The goal of this document is to present an overview of the different approaches to validating the secp256r1 elliptic curve in an EVM setting. The primary goal is to reduce the gas cost of the signature verification, but there are also secondary tradeoffs to consider such as deployment gas costs, pre-computation/proving times, ease of use, and future areas of gas reduction.
Zero Knowledge via Halo2
Single Signature gas cost: 391,331 gas
High Level Approach:
Know Nothing Labs uses a zero knowledge proofs to reduce the gas costs of the secp256r1 signature. Specifically, they support ES256 along the P-256 elliptic curve, which is present on Apple's FaceID/Touch ID, Andriod devices, Intel SGX secure enclaves, hardware devices like Yubikeys, and much more.
End to End Flow: