Currently, the most popular public-key cryptosystem is still RSA. It is even though more sophisticated and secure systems are available (including quantum-resistant ones). It is probably due to the relative simplicity of the algorithm, long history and general technical support. On the other hand, considering the advancement in quantum computers development and programmable hardware, the security of this cryptosystem is becoming more and more questionable.

During the last few years, we could see a revolution in entering passwords into online services (e-shops, email providers, social networks etc.). This revolution ensued in a surge of forgotten passwords. More and more users forget passwords just after entering them, leading to an increasing number of toolkits for storing passwords where each has its vulnerabilities.

The Xilinx Zynq-7000 SoC provides new possibilities for increasing the efficiency of cryptanalysis methods for the public-key systems such as RSA or Diffie-Hellman key exchange algorithm. These cryptosystems are based on the discrete logarithm and integer factorization problem. After a brief introduction to numerical methods for solving these problems, there is an introduction to the distributed system that aims to solve these problems.