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: y2 = x3 + 3
- G2 curve equation: y2 = x3 + B, where
- B = 3/(u+9) where Fq2 is represented as Fq[u]/(u^2+1) = Fq2(19485874751759354771024239261021720505790618469301721065564631296452457478373, 266929791119991161246907387137283842545076965332900288569378510910307636690)