Support proposed Ethereum curves in EIPs 1895, 1962, 2539, 3026

[mratsim]

The following EIPs require support for new curves

• EIP 1895 - https://eips.ethereum.org/EIPS/eip-1895
• EIP 1962 - https://eips.ethereum.org/EIPS/eip-1962
• EIP 2539 - https://eips.ethereum.org/EIPS/eip-2539
• EIP 3026 - https://eips.ethereum.org/EIPS/eip-3026

Reference implementation/documentation:

• https://github.com/matter-labs/eip1962/tree/master/documentation

Implementations

• https://github.com/matter-labs/eip1962
• https://github.com/matter-labs/eip1962_cpp
• https://github.com/saitima/eip1962

Curves

• [x] BN254-Snarks
• [x] BLS12-381
• [x] BLS12-377
• [ ] Secp256k1 with Schnorr signatures and for Bulletproofs
• [ ] BW6-761

Companion curve that embeds BLS12-377

• [ ] BW6-761 from Celo
  • https://github.com/celo-org/celo-bls-snark-rs
  • https://gitlab.inria.fr/zk-curves/bw6-761/
  • https://eprint.iacr.org/2020/351.pdf
  • https://eips.ethereum.org/EIPS/eip-3026
• [ ] CP6-782

Curve cycles: https://eprint.iacr.org/2014/595.pdf

• [ ] MNT4-298
• [ ] MNT6-298
• [ ] MNT4-753
• [ ] MNT6-753

Curve families:

• BN -> Barreto Naehrig
• BLS -> Barreto Lynn Scott
• BW -> Brezing Weng
• CP -> Cocks-Pinch