Sumona Mukhopadhyay, Mala Mitra and Santo Banerjee have proposed a method of digital cryptography inspired from Genetic Algorithm(GA) and synchronization of chaotic delayed system. The chapter introduces a brief idea about the concept of Evolutionary Algorithm(EA) and demonstrates how the potential of dynamical system such as chaos and EA can be utilized in a reliable, efficient and computational cheaper method for secure communication. GA is a subclass of Evolutionary algorithm and as such is governed by the rules of organic evolution. In GA the selection mechanism and both transformation operators-crossover and mutation are probabilistic. In their proposed method for cryptography, the parameters and keys of the system are secure since the synchronized dynamical system does not necessitate the transmission of keys over the communication channel. The random sequence obtained from chaotic generator further transforms it into a powerful stochastic method of searching the solution space in varied directions for an optimal solution escaping points of local optima. But randomicity can sometimes destabilize the system and there is no guarantee that it yields an improved solution. The authors have substituted the random and probabilistic selection operator of GA with problem specific operator to design the cryptosystem to control such random behavior otherwise it would lead to a solution which is uncorrelated with the original message and may also lead to loss of information. The way selection has been modified leads to two versions of the proposed genetic engineering algorithm for cryptography. Simulation results demonstrates that both the flavors of the proposed cryptography successfully recover the message. A comparison of their proposed method of cryptography with cryptography developed from Comma-Based Recombination selection mechanism of Evolutionary Strategy shows a computational edge of their proposed work.
Top1. Chaos Synchronization And Cryptography
The turning point in traditional schemes of cryptography was brought about by the revolutionary work of Pecora and Carroll (Pecora & Carroll, 1990). This opened a gateway to varied areas of applications of chaos synchronization namely secure communication, chaos generators design, chemical reactions, biological systems, information science (Hramov & Koronovskii, 2005a ; Garcia – Ojalio, & Roy, 2001; Yang & Chu 1997; Bowong, 2004; Kittel et al, 1994) and many more significant applications.
Pecora and Carroll experimented on two systems producing their phenomenal work. The first is known as a driver and the other a response system. They used a novel idea of generating a chaotic signal to drive a non linear dynamic system such that the state of the second system is governed by the state of the driving system. This is possible if the two systems are coupled by a proper controlling function. However, it is to be noted that the behavior and system parameters of the response system is dependent on the behavior of the driving system alone, similar to a master-slave relationship. When subjected to suitable conditions, the response system will exhibit a chaotic pattern which is in sync with the driver system. This phenomenon is known as chaos synchronization. Till now many different types of synchronizations have been analyzed in ordinary and time delayed dynamical systems such as complete synchronization (Fujisaka. & Yamada, 1983), generalized synchronization (GS) (Rulkov et al, 1995; Kocarev & Parlitz, 1996; Hramov & Koronovskii, 2005a), generalized projective synchronization of a unified chaotic system (Yan and Li 2005), anticipated synchronization (AS) (Masoller, 2001), lag synchronization (LS) (Rosenblum et al, 1997; Zhan et al, 2002), phase synchronization (PS) (Rosenblum et al, 1996; Koronovskii & Hramov, 2004), antiphase synchronization (APS), time scale synchronization (Hramov et al, 2005b), intermittent generalized synchronization in which the authors (Hramov et al, 2005c) detected that before the transition of unidirectionally coupled chaotic oscillators to generalized synchronization, in some time intervals a non-synchronous behavior occurs and functional synchronization (FS) (Banerjee & Chowdhury, 2009).