Faster NTRU on ARM Cortex-M4 With TMVP-Based Multiplication

Abstract

This paper focuses on speeding up NTRU - one of the lattice-based finalists of the NIST PQC competition - by improving the ring multiplication. The Number Theoretic Transform (NTT), Toom-Cook, and Karatsuba are the most commonly used algorithms for implementing NTRU. In this paper, we propose Toeplitz matrix-vector product (TMVP) based algorithms for multiplication for all parameter sets of NTRU. We implement the proposed algorithms on ARM Cortex-M4. The results show that the TMVP-based multiplication algorithms we propose are more efficient than the others in the literature in most cases. Our algorithm for <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ntruhps2048509</i> outperform the Toom-Cook and NTT methods in the literature by 25.4% and 21.5%. We also observe the impact of these improvements on the overall performance of NTRU. We speed up the key generation, encryption, decryption, encapsulation, and decapsulation algorithms of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ntruhps2048509</i> by 12.5%, 14.3%, 17.7%, 3.9%, and 14.7%, respectively, compared to state-of-the-art implementation. Moreover, our algorithms require less stack space than the others.