Balance-Based Cryptography: Physically Computing Any Boolean Function

TL;DR

This paper introduces a novel physical cryptographic method using a balance scale and coins to securely compute any Boolean function among multiple parties, expanding the toolkit beyond traditional digital protocols.

Contribution

It presents four new protocols that enable secure multi-party computation of any Boolean function using only physical objects like a balance scale and coins.

Findings

Protocols securely compute any Boolean function

Physical approach offers an alternative to digital cryptography

Extends physical cryptographic tools to complex functions

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.