NTTU: An Area-Efficient Low-Power NTT-Uncoupled Architecture for NTT-Based Multiplication

Large integer multiplication, or large degree polynomial multiplication, is the most time-consuming operation in fully homomorphic encryption (FHE). Low area and power consumption are difficult to maintain while achieving high performance for a large size multiplier. To address this issue, an area-efficient low-power architecture for multiplication, named NTTU, is proposed in this article. First, a combined number theoretic transform (NTT) method consisting of decimation-in-time (DIT) NTT for input in natural order and bit-reversed order is proposed to eliminate the steps of zero padding, scramble, and the first stage in NTT, thereby achieving a reduction of $7N/2$7N/2 clock cycles compared with the single-type NTT method. Second, the NTT-uncoupled architecture is proposed to uncouple the multiplication components, decreasing the storage space for coefficients by 1/2 compared with state-of-the-art designs. Third, a parallel computing architecture based on a crossed memory access scheme is proposed, therein reducing the corresponding execution time by one-half compared with serial execution. Synthesized using 65 nm technology, the proposed architecture can multiply two 1024k/768k integers in 1.7 ms at 500 MHz at a cost of 13.66/7.67 million gates and 726.7/550.2 mW, and a 71.17 percent/30.37 percent area time product (ATP) reduction is achieved compared with the state-of-the-art ASIC designs.