ZkFold.Base.Algebra.EllipticCurve.BLS12_381

Documentation

type BLS12_381_Scalar = 52435875175126190479447740508185965837690552500527637822603658699938581184513

type BLS12_381_Base = 4002409555221667393417789825735904156556882819939007885332058136124031650490837864442687629129015664037894272559787

type Fr = Zp BLS12_381_Scalar

type Fq = Zp BLS12_381_Base

type IP1 = "IP1"

type Fq2 = Ext2 Fq IP1

type IP2 = "IP2"

type Fq6 = Ext3 Fq2 IP2

type IP3 = "IP3"

type Fq12 = Ext2 Fq6 IP3

type BLS12_381_G1_Point = Weierstrass "BLS12-381-G1" (Point Fq)

type BLS12_381_G1_CompressedPoint = Weierstrass "BLS12-381-G1" (CompressedPoint Fq)

type BLS12_381_G2_Point = Weierstrass "BLS12-381-G2" (Point Fq2)

type BLS12_381_G2_CompressedPoint = Weierstrass "BLS12-381-G2" (CompressedPoint Fq2)

leBytesOf :: Natural -> [(Natural, Word8)]

bytesOf :: (ToConstant a, Const a ~ Natural) => Int -> a -> [Word8]

ofBytes :: FromConstant Natural a => [Word8] -> a

newtype BLS12_381_GT

An image of a pairing is a cyclic multiplicative subgroup of Fq12 of order BLS12_381_Scalar.

