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Novel Schoolbook-Originated Polynomial Multiplication Accelerators for NTRUbased PQC

April 12, 2024


Jiafeng Xie - Villanova University


NTRU (Number Theory Research Unit)-based postquantum cryptography (PQC) has recently drawn significant attention from the research communities, e.g., the National Institute of Standards and Technology (NIST) PQC standardization process selected algorithm FALCON. As the recent trend in the field has gradually switched to the hardware implementation side, efficient accelerator design for polynomial multiplication (one of the critical components) within NTRU-based PQC is becoming ever more important. Traditionally, the commonly used method for NTRU-based PQC, e.g., FALCON, is the number theoretic transform (NTT). In this paper, however, we have presented an alternative method, i.e., 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 basic version and then through a Toeplitz matrix-vector product (TMVP)-based approach. In total, we have carried out four layers of coherent & interdependent efforts: (i) we have proposed a novel lookup table (LUT)-based point-wise multiplier along with a related modular reduction technique to obtain optimal implementation; (ii) we have then introduced a new hardware accelerator architecture for the targeted polynomial multiplication, deploying the proposed pointwise multiplier design; (iii) we have also extended the proposed architecture to a TMVP-based polynomial multiplication accelerator; (iv) thorough implementation and comparison have shown the efficiency of the proposed accelerators. e.g., they have even better area-time complexities than the existing NTT-based designs (for n = 512). The proposed design strategy is also extended to another NTRU-based scheme (the NIST third-round PQC standardization candidate, NTRU) and other schoolbook- and Toom-Cook-based polynomial multiplications used in other PQC schemes, and the same superior performance is again obtained. We hope the outcome of this research can impact the ongoing NIST PQC standardization process and related full-hardware implementation work for schemes like FALCON.

Presented at

5th PQC Standardization Conference (2024) [in-person]

Event Details


    The NIST PQC conference will be held at the:
    Hilton Washington DC/Rockville Hotel
    1750 Rockville Pike
    Rockville, MD 20852

Related Topics

Security and Privacy: post-quantum cryptography

Created April 11, 2024, Updated April 15, 2024