Paper 2024/1204

A fast heuristic for mapping Boolean circuits to functional bootstrapping

Abstract

Functional bootstrapping in FHE schemes such as FHEW and TFHE allows the evaluation of a function on an encrypted message, in addition to noise reduction. Implementing programs that directly use functional bootstrapping is challenging and error-prone. In this paper, we propose a heuristic that automatically maps Boolean circuits to functional bootstrapping instructions. Unlike other approaches, our method does not limit the encrypted data plaintext space to a power-of-two size, allowing the instantiation of functional bootstrapping with smaller parameters. Furthermore, the negacyclic property of functional bootstrapping is exploited to extend the plaintext space. Despite the inherently greedy nature of the heuristic, experimental results show that the mapped circuits exhibit a significant reduction in evaluation time. Furthermore, our heuristic was able to achieve a $45\%$ improvement in evaluation time when applied to manually implemented Trivium and Kreyvium circuits.