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