How to Solve Millionaires’ Problem with Two Kinds of Cards

Abstract Card-based cryptography, introduced by den Boer aims to realize multiparty computation (MPC) using physical cards. We propose several efficient card-based protocols for the millionaires’ problem introducing a new operation called Private Permutation (PP) instead of shuffle used in most existing cryptography. Shuffle is useful randomization technique exploiting property card shuffling, but it requires strong assumption from viewpoint arithmetic MPC because assumes that public possible. On other hand, private randomness can be PPs, which enables us design taking ideas MPCs into account. Actually, we show Yao’s protocol easily transformed not straightforward shuffles uses randomness. Furthermore, entirely novel and millionaire based on PPs securely updating bitwise comparisons between two numbers, unveil power PPs. As another interest these protocols, point out they have deep connection well-known logical puzzle known as “The fork road.”