Polynomial multiplication is a key component in many post-quantum cryptography and homomorphic encryption schemes. One recurring variation, ternary polynomial multiplication over ring Zq/(xn+1) where one input polynomial has ternary coefficients {−1,0,1} and the other has large integer coefficients {0, q−1}, has recently drawn significant attention from various communities. Following this trend, this paper presents a novel SCALable and area-Efficient Systolic (SCALES) accelerator for ternary polynomial multiplication. In total, we have carried out three layers of coherent interdependent efforts. First, we have rigorously derived a novel block-processing strategy and algorithm based on the schoolbook method for polynomial multiplication. Then, we have innovatively implemented the proposed algorithm as the SCALES accelerator with the help of a number of field-programmable gate array (FPGA)-oriented optimization techniques. Lastly, we have conducted a thorough implementation analysis to showcase the efficiency of the proposed accelerator. The comparison demonstrated that the SCALES accelerator has at least 19.0% and 23.8% less equivalent area-time product (eATP) than the state-of-the-art designs. We hope this work can stimulate continued research in the field.
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Systolic Acceleration of Polynomial Multiplication for KEM Saber and Binary Ring-LWE Post-Quantum Cryptography
Following the rapid progress in the post-quantum cryptography (PQC) field that many efforts have been gradually switched to the hardware implementation side, this paper presents a novel systolic accelerator for polynomial multiplication within two lattice-based PQC algorithms, key encapsulation mechanism (KEM) Saber and binary Ring-Learning-with-Errors (BRLWE)-based encryption scheme. Based on the observation that polynomial multiplication over ring is the key arithmetic operation for the two PQC schemes, we have proposed a novel systolic accelerator for the targeted polynomial multiplications (applicable to two PQC schemes). Mathematical formulation is given to illustrate the proposed algorithmic operation for both schemes. Then, the proposed systolic accelerator is presented. Finally, field-programmable gate array (FPGA) implementation results have been provided to confirm the efficiency of the proposed systolic accelerator under two schemes. The proposed accelerator is highly efficient, and the following work may focus on cryptoprocessor design and side-channel attacks.
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- Award ID(s):
- 2020625
- PAR ID:
- 10358716
- Date Published:
- Journal Name:
- 2022 IEEE International Symposium on Hardware Oriented Security and Trust (HOST)
- Page Range / eLocation ID:
- 157 to 160
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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