Neural networks following a binary approach applied to the integer prime-factorization problem

Abstract — Nowadays, the integer prime-factorization problem finds its application often in modern cryptography. Artificial Neural Networks (ANNs) have been applied to the integer prime-factorization problem. A composed number N is applied to the ANNs, and one of its prime factors p is obtained as the output. Previously, neural networks dealing with the input and output data in a decimal format have been proposed. However, accuracy is not sufficient. In this paper, a neural network following a binary approach is proposed. The input N as well as the desired output p were expressed in a binary form. The proposed neural network is expected to be more stable, i.e. less sensitive to small errors in the network outputs. Simulations have been performed and the results are compared with the results reported in the previous study. The number of required search times for the true prime number can be well reduced. Furthermore, the probability density function of the training patterns is investigated and the need for different data creation and/or selection techniques is shown. I