Curve.Edwards

Documentation

class GaloisField k => PrimeField' k

Minimal complete definition

toInt'

Instances

KnownNat p => PrimeField' (PrimeField p)

Defined in Curve

Methods

toInt' :: PrimeField p -> Integer

data Coordinates

Curve coordinates.

Constructors

Affine

Jacobian

Projective

data Form

Curve forms.

Constructors

Binary

Edwards

Montgomery

Weierstrass

class (GaloisField q, PrimeField' r, Group (Point f c e q r)) => Curve (f :: Form) (c :: Coordinates) e q r where

Elliptic curves.

Minimal complete definition

char, cof, disc, fromA, point, pointX, toA, yX

Associated Types

data Point f c e q r :: *

Curve point.

Methods

char :: Point f c e q r -> Integer

Curve characteristic.

cof :: Point f c e q r -> Integer

Curve cofactor.

disc :: Point f c e q r -> q

Curve discriminant.

mul :: Point f c e q r -> r -> Point f c e q r

Curve point multiplication.

point :: q -> q -> Maybe (Point f c e q r)

Get point from X and Y coordinates.

pointX :: q -> Maybe (Point f c e q r)

Get point from X coordinate.

yX :: Point f c e q r -> q -> Maybe q

Get Y coordinate from X coordinate.

fromA :: Point f Affine e q r -> Point f c e q r

Transform from affine coordinates.

toA :: Point f c e q r -> Point f Affine e q r

Transform to affine coordinates.

Instances

WACurve e q r => Curve Weierstrass Affine (e :: k) q r

Defined in Curve.Weierstrass

Associated Types

data Point Weierstrass Affine e q r :: Type

Methods

char :: Point Weierstrass Affine e q r -> Integer

cof :: Point Weierstrass Affine e q r -> Integer

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

mul :: Point Weierstrass Affine e q r -> r -> Point Weierstrass Affine e q r

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

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

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

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

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

WJCurve e q r => Curve Weierstrass Jacobian (e :: k) q r

Defined in Curve.Weierstrass

Associated Types

data Point Weierstrass Jacobian e q r :: Type

Methods

char :: Point Weierstrass Jacobian e q r -> Integer

cof :: Point Weierstrass Jacobian e q r -> Integer

disc :: Point Weierstrass Jacobian e q r -> q

mul :: Point Weierstrass Jacobian e q r -> r -> Point Weierstrass Jacobian e q r

point :: q -> q -> Maybe (Point Weierstrass Jacobian e q r)

pointX :: q -> Maybe (Point Weierstrass Jacobian e q r)

yX :: Point Weierstrass Jacobian e q r -> q -> Maybe q

fromA :: Point Weierstrass Affine e q r -> Point Weierstrass Jacobian e q r

toA :: Point Weierstrass Jacobian e q r -> Point Weierstrass Affine e q r

WPCurve e q r => Curve Weierstrass Projective (e :: k) q r

Defined in Curve.Weierstrass

Associated Types

data Point Weierstrass Projective e q r :: Type

Methods

char :: Point Weierstrass Projective e q r -> Integer

cof :: Point Weierstrass Projective e q r -> Integer

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

mul :: Point Weierstrass Projective e q r -> r -> Point Weierstrass Projective e q r

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

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

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

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

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

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

Defined in Curve.Montgomery

Associated Types

data Point Montgomery Affine e q r :: Type

Methods

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

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

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

mul :: Point Montgomery Affine e q r -> r -> 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)

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

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

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

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

Defined in Curve.Edwards

Associated Types

data Point Edwards Affine e q r :: Type

Methods

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

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

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

mul :: Point Edwards Affine e q r -> r -> 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)

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

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

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

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

Defined in Curve.Edwards

Associated Types

data Point Edwards Projective e q r :: Type

Methods

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

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

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

mul :: Point Edwards Projective e q r -> r -> 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)

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

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

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

BACurve e q r => Curve Binary Affine (e :: k) q r

Defined in Curve.Binary

Associated Types

data Point Binary Affine e q r :: Type

Methods

char :: Point Binary Affine e q r -> Integer

cof :: Point Binary Affine e q r -> Integer

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

mul :: Point Binary Affine e q r -> r -> Point Binary Affine e q r

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

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

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

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

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

BPCurve e q r => Curve Binary Projective (e :: k) q r

Defined in Curve.Binary

Associated Types

data Point Binary Projective e q r :: Type

Methods

char :: Point Binary Projective e q r -> Integer

cof :: Point Binary Projective e q r -> Integer

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

mul :: Point Binary Projective e q r -> r -> Point Binary Projective e q r

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

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

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

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

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

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 JubJub Fq Fr

Projective JubJub curve is an Edwards projective curve.

