Study on Pseudorandomness of Some Pseudorandom Number Generators with Application

Pseudo random numbers are important in various applications. Pseudo random number generators (PRNGs) have been used widely to provide ideal pseudo random number generating sources. Recently the researches on chaos-based PRNGs have also attracted much attention. Based on Li-York´s chaotic map criteria, this paper introduces a novel piecewise linear chaotic map (PLCM). Combining the PLCM with the logistic map designs a chaotic PRNG (CPRNG). Using the FIPS 140-2 test suit tests the randomness of two 1000 key streams consisting of 20000 bits and 2²⁰ bits, respectively. The results show that for the 1000 key streams consisting of 20000 bits, the statistical properties of the randomness of the sequences generated via the CPRNG and an m-sequence PRNG do not have significant differences. As applications, image encryption examples via the CPRNG and the m-Sequence based PRNG are given.