Balance-Based Cryptography: Physically Computing Any Boolean Function

TL;DR

This work extends secure multi-party computation (MPC) into a physical regime by introducing a balance-scale and coin-based model to securely compute any $n$-variable Boolean function. It develops four protocols: one for AND, one for any threshold function, one for any symmetric function, and one for any Boolean function via Boole expansion, all while using only two coin weights and random shuffles to preserve security. The authors provide concrete resource insights and optimization strategies, including complementing function targets to reduce resources and leveraging Boole expansion to construct general-purpose protocols. This physical MPC framework offers a practical, verifiable approach that can be understood and demonstrated without digital computation, with implications for education and real-world secure computation experiments.

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.

Figures (1)

• Figure 1: Examples of a balance scale and coins (left) and bags (right) used in our protocols