Piecewise Linear Chaotic Map Research Articles

Chaotic hash function based on the dynamic S-Box with variable parameters

We present a chaotic hash function based on the dynamic S-Box with variable parameters in this paper. More specifically, we first exploit the piecewise linear chaotic map to obtain four initial buffers and an initial hash value. Then, we divide a randomly chosen message into message blocks and assign the four buffers and current message block to a transfer function to produce variable parameters and initial values of the PWLCM and logistic map for constructing a dynamic S-Box, which is then used for updating the four buffers. After all the message blocks are processed, the final hash value is generated by cascading the buffers and then applying XOR operation with the last hash value. Finally, we conduct performance evaluation on the proposed hash algorithm in terms of sensitivity, confusion and diffusion properties, collision resistances, speed analysis, randomness tests, and comparison with other algorithms, and the results demonstrate that the proposed algorithm has good statistical properties, strong collision resistances and better performance compared with other schemes.

A novel and effective image encryption algorithm based on chaos and DNA encoding

In this paper, we proposed a novel and effective image encryption algorithm based on Chaos and DNA encoding rules. Piecewise Linear Chaotic Map (PWLCM) and Logistic Map are applied to generate all parameters the presented algorithm needs and DNA encoding technology functions as an auxiliary tool. The proposed algorithm consists of these parts: firstly, use PWLCM to produce a key image, whose pixels are generated by Chaos; Secondly, encode the plain image and the key image with DNA rules by rows respectively and different rows are encoded according to various rules decided by logistic map; After that, employ encoded key image to conduct DNA operations with the encoded plain image row by row to obtain an intermediate image and the specific operation executed every row is chosen by logistic map; Then, decode the intermediate image as the plain image of next step. Finally, repeat steps above by columns again to get the ultimate cipher image. The experiment results and analysis indicate that the proposed algorithm is capable of withstanding typical attacks and has good character of security.

A fast and efficient hash function based on generalized chaotic mapping with variable parameters

We present a fast and efficient hash algorithm based on a generalized chaotic mapping with variable parameters in this paper. We first define a generalized chaotic mapping by utilizing piecewise linear chaotic map and trigonometric functions. Then, we convert the arbitrary length of message into the corresponding ASCII values and perform 6-unit iterations with variable parameters and message values based on the generalized chaotic mapping. The final hash value is obtained by cascading extracted bits from iteration state values. We excessively evaluate the proposed algorithm in terms of distribution of hash value, sensitivity of hash value to the message and secret keys, statistical analysis of diffusion and confusion, analysis of birthday attacks and collision resistance, analysis of secret keys, analysis of speed, and comparison with other algorithms, and the results illustrate that the suggested algorithm is fast, efficient, and enough simple and has good confusion and diffusion capabilities, strong collision resistance, and a high level of security.

A Reliable Image Watermarking Scheme Based on Redistributed Image Normalization and SVD

Digital image watermarking is the process of concealing secret information in a digital image for protecting its rightful ownership. Most of the existing block based singular value decomposition (SVD) digital watermarking schemes are not robust to geometric distortions, such as rotation in an integer multiple of ninety degree and image flipping, which change the locations of the pixels but don’t make any changes to the pixel’s intensity of the image. Also, the schemes have used a constant scaling factor to give the same weightage to the coefficients of different magnitudes that results in visible distortion in some regions of the watermarked image. Therefore, to overcome the problems mentioned here, this paper proposes a novel image watermarking scheme by incorporating the concepts of redistributed image normalization and variable scaling factor depending on the coefficient’s magnitude to be embedded. Furthermore, to enhance the security and robustness the watermark is shuffled by using the piecewise linear chaotic map before the embedding. To investigate the robustness of the scheme several attacks are applied to seriously distort the watermarked image. Empirical analysis of the results has demonstrated the efficiency of the proposed scheme.

A novel bit-level image encryption algorithm based on chaotic maps

Recently, a number of chaos-based image encryption algorithms have been proposed at the pixel level, but little research at the bit level has been conducted. This paper presents a novel bit-level image encryption algorithm that is based on piecewise linear chaotic maps (PWLCM). First, the plain image is transformed into two binary sequences of the same size. Second, a new diffusion strategy is introduced to diffuse the two sequences mutually. Then, we swap the binary elements in the two sequences by the control of a chaotic map, which can permute the bits in one bitplane into any other bitplane. The proposed algorithm has excellent encryption performance with only one round. The simulation results and performance analysis show that the proposed algorithm is both secure and reliable for image encryption.

