AND Protocols Using Only Uniform Shuffles

TL;DR

This paper introduces two card-based secure multi-party computation protocols for Boolean AND operations that exclusively use uniform shuffles, optimizing for minimal card use and finite runtime.

Contribution

It presents the first known protocols for AND computation with only uniform shuffles, requiring four and five cards respectively, with one being restart-free.

Findings

First protocol uses 4 cards, is restart-free, and has finite expected runtime.

Second protocol uses 5 cards and always terminates in finite time.

Both protocols operate under shuffle restrictions to enhance security and efficiency.

Abstract

Secure multi-party computation using a deck of playing cards has been a subject of research since the "five-card trick" introduced by den Boer in 1989. One of the main problems in card-based cryptography is to design committed-format protocols to compute a Boolean AND operation subject to different runtime and shuffle restrictions by using as few cards as possible. In this paper, we introduce two AND protocols that use only uniform shuffles. The first one requires four cards and is a restart-free Las Vegas protocol with finite expected runtime. The second one requires five cards and always terminates in finite time.