Studying OpenCL-based Number Theoretic Transform for heterogeneous platforms

Lattice based cryptography can be considered a candidate alternative for post-quantum cryptosystems offering key exchange, digital signature and encryption functionality. Number Theoretic Transform (NTT) can be utilized to achieve better performance for these functionalities, where polynomials are needed to be multiplied. NTT simplifies the multiplication overhead allowing point-wise multiplication by transforming the polynomials into the spectral domain and then inversing the result to the original domain. It is important to optimize this technique that is used in a wide range of computing systems. In this paper we study the feasibility of using OpenCL, a portable framework, to implement a parallelized version of NTT which allows deployment on heterogeneous platforms, such as Graphic Processing Units (GPUs) and Field Programmable Gate Arrays (FPGAs). We measure the performance of our implementation on a GPU and evaluate when and where such a deployment is beneficial. Our results showed that the proposed parallel implementation is a viable acceleration approach for these algorithms for lattice-based cryptography solutions.