Computational Aspects of Lattice-Based Cryptography on Graphical Processing Unit

Abstract

In this chapter, the aim is to discuss computational aspects of lattice-based cryptographic schemes focused on NTRU in view of the time complexity on a graphical processing unit (GPU). Polynomial multiplication algorithms, having a very important role in lattice-based cryptographic schemes, are implemented on the GPU using the compute unified device architecture (CUDA) platform. They are implemented in both serial and parallel way. Compact and efficient implementation architectures of polynomial multiplication for lattice-based cryptographic schemes are presented for the quotient ring both Zp [x]/(xn-1) and Zp [x]/(xn+1), where p is a prime number. Then, by using these implementations the NTRUEncrypt and signature scheme working over Zp [x]/(xn+1) are implemented on the GPU using CUDA platform. Implementation details are also discussed.