Pairing.Fq6

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.

Documentation

data Fq6

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

Constructors

Fq6

Fields

• fq6x :: Fq2
• fq6y :: Fq2
• fq6z :: Fq2

Instances

Eq Fq6

Defined in Pairing.Fq6

Methods

(==) :: Fq6 -> Fq6 -> Bool

(/=) :: Fq6 -> Fq6 -> Bool

Fractional Fq6

Defined in Pairing.Fq6

Methods

(/) :: Fq6 -> Fq6 -> Fq6

recip :: Fq6 -> Fq6

fromRational :: Rational -> Fq6

Num Fq6

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

Defined in Pairing.Fq6

Methods

showsPrec :: Int -> Fq6 -> ShowS

show :: Fq6 -> String

showList :: [Fq6] -> ShowS

new :: Fq2 -> Fq2 -> Fq2 -> Fq6

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

fq6inv :: Fq6 -> Fq6

Multiplicative inverse

fq6one :: Fq6

Multiplicative identity

fq6zero :: Fq6

Additive identity

fq6sqr :: Fq6 -> Fq6

Squaring operation

mulXi :: Fq6 -> Fq6

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

random :: MonadRandom m => m Fq6