zengo-x / crypto-gmp Goto Github PK

In order to add this lib to curv as another bigint backend, we need cover these operations:

Arithmetic:

• Addition
• • &BigInt + &BigInt
• • &BigInt + {u8, u16, u32} (and vice-versa)
    #1
• • &BigInt + u64 (and vice-versa)
    Note: use crypto_gmp::digits::U64
• Subtraction
• • &BigInt - &BigInt
• • &BigInt - {u8, u16, u32, u64} (and vice-versa)
• Multiplication
• • &BigInt * &BigInt
• • &BigInt * {u8, u16, u32, u64} (and vice-versa)
• Division
• • &BigInt / &BigInt
• • &BigInt / {u8, u16, u32, u64} (no need to do it vice-versa)
• Reminder
• • &BigInt % &BigInt
• • &BigInt % {u8, u16, u32, u64} (no need to do it vice-versa)
• Exponentiation
  Ie fn pow(&self, e: u32) -> Self

Modular arithmetic:

• fn modulus(&self, m: &BigInt) -> BigInt;
• fn mod_pow(&self, e: &BigInt, m: &BigInt) -> BigInt
• fn mod_mul(&self, rhs: &BigInt, m: &BigInt) -> BigInt
• fn mod_sub(&self, rhs: &BigInt, m: &BigInt) -> BigInt
• fn mod_add(&self, rhs: &BigInt, m: &BigInt) -> BigInt
• fn mod_inv(&self, m: &Self) -> Option<Self>;

Primes:

• fn next_prime(&self) -> BigInt
  Function that finds next prime number using probabilistic algorithms
• fn is_probable_prime(&self, n: u32) -> bool
  Function that probabilistically determines whether number is prime

Extended GCD algorithm:

• fn egcd(a: &BigInt, b: &BigInt) -> (BigInt, BigInt, BigInt)
  Function that returns gcd(a,b), p, q such as gcd(a,b) = a*p + b*q

Bits manipulations:

• fn set_bit(&mut self, bit: usize, bit_val: bool)
• fn test_bit(&self, bit: usize) -> bool
• fn bit_length(&self) -> usize
• BitXor: &BigInt ^ &BigInt
• BitAnd: &BigInt & &BigInt
• Shl / Shr: &BigInt << usize, &BigInt >> usize

Conversion:

• BigInt -> u64
  Ie impl TryFrom<&BigInt> for u64
• {u8, u16, u32, u64} -> BigInt
  Ie impl From<u64> for BigInt and so on
• To bytes / from bytes

  impl BigInt {
      pub fn to_bytes(&self) -> Vec<u8> { /* ... */ }
      pub fn from_bytes(bytes: &[u8]) -> Result<Self> { /* ... */ }
  }

Other traits:

• Zeroize
  impl<D: AsMut<[Digit]>> Zeroize for BigInt<D>
• Integer
• Roots
• Num
• One
• Zero