Douglas Stebila

ProofFrog: a tool for verifying game-hopping proofs

ProofFrog's algorithm for checking indistinguishability or interchangeability of two hops in a game-hopping proof

Abstract

Cryptographic proofs allow researchers to provide theoretical guarantees on the security that their constructions provide. A proof of security can completely eliminate a class of attacks by potential adversaries. Human fallibility, however, means that even a proof reviewed by experts may still hide flaws or outright errors. Proof assistants are software tools built for the purpose of formally verifying each step in a proof, and as such have the potential to prevent erroneous proofs from being published and insecure constructions from being implemented.

Unfortunately, existing tooling for verifying cryptographic proofs has found limited adoption in the cryptographic community, in part due to concerns with ease of use. We present ProofFrog: a new tool for verifying cryptographic game-hopping proofs. ProofFrog is designed with the average cryptographer in mind, using an imperative syntax similar to C for specifying games and a syntax for proofs that closely models pen-and-paper arguments. As opposed to other proof assistant tools which largely operate by manipulating logical formulae, ProofFrog manipulates abstract syntax trees (ASTs) into a canonical form to establish indistinguishable or equivalent behaviour for pairs of games in a user-provided sequence. We also detail the domain-specific language developed for use with the ProofFrog proof engine, the exact transformations it applies to canonicalize ASTs, and case studies of verified proofs. A tool like ProofFrog that prioritizes ease of use can lower the barrier of entry to using computer-verified proofs and aid in catching insecure constructions before they are made public.

Keywords: cryptography, game-hopping, proof verification

Reference

Ross Evans, Matthew McKague, Douglas Stebila. ProofFrog: a tool for verifying game-hopping proofs. Technical report. March 2025.

Download

Code

• ProofFrog engine (GitHub)
• ProofFrog examples (GitHub)

BibTeX

@misc{EPRINT:EvaMcKSte25,
 	Author = {Ross Evans and Matthew McKague and Douglas Stebila},
 	Month = mar,
 	Note = {\url{https://eprint.iacr.org/2025/418}},
 	Title = {{ProofFrog}: a tool for verifying game-hopping proofs},
 	Year = {2025}
 }

Funding

• Natural Sciences and Engineering Research Council of Canada (NSERC) Discovery grant RGPIN-2022-03187