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{http://isa-afp.org/entries/Sigma_Commit_Crypto.html}, Formal proof development}, ISSN = {2150-914x}, }
License:	BSD License
Depends on:	CryptHOL
Status: [ok]	This is a development version of this entry. It might change over time and is not stable. Please refer to release versions for citations.

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