Steganographic algorithm based on a chaotic map

In this paper, we suggest a new steganographic spatial domain algorithm based on a single chaotic map. Unlike most existing steganographic algorithms, the proposed algorithm uses one chaotic map to determine the pixel position of the host color image, the channel (red, green or blue) and the bit position of the targeted value in which a sensitive information bit can be hidden. Furthermore, this algorithm can be regarded as a variable-sized embedding algorithm. Experimental results demonstrate that this algorithm can defeat many existing steganalytic attacks. In comparison with existing steganographic spatial domain based algorithms, the suggested algorithm is shown to have some advantages over existing ones, namely, larger key space and a higher level of security against some existing attacks.     

A new approach to pre-processing digital image for wavelet-based watermark

The growth of the Internet has increased the phenomenon of digital piracy, in multimedia objects, like software, image, video, audio and text. Therefore it is strategic to individualize and to develop methods and numerical algorithms, which are stable and have low computational cost, that will allow us to find a solution to these problems. We describe a digital watermarking algorithm for color image protection and authenticity: robust, not blind, and wavelet-based. The use of Discrete Wavelet Transform is motivated by good time-frequency features and a good match with Human Visual System directives. These two combined elements are important for building an invisible and robust watermark. Moreover our algorithm can work with any image, thanks to the step of pre-processing of the image that includes resize techniques that adapt to the size of the original image for Wavelet transform. The watermark signal is calculated in correlation with the image features and statistic properties. In the detection step we apply a re-synchronization between the original and watermarked image according to the Neyman–Pearson statistic criterion. Experimentation on a large set of different images has been shown to be resistant against geometric, filtering, and StirMark attacks with a low rate of false alarm.     

A wavelet filter enhancement scheme with a fast integral B-wavelet transform and pyramidal multi-B-wavelet algorithm

A construction paradigm is proposed to refine a class of wavelet bases such that the filter characteristics are enhanced. In particular, it is shown that the entire Mth order B-wavelet family belong to this class. Exploiting some recent work, a fast integral wavelet transform is found for the refined B-wavelet family. Moreover, this refined basis can be placed into the setting of a multiresolution analysis that has a multiplicity greater than one. Accordingly, a fast, discrete, pyramidal algorithm is realised.     

A novel image encryption algorithm based on a 3D chaotic map

Recently [Solak E, Çokal C, Yildiz OT Biyikogˇlu T. Cryptanalysis of Fridrich’s chaotic image encryption. Int J Bifur Chaos 2010;20:1405-1413] cryptanalyzed the chaotic image encryption algorithm of [Fridrich J. Symmetric ciphers based on two-dimensional chaotic maps. Int J Bifur Chaos 1998;8(6):1259-1284], which was considered a benchmark for measuring security of many image encryption algorithms. This attack can also be applied to other encryption algorithms that have a structure similar to Fridrich’s algorithm, such as that of [Chen G, Mao Y, Chui, C. A symmetric image encryption scheme based on 3D chaotic cat maps. Chaos Soliton Fract 2004;21:749-761]. In this paper, we suggest a novel image encryption algorithm based on a three dimensional (3D) chaotic map that can defeat the aforementioned attack among other existing attacks. The design of the proposed algorithm is simple and efficient, and based on three phases which provide the necessary properties for a secure image encryption algorithm including the confusion and diffusion properties. In phase I, the image pixels are shuffled according to a search rule based on the 3D chaotic map. In phases II and III, 3D chaotic maps are used to scramble shuffled pixels through mixing and masking rules, respectively. Simulation results show that the suggested algorithm satisfies the required performance tests such as high level security, large key space and acceptable encryption speed. These characteristics make it a suitable candidate for use in cryptographic applications.     

边界奇异微分方程的区间样条小波求解

本文基于提升格式的第 2代小波构造方法 ,建立了区间上的三次B样条小波 ,并用于求解有边界奇异性的微分方程 .由于区间小波的边界特性 ,该方法避免了由小波基引起的振荡 .模拟计算结果验证了所提方法     

A chaotic block cipher algorithm for image cryptosystems

Recently, many scholars have proposed chaotic cryptosystems in order to promote communication security. However, there are a number of major problems detected in some of those schemes such as weakness against differential attack, slow performance speed, and unacceptable data expansion. In this paper, we introduce a new chaotic block cipher scheme for image cryptosystems that encrypts block of bits rather than block of pixels. It encrypts 256-bits of plainimage to 256-bits of cipherimage within eight 32-bit registers. The scheme employs the cryptographic primitive operations and a non-linear transformation function within encryption operation, and adopts round keys for encryption using a chaotic system. The new scheme is able to encrypt large size of images with superior performance speed than other schemes. The security analysis of the new scheme confirms a high security level and fairly uniform distribution.     

