An efficient and light weight polynomial multiplication for ideal lattice-based cryptography

Abstract

Ring-Learning With Errors (Ring-LWE) based cryptographic schemes such as signature, key exchange, and encryption require polynomial multiplication. This multiplication operation is the most time consuming and computationally rigorous process in Ring-LWE. In order to improve the efficiency of the Ring-LWE based schemes, most of the existing schemes use Fast Fourier Transform (FFT) based polynomial multiplication algorithm. It is known that Discrete Sine Transformation (DST) and Discrete Cosine Transformation (DCT) are faster than the FFT. The combination of DCT and DST is Discrete Trigonometric Transform (DTT). When we generalize DTT in terms of FFT form, it becomes Generalized Discrete Fourier Transform (GDFT). In this paper, we propose two new polynomial multiplication techniques using DTT and GDFT. When we apply circular convolution and skew-circular convolution on DTT or GDFT for the polynomial multiplication, it gives us wrong results. To overcome this issue, we use symmetric convolution operation on DTT and GDFT. We implemented and compared the proposed polynomial multiplication schemes with the current state-of-the-art schemes in terms of computation and communication costs. The implementation results show that the proposed schemes DTT and GDFT perform more efficiently as compared to current state-of-the-art schemes in terms of computation and communication costs.