Investigation on Pseudorandom Properties of Chaotic Stream Ciphers

This paper presents statistical analysis on the pseudorandom properties of the chaotic sequences, which are widely used as stream ciphers. Sequences generated by different chaotic maps are tested by the NIST's (National institute of standards and technology) STS randomness test suite. To evaluate the pseudorandom properties of the chaotic sequences, frequency, block frequency, run, cumulative sum, and DFT (discrete Fourier transform) tests are performed. By the experimental results, logistic and Henon maps showed the best statistical properties. On the other hand, sequences generated by Tent, sine, and cubic maps failed in some tests and are not recommended to be used individually. Simulation results prove that combination of the strong pseudorandom chaotic sequences with weak sequences can improve statistical performance of the output sequences, as well as the security of the whole chaotic system. In addition, it is also examined that chaotic sequences show better pseudorandom properties than FCSR (feedback carry shift register) based sequences