elliptic-curve-0.3.0: Elliptic curve library

Safe HaskellNone
LanguageHaskell2010

Data.Curve.Edwards

Contents

Synopsis

Documentation

module Data.Curve

Edwards curves

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

Edwards curves.

Methods

a_ Source #

Arguments

:: EPoint c e q r 
-> q

Coefficient A.

d_ Source #

Arguments

:: EPoint c e q r 
-> q

Coefficient D.

h_ Source #

Arguments

:: EPoint c e q r 
-> Natural

Curve cofactor.

q_ Source #

Arguments

:: EPoint c e q r 
-> Natural

Curve characteristic.

r_ Source #

Arguments

:: EPoint c e q r 
-> Natural

Curve order.

Instances
Curve Edwards c Curve1174 Fq Fr => ECurve c Curve1174 Fq Fr Source # 
Instance details

Defined in Data.Curve.Edwards.Curve1174

Methods

a_ :: EPoint c Curve1174 Fq Fr -> Fq Source #

d_ :: EPoint c Curve1174 Fq Fr -> Fq Source #

h_ :: EPoint c Curve1174 Fq Fr -> Natural Source #

q_ :: EPoint c Curve1174 Fq Fr -> Natural Source #

r_ :: EPoint c Curve1174 Fq Fr -> Natural Source #

Curve Edwards c Curve41417 Fq Fr => ECurve c Curve41417 Fq Fr Source # 
Instance details

Defined in Data.Curve.Edwards.Curve41417

Methods

a_ :: EPoint c Curve41417 Fq Fr -> Fq Source #

d_ :: EPoint c Curve41417 Fq Fr -> Fq Source #

h_ :: EPoint c Curve41417 Fq Fr -> Natural Source #

q_ :: EPoint c Curve41417 Fq Fr -> Natural Source #

r_ :: EPoint c Curve41417 Fq Fr -> Natural Source #

Curve Edwards c E222 Fq Fr => ECurve c E222 Fq Fr Source # 
Instance details

Defined in Data.Curve.Edwards.E222

Methods

a_ :: EPoint c E222 Fq Fr -> Fq Source #

d_ :: EPoint c E222 Fq Fr -> Fq Source #

h_ :: EPoint c E222 Fq Fr -> Natural Source #

q_ :: EPoint c E222 Fq Fr -> Natural Source #

r_ :: EPoint c E222 Fq Fr -> Natural Source #

Curve Edwards c E382 Fq Fr => ECurve c E382 Fq Fr Source # 
Instance details

Defined in Data.Curve.Edwards.E382

Methods

a_ :: EPoint c E382 Fq Fr -> Fq Source #

d_ :: EPoint c E382 Fq Fr -> Fq Source #

h_ :: EPoint c E382 Fq Fr -> Natural Source #

q_ :: EPoint c E382 Fq Fr -> Natural Source #

r_ :: EPoint c E382 Fq Fr -> Natural Source #

Curve Edwards c E521 Fq Fr => ECurve c E521 Fq Fr Source # 
Instance details

Defined in Data.Curve.Edwards.E521

Methods

a_ :: EPoint c E521 Fq Fr -> Fq Source #

d_ :: EPoint c E521 Fq Fr -> Fq Source #

h_ :: EPoint c E521 Fq Fr -> Natural Source #

q_ :: EPoint c E521 Fq Fr -> Natural Source #

r_ :: EPoint c E521 Fq Fr -> Natural Source #

Curve Edwards c Ed25519 Fq Fr => ECurve c Ed25519 Fq Fr Source # 
Instance details

Defined in Data.Curve.Edwards.Ed25519

Methods

a_ :: EPoint c Ed25519 Fq Fr -> Fq Source #

d_ :: EPoint c Ed25519 Fq Fr -> Fq Source #

h_ :: EPoint c Ed25519 Fq Fr -> Natural Source #

q_ :: EPoint c Ed25519 Fq Fr -> Natural Source #

r_ :: EPoint c Ed25519 Fq Fr -> Natural Source #

Curve Edwards c Ed3363 Fq Fr => ECurve c Ed3363 Fq Fr Source # 
Instance details

Defined in Data.Curve.Edwards.Ed3363

Methods

a_ :: EPoint c Ed3363 Fq Fr -> Fq Source #

d_ :: EPoint c Ed3363 Fq Fr -> Fq Source #

h_ :: EPoint c Ed3363 Fq Fr -> Natural Source #

q_ :: EPoint c Ed3363 Fq Fr -> Natural Source #

r_ :: EPoint c Ed3363 Fq Fr -> Natural Source #

Curve Edwards c Ed448 Fq Fr => ECurve c Ed448 Fq Fr Source # 
Instance details

Defined in Data.Curve.Edwards.Ed448

Methods

a_ :: EPoint c Ed448 Fq Fr -> Fq Source #

d_ :: EPoint c Ed448 Fq Fr -> Fq Source #

h_ :: EPoint c Ed448 Fq Fr -> Natural Source #

q_ :: EPoint c Ed448 Fq Fr -> Natural Source #

r_ :: EPoint c Ed448 Fq Fr -> Natural Source #

Curve Edwards c JubJub Fq Fr => ECurve c JubJub Fq Fr Source # 
Instance details

Defined in Data.Curve.Edwards.JubJub

Methods

a_ :: EPoint c JubJub Fq Fr -> Fq Source #

d_ :: EPoint c JubJub Fq Fr -> Fq Source #

h_ :: EPoint c JubJub Fq Fr -> Natural Source #

q_ :: EPoint c JubJub Fq Fr -> Natural Source #

r_ :: EPoint c JubJub Fq Fr -> Natural Source #

type EPoint = Point Edwards Source #

Edwards points.

