Data.Curve.Binary

Documentation

module Data.Curve

Binary curves

class (GaloisField q, PrimeField r, Curve Binary c e q r) => BCurve c e q r where

Binary curves.

Methods

a_

Arguments

:: BPoint c e q r

-> q

Coefficient A.

b_

Arguments

:: BPoint c e q r

-> q

Coefficient B.

h_

Arguments

:: BPoint c e q r

-> Natural

Curve cofactor.

p_

Arguments

:: BPoint c e q r

-> Natural

Curve polynomial.

r_

Arguments

:: BPoint c e q r

-> Natural

Curve order.

Instances

Curve Binary c SECT113R1 F2m Fr => BCurve c SECT113R1 F2m Fr

Defined in Data.Curve.Binary.SECT113R1

Methods

a_ :: BPoint c SECT113R1 F2m Fr -> F2m

b_ :: BPoint c SECT113R1 F2m Fr -> F2m

h_ :: BPoint c SECT113R1 F2m Fr -> Natural

p_ :: BPoint c SECT113R1 F2m Fr -> Natural

r_ :: BPoint c SECT113R1 F2m Fr -> Natural

Curve Binary c SECT113R2 F2m Fr => BCurve c SECT113R2 F2m Fr

Defined in Data.Curve.Binary.SECT113R2

Methods

a_ :: BPoint c SECT113R2 F2m Fr -> F2m

b_ :: BPoint c SECT113R2 F2m Fr -> F2m

h_ :: BPoint c SECT113R2 F2m Fr -> Natural

p_ :: BPoint c SECT113R2 F2m Fr -> Natural

r_ :: BPoint c SECT113R2 F2m Fr -> Natural

Curve Binary c SECT131R1 F2m Fr => BCurve c SECT131R1 F2m Fr

Defined in Data.Curve.Binary.SECT131R1

Methods

a_ :: BPoint c SECT131R1 F2m Fr -> F2m

b_ :: BPoint c SECT131R1 F2m Fr -> F2m

h_ :: BPoint c SECT131R1 F2m Fr -> Natural

p_ :: BPoint c SECT131R1 F2m Fr -> Natural

r_ :: BPoint c SECT131R1 F2m Fr -> Natural

Curve Binary c SECT131R2 F2m Fr => BCurve c SECT131R2 F2m Fr

Defined in Data.Curve.Binary.SECT131R2

Methods

a_ :: BPoint c SECT131R2 F2m Fr -> F2m

b_ :: BPoint c SECT131R2 F2m Fr -> F2m

h_ :: BPoint c SECT131R2 F2m Fr -> Natural

p_ :: BPoint c SECT131R2 F2m Fr -> Natural

r_ :: BPoint c SECT131R2 F2m Fr -> Natural

Curve Binary c SECT163K1 F2m Fr => BCurve c SECT163K1 F2m Fr

Defined in Data.Curve.Binary.SECT163K1

Methods

a_ :: BPoint c SECT163K1 F2m Fr -> F2m

b_ :: BPoint c SECT163K1 F2m Fr -> F2m

h_ :: BPoint c SECT163K1 F2m Fr -> Natural

p_ :: BPoint c SECT163K1 F2m Fr -> Natural

r_ :: BPoint c SECT163K1 F2m Fr -> Natural

Curve Binary c SECT163R1 F2m Fr => BCurve c SECT163R1 F2m Fr

Defined in Data.Curve.Binary.SECT163R1

Methods

a_ :: BPoint c SECT163R1 F2m Fr -> F2m

b_ :: BPoint c SECT163R1 F2m Fr -> F2m

h_ :: BPoint c SECT163R1 F2m Fr -> Natural

p_ :: BPoint c SECT163R1 F2m Fr -> Natural

r_ :: BPoint c SECT163R1 F2m Fr -> Natural

Curve Binary c SECT163R2 F2m Fr => BCurve c SECT163R2 F2m Fr

Defined in Data.Curve.Binary.SECT163R2

Methods

a_ :: BPoint c SECT163R2 F2m Fr -> F2m

b_ :: BPoint c SECT163R2 F2m Fr -> F2m

h_ :: BPoint c SECT163R2 F2m Fr -> Natural

p_ :: BPoint c SECT163R2 F2m Fr -> Natural

r_ :: BPoint c SECT163R2 F2m Fr -> Natural

Curve Binary c SECT193R1 F2m Fr => BCurve c SECT193R1 F2m Fr

Defined in Data.Curve.Binary.SECT193R1

