Safe Haskell	None
Language	Haskell2010

Pairing.Fq2

Description

First quadratic 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 following "Multiplication and Squaring on Pairing-Friendly Fields" by Devigili, hEigeartaigh, Scott and Dahab.

Synopsis

data Fq2 = Fq2 {
- fq2x :: Fq
- fq2y :: Fq
}
new :: Fq -> Fq -> Fq2
fq2scalarMul :: Fq -> Fq2 -> Fq2
fq2inv :: Fq2 -> Fq2
fq2one :: Fq2
fq2zero :: Fq2
fq2conj :: Fq2 -> Fq2
fq2sqr :: Fq2 -> Fq2
mulXi :: Fq2 -> Fq2
divXi :: Fq2 -> Fq2
xi :: Fq2
random :: MonadRandom m => m Fq2

Documentation

data Fq2 Source #

Quadratic extension of Fq defined as Fq[u]/x^2 + 1

Constructors

Fq2	Use `new` instead of this contructor
Fields fq2x :: Fq fq2y :: Fq

Instances

Eq Fq2 Source #
Instance details Defined in Pairing.Fq2 Methods (==) :: Fq2 -> Fq2 -> Bool # (/=) :: Fq2 -> Fq2 -> Bool #
Fractional Fq2 Source #
Instance details Defined in Pairing.Fq2 Methods (/) :: Fq2 -> Fq2 -> Fq2 # recip :: Fq2 -> Fq2 # fromRational :: Rational -> Fq2 #
Num Fq2 Source #
Instance details Defined in Pairing.Fq2 Methods (+) :: Fq2 -> Fq2 -> Fq2 # (-) :: Fq2 -> Fq2 -> Fq2 # (*) :: Fq2 -> Fq2 -> Fq2 # negate :: Fq2 -> Fq2 # abs :: Fq2 -> Fq2 # signum :: Fq2 -> Fq2 # fromInteger :: Integer -> Fq2 #
Show Fq2 Source #
Instance details Defined in Pairing.Fq2 Methods showsPrec :: Int -> Fq2 -> ShowS # show :: Fq2 -> String # showList :: [Fq2] -> ShowS #
Generic Fq2 Source #
Instance details Defined in Pairing.Fq2 Associated Types type Rep Fq2 :: Type -> Type # Methods from :: Fq2 -> Rep Fq2 x # to :: Rep Fq2 x -> Fq2 #
Semigroup G2 Source #
Instance details Defined in Pairing.Group Methods (<>) :: G2 -> G2 -> G2 # sconcat :: NonEmpty G2 -> G2 # stimes :: Integral b => b -> G2 -> G2 #
Monoid G2 Source #
Instance details Defined in Pairing.Group Methods mempty :: G2 # mappend :: G2 -> G2 -> G2 # mconcat :: [G2] -> G2 #
NFData Fq2 Source #
Instance details Defined in Pairing.Fq2 Methods rnf :: Fq2 -> () #
CyclicGroup G2 Source #
Instance details Defined in Pairing.Group Methods generator :: G2 Source # order :: Proxy G2 -> Integer Source # expn :: AsInteger e => G2 -> e -> G2 Source # inverse :: G2 -> G2 Source #
Arbitrary (Point Fq2) Source #
Instance details Defined in Pairing.Group Methods arbitrary :: Gen (Point Fq2) # shrink :: Point Fq2 -> [Point Fq2] #
type Rep Fq2 Source #
Instance details Defined in Pairing.Fq2 type Rep Fq2 = D1 (MetaData "Fq2" "Pairing.Fq2" "pairing-0.1.1-LSMyNU2W24Y2zJo2MsJ5lB" False) (C1 (MetaCons "Fq2" PrefixI True) (S1 (MetaSel (Just "fq2x") NoSourceUnpackedness NoSourceStrictness DecidedStrict) (Rec0 Fq) :*: S1 (MetaSel (Just "fq2y") NoSourceUnpackedness NoSourceStrictness DecidedStrict) (Rec0 Fq)))