Distribution of the tree parity machine synchronization time

Neural networks’ synchronization by mutual learning discovered and described by Kanter et al. [12] can be used to construct relatively secure cryptographic key exchange protocol in the open channel. This phenomenon based on simple mathematical operations, can be performed fast on a computer. The latter makes it competitive to the currently used cryptographic algorithms. An additional advantage is the easiness in system scaling by adjusting neutral network’s topology, what results in satisfactory level of security [24] despite different attack attempts [12, 15]. With the aid of previous experiments, it turns out that the above synchronization procedure is a stochastic process. Though the time needed to achieve compatible weights vectors in both partner networks depends on their topology, the histograms generated herein render similar distribution patterns. In this paper the simulations and the analysis of synchronizations’ time are performed to test whether these histograms comply with histograms of a particular well-known statistical distribution. As verified in this work, indeed they coincide with Poisson distribution. The corresponding parameters of the empirically established Poisson distribution are also estimated in this work. Evidently the calculation of such parameters permits to assess the probability of achieving both networks’ synchronization in a given time only upon resorting to the generated distribution tables. Thus, there is no necessity of redoing again time-consuming computer simulations.