A Pseudo Random Bit Generator Based on Chaotic Logistic Map and its Statistical Testing

During last one and half decade an interesting relationship between chaos and cryptography has been developed, according to which many properties of chaotic systems such as: ergodicity, sensitivity to initial conditions/system parameters, mixing property, deterministic dynamics and structural complexity can be considered analogous to the confusion, diffusion with small change in plaintext/secret key, diffusion with a small change within one block of the plaintext, deterministic pseudo randomness and algorithmic complexity properties of traditional cryptosystems. As a result of this close relationship several chaos-based cryptosystems have been put forward since 1990. In one of the stages of the development of chaotic stream ciphers, the application of discrete chaotic dynamical systems in pseudo random bit generation has been widely studied recently. In this communication, we propose a novel pseudo random bit generator (PRBG) based on two chaotic logistic maps running side-by-side and starting from random independent initial conditions. The pseudo random bit sequence is generated by comparing the outputs of both the chaotic logistic maps. We discuss the suitability of the logistic map by highlighting some of its interesting statistical properties, which make it a perfect choice for such random bit generation. Finally, we present the detailed results of the statistical testing on generated bit sequences, done by the most stringent tests of randomness: the NIST suite tests, to detect the specific characteristics expected of truly random sequences.