Comprehensive Guide to BFV Homomorphic Encryption: Architectures for Secure Data Processing 🔒

Fully homomorphic encryption (FHE) is a technique that allows computations on encrypted data without the need for decryption and it provides privacy in various applications such as privacy-preserving cloud computing. In this article, we present two hardware architectures optimized for accelerating the encryption and decryption operations of the Brakerski/Fan-Vercauteren (BFV) homomorphic encryption scheme with high-performance polynomial multipliers. For proof of concept, we utilize our architectures in a hardware/software codesign accelerator framework, in which encryption and decryption operations are offloaded to an FPGA device, while the rest of operations in the BFV scheme are executed in software running on an off-the-shelf desktop computer. Specifically, our accelerator framework is optimized to accelerate Simple Encrypted Arithmetic Library (SEAL), developed by the Cryptography Research Group at Microsoft Research. The hardware part of the proposed framework targets the XILINX VIRTEX7 FPGA device, which communicates with its software part via a peripheral component interconnect express (PCIe) connection. For proof of concept, we implemented our designs targeting 1024- degree polynomials with 8-bit and 32-bit coefficients for plaintext and ciphertext, respectively. The proposed framework achieves almost 12× and 7× latency speedups, including I/O operations for the offloaded encryption and decryption operations, respectively, compared to their pure software implementations.