We address one of the weaknesses of the RSA ciphering systems i.e. the existence of the private keys that are relatively easy to compromise by the attacker. The problem can be mitigated by the Internet services providers, but it requires some computational effort. We propose the proof of concept of the GPGPU-accelerated system that can help detect and eliminate users’ weak keys. We have proposed the algorithms and developed the GPU-optimised program code that is now publicly available and substantially outperforms the tested CPU processor. The source code of the OpenSSL library was adapted for GPGPU, and the resulting code can perform both on the GPU and CPU processors. Additionally, we present the solution how to map a triangular grid into the GPU rectangular grid – the basic dilemma in many problems that concern pair-wise analysis for the set of elements. Also, the comparison of two data caching methods on GPGPU leads to the interesting general conclusions. We present the results of the experiments of the performance analysis of the selected algorithms for the various RSA key length, configurations of GPU grid, and size of the tested key set.