Practical and easy-to-understand card-based implementation of Yao’s millionaire protocol

Yao’s millionaire protocol enables Alice and Bob to know whether or not Bob is richer than Alice by using a public-key cryptosystem without revealing the actual amounts of their properties. In this paper, we present a simple and practical implementation of Yao’s millionaire protocol using a deck of playing cards; we straightforwardly implement the idea behind Yao’s millionaire protocol so that even non-experts can easily understand its correctness and secrecy. Our implementation is based partially on the previous card-based scheme proposed by Nakai, Tokushige, Misawa, Iwamoto, and Ohta; their scheme admits players’ private actions on a sequence of cards called Private Permutation (PP), implying that a malicious player could make an active attack (for example, he/she could exchange some of the cards stealthily when doing such a private action). In contrast, our implementation relies on a familiar shuffling operation called a random cut, and hence, it can be conducted completely publicly so as to avoid any active attack.