International Association
for Cryptologic Research

Fully homomorphic encryption (FHE) enables secure data processing without compromising data access, but its computational cost and slower execution compared to plaintext operations pose challenges. The growing interest in FHE-based secure computation necessitates the acceleration of homomorphic computations. While existing research primarily targets the reduction of the multiplicative depth (MD) of homomorphic circuits, this paper addresses the trade-off between MD reduction and the increase in multiplicative complexity (MC), a critical gap often overlooked during circuit optimization and potentially resulting in suboptimal outcomes. Three contributions are presented: (a) an exact synthesis paradigm for optimal homomorphic circuit implementations, (b) an efficient heuristic algorithm named MC-aware MD minimization, and (c) a homomorphic circuit optimization flow combining MC-aware MD minimization with existing MD reduction techniques. Experimental results demonstrate a 21.32% average reduction in homomorphic computation time and showcase significantly improved efficiency in circuit optimization.