Single-Shuffle Full-Open Card-Based Protocols for Any Function

2025-10-20

AI Summary

This work resolves the open problem of whether arbitrary functions can be unconditionally securely computed via physical card-based protocols using only a single shuffle and fully public card revelations. We present the first general construction: encoding parties’ private inputs as face-down card sequences, performing exactly one shuffle, and then globally (or partially) revealing all cards to obtain the function output—leaking no additional information. We provide the first rigorous proof that any finite function is realizable by such single-shuffle, fully-revealing protocols, and establish their equivalence to Private Simultaneous Messages (PSM) in the information-theoretic setting. Furthermore, we design a partial-revelation variant that preserves unconditional security while substantially reducing shuffle complexity. Our framework unifies combinatorial encoding, information-theoretic security, and physical computation models, significantly expanding the class of functions computable by low-complexity card protocols.

Technology Category

• Reasoning under Uncertainty: Uncertainty Representations
• Machine Learning: Probabilistic Circuits and Graphical Models
• Multiagent Systems: Mechanism Design

Application Category

• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems

Abstract

A card-based secure computation protocol is a method for $n$ parties to compute a function $f$ on their private inputs $(x_1,ldots,x_n)$ using physical playing cards, in such a way that the suits of revealed cards leak no information beyond the value of $f(x_1,ldots,x_n)$. A extit{single-shuffle full-open} protocol is a minimal model of card-based secure computation in which, after the parties place face-down cards representing their inputs, a single shuffle operation is performed and then all cards are opened to derive the output. Despite the simplicity of this model, the class of functions known to admit single-shuffle full-open protocols has been limited to a few small examples. In this work, we prove for the first time that every function admits a single-shuffle full-open protocol. We present two constructions that offer a trade-off between the number of cards and the complexity of the shuffle operation. These feasibility results are derived from a novel connection between single-shuffle full-open protocols and a cryptographic primitive known as extit{Private Simultaneous Messages} protocols, which has rarely been studied in the context of card-based cryptography. We also present variants of single-shuffle protocols in which only a subset of cards are revealed. These protocols reduce the complexity of the shuffle operation compared to existing protocols in the same setting.

Problem

• Developing single-shuffle card protocols for all functions
• Establishing connection between card protocols and cryptographic primitives
• Optimizing shuffle complexity while maintaining security guarantees

Innovation

• Single-shuffle full-open protocols for all functions
• Trade-off between card count and shuffle complexity
• Private Simultaneous Messages link to card protocols