sDPF-RSA: Utilizing Floating-point Computing Power of GPUs for Massive Digital Signature Computations

In financial, electronic and other security-sensitive industries, data centers require various protocols and algorithms to secure massive volumes of transactions. It is well known that digital signature is a computationally expensive task and a potential bottleneck that can restrict overall performance. In this paper, we make the following contributions. First, we propose a novel method called sDPF-RSA to accelerate the core algorithm of RSA, Montgomery multiplication, for Graphics Processing Units (GPUs). The sDPF approach takes advantage of the sign bit to increase the amount of information processed with each double precision floating point value and considerably improves performance. Second, we have comprehensively reviewed and tested the algorithms to ensure they all run in constant time. In particular we improve the standard carry resolution algorithm, introducing two constant time parallel techniques. We thus minimize the potential for timing attacks against GPU based RSA crypto-systems. Finally, we propose a full implementation of RSA, optimized for our GPU-accelerated computing platform to maximize its computing power. With protection against timing attacks, the throughputs of RSA-2048/3072/4096 on an NVIDIA GeForce GTX TITAN Black set a record of 52,747/15,179/6,435 (for signature generation) and 1,237,694/584,083/354,139 (for signature verification with public key 65,537) operations per second with modest latency, outperforming the contemporaneous CPU and many-core processor Xeon Phi by 3.9-11 times.