Generation of perfect random sequences using tailored chaotic maps

Abstract

In this paper, it was intended to investigate the possibility of generating a random chaotic sequence, having a uniform histogram, using a chaotic sequence matching a given histogram and a chaotic sequence matching the complement of this histogram. To study the relation between these two sequences three methods are used to determine the complement of the histogram. Then based on the chaotic map tailoring synthesis method, the given histogram and a chosen starting point are used to generate the first chaotic sequence of a length L. The same procedure is repeated with the complement histogram to generate the second chaotic sequence of same length L. Histograms are computed for each of the sequences. The two generated chaotic sequences are then combined through simple interleaving resulting in a third sequence of length 2L whose histogram is then determined. The process is repeated for the two methods used to determine the complement histogram. Unlike expected, the third sequence histogram is not a uniform one. In the third method, to obtain a sequence having uniform histogram, it is found necessary to combine, through simple concatenation, two relatively computed different lengths of first and second chaotic sequences generated using original and complement histograms of the second or first methods.