twistededwards

Documentation

Overview

Package twistededwards implements the arithmetic of twisted Edwards curves in native fields. This uses associated twisted Edwards curves defined over the scalar field of the SNARK curves.

Examples: Jubjub, Bandersnatch (a twisted Edwards) is defined over BLS12-381's scalar field Baby-Jubjub (a twisted Edwards) is defined over BN254's salar fields

Index

• Variables
• func GetSnarkField(id twistededwards.ID) (*big.Int, error)
• type Curve
  • func NewEdCurve(api frontend.API, id twistededwards.ID) (Curve, error)
• type CurveParams
  • func GetCurveParams(id twistededwards.ID) (*CurveParams, error)
• type EndoParams
• type Point

Variables

var DecomposeScalar = func(scalarField *big.Int, inputs []*big.Int, res []*big.Int) error {

	if scalarField.Cmp(ecc.BLS12_381.ScalarField()) != 0 {
		return errors.New("no efficient endomorphism is available on this curve")
	}
	var glv glvParams
	var init sync.Once
	init.Do(func() {
		glv.lambda.SetString("8913659658109529928382530854484400854125314752504019737736543920008458395397", 10)
		glv.order.SetString("13108968793781547619861935127046491459309155893440570251786403306729687672801", 10)
		ecc.PrecomputeLattice(&glv.order, &glv.lambda, &glv.glvBasis)
	})

	sp := ecc.SplitScalar(inputs[0], &glv.glvBasis)
	res[0].Neg(&(sp[0]))
	res[1].Set(&(sp[1]))

	res[2].Mul(res[1], &glv.lambda).Sub(res[2], res[0])
	res[2].Sub(res[2], inputs[0])
	res[2].Div(res[2], &glv.order)

	return nil
}

Functions

func GetSnarkField

func GetSnarkField(id twistededwards.ID) (*big.Int, error)

GetSnarkField returns the matching snark curve for a twisted edwards curve

Types

type Curve

type Curve interface {
	Params() *CurveParams
	Endo() *EndoParams
	Add(p1, p2 Point) Point
	Double(p1 Point) Point
	Neg(p1 Point) Point
	AssertIsOnCurve(p1 Point)
	ScalarMul(p1 Point, scalar frontend.Variable) Point
	DoubleBaseScalarMul(p1, p2 Point, s1, s2 frontend.Variable) Point
	API() frontend.API
}

Curve methods implemented by a twisted edwards curve inside a circuit

func NewEdCurve

func NewEdCurve(api frontend.API, id twistededwards.ID) (Curve, error)

NewEdCurve returns a new Edwards curve

type CurveParams

type CurveParams struct {
	A, D, Cofactor, Order *big.Int
	Base                  [2]*big.Int // base point coordinates
}

CurveParams twisted edwards curve parameters ax^2 + y^2 = 1 + d*x^2*y^2 Matches gnark-crypto curve specific params

func GetCurveParams

func GetCurveParams(id twistededwards.ID) (*CurveParams, error)

type EndoParams

type EndoParams struct {
	Endo   [2]*big.Int
	Lambda *big.Int
}

EndoParams endomorphism parameters for the curve, if they exist

type Point

type Point struct {
	X, Y frontend.Variable
}

Point represent a pair of X, Y coordinates inside a circuit