Formalization and analysis of the post-quantum signature scheme FALCON with Maude

Abstract

Digital signatures ensure the authenticity and integrity of digital assets, vital properties for any secure communication. The National Institute of Standards and Technologies launched the Post-Quantum Cryptography project to standardise new algorithms and protocols that are secure against quantum attackers. The post-quantum signature scheme FALCON was one of the finalists. We present a continuation of the first steps towards the formal specification and analysis, in the high-performance language Maude, of signature schemes. We have adapted and improved a previous framework, originally aimed to formally specify and analyse post-quantum key encapsulation mechanisms. As a use case of the new framework, we specify an executable symbolic model of FALCON. On the symbolic model, we verify termination and fairness using LTL formulas with Maude's model checker. Furthermore, authentication, integrity and non-repudiation are analysed through invariant analysis. Integrity and non-repudiation hold, meanwhile, authentication does not hold in our symbolic model.