# A Computationally Surveyable Proof of the Group Properties of an Elliptic Curve

## TL;DR

This paper provides an elementary, formal, and mechanically verified proof of the group properties of Curve25519, ensuring correctness of its hardware implementation for Diffie-Hellman key exchange.

## Contribution

It introduces a computationally surveyable proof of elliptic curve group properties, formalized in ACL2, with steps reproducible in any programming language.

## Key findings

- Proof is formalized and mechanically verified in ACL2.
- Proof is computationally surveyable and reproducible.
- Ensures correctness of hardware implementation for Diffie-Hellman.

## Abstract

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.