Card-Based Cryptography Meets Formal Verification

Abstract Card-based cryptography provides simple and practicable protocols for performing secure multi-party computation with just a deck of cards. For the sake simplicity, this is often done using cards only two symbols, e.g., $$\clubsuit $$ ♣ $$\heartsuit ♡ . Within paper, we also target setting where all carry distinct catering use-cases commonly available standard decks weaker indistinguishability assumption. As yet, literature three no proofs non-trivial lower bounds on number such complex (handling very large combinatorial state spaces) tend to be involved error-prone, propose formal verification finding proving bounds. In employ technique software bounded model checking (SBMC), which reduces problem space, automatically searched exhaustively SAT solver as backend. Our contribution threefold: (a) identify converting between different bit encodings overlapping bases, then show them card-minimal. This completes picture tight respect runtime behavior shuffle properties conversion protocols. computing AND, that there protocol finite four distinguishable symbols fixed output encoding, give four-card an expected random cuts. (b) We provide general translation framework card- run-minimal (i.e., has run minimal length) additional confidence in apply validate our method and, example, confirm new AND have its shortest (c) extend handle case , run-minimality from literature.