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Lecture notes in computer science

Necessary and Sufficient Numbers of Cards for Securely Computing Two-Bit Output Functions

Danny Francis, Syarifah Ruqayyah Aljunid, Takuya Nishida, Yu‐ichi Hayashi, Takaaki Mizuki, Hideaki Sone

Published Jan 1, 2017• 16 citations
Publisher
DOI
10.1007/978-3-319-61273-7_10

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Secure computation is a cryptographic primitive that enables mutually distrustful parties to jointly realize a possibly randomized functionality in a secure manner. Card-based secure computation studies the problem of implementing secure computation protocols visually by using physical cards, to help non-experts understand their mechanisms. Although many card-based secure computation protocols have been proposed, most of them focus on deterministic functionalities and only a few protocols for randomized functionalities are tailored to specific applications. In this work, we initiate the study of card-based protocols for generating uniformly random bits, which is the most fundamental randomized functionality in secure computation. We present four constructions of such protocols differing in the types of shuffles they use. We also show a lower-bound result that the number of shuffles required for protocols using complete shuffles must be at least the number of output bits. Furthermore, we demonstrate that our protocols for generating uniformly random bits can be extended to those for generating possibly non-uniform random numbers, when combined with existing card-based protocols for computing deterministic functions.