Safe Haskell	None
Language	Haskell2010

Pairing.Fr

Description

Prime field from which exponents should be chosen

Synopsis

newtype Fr = Fr Integer
new :: Integer -> Fr
frInv :: Fr -> Fr
random :: MonadRandom m => m Fr
isRootOfUnity :: Integer -> Fr -> Bool
isPrimitiveRootOfUnity :: Integer -> Fr -> Bool
primitiveRootOfUnity :: Int -> Fr
precompRootOfUnity :: Int -> Fr

Documentation

newtype Fr Source #

Prime field with characteristic _r

Constructors

Fr Integer

Use new instead of this constructor

Instances

Eq Fr Source #
Instance details Defined in Pairing.Fr Methods (==) :: Fr -> Fr -> Bool # (/=) :: Fr -> Fr -> Bool #
Fractional Fr Source #
Instance details Defined in Pairing.Fr Methods (/) :: Fr -> Fr -> Fr # recip :: Fr -> Fr # fromRational :: Rational -> Fr #
Num Fr Source #
Instance details Defined in Pairing.Fr Methods (+) :: Fr -> Fr -> Fr # (-) :: Fr -> Fr -> Fr # (*) :: Fr -> Fr -> Fr # negate :: Fr -> Fr # abs :: Fr -> Fr # signum :: Fr -> Fr # fromInteger :: Integer -> Fr #
Ord Fr Source #
Instance details Defined in Pairing.Fr Methods compare :: Fr -> Fr -> Ordering # (<) :: Fr -> Fr -> Bool # (<=) :: Fr -> Fr -> Bool # (>) :: Fr -> Fr -> Bool # (>=) :: Fr -> Fr -> Bool # max :: Fr -> Fr -> Fr # min :: Fr -> Fr -> Fr #
Show Fr Source #
Instance details Defined in Pairing.Fr Methods showsPrec :: Int -> Fr -> ShowS # show :: Fr -> String # showList :: [Fr] -> ShowS #
Bits Fr Source #
Instance details Defined in Pairing.Fr Methods (.&.) :: Fr -> Fr -> Fr # (.\|.) :: Fr -> Fr -> Fr # xor :: Fr -> Fr -> Fr # complement :: Fr -> Fr # shift :: Fr -> Int -> Fr # rotate :: Fr -> Int -> Fr # zeroBits :: Fr # bit :: Int -> Fr # setBit :: Fr -> Int -> Fr # clearBit :: Fr -> Int -> Fr # complementBit :: Fr -> Int -> Fr # testBit :: Fr -> Int -> Bool # bitSizeMaybe :: Fr -> Maybe Int # bitSize :: Fr -> Int # isSigned :: Fr -> Bool # shiftL :: Fr -> Int -> Fr # unsafeShiftL :: Fr -> Int -> Fr # shiftR :: Fr -> Int -> Fr # unsafeShiftR :: Fr -> Int -> Fr # rotateL :: Fr -> Int -> Fr # rotateR :: Fr -> Int -> Fr # popCount :: Fr -> Int #
NFData Fr Source #
Instance details Defined in Pairing.Fr Methods rnf :: Fr -> () #
Pretty Fr Source #
Instance details Defined in Pairing.Fr Methods pretty :: Fr -> Doc # prettyList :: [Fr] -> Doc #
AsInteger Fr Source #
Instance details Defined in Pairing.Fr Methods asInteger :: Fr -> Integer Source #

new :: Integer -> Fr Source #

Turn an integer into an Fr number, should be used instead of the Fr constructor.

frInv :: Fr -> Fr Source #

random :: MonadRandom m => m Fr Source #

isRootOfUnity :: Integer -> Fr -> Bool Source #

isPrimitiveRootOfUnity :: Integer -> Fr -> Bool Source #

primitiveRootOfUnity Source #

Arguments

:: Int	exponent of 2 for which we want to get the primitive root of unity
-> Fr

Compute primitive roots of unity for 2^0, 2^1, ..., 2^28. (2^28 is the largest power of two that divides _r - 1, therefore there are no primitive roots of unity for higher powers of 2 in Fr.)

precompRootOfUnity :: Int -> Fr Source #