go-ethereum: github.com/ethereum/go-ethereum/crypto/bn256/cloudflare Index | Files

package bn256

import "github.com/ethereum/go-ethereum/crypto/bn256/cloudflare"

Package bn256 implements a particular bilinear group at the 128-bit security level.

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.

Index

Package Files

bn256.go constants.go curve.go gfp.go gfp12.go gfp2.go gfp6.go gfp_decl.go lattice.go optate.go twist.go

Variables

var Order = bigFromBase10("21888242871839275222246405745257275088548364400416034343698204186575808495617")

Order is the number of elements in both G₁ and G₂: 36u⁴+36u³+18u²+6u+1. Needs to be highly 2-adic for efficient SNARK key and proof generation. Order - 1 = 2^28 * 3^2 * 13 * 29 * 983 * 11003 * 237073 * 405928799 * 1670836401704629 * 13818364434197438864469338081. Refer to https://eprint.iacr.org/2013/879.pdf and https://eprint.iacr.org/2013/507.pdf for more information on these parameters.

var P = bigFromBase10("21888242871839275222246405745257275088696311157297823662689037894645226208583")

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

func PairingCheck Uses

func PairingCheck(a []*G1, b []*G2) bool

PairingCheck calculates the Optimal Ate pairing for a set of points.

type G1 Uses

type G1 struct {
    // contains filtered or unexported fields
}

G1 is an abstract cyclic group. The zero value is suitable for use as the output of an operation, but cannot be used as an input.

func RandomG1 Uses

func RandomG1(r io.Reader) (*big.Int, *G1, error)

RandomG1 returns x and g₁ˣ where x is a random, non-zero number read from r.

func (*G1) Add Uses

func (e *G1) Add(a, b *G1) *G1

Add sets e to a+b and then returns e.

func (*G1) Marshal Uses

func (e *G1) Marshal() []byte

Marshal converts e to a byte slice.

func (*G1) Neg Uses

func (e *G1) Neg(a *G1) *G1

Neg sets e to -a and then returns e.

func (*G1) ScalarBaseMult Uses

func (e *G1) ScalarBaseMult(k *big.Int) *G1

ScalarBaseMult sets e to g*k where g is the generator of the group and then returns e.

func (*G1) ScalarMult Uses

func (e *G1) ScalarMult(a *G1, k *big.Int) *G1

ScalarMult sets e to a*k and then returns e.

func (*G1) Set Uses

func (e *G1) Set(a *G1) *G1

Set sets e to a and then returns e.

func (*G1) String Uses

func (g *G1) String() string

func (*G1) Unmarshal Uses

func (e *G1) Unmarshal(m []byte) ([]byte, error)

Unmarshal sets e to the result of converting the output of Marshal back into a group element and then returns e.

type G2 Uses

type G2 struct {
    // contains filtered or unexported fields
}

G2 is an abstract cyclic group. The zero value is suitable for use as the output of an operation, but cannot be used as an input.

func RandomG2 Uses

func RandomG2(r io.Reader) (*big.Int, *G2, error)

RandomG2 returns x and g₂ˣ where x is a random, non-zero number read from r.

func (*G2) Add Uses

func (e *G2) Add(a, b *G2) *G2

Add sets e to a+b and then returns e.

func (*G2) Marshal Uses

func (e *G2) Marshal() []byte

Marshal converts e into a byte slice.

func (*G2) Neg Uses

func (e *G2) Neg(a *G2) *G2

Neg sets e to -a and then returns e.

func (*G2) ScalarBaseMult Uses

func (e *G2) ScalarBaseMult(k *big.Int) *G2

ScalarBaseMult sets e to g*k where g is the generator of the group and then returns out.

func (*G2) ScalarMult Uses

func (e *G2) ScalarMult(a *G2, k *big.Int) *G2

ScalarMult sets e to a*k and then returns e.

func (*G2) Set Uses

func (e *G2) Set(a *G2) *G2

Set sets e to a and then returns e.

func (*G2) String Uses

func (e *G2) String() string

func (*G2) Unmarshal Uses

func (e *G2) Unmarshal(m []byte) ([]byte, error)

Unmarshal sets e to the result of converting the output of Marshal back into a group element and then returns e.

type GT Uses

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

GT is an abstract cyclic group. The zero value is suitable for use as the output of an operation, but cannot be used as an input.

func Miller Uses

func Miller(g1 *G1, g2 *G2) *GT

Miller applies Miller's algorithm, which is a bilinear function from the source groups to F_p^12. Miller(g1, g2).Finalize() is equivalent to Pair(g1, g2).

func Pair Uses

func Pair(g1 *G1, g2 *G2) *GT

Pair calculates an Optimal Ate pairing.

func (*GT) Add Uses

func (e *GT) Add(a, b *GT) *GT

Add sets e to a+b and then returns e.

func (*GT) Finalize Uses

func (e *GT) Finalize() *GT

Finalize is a linear function from F_p^12 to GT.

func (*GT) Marshal Uses

func (e *GT) Marshal() []byte

Marshal converts e into a byte slice.

func (*GT) Neg Uses

func (e *GT) Neg(a *GT) *GT

Neg sets e to -a and then returns e.

func (*GT) ScalarMult Uses

func (e *GT) ScalarMult(a *GT, k *big.Int) *GT

ScalarMult sets e to a*k and then returns e.

func (*GT) Set Uses

func (e *GT) Set(a *GT) *GT

Set sets e to a and then returns e.

func (*GT) String Uses

func (g *GT) String() string

func (*GT) Unmarshal Uses

func (e *GT) Unmarshal(m []byte) ([]byte, error)

Unmarshal sets e to the result of converting the output of Marshal back into a group element and then returns e.

Package bn256 imports 6 packages (graph) and is imported by 91 packages. Updated 2019-05-28. Refresh now. Tools for package owners.