A Complexity Hierarchy of Shuffles in Card-Based Protocols

TL;DR

This paper introduces a hierarchy of shuffle complexities in card-based cryptography, classifies shuffle operations, and establishes separation results to evaluate protocol complexity.

Contribution

It develops a formal hierarchy of shuffle complexities, proves separation results, and proposes a new measure for evaluating card-based cryptographic protocols.

Findings

Classified shuffle operations into multiple complexity levels.

Proved that certain shuffles cannot be realized with lower-level operations.

Proposed a new complexity measure for protocol evaluation.

Abstract

Card-based cryptography uses physical playing cards to construct protocols for secure multi-party computation. Existing card-based protocols employ various types of shuffles, some of which are easy to implement in practice while others are considerably more complex. In this paper, we classify shuffle operations into several levels according to their implementation complexity. We motivate this hierarchy from both practical and theoretical perspectives, and prove separation results between several levels by showing that certain shuffles cannot be realized using only operations from lower levels. Finally, we propose a new complexity measure for evaluating card-based protocols based on this hierarchy.