A Modified Discretized Chaotic Map and Its Generated Pseudo Binary Random Number

Abstract

In this manuscript, a modified discretized chaotic map is developed which generates a pseudo-random binary number. This Modified Discretized Chaotic Map (MDCM) not only enlarges the range of system parameter of conventional chaotic map but also improves its performance in terms of key space. The numbers generated from MDCM are random in nature and their randomness is investigated with the help of empirical Probability Density Function (PDF) and Lyapunov Exponent. To investigate the randomness of the numbers, these numbers are quantized into two levels and encoded into 1-bit pseudo random binary numbers and then their randomness behavior is investigated by NIST's (National Institute of Standards and Technology) randomness testing methods. The proposed MDCM is compared with the conventional chaotic map in terms of their Lyapunov Exponent. The numbers generated from MDCM can be used not only in various applications of image processing such as image cryptography, image encryption and others, but also applicable where pseudo numbers are necessarily required.