Barrington Plays Cards: The Complexity of Card-based Protocols

TL;DR

This paper analyzes the computational complexity of card-based protocols for secure two-party computation, classifies a broad class of such protocols, and introduces more efficient input encodings requiring fewer cards.

Contribution

It classifies the complexity of functions computed by card protocols and proposes input encodings that reduce the number of cards needed.

Findings

Classified a large class of card protocols by computational complexity.

Proposed input encodings that use fewer cards than traditional methods.

Enhanced understanding of the efficiency and limitations of card-based secure computation.

Abstract

In this paper we study the computational complexity of functions that have efficient card-based protocols. Card-based protocols were proposed by den Boer [EUROCRYPT '89] as a means for secure two-party computation. Our contribution is two-fold: We classify a large class of protocols with respect to the computational complexity of functions they compute, and we propose other encodings of inputs which require fewer cards than the usual 2-card representation.