Mitigating Drawbacks of Logistic Map for Image Encryption Algorithms

Abstract

This paper identifies and analyses some drawbacks of the logistic map which is still one of the most used chaotic maps in image encryption algorithms. As some of the disadvantages are caused by inappropriate implementations of the logistic map, this paper proposes a set of rules which should lead to enhancement of the desired chaotic behavior. Probably the most important rule introduces alternating value of parameter utilized by the logistic map. With careful choice of values and an adapted quantization technique, some of the issues should be fixed and theoretically also the values of numerical parameters should be improved. These assumptions are verified by applying the proposed set of rules on an algorithm from our prior work. Effects of the proposed rules on the used algorithm are investigated and all necessary modifications are thoroughly discussed. The paper also compares obtained values of commonly used numerical parameters and computational complexity with some other image encryption algorithms based on more complex chaotic systems.