How to Solve Millionaires' Problem with Two Kinds of Cards

Takeshi Nakai, Yuto Misawa, Yuuki Tokushige, Mitsugu Iwamoto, Kazuo Ohta
2021 New generation computing  
AbstractCard-based cryptography, introduced by den Boer aims to realize multiparty computation (MPC) by using physical cards. We propose several efficient card-based protocols for the millionaires' problem by introducing a new operation called Private Permutation (PP) instead of the shuffle used in most of existing card-based cryptography. Shuffle is a useful randomization technique by exploiting the property of card shuffling, but it requires a strong assumption from the viewpoint of
more » ... MPC because shuffle assumes that public randomization is possible. On the other hand, private randomness can be used in PPs, which enables us to design card-based protocols taking ideas of arithmetic MPCs into account. Actually, we show that Yao's millionaires' protocol can be easily transformed into a card-based protocol by using PPs, which is not straightforward by using shuffles because Yao's protocol uses private randomness. Furthermore, we propose entirely novel and efficient card-based millionaire protocols based on PPs by securely updating bitwise comparisons between two numbers, which unveil a power of PPs. As another interest of these protocols, we point out they have a deep connection to the well-known logical puzzle known as "The fork in the road."
doi:10.1007/s00354-020-00118-8 fatcat:s5vlwpbomza7zb7d6il53dqhhy