bn256

README

bn256

Package bn256 implements the Optimal Ate pairing over a 256-bit Barreto-Naehrig curve targeting a 128-bit security level as described in the paper New Software Speed Records for Cryptocraphic Pairings. Its output is compatible with the implementation described in that paper.

The basis for this package is Cloudflare's bn256 implementation which itself is an improved version of the official bn256 package. The package at hand maintains compatibility to Cloudflare's library. The biggest difference is the replacement of their public API by a new one that is compatible to Kyber's scalar, point, group, and suite interfaces.

Bilinear groups are the basis for many 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) which is called a pairing.

Documentation

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 (s *Suite) PairingCheck(a []kyber.Point, b []kyber.Point) bool
  • func (s *Suite) Point() kyber.Point
  • func (c Suite) RandomStream() cipher.Stream
  • func (c Suite) Read(r io.Reader, objs ...interface{}) error
  • func (s *Suite) Scalar() kyber.Scalar
  • func (s 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("21888242871839275222246405745257275088548364400416034343698204186575808495617")

Order is the number of elements in both G₁ and G₂: 36u⁴+36u³+18u²+6u+1.

var P = bigFromBase10("21888242871839275222246405745257275088696311157297823662689037894645226208583")

P is a prime over which we form a basic field: 36u⁴+36u³+24u²+6u+1.

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) PairingCheck

func (s *Suite) PairingCheck(a []kyber.Point, b []kyber.Point) bool

PairingCheck calculates the Optimal Ate pairing for a set of points

func (*Suite) Point

func (s *Suite) Point() kyber.Point

Point returns a point in groups G2

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) Scalar

func (s *Suite) Scalar() kyber.Scalar

Scalar returns a scalar in groups G1

func (Suite) String

func (s 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.