Quality evaluation of random numbers generated by chaotic sampling phase-locked loops

The quality of generated random numbers is determined by the independence of consecutive numbers from one another. If the random numbers are used for enciphering plain text then correlation or periodicity destroys the security of the transmission. Chaotic signals are claimed to be suitable for secure communications; however, the quality of the generated sequences has not yet been studied. Physical changes in the parameters of the chaotic circuits used to generate random numbers may alter the parameters determining the chaotic behavior, i.e., the quality of the generated random numbers. This paper evaluates the quality of random sequences generated by chaotic sampling phase-locked loops (PLLs). It shows that micro-Feigenbaum diagrams, i.e., small periodic windows, can be observed in the chaotic PLLs proposed for random number generation. The run test, a much more sensitive tool than the autocorrelation function, is used to evaluate the quality of the random numbers. Because the results have shown that the quality of the generated numbers does not meet the requirements, a simple method is proposed to improve the performance of the chaotic PLLs.