FHEDA: Efficient Circuit Synthesis with Reduced Bootstrapping for Torus FHE

Fully Homomorphic Encryption (FHE) schemes are widely used cryptographic primitives for performing arbitrary computations on encrypted data. However, FHE incorporates a computationally intensive mechanism called bootstrapping, that resets the noise in the ciphertext to a lower level allowing the computation on circuits of arbitrary depth. This process can take significant time, ranging from several minutes to hours. To address the above issue, in this work, we propose an Electronic Design Automation (EDA) framework
$\mathsf{FHEDA}$
that generates efficient Boolean representations of circuits compatible with the Torus-FHE (ASIACRYPT 2020) scheme. To the best of our knowledge, this is the first work in the EDA domain of FHE. We integrate logic synthesis and gate optimization techniques into our
$\mathsf{FHEDA}$
framework for reducing the total number of bootstrapping operations in a Boolean circuit, which leads to a significant (up to 50%) reduction in homomorphic computation time. Our
$\mathsf{FHEDA}$
is built upon the observation that in Torus-FHE two consecutive Boolean gate evaluations over fresh encryptions require only one bootstrapping instead of two, based on appropriate parameter choices. By integrating this observation with logic replacement techniques into
$\mathsf{FHEDA}$
, we could reduce the total number of bootstrapping operations along with the circuit depth. This eventually reduces the homomorphic evaluation time of Boolean circuits. In order to verify the efficacy of our approach, we assess the performance of the proposed EDA flow on a diverse set of representative benchmarks including privacy-preserving machine learning and different symmetric key block ciphers.