A loop structure optimization targeting high-level synthesis of fast number theoretic transform

Multiplication with a large number of digits is heavily used when processing data encrypted by a fully homomorphic encryption, which is a bottleneck in computation time. An algorithm utilizing fast number theoretic transform (FNTT) is known as a high-speed multiplication algorithm and the further speeding up is expected by implementing the FNTT process on an FPGA. A high-level synthesis tool enables efficient hardware implementation even for FNTT with a large number of points. In this paper, we propose a methodology for optimizing the loop structure included in a software description of FNTT so that the performance of the synthesized FNTT processor can be maximized. The loop structure optimization is considered in terms of loop flattening and trip count reduction. We implement a 65,536-point FNTT processor with the loop structure optimization on an FPGA, and demonstrate that it can be executed 6.9 times faster than the execution on a CPU.