Color Image Encryption Algorithm Based on Dynamic Chaos and Matrix Convolution

Images are important information carriers in our lives, and images should be secure when transmitted and stored. Image encryption algorithms based on chaos theory emerge in endlessly. Based on previous various chaotic image fast encryption algorithms, this paper proposes a color image sector fast encryption algorithm based on one-dimensional composite sinusoidal chaotic mapping. The main purpose of this algorithm is to improve the encryption and decryption speed of color images and improve the efficiency of image encryption in the big data era. First, four basic chaos maps are combined in pairs and added with sine operations. Six one-dimensional composite sinusoidal chaos maps (CSCM) were obtained. Secondly, select the two best chaotic mappings LCS and SCS. The randomness of these two chaotic mappings was verified through Lyapunov index and NIST SP 800-22 randomness tests. Thirdly, the encryption process is carried out according to the shape of a traditional Chinese fan, and the diffusion and scrambling of each pixel of the image are performed in parallel. This greatly improves encryption speed. When diffusing, changing the value of one pixel can affect the values of multiple subsequent pixels. When scrambling, each pixel changes position with the three pixels before it according to the chaotic sequence. Finally, through many experiments, it is proved that the image encryption algorithm not only greatly improves the encryption and decryption speed, but also improves various indexes. The key space reached 2192, the average information entropy was 7.9994, the average NPCR was 99.6172, and the average UACI was 33.4646. The algorithm can also resist some common attacks and accidents, such as exhaustion attack, differential attack, noise attack, information loss and so on.

In this paper, a cellular neural network (CNN) chaotic system is constructed and the multiple stability of the system and its rich chaotic properties are confirmed by studying the effect of parameters on the system, coexisting attractors, and offset boosting behavior. As linear feedback shift registers (LFSR) can be applied to cryptography, this paper applies LFSR to generate encrypted key matrices to enhance the randomness of encryption algorithms. Based on CNN and LFSR, a new color image encryption algorithm is designed by combining DNA coding and bit-plane decomposition with high bit-plane Zigzag dislocation changes. Experimental results and security tests show that the algorithm is highly secure and resistant to a variety of common attacks, such as differential attacks, cropping attacks, and noise attacks.

A color image encryption and decryption scheme based on extended DNA coding and fractional-order 5D hyper-chaotic system

Chaotic sequences and chaotic dynamical systems are attractive candidates for use in signal synthesis and analysis as well as in communications applications. In previous works, various methods for the estimation of chaotic sequences under noise were developed. However, although the methods were different, their qualitative performance was the same: for high signal-to-noise ratio (SNR) the performance was good, but below some threshold SNR, a sharp degradation in performance occurred. We prove and quantify the existence of this threshold effect and derive lower bounds on the value of the threshold SNR. Using information-theoretic tools, we prove that for any ergodic chaotic system, there is a certain threshold SNR level below which the ratio between the mean-square error obtained by any estimator of the system's initial state at the output of additive white Gaussian noise (AWGN) channel and the Cramer-Rao bound increases exponentially fast as the number of observations N grows without bound. We explain the connection between the existence of a threshold effect in the estimation of chaotic sequences and the converse to the joint source-channel coding theorem. We derive lower bounds on SNR/sub th/, the value of the threshold SNR, as a function of the system's Lyapunov exponent. Our bounds have two versions, one for a finite number of observations, and one for the asymptotic regime as N/spl rarr//spl infin/. For the asymptotic regime, the bound we develop on the threshold SNR incorporates the key parameters of chaotic systems, the Lyapunov exponent, and the chaotic sequence power spectrum into a simple formula. We demonstrate our results on the chaotic system governed by the r-diadic map.

Chaos is a deterministic, random-like process that occurs in nonlinear dynamic systems. This process is neither periodic nor convergent, and has a sensitive dependence on the initial value. Therefore, the sequence generated by the chaotic dynamic system is widely used in communication encryption systems. However, the phenomenon of “invalid keys” and “quasi-invalid keys” widely existing in chaotic sequences will undoubtedly affect the security of secure communication systems. In this paper, the general existence of invalid keys and quasi-invalid keys in typical one-dimensional chaotic dynamic system is first demonstrated. Then a chaotic binary pseudo-random sequence candidate generation algorithm is proposed, finally the feasibility of this candidate algorithm is verified by the FIPS 140-2 test standard.

The transition from text to images as the primary form of information transmission has recently increased the need for secure and effective encryption techniques due to the expanding information dimensions. The color picture encryption algorithm utilizing chaotic mapping is limited by a small chaotic range, unstable chaotic state, and lengthy encryption duration. This study integrates the Ackley function and the Styblinski–Tang function into a novel two-dimensional hyperchaotic map for optimization testing. A randomness test is run on the chaotic sequence created by the system to check that the new chaotic system can better sustain the chaotic state. This study introduces two techniques, genetic recombination and clock diffusion, to simultaneously disperse and mix images at the bit level. This study utilizes chaotic sequences in genetic recombination and clock drift to propose an image encryption technique. The data indicates that the method demonstrates high encryption efficiency. At the same time, the key also successfully passed the NIST randomness test, verifying its sensitivity and randomness. The algorithm’s dependability has been demonstrated and can be utilized for color image encryption.

