Balance-Based Cryptography: Physically Computing Any Boolean Function

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 unconventional protocols for secure multi-party computation using physical objects have also been developed. The vast majority of them use playing cards as the main tools. In 2024, Kaneko et al. introduced the use of a balance scale and coins in zero-knowledge proof protocols for pencil puzzles. In this paper, we extend the use of these tools to 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.