Package dk.jonaslindstrom.ruffini.elliptic.structures.bn254

Class BN254

java.lang.Object

dk.jonaslindstrom.ruffini.elliptic.structures.bn254.BN254

public class BN254
extends Object

Implementation of the BN254 (aka BN128) pairing-friendly elliptic curve construction.

Field Summary

Fields

Modifier and Type	Field	Description
static BigPrimeField	FP	The base field FP = Fp.
static AlgebraicFieldExtension<Polynomial<Polynomial<BigInteger>>,AlgebraicFieldExtension<Polynomial<BigInteger>,AlgebraicFieldExtension<BigInteger,BigPrimeField>>>	FP12	FP12 = FP6(w) / (w2 - v)) is a quadratic field extension of FP6.
static AlgebraicFieldExtension<BigInteger,BigPrimeField>	FP2	FP2 = FP(u) / (u2 + 1) is a quadratic field extension of base field FP.
static AlgebraicFieldExtension<Polynomial<BigInteger>,AlgebraicFieldExtension<BigInteger,BigPrimeField>>	FP6	FP6 = FP2(v) / (v3 - (u + 9)) is a cubic field extension of FP2.
static BigPrimeField	FQ	Prime field of order q.
static ShortWeierstrassCurveAffine<BigInteger,?>	G1	Curve over FP containing the G1 subgroup.
static AffinePoint<BigInteger>	G1_GENERATOR	Generator for the G1 subgroup of order q.
static ShortWeierstrassCurveAffine<Polynomial<BigInteger>,?>	G2	Curve over FP2 containing the G2 subgroup.
static AffinePoint<Polynomial<BigInteger>>	G2_GENERATOR
static Group<Polynomial<Polynomial<Polynomial<BigInteger>>>>	GT
static BigInteger	p	Modulus of the base field.
static java.util.function.BiFunction<AffinePoint<BigInteger>,AffinePoint<Polynomial<BigInteger>>,Polynomial<Polynomial<Polynomial<BigInteger>>>>	PAIRING	The optimal Ate pairing which is a bilinear function e: G1 x G2 → GT.
static BigInteger	q	Order of subgroups of G1, G2 and GT

Constructor Summary

Constructors

Constructor	Description
BN254()

Method Summary

Modifier and Type	Method	Description
static SamePair<Polynomial<Polynomial<Polynomial<BigInteger>>>>	twist(AffinePoint<BigInteger> p)

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Details

p

public static BigInteger p

Modulus of the base field.

FP

public static BigPrimeField FP

The base field FP = F_p.

FP2

public static AlgebraicFieldExtension<BigInteger,BigPrimeField> FP2

FP2 = FP(u) / (u² + 1) is a quadratic field extension of base field FP.

FP6

public static AlgebraicFieldExtension<Polynomial<BigInteger>,AlgebraicFieldExtension<BigInteger,BigPrimeField>> FP6

FP6 = FP2(v) / (v³ - (u + 9)) is a cubic field extension of FP2.

FP12

public static AlgebraicFieldExtension<Polynomial<Polynomial<BigInteger>>,AlgebraicFieldExtension<Polynomial<BigInteger>,AlgebraicFieldExtension<BigInteger,BigPrimeField>>> FP12

FP12 = FP6(w) / (w² - v)) is a quadratic field extension of FP6.

GT

public static Group<Polynomial<Polynomial<Polynomial<BigInteger>>>> GT

G2

public static ShortWeierstrassCurveAffine<Polynomial<BigInteger>,?> G2

Curve over FP2 containing the G2 subgroup.

G1

public static ShortWeierstrassCurveAffine<BigInteger,?> G1

Curve over FP containing the G1 subgroup.

G2_GENERATOR

public static AffinePoint<Polynomial<BigInteger>> G2_GENERATOR

q

public static BigInteger q

Order of subgroups of G1, G2 and GT

FQ

public static BigPrimeField FQ

Prime field of order q.

G1_GENERATOR

public static AffinePoint<BigInteger> G1_GENERATOR

Generator for the G1 subgroup of order q.

PAIRING

public static java.util.function.BiFunction<AffinePoint<BigInteger>,AffinePoint<Polynomial<BigInteger>>,Polynomial<Polynomial<Polynomial<BigInteger>>>> PAIRING

The optimal Ate pairing which is a bilinear function e: G1 x G2 → GT.

Constructor Details

BN254

public BN254()

Method Details

twist

public static SamePair<Polynomial<Polynomial<Polynomial<BigInteger>>>> twist(AffinePoint<BigInteger> p)