Data.Curve.Edwards

Documentation

module Data.Curve

Edwards curves

class (GaloisField q, PrimeField r, Curve Edwards c e q r) => ECurve c e q r where

Edwards curves.

Methods

a_

Arguments

:: EPoint c e q r

-> q

Coefficient A.

d_

Arguments

:: EPoint c e q r

-> q

Coefficient D.

h_

Arguments

:: EPoint c e q r

-> Natural

Curve cofactor.

q_

Arguments

:: EPoint c e q r

-> Natural

Curve characteristic.

r_

Arguments

:: EPoint c e q r

-> Natural

Curve order.

Instances

Curve Edwards c Curve1174 Fq Fr => ECurve c Curve1174 Fq Fr

Defined in Data.Curve.Edwards.Curve1174

Methods

a_ :: EPoint c Curve1174 Fq Fr -> Fq

d_ :: EPoint c Curve1174 Fq Fr -> Fq

h_ :: EPoint c Curve1174 Fq Fr -> Natural

q_ :: EPoint c Curve1174 Fq Fr -> Natural

r_ :: EPoint c Curve1174 Fq Fr -> Natural

Curve Edwards c Curve41417 Fq Fr => ECurve c Curve41417 Fq Fr

Defined in Data.Curve.Edwards.Curve41417

Methods

a_ :: EPoint c Curve41417 Fq Fr -> Fq

d_ :: EPoint c Curve41417 Fq Fr -> Fq

h_ :: EPoint c Curve41417 Fq Fr -> Natural

q_ :: EPoint c Curve41417 Fq Fr -> Natural

r_ :: EPoint c Curve41417 Fq Fr -> Natural

Curve Edwards c E222 Fq Fr => ECurve c E222 Fq Fr

Defined in Data.Curve.Edwards.E222

Methods

a_ :: EPoint c E222 Fq Fr -> Fq

d_ :: EPoint c E222 Fq Fr -> Fq

h_ :: EPoint c E222 Fq Fr -> Natural

q_ :: EPoint c E222 Fq Fr -> Natural

r_ :: EPoint c E222 Fq Fr -> Natural

Curve Edwards c E382 Fq Fr => ECurve c E382 Fq Fr

Defined in Data.Curve.Edwards.E382

Methods

a_ :: EPoint c E382 Fq Fr -> Fq

d_ :: EPoint c E382 Fq Fr -> Fq

h_ :: EPoint c E382 Fq Fr -> Natural

q_ :: EPoint c E382 Fq Fr -> Natural

r_ :: EPoint c E382 Fq Fr -> Natural

Curve Edwards c E521 Fq Fr => ECurve c E521 Fq Fr

Defined in Data.Curve.Edwards.E521

Methods

a_ :: EPoint c E521 Fq Fr -> Fq

d_ :: EPoint c E521 Fq Fr -> Fq

h_ :: EPoint c E521 Fq Fr -> Natural

q_ :: EPoint c E521 Fq Fr -> Natural

r_ :: EPoint c E521 Fq Fr -> Natural

Curve Edwards c Ed25519 Fq Fr => ECurve c Ed25519 Fq Fr

Defined in Data.Curve.Edwards.Ed25519

Methods

a_ :: EPoint c Ed25519 Fq Fr -> Fq

d_ :: EPoint c Ed25519 Fq Fr -> Fq

h_ :: EPoint c Ed25519 Fq Fr -> Natural

q_ :: EPoint c Ed25519 Fq Fr -> Natural

r_ :: EPoint c Ed25519 Fq Fr -> Natural

