A Complexity Hierarchy of Shuffles in Card-Based Protocols

2026-03-19

AI Summary

This work addresses the disparity in complexity among shuffling operations in card-based cryptography by proposing the first systematic, implementation-complexity-based hierarchical classification framework. Through formal modeling, complexity analysis, and realizability proofs, it rigorously delineates the boundaries of shuffling capabilities across different levels and establishes their mutual non-reducibility. The study not only constructs a clear hierarchy of shuffling operation complexities but also introduces a novel metric for protocol complexity, thereby providing both a theoretical foundation and a practical framework for the design and evaluation of card-based cryptographic protocols.

Technology Category

• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Machine Learning: Probabilistic Circuits and Graphical Models
• Planning, Routing, and Scheduling: Scheduling under Uncertainty

Application Category

• Security and Privacy: Applications of cryptography
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Measurement, analysis, and circumvention of Web censorship

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.

Problem

• card-based cryptography
• shuffle operations
• complexity hierarchy
• secure multi-party computation

Innovation

• card-based cryptography
• shuffle hierarchy
• implementation complexity
• secure multi-party computation
• complexity measure