm(bignum256modm r); /* Barrett reduction, see HAC, Alg. 14.42 Instead of passing in x, pre-process in to q1 and r1 for efficiency */ void barrett_reduce256_modm(bignum256modm r, const bignum256modm q1, const bignum256modm r1); /* addition modulo m */ void add256_modm(bignum256modm r, const bignum256modm x, const bignum256modm y); /* -x modulo m */ void neg256_modm(bignum256modm r, const bignum256modm x); /* subtraction x-y modulo m */ void sub256_modm(bignum256modm r, const bignum256modm x, const bignum256modm y); /* multiplication modulo m */ void mul256_modm(bignum256modm r, const bignum256modm x, const bignum256modm y); void expand256_modm(bignum256modm out, const unsigned char *in, size_t len); void expand_raw256_modm(bignum256modm out, const unsigned char in[32]); int is_reduced256_modm(const bignum256modm in); void contract256_modm(unsigned char out[32], const bignum256modm in); void contract256_window4_modm(signed char r[64], const bignum256modm in); void contract256_slidingwindow_modm(signed char r[256], const bignum256modm s, int windowsize); /* 64bit uint to scalar value */ void set256_modm(bignum256modm r, uint64_t v); /* scalar value to 64bit uint */ int get256_modm(uint64_t * v, const bignum256modm r); /* equality test on two reduced scalar values */ int eq256_modm(const bignum256modm x, const bignum256modm y); /* comparison of two reduced scalar values */ int cmp256_modm(const bignum256modm x, const bignum256modm y); /* scalar null check, has to be reduced */ int iszero256_modm(const bignum256modm x); /* simple copy, no reduction */ void copy256_modm(bignum256modm r, const bignum256modm x); /* check if nonzero && same after reduction */ int check256_modm(const bignum256modm x); /* (cc - aa * bb) % l */ void mulsub256_modm(bignum256modm r, const bignum256modm a, const bignum256modm b, const bignum256modm c); /* (cc + aa * bb) % l */ void muladd256_modm(bignum256modm r, const bignum256modm a, const bignum256modm b, const bignum256modm c);