Novel Methods For Generate Chaotic Sequence And Its Applications In Digital Watermarking

Chaos system has the following features, such as intrinsic randomness of deterministic system, highly sensitive to initial conditions, long-term unpredictability. They have essentially relationship with confusion and diffusion in cipher design.As a new technology and a strong complement to Cryptography, chaotic cryptography has got a lot of research in recent years. Most studies have focused on the generation and analysis of chaotic sequence, numerous literatures suggests that the chaotic sequence has a sufficiently long cycle and good statistical properties. However, with the in-depth study, people found that the dynamic characteristics of chaotic system will be degraded in finite precision, which make the system into short-period. The short-cycle behavior serious damage to the randomness of the chaotic sequence, lead to its statistical characteristics weakened and the corresponding key space narrowed.In order to improve and eliminate the impacts on chaotic sequence, three methods were put forward by researchers, including improving chaotic system structure, mixing multi-chaotic system and using more complex chaotic system. The common characteristics of these methods are the use of experimental simulation verifies its effectiveness, and almost with no theoretical analysis. This paper was first qualitative analysis these characteristics, and used chebyshev sequence as an example in order to qualitative analysis the feature of short-period, then discusses the law of multiple chaotic systems which were series connected, cross-mixed, cascade mixed. In order to verify the validity of the law, we design some new chaotic sequence generating method and apply them in digital watermarking.This article discussed the three aspects about chaotic sequence generation method and its application in digital watermarking.(1) dynamics characteristics degradation and addition of chaosIn recent years, dynamics characteristics degradation of digital chaotic in finite precision has aroused widespread interest. A lot of literatures show that it appears in Logistic map, Tent map and Chebyshev Map, the chaotic sequences which were generated by these map have always lost their value on cryptography. In order to analysis the short-period feature of chaos, we used chebyshev sequence as an example to qualitative analysis of the existence and give the cycle formula of chebyshev sequence finally.To solve the short-period characteristics of digital chaotic system, multi-chaotic system mixed method was commonly used in the industry and experimental simulation always used to illustrates the effectiveness of these methods. It is found that the essential characteristic of these methods is the addition ability of chaos.Unfortunately, few researchers at home and abroad concerned about the addition ability of chaos. This article first defined a series of concept about chaotic system, such as series connected, cross-mixed, cascade mixed. Then using qualitative analysis and simulation experiments to demonstrate the characteristics of chaotic systems exist in several mixed mode. This is a very good guide to design and analysis the chaotic sequences.(2) The new generation method and property analysis of chaotic sequencesBased on the characteristics of degradation and addition ability of chaos, we present some methods, such as an improved chaotic sequence algorithm based on Chebyshev map, a class of multi-scroll Chua chaotic sequence generating method and a new kind of chaotic circuit random sequence generator. The improved chaotic sequence algorithm with Chebyshev by changes the equation parameters before the system enter in short-period, which makes the system not enter the short cycle and got longer sequence. The new method to generate chaotic sequence by multi-scroll Chua chaotic system shows that the short-period problem can be weakened by high-dimensional chaotic system as well as enlarging the key space. Particularly important, the principle of generating random sequence by high-dimensional is the same as by low-dimensional chaotic system. Therefore, we can choose a different multi-scroll Chua chaotic system to generate a random sequence according to the actual situation. In this paper, we first propose a new fourth-order chaotic system, and then implement a random sequence, which provides a new way for the hardware implementation of chaotic sequence.(3) The research of chaos sequence in digital watermarkingIn the field of digital watermarking, chaotic sequence has got more and more researched. These studies generally agreed that the nature of the pseudo-random sequences generated by chaotic systems is better than by traditional algorithms, and ignore the impact of the short-period behavior of the chaotic sequence. In this article, we firstly discuss the key and key space of chaotic cryptosystems and then given some suggestions to design a chaotic cryptographic algorithm, we give two algorithms, one is a digital watermarking algorithm with dual transform domain based on Contourlet and SVD, another one is a digital watermarking algorithm based on grid multi-scroll Chua’s chaotic attractors. Furthermore, we point out that cryptography design principles and evaluation method should be followed in the chaotic digital watermark design.This work was supported by the National Natural Science Foundation of China under Grant Nos.60871025and61172023, the Specialized Research Foundation of Doctoral Subject Point of Education Ministry under Grant No.20114420110003, the Natural Science Foundation of Guangdong Province under Grant Nos.8151009001000060and S2011010001018, and the Science and Technology Program of Guangdong Province under Grant No.2009B010800037.