Card-based protocols for secure ranking computations

Ken Takashima, Yuta Abe, Tatsuya Sasaki, Daiki Miyahara, Kazumasa Shinagawa, Takaaki Mizuki, Hideaki Sone

Research output: Contribution to journalArticlepeer-review

16 Citations (Scopus)


Consider a group of people who want to know the “rich list” among them, namely the ranking in terms of their total assets, without revealing any information about the actual value of their assets. This can be achieved by a “secure ranking computation,” which was first considered by Jiang and Gong (2006) [2]; they constructed a secure ranking computation protocol based on a public-key cryptosystem. In this paper, instead of using a public-key cryptosystem, we use a deck of physical cards to provide secure ranking computation protocols. Therefore, our card-based protocols do not rely on computers, and they are simple and easy for humans to implement. Specifically, we design four protocols considering tradeoffs between the number of cards and the number of shuffles required to execute the protocols. We also present a guide to choose an appropriate protocol according to the number of people participating in the protocol and the size of the input range. To be precise, whereas our protocols make all players know the rich list, the Jiang–Gong scheme makes each player know his/her rank only; to achieve the same task (as the Jiang–Gong scheme) using a deck of cards is an intriguing open problem.

Original languageEnglish
Pages (from-to)122-135
Number of pages14
JournalTheoretical Computer Science
Publication statusPublished - 2020 Dec 12


  • Card-based protocols
  • Deck of cards
  • Secure multi-party computations
  • Secure ranking computation
  • Yao's millionaire protocol


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