Formalising $\Sigma$-Protocols and Commitment Schemes using CryptHOL

David Butler; Andreas Lochbihler; David Aspinall; Adria Gascon

Paper 2019/1185

Formalising $\Sigma$-Protocols and Commitment Schemes using CryptHOL

David Butler, Andreas Lochbihler, David Aspinall, and Adria Gascon

Abstract

Machine-checked proofs of security are important to increase the rigour of provable security. In this work we present a formalised theory of two fundamental two party cryptographic primitives: $\Sigma$-protocols and Commitment Schemes. $\Sigma$-protocols allow a prover to convince a verifier that they possess some knowledge without leaking information about the knowledge. Commitment schemes allow a committer to commit to a message and keep it secret until revealing it at a later time. We use CryptHOL to formalise both primitives and prove secure multiple examples namely; the Schnorr, Chaum-Pedersen and Okamoto $\Sigma$-protocols as well as a construction that allows for compound (AND and OR) $\Sigma$-protocols and the Pedersen and Rivest commitment schemes. A highlight of the work is a formalisation of the construction of commitment schemes from $\Sigma$-protocols. We formalise this proof at an abstract level using the modularity available in Isabelle/HOL and CryptHOL. This way, the proofs of the instantiations come for free.

Metadata

Available format(s): PDF
Category: Foundations
Publication info: Preprint. MINOR revision.
Keywords: Formal methods commitment schemes sigma protocols
Contact author(s): dbutler @ turing ac uk
History: 2019-10-15: received
Short URL: https://ia.cr/2019/1185
License: CC BY

BibTeX

@misc{cryptoeprint:2019/1185,
      author = {David Butler and Andreas Lochbihler and David Aspinall and Adria Gascon},
      title = {Formalising $\Sigma$-Protocols and Commitment Schemes using {CryptHOL}},
      howpublished = {Cryptology {ePrint} Archive, Paper 2019/1185},
      year = {2019},
      url = {https://eprint.iacr.org/2019/1185}
}