Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Card-Based Overwriting Protocol for Equality Function and Applications

Suthee Ruangwises, Tomoki Ono, Yoshiki Abe, Kyosuke Hatsugai, Mitsugu Iwamoto

TL;DR

The paper addresses secure multi-party computation of the $k$-candidate, $n$-variable equality function using card-based protocols. It introduces the overwriting protocol, which uses $\,kn\,$ cards and $n$ shuffles to compute $E:\{0,1,\dots,k-1\\}^n\to\{0,1\}$, achieving improvements over prior $2\lceil\log_2 k\rceil n$-card schemes for many $k$ and eliminating the need for binary input encoding. The authors extend the technique to compute the set function $S$ and set size function $SS$, providing correctness and security proofs for each protocol. The work advances card-based cryptography by delivering concrete, verifiable protocols with reduced resource requirements and clear avenues for future extension to broader $\mathbb{Z}/k\mathbb{Z}$ computations.

Abstract

Research in the area of secure multi-party computation with an unconventional method of using a physical deck of playing cards began in 1989 when den Boer proposed a protocol to compute the logical AND function using five cards. Since then, the area has gained interest from many researchers and several card-based protocols to compute various functions have been developed. In this paper, we propose a card-based protocol called the overwriting protocol that can securely compute the $k$-candidate $n$-variable equality function $f: \{0,1,\ldots ,k-1\}^n \rightarrow \{0,1\}$. We also apply the technique used in this protocol to compute other similar functions.

Card-Based Overwriting Protocol for Equality Function and Applications

TL;DR

The paper addresses secure multi-party computation of the -candidate, -variable equality function using card-based protocols. It introduces the overwriting protocol, which uses cards and shuffles to compute , achieving improvements over prior -card schemes for many and eliminating the need for binary input encoding. The authors extend the technique to compute the set function and set size function , providing correctness and security proofs for each protocol. The work advances card-based cryptography by delivering concrete, verifiable protocols with reduced resource requirements and clear avenues for future extension to broader computations.

Abstract

Research in the area of secure multi-party computation with an unconventional method of using a physical deck of playing cards began in 1989 when den Boer proposed a protocol to compute the logical AND function using five cards. Since then, the area has gained interest from many researchers and several card-based protocols to compute various functions have been developed. In this paper, we propose a card-based protocol called the overwriting protocol that can securely compute the -candidate -variable equality function . We also apply the technique used in this protocol to compute other similar functions.
Paper Structure (21 sections, 3 equations, 3 figures, 2 tables)

This paper contains 21 sections, 3 equations, 3 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Equality Function Protocols
  4. Our Contribution
  5. Preliminaries
  6. Equality Function
  7. Cards
  8. Pile-Scramble Shuffle
  9. Pile-Shifting Shuffle
  10. Protocol for Equality Function
  11. Proofs of Correctness and Security
  12. Proof of Correctness
  13. Proof of Security
  14. Applications to Set and Set Size Functions
  15. Protocol for Set Size Function
  16. ...and 6 more sections

Figures (3)

  • Figure 1: An example of a pile-scramble shuffle on a $5 \times 6$ matrix
  • Figure 2: An example of a pile-shifting shuffle on a $5 \times 6$ matrix
  • Figure 3: An example of a matrix $M$ constructed in Step 1, where $k=6$, $n=5$, $a_1=a_3=a_5=2$, $a_2=3$, and $a_4=0$ (with all cards actually being face-down)