Defined in Curve.Edwards.JubJub

Methods

gP_ :: EPPoint JubJub Fq Fr

EPCurve Ed448 Fq Fr

Projective Ed448 curve is an Edwards projective curve.

Defined in Curve.Edwards.Ed448

Methods

gP_ :: EPPoint Ed448 Fq Fr

EPCurve Ed3363 Fq Fr

Projective Ed3363 curve is an Edwards projective curve.

Defined in Curve.Edwards.Ed3363

Methods

gP_ :: EPPoint Ed3363 Fq Fr

EPCurve Ed25519 Fq Fr

Projective Ed25519 curve is an Edwards projective curve.

Defined in Curve.Edwards.Ed25519

Methods

gP_ :: EPPoint Ed25519 Fq Fr

EPCurve E521 Fq Fr

Projective E521 curve is an Edwards projective curve.

Defined in Curve.Edwards.E521

Methods

gP_ :: EPPoint E521 Fq Fr

EPCurve E382 Fq Fr

Projective E382 curve is an Edwards projective curve.

Defined in Curve.Edwards.E382

Methods

gP_ :: EPPoint E382 Fq Fr

EPCurve E222 Fq Fr

Projective E222 curve is an Edwards projective curve.

Defined in Curve.Edwards.E222

Methods

gP_ :: EPPoint E222 Fq Fr

EPCurve Curve41417 Fq Fr

Projective Curve41417 curve is an Edwards projective curve.

Defined in Curve.Edwards.Curve41417

Methods

gP_ :: EPPoint Curve41417 Fq Fr

EPCurve Curve1174 Fq Fr

Projective Curve1174 curve is an Edwards projective curve.

Defined in Curve.Edwards.Curve1174

Methods

gP_ :: EPPoint Curve1174 Fq Fr

type EPPoint = EPoint Projective

Edwards projective 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 JubJub Fq Fr

Affine JubJub curve is an Edwards affine curve.

Defined in Curve.Edwards.JubJub

Methods

gA_ :: EAPoint JubJub Fq Fr

EACurve Ed448 Fq Fr

Affine Ed448 curve is an Edwards affine curve.

Defined in Curve.Edwards.Ed448

Methods

gA_ :: EAPoint Ed448 Fq Fr

EACurve Ed3363 Fq Fr

Affine Ed3363 curve is an Edwards affine curve.

Defined in Curve.Edwards.Ed3363

Methods

gA_ :: EAPoint Ed3363 Fq Fr

EACurve Ed25519 Fq Fr

Affine Ed25519 curve is an Edwards affine curve.

Defined in Curve.Edwards.Ed25519

Methods

gA_ :: EAPoint Ed25519 Fq Fr

EACurve E521 Fq Fr

Affine E521 curve is an Edwards affine curve.

Defined in Curve.Edwards.E521

Methods

gA_ :: EAPoint E521 Fq Fr

EACurve E382 Fq Fr

Affine E382 curve is an Edwards affine curve.

Defined in Curve.Edwards.E382

Methods

gA_ :: EAPoint E382 Fq Fr

EACurve E222 Fq Fr

Affine E222 curve is an Edwards affine curve.

Defined in Curve.Edwards.E222

Methods

gA_ :: EAPoint E222 Fq Fr

EACurve Curve41417 Fq Fr

Affine Curve41417 curve is an Edwards affine curve.

Defined in Curve.Edwards.Curve41417

Methods

gA_ :: EAPoint Curve41417 Fq Fr

EACurve Curve1174 Fq Fr

Affine Curve1174 curve is an Edwards affine curve.

