Crypto.Number.ModArithmetic

exponentiation

expSafe

Arguments

:: Integer

base

-> Integer

exponant

-> Integer

modulo

-> Integer

result

Compute the modular exponentiation of base^exponant using algorithms design to avoid side channels and timing measurement

Modulo need to be odd otherwise the normal fast modular exponentiation is used.

When used with integer-simple, this function is not different from expFast, and thus provide the same unstudied and dubious timing and side channels claims.

expFast

Arguments

:: Integer

base

-> Integer

exponant

-> Integer

modulo

-> Integer

result

Compute the modular exponentiation of base^exponant using the fastest algorithm without any consideration for hiding parameters.

Use this function when all the parameters are public, otherwise expSafe should be prefered.

exponentiation_rtl_binary :: Integer -> Integer -> Integer -> Integer

exponentiation_rtl_binary computes modular exponentiation as b^e mod m using the right-to-left binary exponentiation algorithm (HAC 14.79)

exponentiation :: Integer -> Integer -> Integer -> Integer

exponentiation computes modular exponentiation as b^e mod m using repetitive squaring.

deprecated name for exponentiation

exponantiation_rtl_binary :: Integer -> Integer -> Integer -> Integer

exponantiation :: Integer -> Integer -> Integer -> Integer

inverse computing

inverse :: Integer -> Integer -> Maybe Integer

inverse computes the modular inverse as in g^(-1) mod m

inverseCoprimes :: Integer -> Integer -> Integer

Compute the modular inverse of 2 coprime numbers. This is equivalent to inverse except that the result is known to exists.

if the numbers are not defined as coprime, this function will raise a CoprimesAssertionError.