A Card-Minimal Three-Input AND Protocol Using Two Shuffles

Raimu Isuzugawa, Kodai Toyoda, Yu Sasaki, Daiki Miyahara, Takaaki Mizuki

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

4 Citations (Scopus)


Card-based cryptography typically uses a physical deck comprising black and red cards to perform secure computations, where a one-bit value is encoded using a pair of cards with different colors such that the order of black to red represents 0 and red to black represents 1. One of the most fundamental classes of card-based protocols is the class of “card-minimal” n-input AND protocols, which require 2n face-down cards as input to securely evaluate the AND value after applying a number of shuffles; here, the 2n cards are minimally required to describe an n-bit input. The best n-input AND protocols currently known use two shuffles for n= 2, five shuffles for n= 3, and n+ 1 shuffles for n> 3. These upper bounds on the numbers of shuffles have not been improved for several years. In this work, we present a better upper bound for the n= 3 case by designing a new card-minimal three-input AND protocol using only two shuffles. Therefore, our proposed protocol reduces the number of required shuffles from five to two; we believe that this is a significant improvement.

Original languageEnglish
Title of host publicationComputing and Combinatorics - 27th International Conference, COCOON 2021, Proceedings
EditorsChi-Yeh Chen, Wing-Kai Hon, Ling-Ju Hung, Chia-Wei Lee
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages12
ISBN (Print)9783030895426
Publication statusPublished - 2021
Event27th International Conference on Computing and Combinatorics, COCOON 2021 - Tainan, Taiwan, Province of China
Duration: 2021 Oct 242021 Oct 26

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume13025 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference27th International Conference on Computing and Combinatorics, COCOON 2021
Country/TerritoryTaiwan, Province of China

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)


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