Defined in Curve.Edwards.Curve1174

Methods

gA_ :: EAPoint Curve1174 Fq Fr

type EAPoint = EPoint Affine

Edwards affine 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

-> Integer

Curve cofactor.

q_

Arguments

:: EPoint c e q r

-> Integer

Curve characteristic.

r_

Arguments

:: EPoint c e q r

-> Integer

Curve order.

x_

Arguments

:: EPoint c e q r

-> q

Coordinate X.

y_

Arguments

:: EPoint c e q r

-> q

Coordinate Y.

Instances

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

JubJub curve is an Edwards curve.

Defined in Curve.Edwards.JubJub

Methods

a_ :: EPoint c JubJub Fq Fr -> Fq

d_ :: EPoint c JubJub Fq Fr -> Fq

h_ :: EPoint c JubJub Fq Fr -> Integer

q_ :: EPoint c JubJub Fq Fr -> Integer

r_ :: EPoint c JubJub Fq Fr -> Integer

x_ :: EPoint c JubJub Fq Fr -> Fq

y_ :: EPoint c JubJub Fq Fr -> Fq

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

Ed448 curve is an Edwards curve.

Defined in Curve.Edwards.Ed448

Methods

a_ :: EPoint c Ed448 Fq Fr -> Fq

d_ :: EPoint c Ed448 Fq Fr -> Fq

h_ :: EPoint c Ed448 Fq Fr -> Integer

q_ :: EPoint c Ed448 Fq Fr -> Integer

r_ :: EPoint c Ed448 Fq Fr -> Integer

x_ :: EPoint c Ed448 Fq Fr -> Fq

y_ :: EPoint c Ed448 Fq Fr -> Fq

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

Ed3363 curve is an Edwards curve.

Defined in Curve.Edwards.Ed3363

Methods

a_ :: EPoint c Ed3363 Fq Fr -> Fq

d_ :: EPoint c Ed3363 Fq Fr -> Fq

h_ :: EPoint c Ed3363 Fq Fr -> Integer

q_ :: EPoint c Ed3363 Fq Fr -> Integer

r_ :: EPoint c Ed3363 Fq Fr -> Integer

x_ :: EPoint c Ed3363 Fq Fr -> Fq

y_ :: EPoint c Ed3363 Fq Fr -> Fq

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

Ed25519 curve is an Edwards curve.

Defined in Curve.Edwards.Ed25519

Methods

a_ :: EPoint c Ed25519 Fq Fr -> Fq

d_ :: EPoint c Ed25519 Fq Fr -> Fq

h_ :: EPoint c Ed25519 Fq Fr -> Integer

q_ :: EPoint c Ed25519 Fq Fr -> Integer

r_ :: EPoint c Ed25519 Fq Fr -> Integer

x_ :: EPoint c Ed25519 Fq Fr -> Fq

y_ :: EPoint c Ed25519 Fq Fr -> Fq

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

E521 curve is an Edwards curve.

Defined in Curve.Edwards.E521

Methods

a_ :: EPoint c E521 Fq Fr -> Fq

d_ :: EPoint c E521 Fq Fr -> Fq

h_ :: EPoint c E521 Fq Fr -> Integer

q_ :: EPoint c E521 Fq Fr -> Integer

r_ :: EPoint c E521 Fq Fr -> Integer

x_ :: EPoint c E521 Fq Fr -> Fq

y_ :: EPoint c E521 Fq Fr -> Fq

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

E382 curve is an Edwards curve.

Defined in Curve.Edwards.E382

Methods

a_ :: EPoint c E382 Fq Fr -> Fq

d_ :: EPoint c E382 Fq Fr -> Fq

h_ :: EPoint c E382 Fq Fr -> Integer

q_ :: EPoint c E382 Fq Fr -> Integer

r_ :: EPoint c E382 Fq Fr -> Integer

x_ :: EPoint c E382 Fq Fr -> Fq

y_ :: EPoint c E382 Fq Fr -> Fq

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

E222 curve is an Edwards curve.