Chaotic sequences and chaotic dynamic systems are attractive candidates for use in signal modelling, synthesis, and analysis as well as in communications applications. In most of the above applications, there is a frequent need to estimate the chaotic sequence from noisy observations. In previous works, various methods for the estimation of chaotic sequences under noise were developed. However, although the methods were different, their qualitative performance was the same: for high SNR the performance was good, but below some threshold SNR, a sharp degradation in performance occurred. Using information-theoretic tools, we quantify this threshold effect and obtain lower bounds on the value of the threshold SNR. We show that the lower bound depends on the system's Lyapunov exponent and the mutual information between the chaotic sequence and the noisy observations. This bound is further simplified to a bound depending on the system's Lyapunov exponent and the power spectrum of the chaotic sequence. Essentially, for SNRs below the threshold, the amount of information that the chaotic system produces about its initial state is larger than the maximum information that the channel can convey with low probability of error. Thus, degradation in distortion performance is unavoidable.

Image encryption based on 3D Cubic-Sine Logistic Coupled Map and Improved Chirikov Map

A chaotic image encryption algorithm based on random dynamic mixing

Transferring data, particularly digital images, over unsecured communication channels has overgrown in the past years. Digital images such as medical images have certain information. Thus, these data should remain protected and inaccessible. According to discussed issues and numerous attack methods, implementing a high secure encryption algorithm is confronted with crucial issues and challenges. This paper proposes a new efficient color image encryption based on a chaotic system and DNA encoding following one round process. Initially, a hash function generates a secret key to be used in the confusion and diffusion stages simultaneously. Subsequently, the pixels' values are changed in the confusion phase through DNA encoding and XORing. Ultimately, the adjacent pixels' positions are shifted by permutation boxes generated from the chaotic system, and the cipher image is achieved. The experimental results and security analysis proves that our scheme has significantly higher security than other methods and can resist statistical attacks, differential attacks, and occlusion attacks.

A new self-embedding and fragile watermarking technique which was used for image integrity authentication was brought up. The assured function of the composite chaotic iterative dynamic system and its initial parameter was put forward. The method using the single pixel value for self-authentication that authenticating bit embedded in the lowest significant bit of the pixel value was brought up. It brought up the prime decomposition function of the pixel value, making the adjacent pixel value completely separated in chaotic calculation. It led up to the facts that no additional information was needed when authenticating, and the algorithm could prevent the safety danger caused by parameter transmission, and it could ascertain the position accurately to a single pixel when tamper occurs, the probability of successful attack was 50%.

In this study, we presented a hybrid method of a new 4D hyper-chaotic system with DNA encoding for the encryption of RGB images. The suggested encryption algorithm consists of three stages: permutation, confusion, and DNA coding. First, color components are permuted utilizing the index of the chaotic sequences are constructed from the new chaotic system to remove the high correlation among adjacent pixels. Second, we performed the XOR between the chaotic sequences and the permuted image from the previous phase. Finally, a set of DNA processes (DNA addition, DNA XOR, and DNA subtraction) are performed between the DNA sequences of the confusing image with the DNA chaotic sequences to obtain the final encoded image. Through tests like key space, key sensitivity, information entropy, and the histogram, the simulation analysis shows that the suggested method is secure and effective, and it has the ability to resist various attacks.

Optical color image encryption based on computer generated hologram and chaotic theory

Recently, many encryption algorithms based on fractional-order chaotic system have been proposed to solve the problem of image encryption. In this paper, we propose a novel color image compression-encryption algorithm based on fractional-order hyperchaotic system and DNA coding. In the data compression stage, the data of R, G, and B channels of the color image are converted to the frequency domain by two-dimensional discrete cosine transform (DCT), and then the amount of encrypted data is reduced by the quantization process. We design a data processing algorithm to ensure that the data after DCT is compatible with DNA coding data format. In the encryption stage, the processes of DNA encoding and decoding, DNA operation, and pixel scrambling are all controlled by the corresponding chaotic sequences, which are generated by the chaotic system. The original image is used to calculate the initial state of the chaotic system, which improves the performance of the algorithm against the chosen-plaintext attack significantly. Experimental results and security analysis illustrate that the proposed algorithm has excellent compression and security performance. It can not only reconstruct the original image well under the condition of low compression ratio, but also provide high security to resist various attacks. Besides, experimental results also indicate that the algorithm proposed can be applied to the fields of color image compression, encryption, and transmission.

As chaotic sequences became more popular within the evolutionary computation community; we choose to address some of the issues that occur when the extremely sensitive chaotic systems are embedded into the Particle Swarm Optimization algorithm. We investigate here the particle trajectory change with changing chaotic systems and with different sequencing. This research highlights several significant trends through the 2D graphical visualizations and 10D statistics, and further, it provides advice for future studies in this area of hybridizing of complex dynamics and swarm based algorithms.