Secure multi-party computation using polarizing cards

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

Research output: Chapter in Book/Report/Conference proceedingConference contribution

12 Citations (Scopus)


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, it has remained an open problem to construct a set of COPY, XOR, and AND protocols based on a two-cards-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-cards-per-bit encoding scheme. Our protocols are optimal in the setting of two-cardsper- bit encoding schemes since four cards are always required to encode the inputs. As applications of our protocols, we show constructions of optimal input-preserving XOR and AND protocols, which we combine to obtain optimal half-adder, full-adder, voting protocols, and more.

Original languageEnglish
Title of host publicationAdvances in Information and Computer Security - 10th International Workshop on Security, IWSEC 2015, Proceedings
EditorsKeisuke Tanaka, Yuji Suga
PublisherSpringer Verlag
Number of pages17
ISBN (Print)9783319224244
Publication statusPublished - 2015
Externally publishedYes
Event10th International Workshop on Security, IWSEC 2015 - Nara, Japan
Duration: Aug 26 2015Aug 28 2015

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference10th International Workshop on Security, IWSEC 2015

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • General Computer Science


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