In the last decade, chaos has emerged as a new promising candidate for cryptography because many chaos fundamental characteristics such as a broadband spectrum, ergodicity, and high sensitivity to initial conditions are directly connected... more
In the last decade, chaos has emerged as a new promising candidate for cryptography because many chaos fundamental characteristics such as a broadband spectrum, ergodicity, and high sensitivity to initial conditions are directly connected with two basic properties of good ciphers: confusion and diffusion. In this chapter we recount some of the saga undergone by this field; we review the main achievements in the field of chaotic cryptography, starting with the definition of chaotic systems and their properties and the difficulties it has to outwit. According to their intrinsic dynamics, chaotic cryptosystems are classified depending on whether the system is discrete or continuous. Due to their simplicity and rapidity the discrete chaotic systems based on iterative maps have received a lot of attention. In spite of the significant achievements accomplished in this field, there are still many problems, basically speed, that restrict the application of existing encoding/decoding algorithms to real systems. The major advantages and drawbacks of the most popular chaotic map ciphers in terms of security and computational cost are analyzed. The most significant cryptanalytic techniques are considered and applied for testing the security of some chaotic algorithms. Finally, future trends in the development of this topic are discussed.
This paper presents the new Lorenz unlike chaotic attractor which is constructed by a three non linear first order differential equations. These equations are arranged in a three dimensional autonomous systems. The dynamic behavior of the... more
This paper presents the new Lorenz unlike chaotic attractor which is constructed by a three non linear first order differential equations. These equations are arranged in a three dimensional autonomous systems. The dynamic behavior of the new chaotic system is shown such as time series, strange attractors, and bifurcations. Numerical experience also shows that when the parameter 'd' is varied, the global non linear amplitude is also varying. The paper ends with some possible research and development recommendations.
Spreading code plays an important role in WCDMA system. Each user in a cell is separated by a unique spread code. WCDMA system generally uses PN sequence such as Walsh codes or gold codes as spread code. In this paper, the chaotic... more
Spreading code plays an important role in WCDMA
system. Each user in a cell is separated by a unique spread code.
WCDMA system generally uses PN sequence such as Walsh
codes or gold codes as spread code. In this paper, the chaotic
spreading sequence is used as spread code instead of Walsh codes
and the chaotic signal is generated using logistic map. The
generated chaotic signal is a real valued signal and it is
inappropriate to be used as spreading sequence. Consequently,
the chaotic signal is transformed into binary sequence using a
threshold function. The performance of chaotic spreading
sequence in WCDMA with PN sequences in terms of bit error
rate for AWGN channel is presented in this paper.
The idea of using chaotic transformations in cryptography is explicit in the foundational papers of Shannon on secrecy systems. Although the word “chaos” was not minted till the 1970s, Shannon clearly refers to this very concept when he... more
The idea of using chaotic transformations in cryptography is explicit in the foundational papers of Shannon on secrecy systems. Although the word “chaos” was not minted till the 1970s, Shannon clearly refers to this very concept when he proposes the construction of secure ciphers by means of measure-preserving, mixing maps which depend ‘sensitively’ on their parameters. The implementation of Shannon’s intuitions had to wait till the development of Chaos Theory in the 1980s. Indeed, it was around 1990 when the first chaos-based ciphers were proposed. Moreover, in 1990 chaos synchronization entered the scene and shortly thereafter, the first applications to secure communications followed. The idea is remarkably simple: mask the message with a chaotic signal and use synchronization at the receiver to filter out the chaotic signal. The realization though had to overcome the desynchronization induced by the message itself. After this initial stage, the number of proposals which exploited the properties of chaotic maps for cryptographical purposes, grew in a spectacular way.
