Exploiting the Floating-Point Computing Power of GPUs for RSA

• Published in: Information Security pp. 198 - 215
• Main Authors: Zheng, Fangyu, Pan, Wuqiong, Lin, Jingqiang, Jing, Jiwu, Zhao, Yuan
• Format: Book Chapter
• Language: English
• Published: Cham Springer International Publishing 2014
• Series: Lecture Notes in Computer Science
• Subjects: CUDA; Floating-Point; GPU; Montgomery Multiplication; RSA
• ISBN: 9783319132563; 3319132563
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/978-3-319-13257-0_12

Asymmetric cryptographic algorithms (e.g., RSA and ECC) have been implemented on Graphics Processing Units (GPUs) for several years. These implementations mainly exploit the highly parallel GPU architecture and port the integer-based algorithms for common CPUs to GPUs, offering high performance. However, the great potential cryptographic computing power of GPUs, especially by the more powerful floating-point instructions, has not been comprehensively investigated in fact. In this paper, we try to fully exploit the floating-point computing power of GPUs for RSA, by various designs, including the floating-point-based Montgomery multiplication algorithm, the optimization for the fundamental operations and the utilization of the latest thread data sharing instruction shuffle. The experimental result on NVIDIA GTX Titan of 2048-bit RSA decryption reaches a throughput of 38,975 operations per second, achieves 2.21 times performance of the existing fastest integer-based work and outperforms the previous floating-point-based implementation by a large margin.