Accelerating Operations on Permutations Using Graphics Processing Units

Abstract

GPUs (graphics processing units) are used in many modern computer systems. They consist of a large number of low-performance computing units that can be used for operations in parallel. In this case, the overall algorithm performance significantly increases compared to the CPU (central processing unit) use. Tests against a brute-force attack of cryptoprotocols that use operations on permutations, such as a three-pass cryptographic protocol, can be performed in parallel for different permutations. Therefore, it is important to determine the ability to use graphics processing units to accelerate operations on permutations. For this, the following tasks have been solved in this study: the most used operations on permutations have been defined; the program code that implements these operations and can use graphics processing units’ hardware has been developed; the performance of different approaches, including computing on CPU and various modes of computing on GPU, has been assessed. The results of the study indicate the effectiveness of using GPU hardware units to accelerate the multiplication of permutations, but if at least 5 such operations are performed simultaneously.