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nistp256-cairo

A cairo implementation of NIST P-256(AKA Secp256R1).

We use canonical ECC way to make this implementation.

implementation notes

Outsourcing computing

We use python to compute the complex field computing, and verify the correctness in cairo. Start from src/p256_example.cairo.

ECDSA-Verify in Projective coordinates

For a signature $(r,s)$ , pubkey $P$ , base point $G$ and msg hash $m$ , we have to verify that: $(x,y,z)=r^{-1}sG+r^{-1}mP$ and if $r*z=x\mod{P}$ or $(r+n)*z=x\mod{P}$

In this form, we avoid division method.