Pseudo Random Bit Generator Using Logistic and Bernoulli Maps

We propose pseudo random bit generator(PRBG) by constructing an ergodic orbit of logistic map generated using intermittent perturbation and sampling the orbit using Bernoulli shift map. The pseudo randomness of the key streams is tested with the standard NIST statistical test suite. The key streams generated by the proposed PRBG pass all the tests of the test suite. As an application of PRBG we propose chaotic stream ciphers. Goodness-of-Fit tests are conducted for these ciphers. Stream ciphers generated using PRBG are shown to generate ciphers in which the distribution of the characters show significant correlation to the uniform distribution. It is also shown that the ciphers exhibit good avalanche effect when the initial seed is varied infinitesimally and we can also clearly observe the avalanche effect at different points within the ciphertext as the ciphertext is being generated. Also we show that the proposed PRBG is on par with conventional PRBG RC4. This indeed vindicates our hypothesis that stream of bits obtained from orbits of logistic map using perturbation and Bernoulli shift map exhibits randomness.