J.S. Armand Eyebe Fouda

Highly secured chaotic block cipher for fast image encryption

Highly secured block ciphering with high encryption speed.Combination of chaos and linear Diophantine equation (LDE).Fast and dynamical generation of large permutations.Exploitation of the true accuracy of the computer.Adaptability of the cipher to any type of chaotic system. The real-time constraint for the codec execution and high security level protection are the two most important multimedia encryption requirements. In this paper, a method is presented for the fast generation of large permutation and diffusion keys, which are based on the sorting of the solutions of the linear Diophantine equation (LDE). The coefficients of the LDE are integers which can be dynamically generated from any type of dynamical chaotic systems, as the maximum precision of the computer can be used for the conversion of floating-point chaotic values into integers. This technique yields a fast image block encryption algorithm in which the security level is considerably strengthened. Although the architecture used in this cipher is the one for which the permutation and diffusion are considered as two separate stages, the generation speed of permutation and diffusion keys allows reducing the computational time required by the duplication of the image-scanning stage during the permutation and diffusion operations.

The three-state test for chaos detection in discrete maps

The three-state test (3ST) - a new approach for chaos detection in discrete chaotic maps is presented. The scheme is based on statistical analyses of patterns obtained from ascending sorting of the system states. In addition to its ability for clear discernment between chaotic, quasi-periodic and periodic dynamical systems, the detection of periods of stable cycles is also automated with 3ST. The method is directly applied on data series generated by chaotic maps and does not require a priori knowledge of the equations of the underlying system. It also presents the advantage of not having to depend on the nature of the vector field as well as its dimensionality and is computationally low cost. The effectiveness of the 3ST is confirmed using two well known and widely studied chaotic maps: the logistic map and the Henon 2D map.

A Modified 0-1 Test for Chaos Detection in Oversampled Time Series Observations

The use of binary 0-1 test for chaos detection is limited to detect chaos in oversampled time series observations. In this paper we propose a modified 0-1 test in which, binary 0-1 test is applied to the discrete map of local maxima and minima of the original observable in contrast to the direct observable. The proposed approach successfully detects chaos in oversampled time series data. This is verified by simulating different numerical simulations of Lorenz and Duffing systems. The simulation results show the efficiency and computational gain of the proposed test for chaos detection in the continuous time dynamical systems.

The EKT method for extraction of periodic signals from noise

Abstract Extracting periodic signal drowned in noise is a challenge in signal processing. Usually, to extract a message made up of several harmonics, it is necessary to have a reference periodic signal made up of as many harmonics. This requires a long processing time if harmonics are extracted one after another. The solution adopted is to simultaneously generate harmonics of the reference signal with the aid of the Dirac comb. This method however has limitations in terms of signal-to-noise ratio. In this paper, we propose a new reference signal which allows extracting the message with a better signal-to-noise ratio than that obtained using the Dirac comb.

Toward a group delay reduction in digital filtering

Finite impulse response (FIR) filters are often used in digital signal processing applications because their linear phase properties do not introduce group delay distortion. While this property is desirable, we may also desire that the filter exhibit zero group delay to suppress the causal time offset between the input and output of the filter. We can minimize the causal delay by the use of recursive minimum phase filters but these introduce an objectionable group delay distortion. We desire both zero group delay and a nonrecursive impulse response (IR). This filter can be applied to input signals indirectly through a modified overlap and save FFT based circular convolution. The desired result is obtained in our proposed new filtering technique: the modified overlap and save method (MOSM). We accomplish this by redefining the time origin of the prototype filters impulse response by circularly shifting the response in the FFT filter time vector till the symmetry point coincides with the vectors zero index.

The EKT method theoretical signal-to-noise ratio expression

The EKT method is a new extraction technique of periodic signals from noise. It is simply a cross-correlation of a periodic message with a reference signal obtained by summation of harmonics of the same amplitude. The only paper [J.S.A. Eyebe Fouda, M. Kom, A. Tiedeu, The EKT method for extraction of periodic signals from noise, Digital Signal Process. 16 (4) (2006) 343-357] published up to now on this method numerically shows that, for examples chosen on simulation, its signal-to-noise ratio (SNR) remains higher than that of the traditional method. However, practical calculation of SNR on some examples does not allow a user having other signals to know which is the best of the multitude methods for an extraction. Only the comparison of SNR literal expressions of the various methods can avoid it proceeding by groping. To this end, we will determine in this text, an expression for theoretical EKT method SNR gain.

Applicability of the permutation largest slope entropy to strange nonchaotic attractors

We extend the permutation largest slope entropy (PLSE) to the detection of strange nonchaotic attractors (SNA). The initial time series derived from a quasi-periodically forced chaotic map is first transformed into a series of symbols using the order relation. These symbols are thereafter combined into m-length words to obtain quantized ordinal matrices (QOM). Finally, the PLSE is applied to the series of QOM for detecting changes in the behavior of the system. Simulation results show that the QOM transform allows to control the complexity of the time series, hence to reduce the entropy of tori and SNA and to increase that of chaotic motions. This result allows to highlight transitions between the three types of motions, thus showing a nonzero entropy for SNA which nevertheless is smaller than that of chaotic dynamics. The approach is effective for the detection of different routes to SNA from time series.

Adaptive EKT method

The EKT method is a recent extraction technique of periodic signals from noise. It is a method presenting a great practical interest because of its easy realization and its high signal-to-noise ratio (SNR)-higher than that of the averaging method. However, it is only valid for signals of known period. Since in practice, periods are not always known with good precision, the EKT method remains limited. To enlarge its application field, we propose in this paper an adaptive EKT method, which could be applied to signals whose variation interval of the fundamental frequency is known.

The matching energy: a novel approach for measuring complexity in time series

We present the matching energy (ME) as a novel approach for nonlinear time series analysis. The time series values are first sorted by ascending and descending order. Thereafter, sequences of length n derived from the sorted and unsorted time series are compared. Finally, the ME is defined as the average of the energies of the set of sequences, where the energy of sequences with matching coordinates is set to zero. We then verified, using both simulation and experimental data, that the ME of periodic time series is equal to zero, while non-regular dynamics present a positive ME. The approach thus defined allows to scale chaos in dynamical systems and presents a high robustness against noise as well as a high-speed performance, hence is useful for real-time analysis of real-world data.

Diophantine Solutions Based Permutation for Image Encryption

A permutation technique based on the resolution of the system of three independent Diophantine equations is presented. Each Diophantine equation parameters are two positive integers generated from a chaotic system. The resulting solutions are then used for rearranging the positions of the bits and pixels in the ciphered sequence. The performance of such a technique is compared to GRP and Xiang permutation algorithms. From this permutation algorithm an efficient chaos-based block cipher using a chaotic logistic map is proposed. Statistical analyses of this system show a high security level and non-propagation of errors.