Crate ark_bn254[−][src]
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[u]=Fq/u+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 |