A Study on Randomness of Sequences Obtained from Piecewise Logistic Map over Integers

We have been studying a design of the pseudo-random number generator by generated sequences with the logistic map over integers. Although it has already been presented that such properties of the generation sequences are good, the range of control parameters that satisfy the properties is not enough wide. To improve this problem, Wang et al. proposed the piecewise logistic map. It is method for increasing the range of control parameters that can generate good sequences for the pseudorandom number generator. However, it is not suitable for computer implementation, because it is defined over real numbers. In this paper, we will propose a piecewise logistic map over integers that uses an integer arithmetic and computers can calculate the map correctly. We will also show some results of numerical experiments for the sequences generated from this map.