package bn256

import "go.dedis.ch/kyber/v3/pairing/bn256"

Package bn256 implements a particular bilinear group.

Bilinear groups are the basis of many of the new cryptographic protocols that have been proposed over the past decade. They consist of a triplet of groups (G₁, G₂ and GT) such that there exists a function e(g₁ˣ,g₂ʸ)=gTˣʸ (where gₓ is a generator of the respective group). That function is called a pairing function.

This package specifically implements the Optimal Ate pairing over a 256-bit Barreto-Naehrig curve as described in http://cryptojedi.org/papers/dclxvi-20100714.pdf. Its output is compatible with the implementation described in that paper.

This package previously claimed to operate at a 128-bit security level. However, recent improvements in attacks mean that is no longer true. See https://moderncrypto.org/mail-archive/curves/2016/000740.html.

Index ¶

• Variables
• type Suite
• func NewSuite() *Suite
• func NewSuiteG1() *Suite
• func NewSuiteG2() *Suite
• func NewSuiteGT() *Suite
• func NewSuiteRand(rand cipher.Stream) *Suite
• func (s *Suite) G1() kyber.Group
• func (s *Suite) G2() kyber.Group
• func (s *Suite) GT() kyber.Group
• func (c Suite) Hash() hash.Hash
• func (c Suite) New(t reflect.Type) interface{}
• func (s *Suite) Pair(p1 kyber.Point, p2 kyber.Point) kyber.Point
• func (c Suite) RandomStream() cipher.Stream
• func (c Suite) Read(r io.Reader, objs ...interface{}) error
• func (c Suite) String() string
• func (c Suite) Write(w io.Writer, objs ...interface{}) error
• func (c Suite) XOF(seed []byte) kyber.XOF

Variables ¶

var Order = bigFromBase10("65000549695646603732796438742359905742570406053903786389881062969044166799969")

Order is the number of elements in both G₁ and G₂: 36u⁴+36u³+18u²+6u+1. order-1 = (2**5) * 3 * 5743 * 280941149 * 130979359433191 * 491513138693455212421542731357 * 6518589491078791937

Types ¶

type Suite ¶

type Suite struct {
	// contains filtered or unexported fields
}

Suite implements the pairing.Suite interface for the BN256 bilinear pairing.

func NewSuite ¶

func NewSuite() *Suite

NewSuite generates and returns a new BN256 pairing suite.

func NewSuiteG1 ¶

func NewSuiteG1() *Suite

NewSuiteG1 returns a G1 suite.

func NewSuiteG2 ¶

func NewSuiteG2() *Suite

NewSuiteG2 returns a G2 suite.

func NewSuiteGT ¶

func NewSuiteGT() *Suite

NewSuiteGT returns a GT suite.

func NewSuiteRand ¶

func NewSuiteRand(rand cipher.Stream) *Suite

NewSuiteRand generates and returns a new BN256 suite seeded by the given cipher stream.

func (*Suite) G1 ¶

func (s *Suite) G1() kyber.Group

G1 returns the group G1 of the BN256 pairing.

func (*Suite) G2 ¶

func (s *Suite) G2() kyber.Group

G2 returns the group G2 of the BN256 pairing.

func (*Suite) GT ¶

func (s *Suite) GT() kyber.Group

GT returns the group GT of the BN256 pairing.

func (Suite) Hash ¶

func (c Suite) Hash() hash.Hash

Hash returns a newly instantiated sha256 hash function.

func (Suite) New ¶

func (c Suite) New(t reflect.Type) interface{}

New implements the kyber.Encoding interface.

func (*Suite) Pair ¶

func (s *Suite) Pair(p1 kyber.Point, p2 kyber.Point) kyber.Point

Pair takes the points p1 and p2 in groups G1 and G2, respectively, as input and computes their pairing in GT.

func (Suite) RandomStream ¶

func (c Suite) RandomStream() cipher.Stream

RandomStream returns a cipher.Stream which corresponds to a key stream from crypto/rand.

func (Suite) Read ¶

func (c Suite) Read(r io.Reader, objs ...interface{}) error

Read is the default implementation of kyber.Encoding interface Read.

func (Suite) String ¶

func (c Suite) String() string

String returns a recognizable string that this is a combined suite.

func (Suite) Write ¶

func (c Suite) Write(w io.Writer, objs ...interface{}) error

Write is the default implementation of kyber.Encoding interface Write.

func (Suite) XOF ¶

func (c Suite) XOF(seed []byte) kyber.XOF

XOF returns a newlly instantiated blake2xb XOF function.

Source Files ¶

constants.go curve.go gfp.go gfp12.go gfp2.go gfp6.go gfp_decl.go group.go optate.go point.go suite.go twist.go