A Machine-Checked Formalization of Sigma-Protocols

Abstract : Zero-knowledge proofs have a vast applicability in the domain of cryptography, stemming from the fact that they can be used to force potentially malicious parties to abide by the rules of a protocol, without forcing them to reveal their secrets. $\Sigma$-protocols are a class of zero-knowledge proofs that can be implemented efficiently and that suffice for a great variety of practical applications. This paper presents a first machine-checked formalization of a comprehensive theory of Sigma-protocols. The development includes basic definitions, relations between different security properties that appear in the literature, and general composability theorems. We show its usefulness by formalizing---and proving the security---of concrete instances of several well-known protocols. The formalization builds on CertiCrypt, a framework that provides support to reason about cryptographic systems in the Coq proof assistant, and that has been previously used to formalize security proofs of encryption and signature schemes
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https://hal.inria.fr/inria-00552886
Contributor : Benjamin Gregoire <>
Submitted on : Monday, January 10, 2011 - 10:06:56 AM
Last modification on : Thursday, January 11, 2018 - 4:24:01 PM
Long-term archiving on : Monday, April 11, 2011 - 2:47:11 AM

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Gilles Barthe, Daniel Hedin, Santiago Zanella-Béguelin, Benjamin Grégoire, Sylvain Heraud. A Machine-Checked Formalization of Sigma-Protocols. CSF'10, Jul 2010, Edinburgh, Sweden. pp.246-260, ⟨10.1109/CSF.2010.24⟩. ⟨inria-00552886⟩

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