SCOPE: Schoolbook-Originated Novel Polynomial Multiplication Accelerators for NTRU-Based PQC

The Nth-degree truncated polynomial ring units (NTRUs)-based postquantum cryptography (PQC) has drawn significant attention from the research communities, e.g., the National Institute of Standards and Technology (NIST) PQC standardization process selected algorithm Fast Fourier lattice-based compact (Falcon). Following the research trend, efficient hardware accelerator design for polynomial multiplication (an important component of the NTRU-based PQC) is crucial. Unlike the commonly used number theoretic transform (NTT) method, in this article, we have presented a novel SChoolbook-Originated Polynomial multiplication accElerators (SCOPE) design framework. Overall, we have proposed the schoolbook-based method in an innovative format to implement the targeted polynomial multiplication, first through a schoolbook-variant version and then through a Toeplitz matrix-vector product (TMVP)-based approach. Four layers of coherent and interdependent efforts have been carried out: 1) a novel lookup table (LUT)-based point-wise multiplier is proposed along with a related modular reduction technique to obtain optimal implementation; 2) a new hardware accelerator is introduced for the targeted polynomial multiplication, deploying the proposed point-wise multiplier; 3) the proposed architecture is extended to a TMVP-based polynomial multiplication accelerator; and 4) the efficiency of the proposed accelerators is demonstrated through implementation and comparison. Finally, the proposed design strategy is also extended to another NTRU-based scheme and other schoolbook- and toom-cook-based polynomial multiplications (used in other PQC), and obtains the same superior performance. We hope that the outcome of this research can impact the ongoing NIST PQC standardization process and related full-hardware implementation work for schemes like Falcon.