Secure computation protocols using polarizing cards

Kazumasa Shinagawa, Takaaki Mizuki, Jacob C.N. Schuldt, Koji Nuida, Naoki Kanayama, Takashi Nishide, Goichiro Hanaoka, Eiji Okamoto

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

It is known that, using just a deck of cards, an arbitrary number of parties with private inputs can securely compute the output of any function of their inputs. In 2009, Mizuki and Sone constructed a six-card COPY protocol, a four-card XOR protocol, and a six-card AND protocol, based on a commonly used encoding scheme in which each input bit is encoded using two cards. However, up until now, there are no known results to construct a set of COPY, XOR, and AND protocols based on a two-card-per-bit encoding scheme, which all can be implemented using only four cards. In this paper, we show that it is possible to construct four-card COPY, XOR, and AND protocols using polarizing plates as cards and a corresponding two-card-per-bit encoding scheme. Our protocols use a minimum number of cards in the setting of two-card-per-bit encoding schemes since four cards are always required to encode the inputs. Moreover, we show that it is possible to construct two-card COPY, two-card XOR, and three-card AND protocols based on a one-card-per-bit encoding scheme using a common reference polarizer which is a polarizing material accessible to all parties.

Original languageEnglish
Pages (from-to)1122-1131
Number of pages10
JournalIEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
VolumeE99A
Issue number6
DOIs
Publication statusPublished - 2016 Jun

Keywords

  • Boolean circuits
  • Card-based protocols
  • Polarizing cards
  • Recreational cryptography
  • Secure computation

ASJC Scopus subject areas

  • Signal Processing
  • Computer Graphics and Computer-Aided Design
  • Electrical and Electronic Engineering
  • Applied Mathematics

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  • Cite this

    Shinagawa, K., Mizuki, T., Schuldt, J. C. N., Nuida, K., Kanayama, N., Nishide, T., Hanaoka, G., & Okamoto, E. (2016). Secure computation protocols using polarizing cards. IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, E99A(6), 1122-1131. https://doi.org/10.1587/transfun.E99.A.1122