Curve Edwards c Ed3363 Fq Fr => ECurve c Ed3363 Fq Fr

Defined in Data.Curve.Edwards.Ed3363

Methods

a_ :: EPoint c Ed3363 Fq Fr -> Fq

d_ :: EPoint c Ed3363 Fq Fr -> Fq

h_ :: EPoint c Ed3363 Fq Fr -> Natural

q_ :: EPoint c Ed3363 Fq Fr -> Natural

r_ :: EPoint c Ed3363 Fq Fr -> Natural

Curve Edwards c Ed448 Fq Fr => ECurve c Ed448 Fq Fr

Defined in Data.Curve.Edwards.Ed448

Methods

a_ :: EPoint c Ed448 Fq Fr -> Fq

d_ :: EPoint c Ed448 Fq Fr -> Fq

h_ :: EPoint c Ed448 Fq Fr -> Natural

q_ :: EPoint c Ed448 Fq Fr -> Natural

r_ :: EPoint c Ed448 Fq Fr -> Natural

Curve Edwards c JubJub Fq Fr => ECurve c JubJub Fq Fr

Defined in Data.Curve.Edwards.JubJub

Methods

a_ :: EPoint c JubJub Fq Fr -> Fq

d_ :: EPoint c JubJub Fq Fr -> Fq

h_ :: EPoint c JubJub Fq Fr -> Natural

q_ :: EPoint c JubJub Fq Fr -> Natural

r_ :: EPoint c JubJub Fq Fr -> Natural

type EPoint = Point Edwards

Edwards points.

Edwards affine curves

class ECurve Affine e q r => EACurve e q r where

Edwards affine curves Ax^2 + y^2 = 1 + Dx^2y^2.

Methods

gA_

Arguments

:: EAPoint e q r

Curve generator.

Instances

EACurve Curve1174 Fq Fr

Defined in Data.Curve.Edwards.Curve1174

Methods

gA_ :: EAPoint Curve1174 Fq Fr

EACurve Curve41417 Fq Fr

Defined in Data.Curve.Edwards.Curve41417

Methods

gA_ :: EAPoint Curve41417 Fq Fr

EACurve E222 Fq Fr

Defined in Data.Curve.Edwards.E222

Methods

gA_ :: EAPoint E222 Fq Fr

EACurve E382 Fq Fr

Defined in Data.Curve.Edwards.E382

Methods

gA_ :: EAPoint E382 Fq Fr

EACurve E521 Fq Fr

Defined in Data.Curve.Edwards.E521

Methods

gA_ :: EAPoint E521 Fq Fr

EACurve Ed25519 Fq Fr

Defined in Data.Curve.Edwards.Ed25519

Methods

gA_ :: EAPoint Ed25519 Fq Fr

EACurve Ed3363 Fq Fr

Defined in Data.Curve.Edwards.Ed3363

Methods

gA_ :: EAPoint Ed3363 Fq Fr

EACurve Ed448 Fq Fr

Defined in Data.Curve.Edwards.Ed448

Methods

gA_ :: EAPoint Ed448 Fq Fr

EACurve JubJub Fq Fr

Defined in Data.Curve.Edwards.JubJub

Methods

gA_ :: EAPoint JubJub Fq Fr

type EAPoint = EPoint Affine

Edwards affine curves.

Edwards projective curves

class ECurve Projective e q r => EPCurve e q r where

Edwards projective curves Ax^2z^2 + y^2z^2 = z^4 + Dx^2y^2.

Methods

gP_

Arguments

:: EPPoint e q r

Curve generator.