Defined in Curve.Edwards.E222

Methods

a_ :: EPoint c E222 Fq Fr -> Fq

d_ :: EPoint c E222 Fq Fr -> Fq

h_ :: EPoint c E222 Fq Fr -> Integer

q_ :: EPoint c E222 Fq Fr -> Integer

r_ :: EPoint c E222 Fq Fr -> Integer

x_ :: EPoint c E222 Fq Fr -> Fq

y_ :: EPoint c E222 Fq Fr -> Fq

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

Curve41417 curve is an Edwards curve.

Defined in Curve.Edwards.Curve41417

Methods

a_ :: EPoint c Curve41417 Fq Fr -> Fq

d_ :: EPoint c Curve41417 Fq Fr -> Fq

h_ :: EPoint c Curve41417 Fq Fr -> Integer

q_ :: EPoint c Curve41417 Fq Fr -> Integer

r_ :: EPoint c Curve41417 Fq Fr -> Integer

x_ :: EPoint c Curve41417 Fq Fr -> Fq

y_ :: EPoint c Curve41417 Fq Fr -> Fq

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

Curve1174 curve is an Edwards curve.

Defined in Curve.Edwards.Curve1174

Methods

a_ :: EPoint c Curve1174 Fq Fr -> Fq

d_ :: EPoint c Curve1174 Fq Fr -> Fq

h_ :: EPoint c Curve1174 Fq Fr -> Integer

q_ :: EPoint c Curve1174 Fq Fr -> Integer

r_ :: EPoint c Curve1174 Fq Fr -> Integer

x_ :: EPoint c Curve1174 Fq Fr -> Fq

y_ :: EPoint c Curve1174 Fq Fr -> Fq

type EPoint = Point Edwards

Edwards points.

class (Arbitrary g, Eq g, Generic g, Monoid g, Pretty g, Random g, Show g) => Group g where

Groups.

Minimal complete definition

add, dbl, def, gen, id, inv, order

Methods

add :: g -> g -> g

Element addition.

dbl :: g -> g

Element doubling.

def :: g -> Bool

Check well-defined.

gen :: g

Group generator.

id :: g

Identity element.

inv :: g -> g

Element inversion.

mul' :: g -> Integer -> g

Element multiplication.

order :: g -> Integer

Curve order.

rnd :: MonadRandom m => m g

Random element.

Instances

FGroup r q => Group (Element r q)

Defined in Group.Field

Methods

add :: Element r q -> Element r q -> Element r q

dbl :: Element r q -> Element r q

def :: Element r q -> Bool

gen :: Element r q

id :: Element r q

inv :: Element r q -> Element r q

mul' :: Element r q -> Integer -> Element r q

order :: Element r q -> Integer

rnd :: MonadRandom m => m (Element r q)

WPCurve e q r => Group (WPPoint e q r)

Defined in Curve.Weierstrass

Methods

add :: WPPoint e q r -> WPPoint e q r -> WPPoint e q r

dbl :: WPPoint e q r -> WPPoint e q r

def :: WPPoint e q r -> Bool

gen :: WPPoint e q r

id :: WPPoint e q r

inv :: WPPoint e q r -> WPPoint e q r

mul' :: WPPoint e q r -> Integer -> WPPoint e q r

order :: WPPoint e q r -> Integer

rnd :: MonadRandom m => m (WPPoint e q r)

WJCurve e q r => Group (WJPoint e q r)

Defined in Curve.Weierstrass

Methods

add :: WJPoint e q r -> WJPoint e q r -> WJPoint e q r

dbl :: WJPoint e q r -> WJPoint e q r

def :: WJPoint e q r -> Bool

gen :: WJPoint e q r

id :: WJPoint e q r

inv :: WJPoint e q r -> WJPoint e q r

mul' :: WJPoint e q r -> Integer -> WJPoint e q r

order :: WJPoint e q r -> Integer

rnd :: MonadRandom m => m (WJPoint e q r)

WACurve e q r => Group (WAPoint e q r)

Defined in Curve.Weierstrass

Methods

add :: WAPoint e q r -> WAPoint e q r -> WAPoint e q r

dbl :: WAPoint e q r -> WAPoint e q r

def :: WAPoint e q r -> Bool

gen :: WAPoint e q r

id :: WAPoint e q r

inv :: WAPoint e q r -> WAPoint e q r

mul' :: WAPoint e q r -> Integer -> WAPoint e q r

order :: WAPoint e q r -> Integer

rnd :: MonadRandom m => m (WAPoint e q r)

