# Sigma Protocols and Commitment Schemes

 Title: Sigma Protocols and Commitment Schemes Authors: David Butler and Andreas Lochbihler Submission date: 2019-10-07 Abstract: We use CryptHOL to formalise commitment schemes and Sigma-protocols. Both are widely used fundamental two party cryptographic primitives. Security for commitment schemes is considered using game-based definitions whereas the security of Sigma-protocols is considered using both the game-based and simulation-based security paradigms. In this work, we first define security for both primitives and then prove secure multiple case studies: the Schnorr, Chaum-Pedersen and Okamoto Sigma-protocols as well as a construction that allows for compound (AND and OR statements) Sigma-protocols and the Pedersen and Rivest commitment schemes. We also prove that commitment schemes can be constructed from Sigma-protocols. We formalise this proof at an abstract level, only assuming the existence of a Sigma-protocol; consequently, the instantiations of this result for the concrete Sigma-protocols we consider come for free. BibTeX: @article{Sigma_Commit_Crypto-AFP, author = {David Butler and Andreas Lochbihler}, title = {Sigma Protocols and Commitment Schemes}, journal = {Archive of Formal Proofs}, month = oct, year = 2019, note = {\url{https://isa-afp.org/entries/Sigma_Commit_Crypto.html}, Formal proof development}, ISSN = {2150-914x}, } License: BSD License Depends on: CryptHOL Used by: Constructive_Cryptography_CM