How to Implement a Non-uniform or Non-closed Shuffle

Takahiro Saito, Daiki Miyahara, Yuta Abe, Takaaki Mizuki, Hiroki Shizuya

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

3 Citations (Scopus)


Card-based protocols allow to perform secure multiparty computations using a deck of physical cards, and rely on shuffle actions such as the (normal) shuffle, the random cut, and the random bisection cut. A shuffle action is mathematically defined by a pair of a permutation set (which is a subset of the symmetric group) and a probability distribution on it; while one can theoretically consider any shuffle action in mind, he or she may be unable to determine whether it can be easily implemented by human hands. As one of the most general results, Koch and Walzer showed that any uniform closed shuffle (meaning that its permutation set is a subgroup and its distribution is uniform) can be implemented by human hands with the help of additional cards. However, there are several existing protocols which use non-uniform and/or non-closed shuffles. To implement these specific shuffles, Nishimura et al. proposed an idea of using (special) physical cases that can store piles of cards as well as Koch and Walzer proposed an implementation of a specific non-closed shuffle with additional cards. Because their implementations handle a limited class of non-uniform and/or non-closed shuffles, it is still open to find a general method for implementing any shuffle. In this paper, we solve the above problem; we implement “any” shuffle with only additional cards, provided that every probability of its distribution is a rational number. Therefore, our implementation works for any non-closed or non-uniform shuffle (if the distribution is rational as above).

Original languageEnglish
Title of host publicationTheory and Practice of Natural Computing - 9th International Conference, TPNC 2020, Proceedings
EditorsCarlos Martín-Vide, Miguel A. Vega-Rodríguez, Miin-Shen Yang
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages12
ISBN (Print)9783030629991
Publication statusPublished - 2020
Event9th International Conference on Theory and Practice of Natural Computing, TPNC 2020 - Taoyuan, Taiwan, Province of China
Duration: 2020 Dec 72020 Dec 9

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume12494 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference9th International Conference on Theory and Practice of Natural Computing, TPNC 2020
Country/TerritoryTaiwan, Province of China


  • Card-based protocols
  • Cryptography
  • Implementation of shuffle
  • Unconventional computation


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