An improved fragile watermarking algorithm for JPEG images

In this paper a new fragile watermarking algorithm is proposed that is built upon the cryptanalysis of the CWSA algorithm (Chaotic Watermarking Scheme for Authentication of JPEG Images – Wang et al. [14]). The proposed algorithm preserves the advantages of CWSA, but is robust against cryptanalysis, faster and less perceptible. It uses two chaotic maps: the piecewise linear chaotic map and a chaotic generator composed of two perturbed recursive filters with a nonlinear function, the Skew Tent map. Experimental results show that the proposed algorithm provides good performances in terms of security, imperceptibility, speed and resistance to cryptographic attacks.

A non-linear preprocessing for opto-digital image encryption using multiple-parameter discrete fractional Fourier transform

In this paper, a novel opto-digital image encryption technique is proposed by introducing a new non-linear preprocessing and using the multiple-parameter discrete fractional Fourier transform (MPDFrFT). The non-linear preprocessing is performed digitally on the input image in the spatial domain using a piecewise linear chaotic map (PLCM) coupled with the bitwise exclusive OR (XOR). The resulting image is multiplied by a random phase mask before applying the MPDFrFT to whiten the image. Then, a chaotic permutation is performed on the output of the MPDFrFT using another PLCM different from the one used in the spatial domain. Finally, another MPDFrFT is applied to obtain the encrypted image. The parameters of the PLCMs together with the multiple fractional orders of the MPDFrFTs constitute the secret key for the proposed cryptosystem. Computer simulation results and security analysis are presented to show the robustness of the proposed opto-digital image encryption technique and the great importance of the new non-linear preprocessing introduced to enhance the security of the cryptosystem and overcome the problem of linearity encountered in the existing permutation-based opto-digital image encryption schemes.

Use of Chebyshev Polynomial Kalman Filter for pseudo-blind demodulation of CD3S signals

Chaos based communication represents an attractive solution in order to design secure multiple access digital communication systems. In this paper we investigate the use of piecewise linear chaotic maps as chaotic generators combined, on the receiver side, with Chebyshev Polynomial Kalman Filters in a dual scheme configuration for demodulation purpose. Piecewise linear maps results into enhanced robustness properties of the spreading chaotic sequence, while approximation of nonlinear systems through Chebyshev polynomial series allows closed form estimation of mean and variance. Therefore, statistical moments can be computed by means of simple algebraic operations on matrices in compact form. In this work we extend these concepts to a dual Chebyshev Polynomial Kalman Filter scheme, suitable for signal recovery in chaos based spread spectrum systems. Numerical simulations show that the proposed method achieves lower error levels on a wide range of the bit-energy-tonoise- power-spectral-density ratio with respect to a state-of-the-art method based on unscented Kalman filters.

Asymmetric color image encryption scheme using discrete-time map and hash value

A chaos-based asymmetric color image encryption scheme is designed. The hash value of the plain image is transformed into three initial values for the piecewise linear chaotic map (PWLCM), which is iterated to generate three pseudo-random sequences to diffuse the red, green and blue components respectively. In the encryption process, the hash value and the initial iteration number m are served as keys, and in the decryption process, three initial values for PWLCM and the initial iteration number n are served as keys. Numerical results demonstrate the feasibility and effectiveness of the proposed asymmetric cryptosystem for color image encryption.

A novel hybrid system for feature selection based on an improved gravitational search algorithm and k-NN method

Feature selection is an important pre-processing step for solving classification problems. This problem is often solved by applying evolutionary algorithms in order to decrease the dimensional number of features involved. In this paper, we propose a novel hybrid system to improve classification accuracy with an appropriate feature subset in binary problems based on an improved gravitational search algorithm. This algorithm makes the best of ergodicity of piecewise linear chaotic map to explore the global search and utilizes the sequential quadratic programming to accelerate the local search. We evaluate the proposed hybrid system on several UCI machine learning benchmark examples, comparing our approaches with feature selection techniques and obtained better predictions with consistently fewer relevant features. Furthermore, the improved gravitational search algorithm is tested on 23 nonlinear benchmark functions and compared with 5 other heuristic algorithms. The obtained results confirm the high performance of the improved gravitational search algorithm in solving function optimization problems.

