Octaviana Datcu

Evaluating the sampling distance to achieve independently and identically distributed data from generalized Hénon map

The paper analyzes, by original statistical, methods the minimum sampling distance that enables to extract statistically independent data sets from the generalized Hénon Map. For the statistical independence analysis, it is necessary to evaluate the entry moment of the chaotic system in the stationarity region. The statistical investigation relies on: the Smirnov test, a method of testing the statistical independence between two continuous random variables of unknown probability laws, a Chi-square test for a bivariate probability law and a Monte-Carlo analysis.

A third-order sliding-mode observer for a continuous delay chaotic system

This paper aims rstly to highlight the possibility of recovering a message included in a chaotic continuous time delay system, secondly to show that it is possible to use the third order sliding mode in order to recover directly all the states and the unknown input (message), thirdly to illustrate the robustness of the proposed observer with respect to a noisy signal. This work is based on the concept of left invertibility and recent advances in sliding mode observers. Some theoretical recalls and assumptions are done previously to the presentation of the observer design and the simulation results.

New enciphering algorithm based on chaotic generalized Hénon map

The paper belongs to the field of chaotic based cryptography. It relies on some ideas from classical fundamentals as mixing functions suggested by C.E. Shannon for secrecy systems, and on the known publication of M.S. Baptista, a paper essentially implying the ergodicity assumption of the chaotic signal in cipher design. In this paper, the first step was to choose a chaotic system of a higher dimension than Baptista used, aiming to obtain a more complex system having a hyperchaotic behavior. The proposed algorithm is based on Generalized Henon Map (3D), stated in literature as hyperchaotic for a number of bifurcation parameters. The paper advances a new mixing enciphering scheme based on the Generalized Henon Map (GHM), which may be used as an inner element in a cipher, providing a good practical diffusion and confusion. A random variable transform is applied on the state of the chaotic system at each iteration in order to obtain a new random variable of a quasi uniform law. This new random variable is further transformed, through a series of other functions containing elements of the secret key, into a discrete random variable. The discrete values - which are ASCII numbers - are combined by a simple relation with the plain message, also in ASCII format. It is obtained a first mask of the original message, involving the GHM. On this result (in its binary representation form) other simple transformations that depend on the state of the GHM are applied. That finally allows getting a transformed version of the message that can be included in one of the states of the GHM without disturbing its chaotic behavior. The results, including a perception of the diffusion and the confusion involved, are illustrated on natural text and jpeg image.

High order sliding mode observers and singular value decomposition in communications

An important issue in communications, in general, and cryptography, in particular, is recovering the information of interest at the reception end. Recent techniques make use of sliding mode observers to achieve this. Another useful method to reconstruct the state space of the transmitter at the receiver end, is the singular value decomposition. Targeting secure communications, the aim of the present paper is to compare the efficiency of the two techniques, when applied to the estimation of the state space of the transmitter at the reception end. For numerical exemplification, a Sprotts jerk-like system was used. The example is taken without loss of generality, being applicable to all differential models expressing the temporal evolution of diode or bipolar-junction transistor based circuits, like the well-known Colpitts oscillator.

Determining chaotic behavior from experimental data: An alternative to the Lyapunov exponents

The present work aims to find an alternative way to the classical Lyapunov exponents of characterizing the chaotic behavior of a system. The procedures that compute Lyapunov exponents use complicated mathematical operations, such as base change and linearization of the investigated system. The main advantage of the proposed procedure is that it can be applied to experimental data records, without knowing the equations that produced the investigated signals. The tridimensional Hénon map is used for exemplification.

Baptista's chaos-based cipher implemented in a field programmable gate array

In the context of the current struggle for information security and computational efficacy, this paper studies Baptistas chaos-based encryption cipher as a resource-efficient alternative to the more popular block cipher algorithms. We evaluate the cipher by encrypting different types of data — text, images and sound — and we present the analysis of cyphertext statistical distribution and obfuscation characteristics. Simulation results illustrate the effectiveness of the algorithm on multimedia content. We present an implementation of the cipher as a digital system in a Xilinx Zynq 7000 series FPGA, and evaluate hardware resource utilization and maximum obtainable frequency. The cipher source code — Matlab simulation and the Verilog hardware description — is made available as a GIT repository. The aim of the demarche is to provide digital circuitry which may be easily integrated in a hybrid analog-digital cryptosystem which employs a dynamically changing secret key.

Secret speech transmission using a high order sliding mode observer

This paper proposes a chaos-based communication scheme which transmits a secret speech signal. To recover the states of the transmitter and the unknown message, the receiver uses a high order sliding mode observer. Its input is one of the states of the transmitter. The control parameters of the observer constitute the secret key of the transmission. The main aspect in which the present work differs from already known algorithms using sliding-mode observers to recover secret messages embedded in the dynamics of chaotic systems is the nature of the hidden information it applies to. To the knowledge of the authors, no work has yet applied this type of reconstruction method — sliding mode estimators, to recover secret speech signals, but only text and image, included in the evolution of chaotic systems. Numerical simulations are used to find the appropriate parameters for the designed encryption and deciphering. Efficiency and future improvement methods are discussed.

Encrypting Multimedia Data Using Modified Baptista’s Chaos-Based Algorithm

One of the easiest to implement, yet complex, symmetric key chaos-based ciphers is the one proposed by Baptista in 1998. It has attracted much interest from scholars, who underlined its deficiencies and proposed different methods to enhance it. The present paper proposes an additional step in the encryption procedure - a modulo two sum between the binary representations of Baptista’s cryptograms and that of the value of the chaotic logistic map at that very iteration. This results in a flat distribution of the cryptograms. Thus, one of the major drawbacks of Baptista’s cryptosystem, the exponential decay of the repartition of the cyphertext values, is surmounted. The original Baptista’s algorithm is described, the proposed method is exemplified on a short message and its results are discussed when applied on multimedia files.

Steganographic embedding of a secret message in a video flow

The paper presents a steganographic method which hides a secret message in a video flow. The secret message represents the result of a chaos-based encryption scheme. One of the flaws which make the algorithm unpractical for real-time applications is that, while the elements of the plain-message are represented using 8 bits (ASCII characters) the corresponding encrypted values need to be represented using 16 bits. Since the pixels of a typical image are represented using 24 bits (8 bits for each color component), each encrypted character fits in only one pixel. Moreover, since the resolution of today’s video materials is very large, the pixel previously established to carry in its evolution the hidden content will not be obvious to unaware spectators, but only to the one which knows its coordinates. In addition to the steganographic procedure, the work presents preliminary results on the degree of pseudo-randomness of video flows. The study is based upon the idea behind Lyapunov exponents. The evolution of two pixels which initially differ only by the minimum possible value (the color representation’s resolution) is followed for a large number of video frames. The distance between such points, for pseudo-random behavior, is known to evolve over time in a Gaussian manner. A Kolmogorov-Smirnov statistic is computed and illustrated in order to conclude over the provenience of the data series representing the evolution of the distance between the two initially neighboring pixels from a standard normal law.

Outputs analysis and dual immersion method for chaotic systems

When secure data transmission is implemented through chaotic systems, the choice of the output is a preliminary problem. In this paper, the quality of the transmitted information is analysed with respect to the observability concept, for each potential output. More-over, in order to overcome observability loss, a dual immersion technique is proposed.The use of high order sliding mode observer on a well known Lorenz system, allows to highlight the well founded of the proposed analysis and method.