Paper 2017/425

Card-Based Protocols Using Unequal Division Shuffle

Akihiro Nishimura and Takuya Nishida and Yu-ichi Hayashi and Takaaki Mizuki and Hideaki Sone

Abstract

Card-based cryptographic protocols can perform secure computation of Boolean functions. Cheung et al. presented an elegant protocol that securely produces a hidden AND value using five cards; however, it fails with a probability of 1/2. The protocol uses an unconventional shuffle operation called unequal division shuffle; after a sequence of five cards is divided into a two-card portion and a three-card portion, these two portions are randomly switched. In this paper, we first show that the protocol proposed by Cheung et al. securely produces not only a hidden AND value but also a hidden OR value (with a probability of 1/2). We then modify their protocol such that, even when it fails, we can still evaluate the AND value. Furthermore, we present two five-card copy protocols using unequal division shuffle. Because the most efficient copy protocol currently known requires six cards, our new protocols improve upon the existing results. We also design a general copy protocol that produces multiple copies using unequal division shuffle.