Pairing.Point

Affine point arithmetic defining the group operation on an elliptic curve E(F), for some field F. In our case the field F is given as some type t with Num and Fractional instances.

Documentation

data Point a

Points on a curve over a field a represented as either affine coordinates or as a point at infinity.

Constructors

Point a a

Affine point

Infinity

Point at infinity

Instances

Functor Point

Defined in Pairing.Point

Methods

fmap :: (a -> b) -> Point a -> Point b

(<$) :: a -> Point b -> Point a

Semigroup G2

Defined in Pairing.Group

Methods

(<>) :: G2 -> G2 -> G2

sconcat :: NonEmpty G2 -> G2

stimes :: Integral b => b -> G2 -> G2

Semigroup G1

Defined in Pairing.Group

Methods

(<>) :: G1 -> G1 -> G1

sconcat :: NonEmpty G1 -> G1

stimes :: Integral b => b -> G1 -> G1

Monoid G2

Defined in Pairing.Group

Methods

mempty :: G2

mappend :: G2 -> G2 -> G2

mconcat :: [G2] -> G2

Monoid G1

Defined in Pairing.Group

Methods

mempty :: G1

mappend :: G1 -> G1 -> G1

mconcat :: [G1] -> G1

CyclicGroup G2

Defined in Pairing.Group

Methods

generator :: G2

order :: Proxy G2 -> Integer

expn :: AsInteger e => G2 -> e -> G2

inverse :: G2 -> G2

CyclicGroup G1

Defined in Pairing.Group

Methods

generator :: G1

order :: Proxy G1 -> Integer

expn :: AsInteger e => G1 -> e -> G1

inverse :: G1 -> G1

Eq a => Eq (Point a)

Defined in Pairing.Point

Methods

(==) :: Point a -> Point a -> Bool

(/=) :: Point a -> Point a -> Bool

Ord a => Ord (Point a)

Defined in Pairing.Point

Methods

compare :: Point a -> Point a -> Ordering

(<) :: Point a -> Point a -> Bool

(<=) :: Point a -> Point a -> Bool

(>) :: Point a -> Point a -> Bool

(>=) :: Point a -> Point a -> Bool

max :: Point a -> Point a -> Point a

min :: Point a -> Point a -> Point a

Show a => Show (Point a)

Defined in Pairing.Point

Methods

showsPrec :: Int -> Point a -> ShowS

show :: Point a -> String

showList :: [Point a] -> ShowS

Generic (Point a)

Defined in Pairing.Point

Associated Types

type Rep (Point a) :: Type -> Type

Methods

from :: Point a -> Rep (Point a) x

to :: Rep (Point a) x -> Point a

Arbitrary (Point Fq)

Defined in Pairing.Group

Methods

arbitrary :: Gen (Point Fq)

shrink :: Point Fq -> [Point Fq]

Arbitrary (Point Fq2)

Defined in Pairing.Group

Methods

arbitrary :: Gen (Point Fq2)

shrink :: Point Fq2 -> [Point Fq2]

NFData a => NFData (Point a)

Defined in Pairing.Point

Methods

rnf :: Point a -> ()

type Rep (Point a)

Defined in Pairing.Point

type Rep (Point a) = D1 (MetaData "Point" "Pairing.Point" "pairing-0.2-I50PwP2iyzj4H1q118vmVa" False) (C1 (MetaCons "Point" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a) :*: S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)) :+: C1 (MetaCons "Infinity" PrefixI False) (U1 :: Type -> Type))

gDouble :: (Fractional t, Eq t) => Point t -> Point t

Point doubling

gAdd :: (Fractional t, Eq t) => Point t -> Point t -> Point t

Point addition, provides a group structure on an elliptic curve with the point at infinity as its unit.

gNeg :: (Fractional t, Eq t) => Point t -> Point t

Negation (flipping the y component)

gMul :: (Eq t, Integral a, Fractional t) => Point t -> a -> Point t

Multiplication by a scalar