Z.Crypto.MPI

This module provide Botan's Multiple Precision Integer, featuring constant-time operations, which is suit for cryptograph usage.

RNG

data MPI

Opaque Botan Multiple Precision Integers.

Instances

Enum MPI

Defined in Z.Crypto.MPI

Methods

succ :: MPI -> MPI

pred :: MPI -> MPI

toEnum :: Int -> MPI

fromEnum :: MPI -> Int

enumFrom :: MPI -> [MPI]

enumFromThen :: MPI -> MPI -> [MPI]

enumFromTo :: MPI -> MPI -> [MPI]

enumFromThenTo :: MPI -> MPI -> MPI -> [MPI]

Eq MPI

Defined in Z.Crypto.MPI

Methods

(==) :: MPI -> MPI -> Bool

(/=) :: MPI -> MPI -> Bool

Integral MPI

Defined in Z.Crypto.MPI

Methods

quot :: MPI -> MPI -> MPI

rem :: MPI -> MPI -> MPI

div :: MPI -> MPI -> MPI

mod :: MPI -> MPI -> MPI

quotRem :: MPI -> MPI -> (MPI, MPI)

divMod :: MPI -> MPI -> (MPI, MPI)

toInteger :: MPI -> Integer

Num MPI

Defined in Z.Crypto.MPI

Methods

(+) :: MPI -> MPI -> MPI

(-) :: MPI -> MPI -> MPI

(*) :: MPI -> MPI -> MPI

negate :: MPI -> MPI

abs :: MPI -> MPI

signum :: MPI -> MPI

fromInteger :: Integer -> MPI

Ord MPI

Defined in Z.Crypto.MPI

Methods

compare :: MPI -> MPI -> Ordering

(<) :: MPI -> MPI -> Bool

(<=) :: MPI -> MPI -> Bool

(>) :: MPI -> MPI -> Bool

(>=) :: MPI -> MPI -> Bool

max :: MPI -> MPI -> MPI

min :: MPI -> MPI -> MPI

Real MPI

Defined in Z.Crypto.MPI

Methods

toRational :: MPI -> Rational

Show MPI

Defined in Z.Crypto.MPI

Methods

showsPrec :: Int -> MPI -> ShowS

show :: MPI -> String

showList :: [MPI] -> ShowS

JSON MPI

Defined in Z.Crypto.MPI

Methods

fromValue :: Value -> Converter MPI

toValue :: MPI -> Value

encodeJSON :: MPI -> Builder ()

Print MPI

Defined in Z.Crypto.MPI

Methods

toUTF8BuilderP :: Int -> MPI -> Builder ()

Bits MPI

The testBit implementation ignore sign.

Defined in Z.Crypto.MPI

Methods

(.&.) :: MPI -> MPI -> MPI

(.|.) :: MPI -> MPI -> MPI

xor :: MPI -> MPI -> MPI

complement :: MPI -> MPI

shift :: MPI -> Int -> MPI

rotate :: MPI -> Int -> MPI

zeroBits :: MPI

bit :: Int -> MPI

setBit :: MPI -> Int -> MPI

clearBit :: MPI -> Int -> MPI

complementBit :: MPI -> Int -> MPI

testBit :: MPI -> Int -> Bool

bitSizeMaybe :: MPI -> Maybe Int

bitSize :: MPI -> Int

isSigned :: MPI -> Bool

shiftL :: MPI -> Int -> MPI

unsafeShiftL :: MPI -> Int -> MPI

shiftR :: MPI -> Int -> MPI

unsafeShiftR :: MPI -> Int -> MPI

rotateL :: MPI -> Int -> MPI

rotateR :: MPI -> Int -> MPI

popCount :: MPI -> Int

fromCInt :: CInt -> MPI

Set MPI from an integer value.

toWord32 :: HasCallStack => MPI -> Word32

Convert a MPI to Word32, the sign is ignored.

byteSize :: MPI -> Int

Get MPI 's byte size.

bitSize :: MPI -> Int

Get MPI 's bit size.

Builder & Parser

toHex :: MPI -> Builder ()

Write a MPI in hexadecimal format(without '0x' prefix), the sign is ignored.

toDecimal :: MPI -> Builder ()

Write a MPI in decimal format, with negative sign if < 0.

fromHex :: Parser MPI

Parse a MPI in hexadecimal format(without '0x' prefix), no sign is allowed.

fromDecimal :: Parser MPI

Parse a MPI in decimal format, parse leading minus sign.

Predicator

isNegative :: MPI -> Bool

isZero :: MPI -> Bool

isOdd :: MPI -> Bool

isEven :: MPI -> Bool

isPrim :: RNG -> MPI -> Int -> IO Bool

Test if n is prime.

The algorithm used (Miller-Rabin) is probabilistic, set test_prob to the desired assurance level. For example if test_prob is 64, then sufficient Miller-Rabin iterations will run to assure there is at most a 1/2**64 chance that n is composite.

MPI specific

mulMod :: MPI -> MPI -> MPI -> MPI

mulMod x y mod = x times y modulo mod

powMod :: MPI -> MPI -> MPI -> MPI

Modular exponentiation. powMod base exp mod = base power exp module mod

modInverse :: MPI -> MPI -> MPI

Modular inverse, find an integer x so that a⋅x ≡ 1 mod m

If no modular inverse exists (for instance because in and modulus are not relatively prime), return 0.

gcd :: MPI -> MPI -> MPI

Compute the greatest common divisor of x and y.

Random MPI

randBits :: RNG -> Int -> IO MPI

Create a random MPI of the specified bit size.

randRange

Arguments

:: RNG

-> MPI

lower bound

-> MPI

upper bound

-> IO MPI

Create a random MPI within the provided range.

Internal

copyMPI :: MPI -> IO MPI

newMPI :: (BotanStructT -> IO a) -> IO MPI

unsafeNewMPI :: (BotanStructT -> IO a) -> MPI

newMPI' :: (BotanStructT -> IO a) -> IO (MPI, a)

unsafeNewMPI' :: (BotanStructT -> IO a) -> (MPI, a)

withMPI :: MPI -> (BotanStructT -> IO a) -> IO a

unsafeWithMPI :: MPI -> (BotanStructT -> IO a) -> a