Speeding up the Montgomery Exponentiation with CMM-SDR Over GPU with Maxwell and Pascal Architecture

Abstract

RSA is an algorithm widely used in protecting the key exchange between two parties for secure mobile and wireless communication. Modular exponentiation is the main operation involved in RSA, which is very time consuming when the bit-size is large, usually in the range of 1024-bit to 4096-bit. The speed performance of RSA comes to concerns when thousands or millions of authentication requests are needed to handle by the server at a time, through a massive number of connected mobile and wireless devices. The performance of RSA can be improved by utilizing parallel computing architecture or enhancing existing modular exponentiation algorithm. In this paper, we exploit the massively parallel architecture in GPU to perform RSA computations. Various optimization techniques were proposed in this paper to achieve higher throughput in RSA computation in two GPU platforms. Moreover, we also incorporated signed-digit recoding to further improve the performance. To allow a fair comparison with existing implementation techniques, we proposed to evaluate the speed performance in the best case (least ‘0’ in exponent bits), average case (random exponent bits) and worse case (all ‘1’ in exponent bits). The overall throughput achieved by our implementation is about 12% higher in random exponent bits and 50% higher in all 1’s exponent bits compared to the implementation without signed-digit recoding technique. Our implementation is able to achieve 17713 and 89043 1024-bit modular exponentiation per second on random exponent bits in GTX 960 M and GTX 1080, which represent the two state of the art GPU architecture.