Exploring Energy Efficient Quantum-Resistant Signal Processing Using Array Processors

Quantum computers threaten to compromise public-key cryptography which poses an imminent threat to secure signal processing. The cryptography community has responded with the development and standardization of post-quantum cryptography (PQC) algorithms. Ring learning with error (RLWE) lattice-based cryptographic (LBC) protocols are one of the most promising families of PQC schemes. Two common methods to compute polynomial multiplication, the most compute-intensive routine in RLWE schemes, are convolutions and Number Theoretic Transform (NTT). In this work, we explore the energy efficiency of polynomial multiplier using systolic architecture for the first time. We design two high-throughput systolic array polynomial multipliers, including NTT-based and convolution-based, and compare with our low-cost sequential (non-systolic) NTT-based multiplier. Our sequential NTT-based multiplier achieves more than 3x speedup over the state-of-the-art FGPA implementation of the polynomial multiplier in the NewHope-Simple key exchange mechanism on a low-cost Artix7 FPGA. When synthesized on a Zynq UltraScale+ FPGA, the NTT-based and convolution-based systolic designs achieve on average 1.7x and 7.5x speedup over our sequential NTT-based multiplier respectively, which leads to generating over 2x more signatures per second by CRYSTALS-Dilithium, a PQC digital signature scheme. These explorations help designers select the right PQC implementations for making future signal processing applications quantum-resistant.