Methods

a_ :: BPoint c SECT193R1 F2m Fr -> F2m

b_ :: BPoint c SECT193R1 F2m Fr -> F2m

h_ :: BPoint c SECT193R1 F2m Fr -> Natural

p_ :: BPoint c SECT193R1 F2m Fr -> Natural

r_ :: BPoint c SECT193R1 F2m Fr -> Natural

Curve Binary c SECT193R2 F2m Fr => BCurve c SECT193R2 F2m Fr

Defined in Data.Curve.Binary.SECT193R2

Methods

a_ :: BPoint c SECT193R2 F2m Fr -> F2m

b_ :: BPoint c SECT193R2 F2m Fr -> F2m

h_ :: BPoint c SECT193R2 F2m Fr -> Natural

p_ :: BPoint c SECT193R2 F2m Fr -> Natural

r_ :: BPoint c SECT193R2 F2m Fr -> Natural

Curve Binary c SECT233K1 F2m Fr => BCurve c SECT233K1 F2m Fr

Defined in Data.Curve.Binary.SECT233K1

Methods

a_ :: BPoint c SECT233K1 F2m Fr -> F2m

b_ :: BPoint c SECT233K1 F2m Fr -> F2m

h_ :: BPoint c SECT233K1 F2m Fr -> Natural

p_ :: BPoint c SECT233K1 F2m Fr -> Natural

r_ :: BPoint c SECT233K1 F2m Fr -> Natural

Curve Binary c SECT233R1 F2m Fr => BCurve c SECT233R1 F2m Fr

Defined in Data.Curve.Binary.SECT233R1

Methods

a_ :: BPoint c SECT233R1 F2m Fr -> F2m

b_ :: BPoint c SECT233R1 F2m Fr -> F2m

h_ :: BPoint c SECT233R1 F2m Fr -> Natural

p_ :: BPoint c SECT233R1 F2m Fr -> Natural

r_ :: BPoint c SECT233R1 F2m Fr -> Natural

Curve Binary c SECT239K1 F2m Fr => BCurve c SECT239K1 F2m Fr

Defined in Data.Curve.Binary.SECT239K1

Methods

a_ :: BPoint c SECT239K1 F2m Fr -> F2m

b_ :: BPoint c SECT239K1 F2m Fr -> F2m

h_ :: BPoint c SECT239K1 F2m Fr -> Natural

p_ :: BPoint c SECT239K1 F2m Fr -> Natural

r_ :: BPoint c SECT239K1 F2m Fr -> Natural

Curve Binary c SECT283K1 F2m Fr => BCurve c SECT283K1 F2m Fr

Defined in Data.Curve.Binary.SECT283K1

Methods

a_ :: BPoint c SECT283K1 F2m Fr -> F2m

b_ :: BPoint c SECT283K1 F2m Fr -> F2m

h_ :: BPoint c SECT283K1 F2m Fr -> Natural

p_ :: BPoint c SECT283K1 F2m Fr -> Natural

r_ :: BPoint c SECT283K1 F2m Fr -> Natural

Curve Binary c SECT283R1 F2m Fr => BCurve c SECT283R1 F2m Fr

Defined in Data.Curve.Binary.SECT283R1

Methods

a_ :: BPoint c SECT283R1 F2m Fr -> F2m

b_ :: BPoint c SECT283R1 F2m Fr -> F2m

h_ :: BPoint c SECT283R1 F2m Fr -> Natural

p_ :: BPoint c SECT283R1 F2m Fr -> Natural

r_ :: BPoint c SECT283R1 F2m Fr -> Natural

Curve Binary c SECT409K1 F2m Fr => BCurve c SECT409K1 F2m Fr

Defined in Data.Curve.Binary.SECT409K1

Methods

a_ :: BPoint c SECT409K1 F2m Fr -> F2m

b_ :: BPoint c SECT409K1 F2m Fr -> F2m

h_ :: BPoint c SECT409K1 F2m Fr -> Natural

p_ :: BPoint c SECT409K1 F2m Fr -> Natural

r_ :: BPoint c SECT409K1 F2m Fr -> Natural

Curve Binary c SECT409R1 F2m Fr => BCurve c SECT409R1 F2m Fr

Defined in Data.Curve.Binary.SECT409R1

Methods

a_ :: BPoint c SECT409R1 F2m Fr -> F2m

b_ :: BPoint c SECT409R1 F2m Fr -> F2m

h_ :: BPoint c SECT409R1 F2m Fr -> Natural

p_ :: BPoint c SECT409R1 F2m Fr -> Natural

r_ :: BPoint c SECT409R1 F2m Fr -> Natural

Curve Binary c SECT571K1 F2m Fr => BCurve c SECT571K1 F2m Fr

