Public Key Cryptography on Modern Graphics Hardware

Graphics processing units (GPUs) are increasingly being used for general purpose processing. We present implementations of large integer modular exponentiation, the core of public-key cryptosystems such as RSA, on a DirectX 10 compliant GPU. DirectX 10 compliant graphics processors are the latest generation of GPU architecture, which provide increased programming flexibility and support for integer operations. We present high performance modular exponentiation implementations based on integers represented in both standard radix form and residue number system (RNS) form. We show how a GPU implementation of a 1024-bit RSA decrypt primitive can outperform for the first time a comparable CPU implementation by up to 4 times. We present how an adaptive approach to modular exponentiation involving implementations based on both a radix and a residue number system gives the best all-around performance on the GPU. We also highlight the criteria necessary to allow the GPU to improve the performance of public key cryptographic operations.