Construction of Substitution Box Based on Piecewise Linear Chaotic Map and S8 Group

In this paper, a scheme for the construction of substitution boxes (S-boxes) based on chaotic map and S8 (symmetric group of permutation) is presented. The properties such as nonlinearity, strict avalanche and resistance against the differential cryptanalysis are analyzed in detail. The result shows that the criterion for designing good S-box can be met approximately. As a result, our approach is suitable for practical application in designing block cryptosystem.

An audio encryption technique through compressive sensing and Arnold transform

In this paper, an audio encryption scheme using compressive sensing (CS) and Arnold transform-based scrambling is presented. In the proposed method, compressive sensing is done by using a key-based measurement matrix and the scrambling is carried out with the help of a key-based Arnold matrix. The use of these key-based matrices not only provides better security but also do away with their transmission and storage requirement. The measurement matrix is constructed by using the random numbers generated by a linear feedback shift register (LFSR) whose initial state is generated by a piece wise linear chaotic map (PWLCM), using three 32-bit keys whereas the Arnold matrix is constructed by the random numbers generated by using another 32-bit secret key, PWLCM and a logistic map. By combining secure compressive sensing and Arnold scrambling techniques, very high security can be ensured in addition to efficient channel usage, good resistivity to noise, best reconstruction performance, little encoder complexity and excellent scrambling of data. Experimental results prove the effectiveness of the proposed scheme.

On the Cryptanalysis of Two Cryptographic Algorithms That Utilize Chaotic Neural Networks

This paper deals with the security and efficiency issues of two cipher algorithms which utilize the principles of Chaotic Neural Networks (CNNs). The two algorithms that we consider are (1) the CNN-Hash, which is a one-way hash function based on the Piece-Wise Linear Chaotic Map (PWLCM) and the One-Way Coupled Map Lattice (OCML), and (2) the Delayed CNN-Based Encryption (DCBE), which is an encryption algorithm based on the delayed CNN. Although both of these cipher algorithms have their own salient characteristics, our analysis shows that, unfortunately, the CNN-Hash is not secure because it is neither Second-Preimage resistant nor collision resistant. Indeed, one can find a collision with relative ease, demonstrating that its potential as a hash function is flawed. Similarly, we show that the DCBE is also not secure since it is not capable of resisting known plaintext, chosen plaintext, and chosen ciphertext attacks. Furthermore, unfortunately, both schemes are not efficient either, because of the large number of iteration steps involved in their respective implementations.

An efficient and noise resistive selective image encryption scheme for gray images based on chaotic maps and DNA complementary rules

A novel image encryption algorithm in streaming mode is proposed which exhaustively employs an entire set of DNA complementary rules alongwith one dimensional chaotic maps. The proposed algorithm is highly efficient due to encrypting the subset of digital image which contains 92.125 % of information. DNA addition operation is carried out on this MSB part. The core idea of the proposed scheme is to scramble the whole image by means of piecewise linear chaotic map (PWLCM) followed by decomposition of image into most significant bits (MSB) and least significant bits (LSB). The logistic sequence is XORed with the decoded MSB and LSB parts separately and finally these two parts are combined to get the ciphered image. The parameters for PWLCM, logistic map and selection of different DNA rules for encoding and decoding of both parts of an image are derived from 128-bit MD5 hash of the plain image. Simulated experimental results in terms of quantitative and qualitative ways prove the encryption quality. Efficiency and robustness against different noises make the proposed cipher a good candidate for real time applications.

Optimal image watermarking scheme based on chaotic map and quaternion wavelet transform

In this paper, an intelligent watermarking scheme optimized by adaptive differential evolution (ADE) is proposed based on chaotic map and quaternion wavelet transform (QWT). Watermark is first scrambled by a piecewise linear chaotic map to increase security and then inserted into the real QWT amplitude coefficients intelligently. ADE algorithm is explored to optimize the watermarking parameter (i.e., scaling factors) automatically. The experimental results demonstrate the high robustness against common signal processing operations, especially geometrical distortions of the proposed algorithm. Comparison results also indicate the superiority of the proposed algorithm over the existing watermarking algorithm.

