Card-Based Protocols Using Regular Polygon Cards

Special Section on Discrete Mathematics and Its Applications

National Institute of Advanced Industrial Science and Technology">Kazumasa SHINAGAWA, Takaaki MIZUKI, Jacob C.N. SCHULDT, Koji NUIDA, Naoki KANAYAMA, Takashi NISHIDE, Goichiro HANAOKA, Eiji OKAMOTO

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Keywords: card-based protocol, regular polygon cards

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2017 Volume E100.A Issue 9 Pages 1900-1909

DOI https://doi.org/10.1587/transfun.E100.A.1900

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Abstract

Cryptographic protocols enable participating parties to compute any function of their inputs without leaking any information beyond the output. A card-based protocol is a cryptographic protocol implemented by physical cards. In this paper, for constructing protocols with small numbers of shuffles, we introduce a new type of cards, regular polygon cards, and a new protocol, oblivious conversion. Using our cards, we construct an addition protocol on non-binary inputs with only one shuffle and two cards. Furthermore, using our oblivious conversion protocol, we construct the first protocol for general functions in which the number of shuffles is linear in the number of inputs.

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