Linear codes for high payload steganography

Steganography is concerned with communicating hidden messages in such a way that no one apart from the sender and the intended recipient can detect the very existence of the message. We study the syndrome coding method (sometimes also called the “matrix embedding method”), which uses a linear code as an ingredient. Among all codes of a fixed block length and fixed dimension (and thus of a fixed information rate), an optimal code is one that makes it most difficult for an eavesdropper to detect the presence of the hidden message. We show that the average distance to code is the appropriate concept that replaces the covering radius for this particular application. We completely classify the optimal codes in the cases when the linear code used in the syndrome coding method is a one- or two-dimensional code over . In the steganography application this translates to cases when the code carries a high payload (has a high information rate).     

Invertible chaotic fragile watermarking for robust image authentication

Fragile watermarking is a popular method for image authentication. In such schemes, a fragile signal that is sensitive to manipulations is embedded in the image, so that it becomes undetectable after any modification of the original work. Most algorithms focus either on the ability to retrieve the original work after watermark detection (invertibility) or on detecting which image parts have been altered (localization). Furthermore, the majority of fragile watermarking schemes suffer from robustness flaws. We propose a new technique that combines localization and invertibility. Moreover, watermark dependency on the original image and the non-linear watermark embedding procedure guarantees that no malicious attacks will manage to create information leaks.     

A coding problem in steganography

To study how to design a steganographic algorithm more efficiently, a new coding problem—steganographic codes (abbreviated stego-codes)—is presented in this paper. The stego-codes are defined over the field with q(q ≥ 2) elements. A method of constructing linear stego-codes is proposed by using the direct sum of vector subspaces. And the problem of linear stego-codes is converted to an algebraic problem by introducing the concept of the tth dimension of a vector space. Some bounds on the length of stego-codes are obtained, from which the maximum length embeddable (MLE) code arises. It is shown that there is a corresponding relation between MLE codes and perfect error-correcting codes. Furthermore the classification of all MLE codes and a lower bound on the number of binary MLE codes are obtained based on the corresponding results on perfect codes. Finally hiding redundancy is defined to value the performance of stego-codes.      

Contrast enhancement for image by WNN and GA combining PSNR with information entropy

A new contrast enhancement algorithm for image is proposed combining genetic algorithm (GA) with wavelet neural network (WNN). In-complete Beta transform (IBT) is used to obtain non-linear gray transform curve so as to enhance global contrast for an image. GA determines optimal gray transform parameters. In order to avoid the expensive time for traditional contrast enhancement algorithms, which search optimal gray transform parameters in the whole parameters space, based on gray distribution of an image, a classification criterion is proposed. Contrast type for original image is determined by the new criterion. Parameters space is, respectively, determined according to different contrast types, which greatly shrink parameters space. Thus searching direction of GA is guided by the new parameter space. Considering the drawback of traditional histogram equalization that it reduces the information and enlarges noise and background blur in the processed image, a synthetic objective function is used as fitness function of GA combining peak signal-noise-ratio (PSNR) and information entropy. In order to calculate IBT in the whole image, WNN is used to approximate the IBT. In order to enhance the local contrast for image, discrete stationary wavelet transform (DSWT) is used to enhance detail in an image. Having implemented DSWT to an image, detail is enhanced by a non-linear operator in three high frequency sub-bands. The coefficients in the low frequency sub-bands are set as zero. Final enhanced image is obtained by adding the global enhanced image with the local enhanced image. Experimental results show that the new algorithm is able to well enhance the global and local contrast for image while keeping the noise and background blur from being greatly enlarged.     

ESL-SELO: A robust image denoising algorithm with penalty

Robust image recovery methods have been attracted more and more attention in recent decades for its good property of tolerating system errors or measuring noise. In this paper, we propose a new robust method (ESL-SELO) to recover nosing image, which combine exponential loss function and seamless-L0 (SELO) penalty function to guarantee both accuracy and robustness of the estimator. Theoretical result showed that our method has a local optimal solution and good asymptotic properties. Finally, we compare our method with other methods in simulation which shows better robustness and takes much less time.     

An efficient self-adaptive model for chaotic image encryption algorithm

In this paper, an efficient self-adaptive model for chaotic image encryption algorithm is proposed. With the help of the classical structure of permutation-diffusion and double simple two-dimensional chaotic systems, an efficient and fast encryption algorithm is designed. However, different from most of the existing methods which are found insecure upon chosen-plaintext or known-plaintext attack in the process of permutation or diffusion, the keystream generated in both operations of our method is dependent on the plain-image. Therefore, different plain-images will have different keystreams in both processes even just only a bit is changed in the plain-image. This design can solve the problem of fixed chaotic sequence produced by the same initial conditions but for different images. Moreover, the operation speed is high because complex mathematical methods, such as Runge–Kutta method, of solving the high-dimensional partial differential equations are avoided. Numerical experiments show that the proposed self-adaptive method can well resist against chosen-plaintext and known-plaintext attacks, and has high security and efficiency.     

