A Secure Three-Input AND Protocol with a Standard Deck of Minimal Cards

Abstract

Card-based protocols are used to perform cryptographic tasks such as secure multiparty computation using a deck of physical cards. While most of the existing protocols use a two-colored deck consisting of red cards and black cards, Niemi and Renvall in 1999 constructed protocols for securely computing two-input Boolean functions (such as secure logical AND and XOR computations) using a commonly available standard deck of playing cards. Since this initial investigation, two-input protocols with fewer cards and/or shuffles have been designed, and by combining them, one can perform a secure computation of any Boolean circuit. In this paper, we directly construct a simple card-based protocol for the three-input AND computation. Our three-input AND protocol requires fewer cards and shuffles compared to that required when applying any existing two-input AND protocol twice to perform the three-input AND computation. Our protocol is unique in the sense that it is card minimal if we use two cards to encode a single bit.