[isabelle] New in the AFP: Sigma Protocols and Commitment Schemes



This new entry is by David Butler and Andreas Lochbihler:

> 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.


You’ll find it online at https://www.isa-afp.org/entries/Sigma_Commit_Crypto.html.

Incidentally, you might want to take look at the session graph:

https://www.isa-afp.org/browser_info/current/AFP/Sigma_Commit_Crypto/session_graph.pdf

This entry depends on numerous other AFP entries, showing the extent to which material here can be reused.

Larry





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