Continuous and discrete Bessel wavelet transforms

Using the theory of Hankel convolution, continuous and discrete Bessel wavelet transforms are defined. Certain boundedness results and inversion formula for the continuous Bessel wavelet transform are obtained. Important properties of the discrete Bessel wavelet transform are given.     

Hybrid chaos control of continuous unified chaotic systems using discrete rippling sliding mode control

In this paper, a new systematic design procedure to stabilize continuous unified chaotic systems based on discrete sliding mode control (DSMC) is presented. In contrast to the previous works, the concept of rippling control is newly introduced such that the design of DSMC can be simplified and only a single controller is needed to realize chaos suppression. As expected, under the proposed DSMC law, the unified system can be stabilized in a manner of ripple effect, even when the external uncertainty is present. Last, two examples are included to illustrate the effectiveness of the proposed rippling DSMC developed in this paper.     

Improving the complexity of chaotic sequence based on the PCA algorithm

The principal component analysis (PCA) is an effective statistical analysis method in statistical data analysis, feature extraction and data compression. The method simplifies multiple related variables into a linear combination of several irrelevant variables, through the less-comprehensive index as far as possible to replace many of the original data, and can reflect the information provided by the original data. This paper studies the signal feature extraction algorithm based on PCA, and extracts sequences’ feature which generated by Logistic mapping. Then we measured the complexity of the reconstructed chaotic sequences by the permutation entropy algorithm. The testing results show that the complexity of the reconstruction sequences is significantly higher than the original sequences.     

Global optimization using a synchronization of multiple search Points autonomously driven by a chaotic dynamic model

In the present paper, we propose a new multipoint type global optimization model using a chaotic dynamic model and a synchronization phenomenon in nonlinear dynamic systems for a continuously differentiable optimization problem. We first improve the Discrete Gradient Chaos Model (DGCM), which drives each search point’s autonomous movement, based on theoretical analysis. We then derive a new coupling structure called PD type coupling in order to obtain stable synchronization of all search points with the chaotic dynamic model in a discrete time system. Finally, we propose a new multipoint type global optimization model, in which each search point moves autonomously by improved DGCM and their trajectories are synchronized to elite search points by the PD type coupling model. The proposed model properly achieves diversification and intensification, which are reported to be important strategies for global optimization in the Meta-heuristics research field. Through application to proper benchmark problems [Liang et al. Novel composition test functions for numerical global optimization. In: Proceedings of Swarm Intelligence Symposium, 2005 (SIS 2005), pp. 68–75 (2005); Liang et al. Nat. Comput. 5(1), 83–96, 2006] (in which the drawbacks of typical benchmark problems are improved) with 100 or 1000 variables, we confirm that the proposed model is more effective than other gradient-based methods.     

WAVELET TRANSFORM IN FRACTAL IMAGE ENCODING

This paper presents some results of the relation between wavelet transform and fractal transform. The wavelet transform of the attractor of fractal transform posseses translational and scale invariance. So we speed the fractal image encoding by testing the invariance of the wavelet transform appropriate for image encoding. The classfication scheme of range blocks by wavelet transform is given in this paper.     

Cryptanalyzing a nonlinear chaotic algorithm (NCA) for image encryption

This paper describes the security weakness of a recently proposed image encryption algorithm based on a logistic-like new chaotic map. We show that the chaotic map’s distribution is far from ideal, thus making it a bad candidate as a pseudo-random stream generator. As a consequence, the images encrypted with this algorithm are shown to be breakable through different attacks of variable complexity.     

A capacity scaling algorithm for M-convex submodular flow

This paper presents a faster algorithm for the M-convex submodular flow problem, which is a generalization of the minimum-cost flow problem with an M-convex cost function for the flow-boundary, where an M-convex function is a nonlinear nonseparable discrete convex function on integer points. The algorithm extends the capacity scaling approach for the submodular flow problem by Fleischer, Iwata and McCormick (2002) with the aid of a novel technique of changing the potential by solving maximum submodular flow problems.Mathematics Subject Classification (1991): 90C27A preliminary version of this paper has appeared in Proceedings of the Tenth International Conference on Integer Programming and Combinatorial Optimization (IPCO X), LNCS 3064, Springer-Verlag, 2004, pp. 352–367.