Committed AND protocol using three cards with more handy shuffle

Kazumasa Shinagawa, Koji Nuida, Takashi Nishide, Goichiro Hanaoka, Eiji Okamoto

Abstract: A card-based protocol enables parties to securely compute a desired function by using physical cards instead of computer devices. Most of the previous works have aimed to achieve protocols with a smaller number of cards for elementary functions (e.g., AND/XOR/COPY). Mizuki and Shizuya's protocols achieve the smallest numbers of cards among the existing protocols. Their XOR and COPY protocols can be done easily, however, their AND protocol does not have an easy physical implementation due to the complicated underlying shuffle. We propose a new shuffle, tornado shuffle, which has an easy physical implementation and is also sufficient to construct three-card AND protocol.