A Computationally Surveyable Proof of the Group Properties of an Elliptic Curve
This work provides a verified foundation for cryptographic hardware implementations, but it is incremental as it focuses on a specific curve and proof method.
The authors tackled the problem of verifying the group properties of the Curve25519 elliptic curve as part of a hardware implementation proof, resulting in a formalized and mechanically verified proof using ACL2 that is computationally surveyable for reproduction.
We present an elementary proof of the group properties of the elliptic curve known as "Curve25519", as a component of a comprehensive proof of correctness of a hardware implementation of the associated Diffie-Hellman key agreement algorithm. The entire proof has been formalized and mechanically verified with ACL2, and is computationally surveyable in the sense that all steps that require mechanical support are presented in such a way that they may readily reproduced in any suitable programming language.