There is a fundamental relationship between Σ-protocols and commitment schemes whereby the former can be used to construct the latter. In this work we provide the first formal analysis in a proof assistant of such a relationship and in doing so formalise Σ-protocols and commitment schemes and provide proofs of security for well known instantiations of both primitives.
Every definition and every theorem presented in this paper has been checked mechanically by the Isabelle/HOL proof assistant.
Butler D., Aspinall D., Gascón A. (2019) On the Formalisation of Σ-Protocols and Commitment Schemes. In: Nielson F., Sands D. (eds) Principles of Security and Trust. POST 2019. Lecture Notes in Computer Science, vol 11426. Springer, Cham