A New Pseudo-Random Number Generator Based on Chaotic Maps and Linear Feedback Shift Register

Abstract

Random numbers have a significant role in cryptography, and methods of generating these numbers always require serious attention in order to ensure proper security of cryptography. In this paper, we introduce a linear congruential pseudo-random number generator that operates by utilizing chaotic maps and shift register. In each stage, LFSR's perform (XOR) sum on specific positions in the binary field. The aim of this paper is to use chaotic maps to randomly select positions at each stage, and then perform summing operation in binary field on least significant bits produced by linear congruential generator to produce a good pseudo-random sequence. In fact, weakness of linear congruential generator which is its short period and weakness of LFSR which is its linearity are both resolved by implementing chaotic maps in the design. The proposed generator merges two layers of cryptography and scrambling, which operate separately in image, audio and video signals, into one layer. Statistical analysis by NIST and DIEHARD packages and results of statistical evaluations on the quality of generator output confirm the efficiency of the proposed generator. Algorithm speed and it security in terms of key space is assessed, and given its robustness against different attacks, it can be concluded that this pseudo-random number generator is suitable for cryptography application.