A New Method for Improving Pseudorandomness of Pseudorandom Sequences with Applications

This paper first presents a new method to improve the pseudorandomness of pseudorandom sequences in the meaning defined by Golomb’s assumptions. Next, using 4 chaotic maps constructs a new 8-dimensional generalized synchronization system (8DCGSS). Third using the 8DCGSS introduces a chaotic pseudorandom number generator (chaotic PRNG) with keyspace larger than \(2^{1117}\) . Then, using FIPS 140-2 test criteria and generalized FIPS 140-2 test criteria tests the pseudorandomness of the keystreams with length 20 000 bits, 100 000 bits and 1 000 000 bits generated by the chaotic PRNG, an Matlab PRNG, an RC4 PRNG, and an m-sequence PRNG with period \(2^{20} - 1\) . The corresponding improved keystreams by our method are also tested. The results show that the presented method significantly increases the pseudorandomness of keystreams generated by the 4 PRNGs. However, the keystreams generated by the m-sequence PRNG do not exhibit strong pseudorandomness when their lengths are less than 100 000.