Safe Haskell	None
Language	Haskell2010

Pairing.Point

Description

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.

Synopsis

data Point a
- = Point a a
- | Infinity
gDouble :: GaloisField k => Point k -> Point k
gAdd :: GaloisField k => Point k -> Point k -> Point k
gNeg :: GaloisField k => Point k -> Point k
gMul :: (Integral a, GaloisField k) => Point k -> a -> Point k

Documentation

data Point a Source #

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 Source #
Instance details Defined in Pairing.Point Methods fmap :: (a -> b) -> Point a -> Point b # (<$) :: a -> Point b -> Point a #
Semigroup G2 Source #
Instance details Defined in Pairing.Group Methods (<>) :: G2 -> G2 -> G2 # sconcat :: NonEmpty G2 -> G2 # stimes :: Integral b => b -> G2 -> G2 #
Semigroup G1 Source #
Instance details Defined in Pairing.Group Methods (<>) :: G1 -> G1 -> G1 # sconcat :: NonEmpty G1 -> G1 # stimes :: Integral b => b -> G1 -> G1 #
Monoid G2 Source #
Instance details Defined in Pairing.Group Methods mempty :: G2 # mappend :: G2 -> G2 -> G2 # mconcat :: [G2] -> G2 #
Monoid G1 Source #
Instance details Defined in Pairing.Group Methods mempty :: G1 # mappend :: G1 -> G1 -> G1 # mconcat :: [G1] -> G1 #
Arbitrary G2 Source #
Instance details Defined in Pairing.Group Methods arbitrary :: Gen G2 # shrink :: G2 -> [G2] #
Arbitrary G1 Source #
Instance details Defined in Pairing.Group Methods arbitrary :: Gen G1 # shrink :: G1 -> [G1] #
Validate G2 Source #
Instance details Defined in Pairing.Group Methods isValidElement :: G2 -> Bool Source #
Validate G1 Source #
Instance details Defined in Pairing.Group Methods isValidElement :: G1 -> Bool Source #
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 # random :: MonadRandom m => m G2 Source #
CyclicGroup G1 Source #
Instance details Defined in Pairing.Group Methods generator :: G1 Source # order :: Proxy G1 -> Integer Source # expn :: AsInteger e => G1 -> e -> G1 Source # inverse :: G1 -> G1 Source # random :: MonadRandom m => m G1 Source #
Eq a => Eq (Point a) Source #
Instance details Defined in Pairing.Point Methods (==) :: Point a -> Point a -> Bool # (/=) :: Point a -> Point a -> Bool #
Ord a => Ord (Point a) Source #
Instance details 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) Source #
Instance details Defined in Pairing.Point Methods showsPrec :: Int -> Point a -> ShowS # show :: Point a -> String # showList :: [Point a] -> ShowS #
Generic (Point a) Source #
Instance details 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 #
NFData a => NFData (Point a) Source #
Instance details Defined in Pairing.Point Methods rnf :: Point a -> () #
type Rep (Point a) Source #
Instance details Defined in Pairing.Point type Rep (Point a) = D1 (MetaData "Point" "Pairing.Point" "pairing-0.4.1-Ig2Nbmhb1EL9wYT1sJSiHq" 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 :: GaloisField k => Point k -> Point k Source #

Point doubling

gAdd :: GaloisField k => Point k -> Point k -> Point k Source #

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

gNeg :: GaloisField k => Point k -> Point k Source #

Negation (flipping the y component)

gMul :: (Integral a, GaloisField k) => Point k -> a -> Point k Source #

Multiplication by a scalar