Safe Haskell	None
Language	Haskell2010

Pairing.Fq12

Description

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

Synopsis

data Fq12 = Fq12 {
- fq12x :: Fq6
- fq12y :: Fq6
}
new :: [Fq] -> Fq12
deconstruct :: Fq12 -> [Fq]
fq12inv :: Fq12 -> Fq12
fq12one :: Fq12
fq12zero :: Fq12
fq12conj :: Fq12 -> Fq12
fq12frobenius :: Int -> Fq12 -> Fq12
random :: MonadRandom m => m Fq12

Documentation

data Fq12 Source #

Field extension defined as Fq6[w]/w^2 - v

Constructors

Fq12	Use `new` instead of this constructor
Fields fq12x :: Fq6 fq12y :: Fq6

Instances

Eq Fq12 Source #
Instance details Defined in Pairing.Fq12 Methods (==) :: Fq12 -> Fq12 -> Bool # (/=) :: Fq12 -> Fq12 -> Bool #
Fractional Fq12 Source #
Instance details Defined in Pairing.Fq12 Methods (/) :: Fq12 -> Fq12 -> Fq12 # recip :: Fq12 -> Fq12 # fromRational :: Rational -> Fq12 #
Num Fq12 Source #
Instance details Defined in Pairing.Fq12 Methods (+) :: Fq12 -> Fq12 -> Fq12 # (-) :: Fq12 -> Fq12 -> Fq12 # (*) :: Fq12 -> Fq12 -> Fq12 # negate :: Fq12 -> Fq12 # abs :: Fq12 -> Fq12 # signum :: Fq12 -> Fq12 # fromInteger :: Integer -> Fq12 #
Show Fq12 Source #
Instance details Defined in Pairing.Fq12 Methods showsPrec :: Int -> Fq12 -> ShowS # show :: Fq12 -> String # showList :: [Fq12] -> ShowS #
Generic Fq12 Source #
Instance details Defined in Pairing.Fq12 Associated Types type Rep Fq12 :: Type -> Type # Methods from :: Fq12 -> Rep Fq12 x # to :: Rep Fq12 x -> Fq12 #
Semigroup GT Source #
Instance details Defined in Pairing.Group Methods (<>) :: GT -> GT -> GT # sconcat :: NonEmpty GT -> GT # stimes :: Integral b => b -> GT -> GT #
Monoid GT Source #
Instance details Defined in Pairing.Group Methods mempty :: GT # mappend :: GT -> GT -> GT # mconcat :: [GT] -> GT #
NFData Fq12 Source #
Instance details Defined in Pairing.Fq12 Methods rnf :: Fq12 -> () #
ByteRepr Fq12 Source #
Instance details Defined in Pairing.Fq12 Methods mkRepr :: Fq12 -> Maybe ByteString Source # fromRepr :: Fq12 -> ByteString -> Maybe Fq12 Source # reprLength :: Fq12 -> Int Source #
Validate GT Source #
Instance details Defined in Pairing.Group Methods isValidElement :: GT -> Bool Source #
CyclicGroup GT Source #
Instance details Defined in Pairing.Group Methods generator :: GT Source # order :: Proxy GT -> Integer Source # expn :: AsInteger e => GT -> e -> GT Source # inverse :: GT -> GT Source # random :: MonadRandom m => GT -> m GT Source #
ToUncompressedForm GT Source #
Instance details Defined in Pairing.Group Methods serializeUncompressed :: GT -> Maybe ByteString Source #
type Rep Fq12 Source #
Instance details Defined in Pairing.Fq12 type Rep Fq12 = D1 (MetaData "Fq12" "Pairing.Fq12" "pairing-0.3.0-DeuZ5Z2okCW8lwO8f8VUj3" False) (C1 (MetaCons "Fq12" PrefixI True) (S1 (MetaSel (Just "fq12x") NoSourceUnpackedness NoSourceStrictness DecidedStrict) (Rec0 Fq6) :*: S1 (MetaSel (Just "fq12y") NoSourceUnpackedness NoSourceStrictness DecidedStrict) (Rec0 Fq6)))

new :: [Fq] -> Fq12 Source #

Create a new value in Fq12 by providing a list of twelve coefficients in Fq, should be used instead of the Fq12 constructor.

deconstruct :: Fq12 -> [Fq] Source #

Deconstruct a value in Fq12 into a list of twelve coefficients in Fq.

fq12inv :: Fq12 -> Fq12 Source #

Multiplicative inverse

fq12one :: Fq12 Source #

Multiplicative identity

fq12zero :: Fq12 Source #

Additive identity

fq12conj :: Fq12 -> Fq12 Source #

Conjugation

fq12frobenius :: Int -> Fq12 -> Fq12 Source #

Iterated Frobenius automorphism

random :: MonadRandom m => m Fq12 Source #