Efficient montgomery multiplication on GPUs

Abstract

Public-key cryptosystems and algorithms, including RSA [20], EC and Diffie-Hellman key exchange [5], require efficient large integer arithmetic in finite fields. Contemporary processors are not designed to support such operations in a productive manner, since most of them natively work on 8 to 64 bit word sizes. Thus, an expensive cryptographic accelerator is frequently required to offload the computational burden. In this paper, we focus on a highly parallel architecture which is commonly found in commodity computers, i.e. the Graphical Processing Unit (GPU). Recently, GPUs have known an exponential growth in terms of computing power, becoming a cost-effective option for offloading computationally intensive tasks. This paper describes a parallel implementation of the Montgomery Multiplication, as well as optimizations that enable efficient exploitation of the CUDA GPU architecture.