Accelerating N-Bit Operations over TFHE on Commodity CPU-FPGA

TFHE is a fully homomorphic encryption (FHE) scheme that evaluates Boolean gates, which we will hereafter call Tgates, over encrypted data. TFHE is considered to have higher expressive power than many existing schemes in that it is able to compute not only N-bit Arithmetic operations but also Logical/Relational ones as arbitrary ALR operations can be represented by Tgate circuits. Despite such strength, TFHE has a weakness that like all other schemes, it suffers from colossal computational overhead. Incessant efforts to reduce the overhead have been made by exploiting the inherent parallelism of FHE operations on ciphertexts. Unlike other FHE schemes, the parallelism of TFHE can be decomposed into multilayers: one inside each FHE operation (equivalent to a single Tgate) and the other between Tgates. Unfortunately, previous works focused only on exploiting the parallelism inside Tgate. However, as each N-bit operation over TFHE corresponds to a Tgate circuit constructed from multiple Tgates, it is also necessary to utilize the parallelism between Tgates for optimizing an entire operation. This paper proposes an acceleration technique to maximize performance of a TFHE N-bit operation by simultaneously utilizing both parallelism comprising the operation. To fully profit from both layers of parallelism, we have implemented our technique on a commodity CPU-FPGA hybrid machine with parallel execution capabilities in hardware. Our implementation outperforms prior ones by 2.43× in throughput and 12.19× in throughput per watt when performing N-bit operations under the 128-bit quantum security parameters.