A design guide of renewal of a parameter of the logistic map over integers on pseudorandom number generator

A purpose of our research is to provide a design of a pseudorandom number generator with the logistic map over integers. In the presented paper, we will discuss an influence of a control parameter on outputs generated by the logistic map. Additionally, this result will give a design guide about an interval of a bit extraction from values by the logistic map. Concretely, we will analyze experimentally a rate that two mapping values for different parameters differ from each other on the logistic map over integers, and will show theoretically a probability that the maps for different parameters output different values. Based on these results, we will obtain the number of iteration that for an initial value different mapped values appear in iterative mapping with different parameters.