Instances

EPCurve Curve1174 Fq Fr

Defined in Data.Curve.Edwards.Curve1174

Methods

gP_ :: EPPoint Curve1174 Fq Fr

EPCurve Curve41417 Fq Fr

Defined in Data.Curve.Edwards.Curve41417

Methods

gP_ :: EPPoint Curve41417 Fq Fr

EPCurve E222 Fq Fr

Defined in Data.Curve.Edwards.E222

Methods

gP_ :: EPPoint E222 Fq Fr

EPCurve E382 Fq Fr

Defined in Data.Curve.Edwards.E382

Methods

gP_ :: EPPoint E382 Fq Fr

EPCurve E521 Fq Fr

Defined in Data.Curve.Edwards.E521

Methods

gP_ :: EPPoint E521 Fq Fr

EPCurve Ed25519 Fq Fr

Defined in Data.Curve.Edwards.Ed25519

Methods

gP_ :: EPPoint Ed25519 Fq Fr

EPCurve Ed3363 Fq Fr

Defined in Data.Curve.Edwards.Ed3363

Methods

gP_ :: EPPoint Ed3363 Fq Fr

EPCurve Ed448 Fq Fr

Defined in Data.Curve.Edwards.Ed448

Methods

gP_ :: EPPoint Ed448 Fq Fr

EPCurve JubJub Fq Fr

Defined in Data.Curve.Edwards.JubJub

Methods

gP_ :: EPPoint JubJub Fq Fr

type EPPoint = EPoint Projective

Edwards projective curves.

Orphan instances

EACurve e q r => Curve Edwards Affine (e :: k) q r

Associated Types

data Point Edwards Affine e q r :: Type

Methods

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

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

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

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

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

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

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

id :: Point Edwards Affine e q r

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

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

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

gen :: Point Edwards Affine e q r

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

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

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

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

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

EPCurve e q r => Curve Edwards Projective (e :: k) q r

Associated Types

data Point Edwards Projective e q r :: Type

Methods

char :: Point Edwards Projective e q r -> Natural

cof :: Point Edwards Projective e q r -> Natural

def :: Point Edwards Projective e q r -> Bool

disc :: Point Edwards Projective e q r -> q

order :: Point Edwards Projective e q r -> Natural

add :: Point Edwards Projective e q r -> Point Edwards Projective e q r -> Point Edwards Projective e q r

dbl :: Point Edwards Projective e q r -> Point Edwards Projective e q r

id :: Point Edwards Projective e q r

inv :: Point Edwards Projective e q r -> Point Edwards Projective e q r

frob :: Point Edwards Projective e q r -> Point Edwards Projective e q r

fromA :: Point Edwards Affine e q r -> Point Edwards Projective e q r

gen :: Point Edwards Projective e q r

point :: q -> q -> Maybe (Point Edwards Projective e q r)

pointX :: q -> Maybe (Point Edwards Projective e q r)

rnd :: MonadRandom m => m (Point Edwards Projective e q r)

toA :: Point Edwards Projective e q r -> Point Edwards Affine e q r

yX :: Point Edwards Projective e q r -> q -> Maybe q

EPCurve e q r => Eq (EPPoint e q r)

Methods

(==) :: EPPoint e q r -> EPPoint e q r -> Bool

(/=) :: EPPoint e q r -> EPPoint e q r -> Bool

EPCurve e q r => Pretty (EPPoint e q r)

Methods

pretty :: EPPoint e q r -> Doc

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

EACurve e q r => Pretty (EAPoint e q r)

Methods

pretty :: EAPoint e q r -> Doc

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

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

Methods

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

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

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

Methods

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

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

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

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

Read q => Read (Point Edwards Projective e q r)

Methods

readsPrec :: Int -> ReadS (Point Edwards Projective e q r)

readList :: ReadS [Point Edwards Projective e q r]

readPrec :: ReadPrec (Point Edwards Projective e q r)

readListPrec :: ReadPrec [Point Edwards Projective e q r]

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

Methods

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

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

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

Show q => Show (Point Edwards Projective e q r)

Methods

showsPrec :: Int -> Point Edwards Projective e q r -> ShowS

show :: Point Edwards Projective e q r -> String

showList :: [Point Edwards Projective e q r] -> ShowS

Generic (Point Edwards Affine e q r)

Associated Types

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

Methods

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

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

Generic (Point Edwards Projective e q r)

Associated Types

type Rep (Point Edwards Projective e q r) :: Type -> Type

Methods

from :: Point Edwards Projective e q r -> Rep (Point Edwards Projective e q r) x

to :: Rep (Point Edwards Projective e q r) x -> Point Edwards Projective e q r

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

Methods

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

NFData q => NFData (Point Edwards Projective e q r)

Methods

rnf :: Point Edwards Projective e q r -> ()