Defined in Data.Curve.Binary.SECT571K1

Methods

a_ :: BPoint c SECT571K1 F2m Fr -> F2m

b_ :: BPoint c SECT571K1 F2m Fr -> F2m

h_ :: BPoint c SECT571K1 F2m Fr -> Natural

p_ :: BPoint c SECT571K1 F2m Fr -> Natural

r_ :: BPoint c SECT571K1 F2m Fr -> Natural

Curve Binary c SECT571R1 F2m Fr => BCurve c SECT571R1 F2m Fr

Defined in Data.Curve.Binary.SECT571R1

Methods

a_ :: BPoint c SECT571R1 F2m Fr -> F2m

b_ :: BPoint c SECT571R1 F2m Fr -> F2m

h_ :: BPoint c SECT571R1 F2m Fr -> Natural

p_ :: BPoint c SECT571R1 F2m Fr -> Natural

r_ :: BPoint c SECT571R1 F2m Fr -> Natural

type BPoint = Point Binary

Binary points.

Binary affine curves

class BCurve Affine e q r => BACurve e q r where

Binary affine curves y^2 + xy = x^3 + Ax^2 + B.

Methods

gA_

Arguments

:: BAPoint e q r

Curve generator.

Instances

BACurve SECT113R1 F2m Fr

Defined in Data.Curve.Binary.SECT113R1

Methods

gA_ :: BAPoint SECT113R1 F2m Fr

BACurve SECT113R2 F2m Fr

Defined in Data.Curve.Binary.SECT113R2

Methods

gA_ :: BAPoint SECT113R2 F2m Fr

BACurve SECT131R1 F2m Fr

Defined in Data.Curve.Binary.SECT131R1

Methods

gA_ :: BAPoint SECT131R1 F2m Fr

BACurve SECT131R2 F2m Fr

Defined in Data.Curve.Binary.SECT131R2

Methods

gA_ :: BAPoint SECT131R2 F2m Fr

BACurve SECT163K1 F2m Fr

Defined in Data.Curve.Binary.SECT163K1

Methods

gA_ :: BAPoint SECT163K1 F2m Fr

BACurve SECT163R1 F2m Fr

Defined in Data.Curve.Binary.SECT163R1

Methods

gA_ :: BAPoint SECT163R1 F2m Fr

BACurve SECT163R2 F2m Fr

Defined in Data.Curve.Binary.SECT163R2

Methods

gA_ :: BAPoint SECT163R2 F2m Fr

BACurve SECT193R1 F2m Fr

Defined in Data.Curve.Binary.SECT193R1

Methods

gA_ :: BAPoint SECT193R1 F2m Fr

BACurve SECT193R2 F2m Fr

Defined in Data.Curve.Binary.SECT193R2

Methods

gA_ :: BAPoint SECT193R2 F2m Fr

BACurve SECT233K1 F2m Fr

Defined in Data.Curve.Binary.SECT233K1

Methods

gA_ :: BAPoint SECT233K1 F2m Fr

BACurve SECT233R1 F2m Fr

Defined in Data.Curve.Binary.SECT233R1

Methods

gA_ :: BAPoint SECT233R1 F2m Fr

BACurve SECT239K1 F2m Fr

Defined in Data.Curve.Binary.SECT239K1

Methods

gA_ :: BAPoint SECT239K1 F2m Fr

BACurve SECT283K1 F2m Fr

Defined in Data.Curve.Binary.SECT283K1

Methods

gA_ :: BAPoint SECT283K1 F2m Fr

BACurve SECT283R1 F2m Fr

Defined in Data.Curve.Binary.SECT283R1

Methods

gA_ :: BAPoint SECT283R1 F2m Fr

BACurve SECT409K1 F2m Fr

Defined in Data.Curve.Binary.SECT409K1

Methods

gA_ :: BAPoint SECT409K1 F2m Fr

BACurve SECT409R1 F2m Fr

Defined in Data.Curve.Binary.SECT409R1

Methods

gA_ :: BAPoint SECT409R1 F2m Fr

BACurve SECT571K1 F2m Fr

Defined in Data.Curve.Binary.SECT571K1

Methods

gA_ :: BAPoint SECT571K1 F2m Fr

BACurve SECT571R1 F2m Fr

Defined in Data.Curve.Binary.SECT571R1

Methods

gA_ :: BAPoint SECT571R1 F2m Fr

type BAPoint = BPoint Affine

Binary affine points.