Audio security through compressive sampling and cellular automata

In this paper, a new approach for scrambling the compressive sensed (CS) audio data using two dimensional cellular automata is presented. In order to improve the security, linear feedback shift register (LFSR) based secure measurement matrix for compressive sensing is used. The basic idea is to select the different states of LFSR as the entries of a random matrix and orthonormalize these values to generate a Gaussian random measurement matrix. It is proposed to generate the initial state matrix of cellular automata using an LFSR based random bitstream generator. In order to improve the security and key space of the proposed cryptosystem, piecewise linear chaotic map (PWLCM) based initial seeds generation for LFSRs is used. In the proposed approach, the initial value, parameter value and the number of iterations of PWLCM are kept as secret to provide security. The proposed audio encryption method for CS audio data is validated with different compressive sensing reconstruction approaches. Experimental and analytical verification shows that the proposed encryption system gives good reconstruction performance, robustness to noise, high level of scrambling and good security against several forms of attack. Moreover, since the measurement matrix used for CS operation and the initial state matrix used for 2D cellular automata are generated using the secret key, the storage/transmission requirement of the same can be avoided.

Hiding message into DNA sequence through DNA coding and chaotic maps

The paper proposes an improved reversible substitution method to hide data into deoxyribonucleic acid (DNA) sequence, and four measures have been taken to enhance the robustness and enlarge the hiding capacity, such as encode the secret message by DNA coding, encrypt it by pseudo-random sequence, generate the relative hiding locations by piecewise linear chaotic map, and embed the encoded and encrypted message into a randomly selected DNA sequence using the complementary rule. The key space and the hiding capacity are analyzed. Experimental results indicate that the proposed method has a better performance compared with the competing methods with respect to robustness and capacity.

A Chaotic Image Encryption Algorithm Based on a Dynamical Feedback Operation

This paper designs an image encryption algorithm with a dynamical feedback operation based on sensitive chaotic system. In the proposed algorithm, the piece wise linear chaotic map is selected to construct pseudo-random keystream sequences. The pseudorandom keystream sequences are used to permute and substitute the plain image data. To enhance the complexity and security of the algorithm, each pixel is dynamically confused by its two previous adjacent encrypted pixels which are specified by a quantized binary tuple derived from a chaotic element. Both theoretical analysis and experimental tests show that the proposed algorithm is secure and efficient.

A Novel Encryption Scheme based on Piecewise Linear Chaotic Maps for Multimedia Data

recent years, many multimedia and image encryption techniques based on chaotic maps have been proposed. In this paper, we propose a novel multimedia data encryption technique called MDEA (Multimedia Data Encryption Algorithm). Proposed encryption scheme is based on two digital chaotic maps, which in turn are used to generate two different chaotic sequences. Detail description of the proposed encryption technique and performance analysis of MDEA on various parameters of security is given in later sections of this paper.

Feature subset selection by gravitational search algorithm optimization

A new method for feature subset selection in machine learning, FSS-MGSA (Feature Subset Selection by Modified Gravitational Search Algorithm), is presented. FSS-MGSA is an evolutionary, stochastic search algorithm based on the law of gravity and mass interactions, and it can be executed when domain knowledge is not available. A wrapper approach, over Naive-Bayes, ID3, K-Nearest Neighbor and Support Vector Machine learning algorithms, is used to evaluate the goodness of each visited solution. The key to the success of the MGSA is to utilize the piecewise linear chaotic map for increasing its diversity of species, and to use sequential quadratic programming for accelerating local exploitation. Promising results are achieved in a variety of tasks where domain knowledge is not available. The experimental results show that the proposed method has the ability of selecting the discriminating input features correctly and can achieve high accuracy of classification, which is comparable to or better than well-known similar classifier systems. Furthermore, the MGSA is tested on ten functions provided by CEC 2005 special session and compared with various modified Gravitational Search Algorithm, Particle Swarm Optimization, and Genetic Algorithm. The obtained results confirm the high performance of the MGSA in solving various problems in optimization.