Crate ark_bn254[][src]

Expand description

This library implements the BN254 curve that was sampled as part of the [BCTV14] paper . The name denotes that it is a Barreto–Naehrig curve of embedding degree 12, defined over a 254-bit (prime) field. The scalar field is highly 2-adic.

This curve is also implemented in libff under the name bn128. It is the same as the bn256 curve used in Ethereum (eg: go-ethereum).

#CAUTION This curve does not satisfy the 128-bit security level anymore.

Curve information:

  • Base field: q = 21888242871839275222246405745257275088696311157297823662689037894645226208583
  • Scalar field: r = 21888242871839275222246405745257275088548364400416034343698204186575808495617
  • valuation(q - 1, 2) = 1
  • valuation(r - 1, 2) = 28
  • G1 curve equation: y^2 = x^3 + 3
  • G2 curve equation: y^2 = x^3 + B, where
    • B = 3/(u+9) where Fq2 is represented as Fq[u]/(u^2+1) = Fq2(19485874751759354771024239261021720505790618469301721065564631296452457478373, 266929791119991161246907387137283842545076965332900288569378510910307636690)

Modules

fq
fq2
fq6
fq12
fr
g1
g2

Structs

Fq2Parameters
Fq6Parameters
Fq12Parameters
FqParameters
FrParameters
Parameters

Constants

FQ2_ONE
FQ2_ZERO
FQ_ONE
FQ_ZERO

Type Definitions

Bn254
Fq
Fq2
Fq6
Fq12
Fr
G1Affine
G1Projective
G2Affine
G2Projective