New Approach for Improving Pseudorandomness of Pseudorandom Sequences with Applications

br />Based on the Golomb&#39;s pseudorandomness &nbsp;assumptions &nbsp;on idea pseudorandom sequences &nbsp;and FIPS 140-2 pseudorandomness&nbsp;test, &nbsp;this paper first presents a new approach for improving the&nbsp;pseudorandomness of pseudorandom sequences. Second, using a&nbsp;generalized synchronization theorem, &nbsp;and three chaotic maps&nbsp;constructs one &nbsp;8-dimensional chaotic generalized synchronization&nbsp;system (8DCGSS). Then using the 8DCGSS designs a chaotic<br />pseudorandom number generator (CPRNG). The keyspace of the CPRNG is&nbsp;larger than 2^{1117}. Third, using &nbsp;FIPS 140-2 pseudorandomness&nbsp;test criterions and generalized FIPS 140-2 pseudorandomness test&nbsp;criterions measures, respectively, the pseudorandomness of the&nbsp;keystreams with length 20 000, 100 000 and 1 000 000 generated via&nbsp;the CPRNG, an Matlab PRNG, an RC4 algorithm, and an m-sequence with&nbsp;period 2^{20} - 1, and the corresponding improved keystreams by&nbsp;our approach. &nbsp;The results show that the presented approach can&nbsp;increase significantly the pseudorandomness of the keystreams&nbsp;generated by the four PRNGs. The key streams generated by the&nbsp;m-sequence do not have sound pseudorandomness &nbsp;when the lengths of&nbsp;the key streams are less than 100 000.