Edwards affine curves

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

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

Methods

gA_ Source #

Arguments

:: EAPoint e q r

Curve generator.

Instances
EACurve Curve1174 Fq Fr Source # 
Instance details

Defined in Data.Curve.Edwards.Curve1174

Methods

gA_ :: EAPoint Curve1174 Fq Fr Source #

EACurve Curve41417 Fq Fr Source # 
Instance details

Defined in Data.Curve.Edwards.Curve41417

Methods

gA_ :: EAPoint Curve41417 Fq Fr Source #

EACurve E222 Fq Fr Source # 
Instance details

Defined in Data.Curve.Edwards.E222

Methods

gA_ :: EAPoint E222 Fq Fr Source #

EACurve E382 Fq Fr Source # 
Instance details

Defined in Data.Curve.Edwards.E382

Methods

gA_ :: EAPoint E382 Fq Fr Source #

EACurve E521 Fq Fr Source # 
Instance details

Defined in Data.Curve.Edwards.E521

Methods

gA_ :: EAPoint E521 Fq Fr Source #

EACurve Ed25519 Fq Fr Source # 
Instance details

Defined in Data.Curve.Edwards.Ed25519

Methods

gA_ :: EAPoint Ed25519 Fq Fr Source #

EACurve Ed3363 Fq Fr Source # 
Instance details

Defined in Data.Curve.Edwards.Ed3363

Methods

gA_ :: EAPoint Ed3363 Fq Fr Source #

EACurve Ed448 Fq Fr Source # 
Instance details

Defined in Data.Curve.Edwards.Ed448

Methods

gA_ :: EAPoint Ed448 Fq Fr Source #

EACurve JubJub Fq Fr Source # 
Instance details

Defined in Data.Curve.Edwards.JubJub

Methods

gA_ :: EAPoint JubJub Fq Fr Source #

type EAPoint = EPoint Affine Source #

Edwards affine curves.

Edwards projective curves

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

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

Methods

gP_ Source #

Arguments

:: EPPoint e q r

Curve generator.

Instances
EPCurve Curve1174 Fq Fr Source # 
Instance details

Defined in Data.Curve.Edwards.Curve1174

Methods

gP_ :: EPPoint Curve1174 Fq Fr Source #

EPCurve Curve41417 Fq Fr Source # 
Instance details

Defined in Data.Curve.Edwards.Curve41417

Methods

gP_ :: EPPoint Curve41417 Fq Fr Source #

EPCurve E222 Fq Fr Source # 
Instance details

Defined in Data.Curve.Edwards.E222

Methods

gP_ :: EPPoint E222 Fq Fr Source #

EPCurve E382 Fq Fr Source # 
Instance details

Defined in Data.Curve.Edwards.E382

Methods

gP_ :: EPPoint E382 Fq Fr Source #

EPCurve E521 Fq Fr Source # 
Instance details

Defined in Data.Curve.Edwards.E521

Methods

gP_ :: EPPoint E521 Fq Fr Source #

EPCurve Ed25519 Fq Fr Source # 
Instance details

Defined in Data.Curve.Edwards.Ed25519

Methods

gP_ :: EPPoint Ed25519 Fq Fr Source #

EPCurve Ed3363 Fq Fr Source # 
Instance details

Defined in Data.Curve.Edwards.Ed3363

Methods

gP_ :: EPPoint Ed3363 Fq Fr Source #

EPCurve Ed448 Fq Fr Source # 
Instance details

Defined in Data.Curve.Edwards.Ed448

Methods

gP_ :: EPPoint Ed448 Fq Fr Source #

EPCurve JubJub Fq Fr Source # 
Instance details

Defined in Data.Curve.Edwards.JubJub

Methods

gP_ :: EPPoint JubJub Fq Fr Source #

type EPPoint = EPoint Projective Source #

Edwards projective curves.

Orphan instances

EACurve e q r => Curve Edwards Affine (e :: k) q r Source # 
Instance details

Associated Types

data Point Edwards Affine e q r :: Type Source #

Methods

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

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

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

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

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

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

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

id :: Point Edwards Affine e q r Source #

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

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

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

gen :: Point Edwards Affine e q r Source #

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

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

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

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

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

EPCurve e q r => Curve Edwards Projective (e :: k) q r Source # 
Instance details

Associated Types

data Point Edwards Projective e q r :: Type Source #

Methods

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

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

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

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

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

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

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

id :: Point Edwards Projective e q r Source #

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

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

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

gen :: Point Edwards Projective e q r Source #

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

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

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

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

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

EPCurve e q r => Eq (EPPoint e q r) Source # 
Instance details

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) Source # 
Instance details

Methods

pretty :: EPPoint e q r -> Doc #

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

EACurve e q r => Pretty (EAPoint e q r) Source # 
Instance details

Methods

pretty :: EAPoint e q r -> Doc #

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

Eq q => Eq (Point Edwards Affine e q r) Source # 
Instance details

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) Source # 
Instance details

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) Source # 
Instance details

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) Source # 
Instance details

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) Source # 
Instance details

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) Source # 
Instance details

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) Source # 
Instance details

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) Source # 
Instance details

Methods

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

NFData q => NFData (Point Edwards Projective e q r) Source # 
Instance details

Methods

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