Data.Curve.Montgomery

Documentation

module Data.Curve

Montgomery curves

class (GaloisField q, PrimeField r, Curve Montgomery c e q r) => MCurve c e q r where

Montgomery curves.

Methods

a_

Arguments

:: MPoint c e q r

-> q

Coefficient A.

b_

Arguments

:: MPoint c e q r

-> q

Coefficient B.

h_

Arguments

:: MPoint c e q r

-> Natural

Curve cofactor.

q_

Arguments

:: MPoint c e q r

-> Natural

Curve characteristic.

r_

Arguments

:: MPoint c e q r

-> Natural

Curve order.

Instances

Curve Montgomery c Curve25519 Fq Fr => MCurve c Curve25519 Fq Fr

Defined in Data.Curve.Montgomery.Curve25519

Methods

a_ :: MPoint c Curve25519 Fq Fr -> Fq

b_ :: MPoint c Curve25519 Fq Fr -> Fq

h_ :: MPoint c Curve25519 Fq Fr -> Natural

q_ :: MPoint c Curve25519 Fq Fr -> Natural

r_ :: MPoint c Curve25519 Fq Fr -> Natural

Curve Montgomery c Curve383187 Fq Fr => MCurve c Curve383187 Fq Fr

Defined in Data.Curve.Montgomery.Curve383187

Methods

a_ :: MPoint c Curve383187 Fq Fr -> Fq

b_ :: MPoint c Curve383187 Fq Fr -> Fq

h_ :: MPoint c Curve383187 Fq Fr -> Natural

q_ :: MPoint c Curve383187 Fq Fr -> Natural

r_ :: MPoint c Curve383187 Fq Fr -> Natural

Curve Montgomery c Curve448 Fq Fr => MCurve c Curve448 Fq Fr

Defined in Data.Curve.Montgomery.Curve448

Methods

a_ :: MPoint c Curve448 Fq Fr -> Fq

b_ :: MPoint c Curve448 Fq Fr -> Fq

h_ :: MPoint c Curve448 Fq Fr -> Natural

q_ :: MPoint c Curve448 Fq Fr -> Natural

r_ :: MPoint c Curve448 Fq Fr -> Natural

Curve Montgomery c M221 Fq Fr => MCurve c M221 Fq Fr

Defined in Data.Curve.Montgomery.M221

Methods

a_ :: MPoint c M221 Fq Fr -> Fq

b_ :: MPoint c M221 Fq Fr -> Fq

h_ :: MPoint c M221 Fq Fr -> Natural

q_ :: MPoint c M221 Fq Fr -> Natural

r_ :: MPoint c M221 Fq Fr -> Natural

Curve Montgomery c M383 Fq Fr => MCurve c M383 Fq Fr

Defined in Data.Curve.Montgomery.M383

Methods

a_ :: MPoint c M383 Fq Fr -> Fq

b_ :: MPoint c M383 Fq Fr -> Fq

h_ :: MPoint c M383 Fq Fr -> Natural

q_ :: MPoint c M383 Fq Fr -> Natural

r_ :: MPoint c M383 Fq Fr -> Natural

Curve Montgomery c M511 Fq Fr => MCurve c M511 Fq Fr

Defined in Data.Curve.Montgomery.M511

Methods

a_ :: MPoint c M511 Fq Fr -> Fq

b_ :: MPoint c M511 Fq Fr -> Fq

h_ :: MPoint c M511 Fq Fr -> Natural

q_ :: MPoint c M511 Fq Fr -> Natural

r_ :: MPoint c M511 Fq Fr -> Natural

type MPoint = Point Montgomery

Montgomery points.

Montgomery affine curves

class MCurve Affine e q r => MACurve e q r where

Montgomery affine curves By^2 = x^3 + Ax^2 + x.

Methods

gA_

Arguments

:: MAPoint e q r

Curve generator.

Instances

MACurve Curve25519 Fq Fr

Defined in Data.Curve.Montgomery.Curve25519

Methods

gA_ :: MAPoint Curve25519 Fq Fr

MACurve Curve383187 Fq Fr

Defined in Data.Curve.Montgomery.Curve383187

Methods

gA_ :: MAPoint Curve383187 Fq Fr

MACurve Curve448 Fq Fr

Defined in Data.Curve.Montgomery.Curve448

Methods

gA_ :: MAPoint Curve448 Fq Fr

MACurve M221 Fq Fr

Defined in Data.Curve.Montgomery.M221

Methods

gA_ :: MAPoint M221 Fq Fr

MACurve M383 Fq Fr

Defined in Data.Curve.Montgomery.M383

Methods

gA_ :: MAPoint M383 Fq Fr

MACurve M511 Fq Fr

Defined in Data.Curve.Montgomery.M511

Methods

gA_ :: MAPoint M511 Fq Fr

type MAPoint = MPoint Affine

Montgomery affine points.

Orphan instances

MACurve e q r => Curve Montgomery Affine (e :: k) q r

Associated Types

data Point Montgomery Affine e q r :: Type

Methods

char :: Point Montgomery Affine e q r -> Natural

cof :: Point Montgomery Affine e q r -> Natural

def :: Point Montgomery Affine e q r -> Bool

disc :: Point Montgomery Affine e q r -> q

order :: Point Montgomery Affine e q r -> Natural

add :: Point Montgomery Affine e q r -> Point Montgomery Affine e q r -> Point Montgomery Affine e q r

dbl :: Point Montgomery Affine e q r -> Point Montgomery Affine e q r

id :: Point Montgomery Affine e q r

inv :: Point Montgomery Affine e q r -> Point Montgomery Affine e q r

frob :: Point Montgomery Affine e q r -> Point Montgomery Affine e q r

fromA :: Point Montgomery Affine e q r -> Point Montgomery Affine e q r

gen :: Point Montgomery Affine e q r

point :: q -> q -> Maybe (Point Montgomery Affine e q r)

pointX :: q -> Maybe (Point Montgomery Affine e q r)

rnd :: MonadRandom m => m (Point Montgomery Affine e q r)

toA :: Point Montgomery Affine e q r -> Point Montgomery Affine e q r

yX :: Point Montgomery Affine e q r -> q -> Maybe q

MACurve e q r => Pretty (MAPoint e q r)

Methods

pretty :: MAPoint e q r -> Doc

prettyList :: [MAPoint e q r] -> Doc

Eq q => Eq (Point Montgomery Affine e q r)

Methods

(==) :: Point Montgomery Affine e q r -> Point Montgomery Affine e q r -> Bool

(/=) :: Point Montgomery Affine e q r -> Point Montgomery Affine e q r -> Bool

Read q => Read (Point Montgomery Affine e q r)

Methods

readsPrec :: Int -> ReadS (Point Montgomery Affine e q r)

readList :: ReadS [Point Montgomery Affine e q r]

readPrec :: ReadPrec (Point Montgomery Affine e q r)

readListPrec :: ReadPrec [Point Montgomery Affine e q r]

Show q => Show (Point Montgomery Affine e q r)

Methods

showsPrec :: Int -> Point Montgomery Affine e q r -> ShowS

show :: Point Montgomery Affine e q r -> String

showList :: [Point Montgomery Affine e q r] -> ShowS

Generic (Point Montgomery Affine e q r)

Associated Types

type Rep (Point Montgomery Affine e q r) :: Type -> Type

Methods

from :: Point Montgomery Affine e q r -> Rep (Point Montgomery Affine e q r) x

to :: Rep (Point Montgomery Affine e q r) x -> Point Montgomery Affine e q r

NFData q => NFData (Point Montgomery Affine e q r)

Methods

rnf :: Point Montgomery Affine e q r -> ()