A novel method to identify initial values of chaotic maps in cybersecurity

Abstract

Chaos theory has applications in several disciplines and is focusing on the behavior of dynamical systems that are highly sensitive to initial conditions. Chaotic dynamics are the impromptu behavior displayed by some nonlinear dynamical frameworks and have been used as a source of diffusion in cybersecurity for more than two decades. With the addition of chaos, the overall strength of communication security systems can be increased, as seen in recent proposals. However, there is a major drawback of using chaos in communication security systems. Chaotic communication security systems rely on private keys, which are the initial values and parameters of chaotic systems. This paper shows that these chaotic communication security systems can be broken by identifying those initial values through the statistical analysis of standard deviation and variance. The proposed analyses are done on the chaotic sequences of Lorenz chaotic system and Logistic chaotic map and show that the initial values and parameters, which serve as security keys, can be retrieved and broken in short computer times. Furthermore, the proposed model of identifying the initial values can also be applied on other chaotic maps as well.