Safe Haskell	None
Language	Haskell2010

Pairing.Fq6

Description

Cubic extension of the tower:

Fq
Fq2 := Fq[u]/u^2 + 1
Fq6 := Fq2[v]/v^3 - (9 + u)
Fq12 := Fq6[w]/w^2 - v

Implementation follows "Multiplication and Squaring on Pairing-Friendly Fields" by Devigili, hEigeartaigh, Scott and Dahab.

Synopsis

data Fq6 = Fq6 {
- fq6x :: Fq2
- fq6y :: Fq2
- fq6z :: Fq2
}
new :: Fq2 -> Fq2 -> Fq2 -> Fq6
fq6inv :: Fq6 -> Fq6
fq6one :: Fq6
fq6zero :: Fq6
fq6sqr :: Fq6 -> Fq6
mulXi :: Fq6 -> Fq6
random :: MonadRandom m => m Fq6

Documentation

data Fq6 Source #

Field extension defined as Fq2[v]/v^3 - (9 + u)

Constructors

Fq6
Fields fq6x :: Fq2 fq6y :: Fq2 fq6z :: Fq2

Instances

Eq Fq6 Source #
Instance details Defined in Pairing.Fq6 Methods (==) :: Fq6 -> Fq6 -> Bool # (/=) :: Fq6 -> Fq6 -> Bool #
Fractional Fq6 Source #
Instance details Defined in Pairing.Fq6 Methods (/) :: Fq6 -> Fq6 -> Fq6 # recip :: Fq6 -> Fq6 # fromRational :: Rational -> Fq6 #
Num Fq6 Source #
Instance details Defined in Pairing.Fq6 Methods (+) :: Fq6 -> Fq6 -> Fq6 # (-) :: Fq6 -> Fq6 -> Fq6 # (*) :: Fq6 -> Fq6 -> Fq6 # negate :: Fq6 -> Fq6 # abs :: Fq6 -> Fq6 # signum :: Fq6 -> Fq6 # fromInteger :: Integer -> Fq6 #
Show Fq6 Source #
Instance details Defined in Pairing.Fq6 Methods showsPrec :: Int -> Fq6 -> ShowS # show :: Fq6 -> String # showList :: [Fq6] -> ShowS #
Generic Fq6 Source #
Instance details Defined in Pairing.Fq6 Associated Types type Rep Fq6 :: Type -> Type # Methods from :: Fq6 -> Rep Fq6 x # to :: Rep Fq6 x -> Fq6 #
NFData Fq6 Source #
Instance details Defined in Pairing.Fq6 Methods rnf :: Fq6 -> () #
ByteRepr Fq6 Source #
Instance details Defined in Pairing.Fq6 Methods mkRepr :: Fq6 -> Maybe ByteString Source # fromRepr :: Fq6 -> ByteString -> Maybe Fq6 Source # reprLength :: Fq6 -> Int Source #
type Rep Fq6 Source #
Instance details Defined in Pairing.Fq6 type Rep Fq6 = D1 (MetaData "Fq6" "Pairing.Fq6" "pairing-0.3.1-JhhvluXyNup3CB27ybng3m" False) (C1 (MetaCons "Fq6" PrefixI True) (S1 (MetaSel (Just "fq6x") NoSourceUnpackedness NoSourceStrictness DecidedStrict) (Rec0 Fq2) :: (S1 (MetaSel (Just "fq6y") NoSourceUnpackedness NoSourceStrictness DecidedStrict) (Rec0 Fq2) :: S1 (MetaSel (Just "fq6z") NoSourceUnpackedness NoSourceStrictness DecidedStrict) (Rec0 Fq2))))

new :: Fq2 -> Fq2 -> Fq2 -> Fq6 Source #

Create a new value in Fq6, should be used instead of the Fq6 constructor.

fq6inv :: Fq6 -> Fq6 Source #

Multiplicative inverse

fq6one :: Fq6 Source #

Multiplicative identity

fq6zero :: Fq6 Source #

Additive identity

fq6sqr :: Fq6 -> Fq6 Source #

Squaring operation

mulXi :: Fq6 -> Fq6 Source #

Multiply by xi (cubic nonresidue in Fq2) and reorder coefficients

random :: MonadRandom m => m Fq6 Source #