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

Defined in Curve.Montgomery

Methods

add :: MAPoint e q r -> MAPoint e q r -> MAPoint e q r

dbl :: MAPoint e q r -> MAPoint e q r

def :: MAPoint e q r -> Bool

gen :: MAPoint e q r

id :: MAPoint e q r

inv :: MAPoint e q r -> MAPoint e q r

mul' :: MAPoint e q r -> Integer -> MAPoint e q r

order :: MAPoint e q r -> Integer

rnd :: MonadRandom m => m (MAPoint e q r)

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

Defined in Curve.Edwards

Methods

add :: EPPoint e q r -> EPPoint e q r -> EPPoint e q r

dbl :: EPPoint e q r -> EPPoint e q r

def :: EPPoint e q r -> Bool

gen :: EPPoint e q r

id :: EPPoint e q r

inv :: EPPoint e q r -> EPPoint e q r

mul' :: EPPoint e q r -> Integer -> EPPoint e q r

order :: EPPoint e q r -> Integer

rnd :: MonadRandom m => m (EPPoint e q r)

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

Defined in Curve.Edwards

Methods

add :: EAPoint e q r -> EAPoint e q r -> EAPoint e q r

dbl :: EAPoint e q r -> EAPoint e q r

def :: EAPoint e q r -> Bool

gen :: EAPoint e q r

id :: EAPoint e q r

inv :: EAPoint e q r -> EAPoint e q r

mul' :: EAPoint e q r -> Integer -> EAPoint e q r

order :: EAPoint e q r -> Integer

rnd :: MonadRandom m => m (EAPoint e q r)

BPCurve e q r => Group (BPPoint e q r)

Defined in Curve.Binary

Methods

add :: BPPoint e q r -> BPPoint e q r -> BPPoint e q r

dbl :: BPPoint e q r -> BPPoint e q r

def :: BPPoint e q r -> Bool

gen :: BPPoint e q r

id :: BPPoint e q r

inv :: BPPoint e q r -> BPPoint e q r

mul' :: BPPoint e q r -> Integer -> BPPoint e q r

order :: BPPoint e q r -> Integer

rnd :: MonadRandom m => m (BPPoint e q r)

BACurve e q r => Group (BAPoint e q r)

Defined in Curve.Binary

Methods

add :: BAPoint e q r -> BAPoint e q r -> BAPoint e q r

dbl :: BAPoint e q r -> BAPoint e q r

def :: BAPoint e q r -> Bool

gen :: BAPoint e q r

id :: BAPoint e q r

inv :: BAPoint e q r -> BAPoint e q r

mul' :: BAPoint e q r -> Integer -> BAPoint e q r

order :: BAPoint e q r -> Integer

rnd :: MonadRandom m => m (BAPoint e q r)

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 -> Integer

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

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

mul :: Point Edwards Affine e q r -> r -> 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)

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

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

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

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 -> Integer

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

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

mul :: Point Edwards Projective e q r -> r -> 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)

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

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

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

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

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

Methods

add :: EPPoint e q r -> EPPoint e q r -> EPPoint e q r

dbl :: EPPoint e q r -> EPPoint e q r

def :: EPPoint e q r -> Bool

gen :: EPPoint e q r

id :: EPPoint e q r

inv :: EPPoint e q r -> EPPoint e q r

mul' :: EPPoint e q r -> Integer -> EPPoint e q r

order :: EPPoint e q r -> Integer

rnd :: MonadRandom m => m (EPPoint e q r)

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

Methods

add :: EAPoint e q r -> EAPoint e q r -> EAPoint e q r

dbl :: EAPoint e q r -> EAPoint e q r

def :: EAPoint e q r -> Bool

gen :: EAPoint e q r

id :: EAPoint e q r

inv :: EAPoint e q r -> EAPoint e q r

mul' :: EAPoint e q r -> Integer -> EAPoint e q r

order :: EAPoint e q r -> Integer

rnd :: MonadRandom m => m (EAPoint e q r)

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 -> ()