Constructors

BLS12_381_GT Fq12

Instances

Show BLS12_381_GT

Defined in ZkFold.Base.Algebra.EllipticCurve.BLS12_381

Methods

showsPrec :: Int -> BLS12_381_GT -> ShowS

show :: BLS12_381_GT -> String

showList :: [BLS12_381_GT] -> ShowS

Eq BLS12_381_GT

Defined in ZkFold.Base.Algebra.EllipticCurve.BLS12_381

Methods

(==) :: BLS12_381_GT -> BLS12_381_GT -> Bool

(/=) :: BLS12_381_GT -> BLS12_381_GT -> Bool

Finite BLS12_381_GT

Defined in ZkFold.Base.Algebra.EllipticCurve.BLS12_381

Associated Types

type Order BLS12_381_GT :: Natural

MultiplicativeGroup BLS12_381_GT

Defined in ZkFold.Base.Algebra.EllipticCurve.BLS12_381

Methods

(/) :: BLS12_381_GT -> BLS12_381_GT -> BLS12_381_GT

invert :: BLS12_381_GT -> BLS12_381_GT

MultiplicativeMonoid BLS12_381_GT

Defined in ZkFold.Base.Algebra.EllipticCurve.BLS12_381

Methods

one :: BLS12_381_GT

MultiplicativeSemigroup BLS12_381_GT

Defined in ZkFold.Base.Algebra.EllipticCurve.BLS12_381

Methods

(*) :: BLS12_381_GT -> BLS12_381_GT -> BLS12_381_GT

Eq BLS12_381_GT

Defined in ZkFold.Base.Algebra.EllipticCurve.BLS12_381

Associated Types

type BooleanOf BLS12_381_GT

Methods

(==) :: BLS12_381_GT -> BLS12_381_GT -> BooleanOf BLS12_381_GT

(/=) :: BLS12_381_GT -> BLS12_381_GT -> BooleanOf BLS12_381_GT

Exponent BLS12_381_GT Integer

Defined in ZkFold.Base.Algebra.EllipticCurve.BLS12_381

Methods

(^) :: BLS12_381_GT -> Integer -> BLS12_381_GT

Exponent BLS12_381_GT Natural

Defined in ZkFold.Base.Algebra.EllipticCurve.BLS12_381

Methods

(^) :: BLS12_381_GT -> Natural -> BLS12_381_GT

Conditional Bool BLS12_381_GT

Defined in ZkFold.Base.Algebra.EllipticCurve.BLS12_381

Methods

bool :: BLS12_381_GT -> BLS12_381_GT -> Bool -> BLS12_381_GT

Pairing BLS12_381_G1_Point BLS12_381_G2_Point BLS12_381_GT

Defined in ZkFold.Base.Algebra.EllipticCurve.BLS12_381

Methods

pairing :: BLS12_381_G1_Point -> BLS12_381_G2_Point -> BLS12_381_GT

type Order BLS12_381_GT

Defined in ZkFold.Base.Algebra.EllipticCurve.BLS12_381

type Order BLS12_381_GT = BLS12_381_Scalar

type BooleanOf BLS12_381_GT

Defined in ZkFold.Base.Algebra.EllipticCurve.BLS12_381

type BooleanOf BLS12_381_GT = BooleanOf Fq12

Orphan instances

Binary BLS12_381_G1_CompressedPoint

Methods

put :: BLS12_381_G1_CompressedPoint -> Put

get :: Get BLS12_381_G1_CompressedPoint

putList :: [BLS12_381_G1_CompressedPoint] -> Put

Binary BLS12_381_G1_Point

Methods

put :: BLS12_381_G1_Point -> Put

get :: Get BLS12_381_G1_Point

putList :: [BLS12_381_G1_Point] -> Put

Binary BLS12_381_G2_CompressedPoint

Methods

put :: BLS12_381_G2_CompressedPoint -> Put

get :: Get BLS12_381_G2_CompressedPoint

putList :: [BLS12_381_G2_CompressedPoint] -> Put

Binary BLS12_381_G2_Point

Methods

put :: BLS12_381_G2_Point -> Put

get :: Get BLS12_381_G2_Point

putList :: [BLS12_381_G2_Point] -> Put

Prime BLS12_381_Base

Prime BLS12_381_Scalar

Compressible BLS12_381_G1_Point

Associated Types

type Compressed BLS12_381_G1_Point

Methods

pointCompressed :: BaseFieldOf BLS12_381_G1_Point -> BooleanOf (BaseFieldOf BLS12_381_G1_Point) -> Compressed BLS12_381_G1_Point

compress :: BLS12_381_G1_Point -> Compressed BLS12_381_G1_Point

decompress :: Compressed BLS12_381_G1_Point -> BLS12_381_G1_Point

Compressible BLS12_381_G2_Point

Associated Types

type Compressed BLS12_381_G2_Point

Methods

pointCompressed :: BaseFieldOf BLS12_381_G2_Point -> BooleanOf (BaseFieldOf BLS12_381_G2_Point) -> Compressed BLS12_381_G2_Point

compress :: BLS12_381_G2_Point -> Compressed BLS12_381_G2_Point

decompress :: Compressed BLS12_381_G2_Point -> BLS12_381_G2_Point

CyclicGroup BLS12_381_G1_Point

Associated Types

type ScalarFieldOf BLS12_381_G1_Point

Methods

pointGen :: BLS12_381_G1_Point

CyclicGroup BLS12_381_G2_Point

Associated Types

type ScalarFieldOf BLS12_381_G2_Point

Methods

pointGen :: BLS12_381_G2_Point

Scale Fr BLS12_381_G1_Point

Methods

scale :: Fr -> BLS12_381_G1_Point -> BLS12_381_G1_Point

Scale Fr BLS12_381_G2_Point

Methods

scale :: Fr -> BLS12_381_G2_Point -> BLS12_381_G2_Point

IrreduciblePoly Fq IP1

Methods

irreduciblePoly :: Poly Fq

IrreduciblePoly Fq2 IP2

Methods

irreduciblePoly :: Poly Fq2

IrreduciblePoly Fq6 IP3

Methods

irreduciblePoly :: Poly Fq6

Field field => WeierstrassCurve "BLS12-381-G1" field

Methods

weierstrassB :: field

WeierstrassCurve "BLS12-381-G2" Fq2

Methods

weierstrassB :: Fq2

Pairing BLS12_381_G1_Point BLS12_381_G2_Point BLS12_381_GT

Methods

pairing :: BLS12_381_G1_Point -> BLS12_381_G2_Point -> BLS12_381_GT