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• W3086061451 abstract "Abstract Machine-checked proofs of security are important to increase the rigour of provable security. In this work we present a formalised theory of two fundamental two party cryptographic primitives: $$varSigma $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mi>Σ</mml:mi></mml:math> -protocols and Commitment Schemes. $$varSigma $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mi>Σ</mml:mi></mml:math> -protocols allow a prover to convince a verifier that they possess some knowledge without leaking information about the knowledge. Commitment schemes allow a committer to commit to a message and keep it secret until revealing it at a later time. We use CryptHOL (Lochbihler in Archive of formal proofs, 2017) to formalise both primitives and prove secure multiple examples namely; the Schnorr, Chaum-Pedersen and Okamoto $$varSigma $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mi>Σ</mml:mi></mml:math> -protocols as well as a construction that allows for compound (AND and OR) $$varSigma $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mi>Σ</mml:mi></mml:math> -protocols and the Pedersen and Rivest commitment schemes. A highlight of the work is a formalisation of the construction of commitment schemes from $$varSigma $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mi>Σ</mml:mi></mml:math> -protocols (Damgard in Lecture notes, 2002). We formalise this proof at an abstract level using the modularity available in Isabelle/HOL and CryptHOL. This way, the proofs of the instantiations come for free." @default.
• W3086061451 created "2020-09-21" @default.
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• W3086061451 date "2020-09-09" @default.
• W3086061451 modified "2023-10-09" @default.
• W3086061451 title "Formalising $$varSigma $$-Protocols and Commitment Schemes Using CryptHOL" @default.
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• W3086061451 doi "https://doi.org/10.1007/s10817-020-09581-w" @default.
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