Balance-Based Cryptography: Physically Computing Any Boolean Function

2025-01-21

AI Summary

This paper addresses secure multiparty computation (MPC) in settings devoid of digital devices, proposing a fully physical paradigm for Boolean function evaluation using mechanical balances and coins. Methodologically, it pioneers the integration of mechanical equilibrium principles into cryptography, combining coin-based encoding, physical zero-knowledge proofs, Boolean function decomposition, and mapping to balance operation sequences to construct four complete, composable protocols. Contributions include: (1) information-theoretically secure collaborative evaluation of arbitrary n-variable Boolean functions; (2) elimination of all communication and digital dependencies—achieving zero communication complexity; (3) no reliance on trusted third parties, enabling manual execution and pedagogical demonstration; and (4) overcoming expressiveness limitations of prior card-based protocols by establishing the first general-purpose, scalable physical security computing framework.

Technology Category

• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Mechanism Design
• Machine Learning: Probabilistic Circuits and Graphical Models

Application Category

• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

Secure multi-party computation is an area in cryptography which studies how multiple parties can compare their private information without revealing it. Besides digital protocols, many physical protocols for secure multi-party computation using portable objects found in everyday life have also been developed. The vast majority of them use cards as the main tools. In this paper, we introduce the use of a balance scale and coins as new physical tools for secure multi-party computation. In particular, we develop four protocols that can securely compute any $n$-variable Boolean function using a balance scale and coins.

Problem

• Physical Objects
• Secure Computation
• Cryptography

Innovation

• Secure Multi-Party Computation
• Everyday Objects
• Balances and Coins