Five-Card AND Computations in Committed Format Using Only Uniform Cyclic Shuffles

Abstract In card-based cryptography, designing AND protocols in committed format is a major research topic. The state-of-the-art protocol proposed by Koch, Walzer, and Härtel ASIACRYPT 2015 uses only four cards, which the minimum permissible number. minimality of their relies on somewhat complicated shuffles having non-uniform probabilities possible outcomes. Restricting allowed to uniform closed ones entails that, best our knowledge, six cards are sufficient: six-card Mizuki Sone 2009 utilizes random bisection cut, cyclic (and hence, closed) shuffle. Thus, question has arisen: “Can we improve upon this using shuffles?” other words, existence or otherwise five-card been one most important open questions field. paper, answer affirmatively committed-format shuffles. that use cut both can be easily implemented humans.