Efficient TMVP-Based Polynomial Convolution on GPU for Post-Quantum Cryptography Targeting IoT Applications

Recently proposed lattice-based cryptography algorithms can be used to protect the IoT communication against the threat from quantum computers, but they are computationally heavy. In particular, polynomial convolution is one of the most time-consuming operations in lattice-based cryptography. To achieve efficient implementation, the number theoretic transform (NTT) algorithm is an ideal choice, but it has certain limitations on the parameters, which not all lattice-based schemes can employ directly. Hence, alternative techniques are proposed to accelerate polynomial convolution on lattice-based schemes that cannot utilize the NTT directly. In this article, we propose a parallel Toeplitz matrix-vector product (TMVP) version to accelerate the polynomial convolution in post-quantum cryptography algorithms implemented it on a graphics processing unit (GPU). This is the first time a TMVP parallel version has been proposed and experimented on different GPU cores (i.e., CUDA-cores and Tensor-cores). The effectiveness of the proposed solution is validated on Saber (the National Institute of Standards and Technology post-quantum standardization finalist) and Sable (an improved version of Saber) schemes. Experimental results show that TMVP-based polynomial convolution using CUDA-cores fails to exhibit a significant enhancement compared to the schoolbook CUDA-core method already proposed by Hafeez et al. in 2023. However, when the TMVP technique is applied to Tensor-cores, it outperformed state-of-the-art implementations. The proposed Tensor-core approach outperformed the schoolbook Tensor-core method by up to
$1.21\times $
, and outperformed the dot-product-instructions method (Lee et al. in 2022) by up to
$3.63\times $
. The proposed TMVP Tensor-cores is also faster than the TMVP CUDA-cores method by
$13.76\times $
.