PSEUDO RANDOM NUMBER GENERATOR BASED ON LOOK-UP TABLE AND CHAOTIC MAPS

Abstract

Pseudo-Random Number Generators (PRNGs) play an important role in many cryptographic applications. Many network security algorithms and protocols that are based on cryptography also require random or pseudorandom numbers at certain points. PRNG is an algorithm that is used to generate a random sequence that has the same behavior of truly random numbers. Each generated number should not depend on the previously generated numbers, and thus it is not possible to predict such numbers. However, not all PRNGs are suitable for cryptographic applications. Therefore, various statistical tests can be applied to the obtained sequence to evaluate and compare it with truly random sequences. A PRNG that passes all statistical tests can be considered as a statistically secure PRNG. Based on some properties of chaos, such as randomness, unpredictability, and high sensitivity to the secret key, we proposed a new PRNG. The proposed PRNG is based on a modified chaotic map proposed in [20], and a new lookup table, which is created in such way that the stored numbers will not be duplicated in the same row, column, or diameter. The proposed map and lookup table are used to produce non-linear and non-invertible functions, which are the main targets of any secure PRNG. As a result, the behavior of the proposed PRNG simulates the behavior of TRNGs. The obtained results from the cryptographic analysis and the standard statistical National Institute of Standards and Technology (NIST) tests indicate the robustness of the proposed PRNG. Furthermore, it is robust against known cryptographic attacks, and it has a strong non-linearity compared to the other systems. A comparison study of efficiency in terms of both speed performance and robustness against cryptanalysis was done, and the results demonstrate the superiority of the proposed algorithm.