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Card-Based Cryptography Meets Formal Verification

Koch, Alexander; Schrempp, Michael; Kirsten, Michael

Abstract:
Card-based cryptography provides simple and practicable protocols for performing secure multi-party computation (MPC) with just a deck of cards. For the sake of simplicity, this is often done using cards with only two symbols, e.g., ♣ and ♡. Within this paper, we target the setting where all cards carry distinct symbols, catering for use-cases with commonly available standard decks and a weaker indistinguishability assumption. As of yet, the literature provides for only three protocols and no proofs for non-trivial lower bounds on the number of cards. As such complex proofs (handling very large combinatorial state spaces) tend to be involved and error-prone, we propose using formal verification for finding protocols and proving lower bounds. In this paper, we employ the technique of software bounded model checking (SBMC), which reduces the problem to a bounded state space, which is automatically searched exhaustively using a SAT solver as a backend.
Our contribution is twofold: (a) We identify two protocols for converting between different bit encodings with overlapping bases, and then show them to be card-minimal. This completes the picture of tight lower bounds on the number of cards with respect to runtime behavior and shuffle properties of conversion protocols. ... mehr

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Volltext §
DOI: 10.5445/IR/1000120005
Veröffentlicht am 18.11.2020
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Theoretische Informatik (ITI)
Kompetenzzentrum für angewandte Sicherheitstechnologie (KASTEL)
Publikationstyp Forschungsbericht/Preprint
Publikationsdatum 16.09.2019
Sprache Englisch
Identifikator KITopen-ID: 1000120005
Serie Cryptology ePrint Archive ; 2019/1037
Externe Relationen Siehe auch
Schlagwörter secure multiparty computation, card-based cryptography, formal verification, bounded model checking, standard decks
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