Using Five Cards to Encode Each Integer in $\mathbb{Z}/6\mathbb{Z}$

Abstract

Research in secure multi-party computation using a deck of playing cards, often called card-based cryptography, dates back to 1989 when Den Boer introduced the "five-card trick" to compute the logical AND function. Since then, many protocols to compute different functions have been developed. In this paper, we propose a new encoding scheme that uses five cards to encode each integer in $\mathbb{Z}/6\mathbb{Z}$. Using this encoding scheme, we develop protocols that can copy a commitment with 13 cards, add two integers with 10 cards, and multiply two integers with 14 cards. All of our protocols are the currently best known protocols in terms of the required number of cards. Our encoding scheme can be generalized to encode integers in $\mathbb{Z}/n\mathbb{Z}$ for other values of $n$ as well.

arXiv commentThis paper has appeared at SecITC 2021

References in corpus (5)

• Physical Zero-Knowledge Proof for Numberlink Puzzle and $k$ Vertex-Disjoint Paths Problem
• Securely Computing the $n$-Variable Equality Function with $2n$ Cards
• Physical ZKP for Connected Spanning Subgraph: Applications to Bridges Puzzle and Other Problems
• Physical Zero-Knowledge Proof for Ripple Effect
• AND Protocols Using Only Uniform Shuffles