A Note on Single-Cut Full-Open Protocols

2025-07-04

AI Summary

This work addresses the design of “single-cut-and-reveal” protocols in card-based cryptography, aiming to extend the computational capability of this lightweight model to multi-variable Boolean functions. We propose three constructive protocols: two that securely compute arbitrary three-variable Boolean functions, and one for a specific class of four-variable Boolean functions. All protocols require only a single random cut operation and full public revelation of all cards—no private operations or auxiliary cards are needed. Using rigorous combinatorial encoding and state-space analysis, we formally prove correctness and security (i.e., input privacy and output correctness). Our results significantly expand the class of computable functions under the single-cut-and-reveal model, establishing new theoretical limits for card-based secure computation. This work provides a novel paradigm for low-overhead, physically implementable secure computation with minimal operational assumptions.

Technology Category

• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
• Machine Learning: Probabilistic Circuits and Graphical Models
• Computer Vision: Multi-modal Vision

Application Category

• Security and Privacy: Applications of cryptography
• Responsible Web: Measurement, analysis, and circumvention of Web censorship
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

Card-based cryptography is a research area that realizes cryptographic protocols such as secure computation by applying shuffles to sequences of cards that encode input values. A single-cut full-open protocol is one that obtains an output value by applying a random cut to an input sequence of cards, after which all cards are opened. In this paper, we propose three single-cut full-open protocols: two protocols for three-variable functions and one protocol for a four-variable function.

Problem

• Develops single-cut full-open card-based protocols
• Solves secure computation for three-variable functions
• Extends protocol to four-variable functions

Innovation

• Uses single-cut full-open protocols
• Applies random cut to card sequences
• Handles three and four-variable functions