### 5 unstable releases

0.4.0 | Jan 17, 2023 |
---|---|

0.4.0-alpha.2 | Dec 28, 2022 |

0.4.0-alpha.1 | Nov 29, 2022 |

0.3.0 | Jun 6, 2021 |

0.2.0 | Mar 25, 2021 |

#**1125** in Cryptography

**172,999** downloads per month

Used in **1,083** crates
(34 directly)

**MIT/Apache**

25KB

515 lines

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

.
It is the same as the `bn128`

curve used in Ethereum (eg: go-ethereum).`bn256`

#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)

#### Dependencies

~5MB

~92K SLoC