Low-Latency Preprocessing Architecture for Residue Number System via Flexible Barrett Reduction for Homomorphic Encryption

Data privacy has become a significant concern due to the rapid development of cloud services, Internet of Things, edge devices, and other applications. Homomorphic encryption (HE) addresses the issue by enabling computations to be performed without the decryption of the encrypted message. However, the bottleneck of designing homomorphic encryption hardware is the complexity of computation. To tackle the long integer arithmetic, the residue number system based on the Chinese remainder theorem is used. In this paper, we propose a novel modular reduction architecture that computes the mapping of residual polynomials in parallel with high speed and low latency. We implement our proposed design in the Xilinx Ultrascale+ FPGA board (VCU118). When the input sizes are 360-bit (1440-bit), the frequency is 180MHz (168MHz) with 4 pipelining stages. Also, the area delay product (ADP) of DSP blocks of our design is reduced by 23 and 31 percent, respectively, for 360 and 1440 bits, compared to prior work.