Binary projective curves

class BCurve Projective e q r => BPCurve e q r where

Binary projective curves y^2z + xyz = x^3 + Ax^2z + Bz.

Methods

gP_

Arguments

:: BPPoint e q r

Curve generator.

Instances

BPCurve SECT113R1 F2m Fr

Defined in Data.Curve.Binary.SECT113R1

Methods

gP_ :: BPPoint SECT113R1 F2m Fr

BPCurve SECT113R2 F2m Fr

Defined in Data.Curve.Binary.SECT113R2

Methods

gP_ :: BPPoint SECT113R2 F2m Fr

BPCurve SECT131R1 F2m Fr

Defined in Data.Curve.Binary.SECT131R1

Methods

gP_ :: BPPoint SECT131R1 F2m Fr

BPCurve SECT131R2 F2m Fr

Defined in Data.Curve.Binary.SECT131R2

Methods

gP_ :: BPPoint SECT131R2 F2m Fr

BPCurve SECT163K1 F2m Fr

Defined in Data.Curve.Binary.SECT163K1

Methods

gP_ :: BPPoint SECT163K1 F2m Fr

BPCurve SECT163R1 F2m Fr

Defined in Data.Curve.Binary.SECT163R1

Methods

gP_ :: BPPoint SECT163R1 F2m Fr

BPCurve SECT163R2 F2m Fr

Defined in Data.Curve.Binary.SECT163R2

Methods

gP_ :: BPPoint SECT163R2 F2m Fr

BPCurve SECT193R1 F2m Fr

Defined in Data.Curve.Binary.SECT193R1

Methods

gP_ :: BPPoint SECT193R1 F2m Fr

BPCurve SECT193R2 F2m Fr

Defined in Data.Curve.Binary.SECT193R2

Methods

gP_ :: BPPoint SECT193R2 F2m Fr

BPCurve SECT233K1 F2m Fr

Defined in Data.Curve.Binary.SECT233K1

Methods

gP_ :: BPPoint SECT233K1 F2m Fr

BPCurve SECT233R1 F2m Fr

Defined in Data.Curve.Binary.SECT233R1

Methods

gP_ :: BPPoint SECT233R1 F2m Fr

BPCurve SECT239K1 F2m Fr

Defined in Data.Curve.Binary.SECT239K1

Methods

gP_ :: BPPoint SECT239K1 F2m Fr

BPCurve SECT283K1 F2m Fr

Defined in Data.Curve.Binary.SECT283K1

Methods

gP_ :: BPPoint SECT283K1 F2m Fr

BPCurve SECT283R1 F2m Fr

Defined in Data.Curve.Binary.SECT283R1

Methods

gP_ :: BPPoint SECT283R1 F2m Fr

BPCurve SECT409K1 F2m Fr

Defined in Data.Curve.Binary.SECT409K1

Methods

gP_ :: BPPoint SECT409K1 F2m Fr

BPCurve SECT409R1 F2m Fr

Defined in Data.Curve.Binary.SECT409R1

Methods

gP_ :: BPPoint SECT409R1 F2m Fr

BPCurve SECT571K1 F2m Fr

Defined in Data.Curve.Binary.SECT571K1

Methods

gP_ :: BPPoint SECT571K1 F2m Fr

BPCurve SECT571R1 F2m Fr

Defined in Data.Curve.Binary.SECT571R1

Methods

gP_ :: BPPoint SECT571R1 F2m Fr

type BPPoint = BPoint Projective

Binary projective points.

Orphan instances

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

Associated Types

data Point Binary Affine e q r :: Type

Methods

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

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

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

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

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

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

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

id :: Point Binary Affine e q r

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

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

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

gen :: 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)

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

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

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

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

Associated Types

data Point Binary Projective e q r :: Type

Methods

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

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

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

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

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

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

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

id :: Point Binary Projective e q r

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

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

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

gen :: 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)

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

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

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

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

Methods

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

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

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

Methods

pretty :: BPPoint e q r -> Doc

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

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

Methods

pretty :: BAPoint e q r -> Doc

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

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

Methods

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

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

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

Methods

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

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

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

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

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

Methods

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

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

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

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

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

Methods

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

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

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

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

Methods

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

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

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

Generic (Point Binary Affine e q r)

Associated Types

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

Methods

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

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

Generic (Point Binary Projective e q r)

Associated Types

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

Methods

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

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

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

Methods

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

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

Methods

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