README
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Curves
This library currently supports Bls12-381, and Alt bn128. Currently it wraps existing golang libraries into a common interface, and provides hashing methods for these curves.
Bls12-381
This is the set of curves which zcash is switching too. Its official documentation is located here. The underlying bls12-381 implementation used in this library is dis2's repository.
Alt bn128
The group G_1 is a cyclic group of prime order on the curve Y^2 = X^3 + 3 defined over the field F_p with p = 21888242871839275222246405745257275088696311157297823662689037894645226208583.
The generator g_1 is (1,2)
Since this curve is of prime order, every non-identity point is a generator, therefore the cofactor is 1.
The group G_2 is a cyclic subgroup of the non-prime order elliptic curve Y^2 = X^3 + 3*((i + 9)^(-1)) over the field F_p^2 = F_p[X] / (X^2 + 1) (where p is the same as above). We can write our irreducible element as i. The cofactor of this group is 21888242871839275222246405745257275088844257914179612981679871602714643921549.
The generator g_2 is defined as: (11559732032986387107991004021392285783925812861821192530917403151452391805634*i + 10857046999023057135944570762232829481370756359578518086990519993285655852781, 4082367875863433681332203403145435568316851327593401208105741076214120093531*i + 8495653923123431417604973247489272438418190587263600148770280649306958101930)
The identity element for both groups (The point at infinity in affine space) is internally represented as (0,0).
The underlying alt bn128 implementation used in this library is go-ethereums.
Benchmarks
The following benchmarks are from a 3.80GHz i7-7700HQ CPU with 16GB ram.
The pairing operation on Altbn128 takes ~1.9 milliseconds.
BenchmarkPairing-8 1000 1958898 ns/op
and for Bls12 it takes ~1.5 ms:
BenchmarkPairGT-8 1000 1539918 ns/op
Hashing
Currently only hashing to G1 is supported. Hashing to G2 is planned. For altbn128, the hashing algorithm is currently try-and-increment, and we support SHA3, Kangaroo twelve, Keccak256, and Blake2b.
For bls12-381, we are using Fouque-Tibouchi hashing using blake2b. This is interoperable with ebfull's repository.
References
- Pierre-Alain Fouque and Mehdi Tibouchi. Indifferentiable Hashing to Barreto–Naehrig Curves
Documentation
¶
Index ¶
Constants ¶
This section is empty.
Variables ¶
var Altbn128 = &altbn128{}
Altbn128Inst is the instance for the altbn128 curve, with all of its functions.
var Bls12 = &bls12Curve{}
Bls12 is the instance for the bls12 curve, with all of its functions.
Functions ¶
func AltbnBlake2b ¶
AltbnBlake2b Hashes a message to a point on Altbn128 using Blake2b and try and increment The return value is the x,y affine coordinate pair.
func AltbnKeccak3 ¶
AltbnKeccak3 Hashes a message to a point on Altbn128 using Keccak3 and try and increment Keccak3 is only for compatability with Ethereum hashing. The return value is the x,y affine coordinate pair.
func AltbnSha3 ¶
AltbnSha3 Hashes a message to a point on Altbn128 using SHA3 and try and increment The return value is the x,y affine coordinate pair.
func EthereumSum256 ¶
EthereumSum256 returns the Keccak3-256 digest of the data. This is because Ethereum uses a non-standard hashing algo.
Types ¶
type CurveSystem ¶
type CurveSystem interface {
Name() string
MakeG1Point([]*big.Int, bool) (Point, bool)
MakeG2Point([]*big.Int, bool) (Point, bool)
UnmarshalG1([]byte) (Point, bool)
UnmarshalG2([]byte) (Point, bool)
UnmarshalGT([]byte) (PointT, bool)
GetG1() Point
GetG2() Point
GetGT() PointT
GetG1Infinity() Point
GetG2Infinity() Point
GetGTIdentity() PointT
HashToG1(message []byte) Point
GetG1Q() *big.Int
GetG1Order() *big.Int
Pair(Point, Point) (PointT, bool)
// Product of Pairings
PairingProduct([]Point, []Point) (PointT, bool)
// contains filtered or unexported methods
}
CurveSystem is a set of parameters and functions for a pairing based cryptosystem It has everything necessary to support all bgls functionality which we use.
type Point ¶
type Point interface {
Add(Point) (Point, bool)
Copy() Point
Equals(Point) bool
Marshal() []byte
MarshalUncompressed() []byte
Mul(*big.Int) Point
ToAffineCoords() []*big.Int
}
Point is a way to represent a point on G1 or G2, in the first two elliptic curves.
func AggregatePoints ¶
AggregatePoints takes the sum of points.
Source Files