Quantum computers are imminent threat to secure signal processing because they can break the contemporary public-key cryptography schemes in polynomial time. Ring learning with error (RLWE) lattice-based cryptography (LBC) is considered as the most versatile and efficient family of post-quantum cryptography (PQC). Polynomial multiplication is the most compute-intensive routine in the RLWE schemes. Convolutions and Number Theoretic Transform (NTT) are two common methods to perform the polynomial multiplication. In this paper, we explore the energy efficiency of different polynomial multipliers, NTT-based and convolution-based, on GPU and FPGA. When synthesized on a Zynq UltraScale+ FPGA, our NTT-based and convolution-based designs achieve on average 5.1x and 22.5x speedup over state-of-the-art. Our convolution-based design, on a Zynq UltraScale+ FPGA, can generate more than 2x signatures per second by CRYSTALS-Dilithium. The designed NTT-based multiplier on NVIDIA Jetson TX2 is 1.2x and 2x faster than our baseline NTT-based multiplier on FPGA for polynomial degrees of 512 and 1024, respectively. Our explorations and guidelines can help designers choose proper implementations to realize quantum-resistant signal processing.

量子计算机即将对安全的信号处理构成威胁，因为它们可以在多项式时间内破坏当代的公共密钥加密方案。带有错误的环学习（RLWE）基于晶格的密码学（LBC）被认为是功能最齐全，效率最高的后量子密码学（PQC）系列。多项式乘法是RLWE方案中计算量最大的例程。卷积和数论变换（NTT）是执行多项式乘法的两种常用方法。在本文中，我们将探讨不同的多项式乘法的能源效率，NTT为基础，并基于卷积，在GPU和FPGA。当在ZYNQ的UltraScale + FPGA合成，我们的NTT基础和卷积为主与最新技术相比，这些设计的平均速度提高了5.1倍和22.5倍。我们在Zynq UltraScale + FPGA上进行的基于卷积的设计每秒可以产生超过2x的CRYSTALS-Dilithium签名。NVIDIA Jetson TX2上设计的基于NTT的乘法器分别比我们的基准上基于FPGA的基于NTT的乘法器快1.2倍和2倍，分别针对512和1024的多项式。我们的探索和指南可以帮助设计人员选择适当的实现方式，以实现抗量子信号处理。