Ina Taralova

Design and Analyses of Efficient Chaotic Generators for Crypto-systems

In this paper, we design and implement under Matlab/Simulink some efficient digital chaotic generators for data encryption/decryption process. Some of these generators (logistic, PWLCM, Frey) are known, the others xcos(x), xexp[cos(x)], 2-D Tmap) are proposed. A number of designed generators contain cascaded layer to improve the statistical properties of the generated sequences. We introduce and demonstrate the importance of the perturbing orbit technique to avoid the dynamical degradation caused by the 2N-dimensional finite state space. This technique increases also the orbit cycle length. Finally, to quantify the security level of the proposed generators, we analyze their global dynamical properties using system and signal processing tools (Lyapunov exponents, bifurcation diagrams, distribution, pseudo phase space, autonotcorrelation, cross correlation, NIST tests ldquoNational Institute of Standards and Technology ldquo). Experimental and theoretical analyses show that the proposed generators have good cryptographic properties.

New nonlinear CPRNG based on tent and logistic maps

This paper is devoted to the design of new chaotic Pseudo Random Number Generator (CPRNG). Exploring several topologies of network of 1-D coupled chaotic mapping, we focus first on two dimensional networks. Two coupled maps are studied: TTL^{RC} non-alternate, and TTL^{SC} alternate. The primary idea of the novel maps has been based on an original coupling of the tent and logistic maps to achieve excellent random properties and homogeneous /uniform/ density in the phase plane, thus guaranteeing maximum security when used for chaos base cryptography. In this aim a new nonlinear CPRNG: MTTL_{2}^{SC} is proposed. In addition, we explore higher dimension and the proposed ring coupling with injection mechanism enables us to achieve the strongest security requirements.

Dynamical study of a second-order DPCM transmission system modeled by a piecewise-linear function

This paper analyzes the behavior of a second-order differential pulse code modulation (DPCM) transmission system when the nonlinear characteristic of the quantizer is taken into consideration. In this way, qualitatively new properties of the DPCM system have been unraveled, which cannot be observed and explained if the nonlinearity of the quantizer is neglected. For the purpose of this study, a piecewise-linear nondifferentiable quantizer characteristic is considered. The resulting model of the DPCM is of the form of iteration equations (i.e., map), where the inverse iterate is not unique (i.e., noninvertible map). Therefore, the mathematical theory of noninvertible maps is particularly suitable for this analysis, together with the more classic tools of nonlinear dynamics. This study allowed us, in addition, to show, from a theoretical point of view, some new properties of nondifferentiable maps, in comparison with differentiable ones. After a short review of noninvertible maps, the presented methods and tools for noninvertible maps are applied to the DPCM system. An original algorithm for calculation of bifurcation curves for the DPCM map is proposed. Via the studies in the parameter and phase plane, different nonlinear phenomena such as the overlapping of bifurcation curves causing multistability, chaotic behavior, or multiple basins with fractal boundary are pointed out. All observed phenomena show a very complex dynamical behavior even in the constant input signal case, discussed here.

Efficient Cascaded 1-D and 2-D Chaotic Generators

In order to improve the communication security, two novel chaotic generators are proposed. The first one is a single order chaotic generator using two cascading stages, and the second one is a second order chaotic generator with single and cascaded layer. The goal is to generate binary pseudo random chaotic signal with high degree of randomness. We analyze their global dynamics properties using system and signal processing tools (Lyapunov exponents, bifurcation diagrams, distribution, pseudo phase, autocorrelation, cross correlation, NIST test). A complete analysis is provided. Experimental and theoretical analyses show that the proposed generators have good cryptographic properties.

Application of observer-based chaotic synchronization and identifiability to original CSK model for secure information transmission

The modified Lozi system is analyzed as chaotic PRNG and synchronized via observers. The objective of the study is to investigate chaotic-based encryption method that preserves CSK model advantages, but improves the security level. The CSK model have been discussed to message encryption because it implies better resistance against noise, but there are many evidences of the model weaknesses. The investigation provides the original CSK model analyses of secure message transmission over the communication channel by examining identifiability and observability; switched regimes detection; sensitivity to initial conditions and session key; NIST tests of the encrypted signal; correlation between wrong decrypted messages; system ergodicity. The proposed model has a significant effect on the security level of the transmitted signal that successfully passed chaotic and randomness tests. The results suggest that the original CSK model can be used for information security applications.

Key requirements for the design of robust chaotic PRNG

The increasing number of e-transactions requires more secure and innovative schemes for secure information storage and transmission. Since the encryption should be unique for each transaction, there is a big necessity of new generators of very huge numbers of encryption keys, and chaotic random number generators seem to be perfectly suitable for this application. In this paper a new robust, gigaperiodic and simple in implementation chaotic generator is proposed. The generator construction is based on the principle of ring-coupling. The proposed chaotic generator successfully passed statistical and analytical tests: NIST, largest Lyapunov exponent, autocorrelation, cross-correlation, uniform distribution. For the best precision of uniform distribution, approximate density function has been applied, the distribution errors are analyzed by written software. The resulting chaotic system promises the designed robust implementation to cryptosystems.