A modernistic approach for chaotic based pseudo random number generator secured with gene dominance

Random numbers play a key role in diverse fields of cryptography, stochastic simulations, gaming, etc. Random numbers used in cryptography must satisfy additional properties of forward secrecy. Chaotic systems have been a potential source of random number generators. Both lower (One-dimension) and higher (two, three-dimension) chaotic systems are popularized in the generation of random bit sequences. Higher-order chaotic systems have a higher resistance to attacks owing to multiple dimensional outputs. Logistic map initially designed in one-dimension has been extended to two- dimensions to improve security. This paper proposes to use the concept of biological Gene Dominance to further improvise the randomness of 2D Logistic map. The sequences X and Y are considered to be parent genes that determine the value of parameter 'r' for the next iteration. The scatter plot of the proposed 2D Logistic Map with Gene Dominance (2DLMGD) shows almost uniform distribution of points in the region. The generated sequences are statistically tested using NIST SP 800-22 test suite and the results show that all sequences pass the tests. The random sequences are analysed for key sensitivity, information entropy, linear complexity, correlation to verify their conformity for use in cryptographic applications.