Paper 2025/048

ABLE: Optimizing Mixed Arithmetic and Boolean Garbled Circuit

Abstract

Privacy and security have become critical priorities in many scenarios. Privacy-preserving computation (PPC) is a powerful solution that allows functions to be computed directly on encrypted data. Garbled circuit (GC) is a key PPC technology that enables secure, confidential computing. GC comes in two forms: Boolean GC supports all operations by expressing functions as logic circuits; arithmetic GC is a newer technique to efficiently compute a set of arithmetic operations like addition and multiplication. Mixed GC combines both Boolean and arithmetic GC, in an attempt to optimize performance by computing each function in its most natural form. However, this introduces additional costly conversions between the two forms and it remains unclear if and when the efficiency gains of arithmetic GC outweigh these conversion costs. In this paper, we present Arithmetic Boolean Logic Exchange for Garbled Circuit, the first real implementation of mixed GC. ABLE profiles the performance of Boolean and arithmetic GC operations along with their conversions. We assess not only communication but also computation latency, a crucial factor in evaluating the end-to-end runtime of GC. Based on these insights, we propose a method to determine whether it is more efficient to use general Boolean GC or mixed GC for a given application. Rather than implementing both approaches to identify the better solution for each unique case, our method enables users to select the most suitable GC realization early in the design process. This method evaluates whether the benefits of transitioning operations from Boolean to arithmetic GC offset the associated conversion costs. We apply this approach to a neural network task as a case study. We propose an optimization to reduce the number of primes in arithmetic GC, cutting communication and compute latency by up to 14.1% and 15.7%, respectively. Additionally, we optimize mixed GC conversions with a row reduction technique, achieving a 48.6%reduction in garbled table size for bit-decomposition and a 50%reduction for bit-composition operation. Our code is open-sourced for community use.