- EIP-196: Precompiled contracts for addition and scalar multiplication on the elliptic curve alt_bn128
- EIP-197: Precompiled contracts for optimal ate pairing check on the elliptic curve alt_bn128
- EIP-198: Big integer modular exponentiation
- LambdaWorks
- Montgomery Modular Multiplication
- go-ethereum
- gnark
- Faster big-integer modular multiplication for most moduli
- LambdaWorks
- gnark
- go-ethereum
- BN254 for the rest of us
- Elliptic curve point addition in projective coordinates
- LambdaWorks
- Pairing for Beginners
- gnark
- py_pairing
- BN254 for the rest of us
- High-Speed Software Implementation of the Optimal Ate Pairing over Barreto–Naehrig Curves
- Efficient Optimal Ate Pairing at 128-bit Security Level
- Faster Computation of the Tate Pairing -New software speed records for cryptographic pairings
- https://eprint.iacr.org/2002/088.pdf
- https://eprint.iacr.org/2005/133.pdf
- https://eprint.iacr.org/2007/013.pd
- https://eprint.iacr.org/2007/247.pdf
- https://eprint.iacr.org/2008/096.pdf
- Final exponentiation
- https://eprint.iacr.org/2010/354.pdf
- https://eprint.iacr.org/2010/526.pdf
- https://eprint.iacr.org/2010/542.pdf
- https://eprint.iacr.org/2012/232.pdf
- Mixed addition
- Final exponentiation BN curves
- https://hal.science/hal-01620848/document (2017)
- https://link.springer.com/article/10.1007/s12190-018-1167-y
- https://eprint.iacr.org/2019/077.pdf
- https://eprint.iacr.org/2020/875.pdf
- Improving the computation of the optimal ate pairing for a high security level
- Cyclotomic Squaring