A Research On The Chaotic Dynamical Complexity And Cryptographic Security

Currently, more and more dynamical systems has been applied in the field of information security and cryptography because of its complex dynamic characteristics. Chaotic cryptography is such a new technology of cryptography based on the dynamical system. The properties of Chaotic systems such as sensitive dependence on initial conditions, randomness and short-term predictable, long-term unpredictable, which are well related to confusion and diffusion cryptographic design principles.Chaos and traditional cryptography is so closed in their research to each other, that they absorb the other’s research achievements to promote themselves. The dynamic properties of chaotic systems can be measured by dynamic complexity, and for the security of chaotic cryptosystem, we still need to use cryptographic complexity to analyze. So in the study of chaotic cryptography, the relationship between dynamic complexity and the complexity of cryptography is a very meaningful topic, which laid a foundation for creating a chaotic system that could satisfy the requirement of cryptographic security as well as establishing the security of chaotic cryptography theory.In this paper, the relationship between the chaotic dynamical complexity and the cryptographic complexity were studied. Research established the relationship between Lyapunov exponent of chaotic systems and cryptographic complexities such as Lempel-Ziv complexity, nonlinear complexity. Research results show that there is a strong correlation between these two kinds of complexities, and with the Lyapunov exponent increases, the binary sequences generated by chaotic systems are more satisfying the requirements of the cryptographic complexity.In the complexity analysis of sequences generated by the chaotic systems, we found that we found dynamical complexity have a quite strong correlation with cryptographic complexities. These conclusions make a contribution to designing chaotic pseudo-random generator with high cryptographic complexity, put forward the chaotic stream cipher scheme satisfying the requirement of cryptographic security, which laid a foundation for establishing the security of chaotic cryptography theory.