A novel image encryption method based on total shuffling scheme

In this paper, a novel image encryption method based on skew tent chaotic map and permutation-diffusion architecture is proposed. In the proposed method, the P-box is chosen as the same size of plain-image, which shuffles the positions of pixels totally. The keystream generated by skew tent chaotic map is related to the plain-image. Statistical analysis, information entropy analysis, and sensitivity analysis to plaintext and key on the proposed scheme are provided in this paper. It can be seen that this algorithm is efficient and reliable, with high potential to be adopted for network security and secure communications.     

Encrypting the compressed image by chaotic map and arithmetic coding

Due to the efficient and secure requirements of image transmission, a number of research works have been done to encrypt the compressed image. Inspired by the arithmetic coding and chaotic map which are used to compress and encrypt image, respectively. In this paper, a scheme is proposed to encrypt the compressed image by chaotic map and arithmetic coding. This scheme compresses the image row by row which is firstly permuted by two logistic maps before arithmetic coding. It not only enhances the security of arithmetic coding, but also improves the compression ratio. To further improve the security of binary data which has been compressed, we use the chaotic maps to encrypt the data, and set different parameters and initial value for chaotic maps. In order to possess high sensitivities of key and plain-image, the keys that are employed to determine the parameter and initial value of chaotic maps are related to the plain-image. The experimental results validate the effect of the proposed scheme and demonstrate that the compressed and encrypted image is secure and convenient for transmission.     

Wave atom transform generated strong image hashing scheme

The rapid development of multimedia technology has resulted in a rising rate on digital unauthorized utilization and forgery, which makes the situation of image authentication increasingly severe. A novel strong image hashing scheme is proposed based on wave atom transform, which can better authenticate images by precisely distinguishing the malicious tampered images from the non-maliciously processed ones. Wave atom transform is employed since it has significantly sparser expansion and better characteristics of texture feature extraction than other traditional transforms. For better detection sensitivity, gray code is applied instead of natural binary code to optimize the hamming distance. Randomizations are also performed using Rényi chaotic map for the purposes of secure image hashing and key sensitivity. The experimental results show that the proposed strong scheme is robust to non-malicious content-preserving operations and also fragile to malicious content-altering operations. The scheme also outperforms DCT and DWT based schemes in terms of receiving operating characteristic (ROC) curves. Moreover, to provide an application-defined tradeoff, a security enhancement approach based on Rényi map is presented, which can further protect the integrity and secrecy of images.     

一种基于保守混沌的密钥分发协议及图像加密算法

耗散混沌系统可以通过时滞嵌入法重构混沌吸引子,因而耗散混沌在基于混沌的信息加密技术中存在一定隐患。针对这一问题提出一种基于保守混沌的密钥分发协议及图像加密算法,该算法将图像数据通过Hash算法转换为保守混沌系统的初始值,形成一次一密的加密结构。然后利用保守混沌信号结合密钥分发协议生成二进制密钥流,该过程由发送方和接受方双方共同完成。使用得到的二进制密钥流对图像数据置乱和扩散,得到加密图像数据。仿真结果表明：该算法安全可靠,能够有效地隐藏原图像信息,并能抵御一些常见的攻击。此外,该加密算法所使用的保守混沌不存在吸引子难以被破解,算法的安全性进一步加强。     

Image encryption using high-dimension chaotic system

In recent years, the chaos based cryptographic algorithms have suggested some new and efficient ways to develop secure image encryption techniques. This paper proposes a new approach for image encryption based on a high-dimensional chaotic map. The new scheme employs the Cat map to shuffle the positions, then to confuse the relationship between the cipher-image and the plain-image using the high-dimensional Lorenz chaotic map preprocessed. The results of experimental, statistical analysis and key space analysis show that the proposed image encryption scheme provides an efficient and secure way for real-time image encryption and transmission.     

Digital image encryption with chaotic map lattices

This paper proposes a secure approach for encryption and decryption of digital images with chaotic map lattices. In the proposed encryption process,eight different types of operations are used to encrypt the pixels of an image and one of them will be used for particular pixels decided by the outcome of the chaotic map lattices. To make the cipher more robust against any attacks,the secret key is modified after encrypting each block of sixteen pixels of the image. The experimental results and security analysis show that the proposed image encryption scheme achieves high security and efficiency.     

Relaxation properties of chaotic dynamical systems: Operator approach

A method of analytically determining eigenvalues and the piecewise-continuous eigenfunction systems of the Perron-Frobenius operator for Rényi chaotic map x _n+1 = βx _n mod 1, 1 < β < 2 based on introducing the generating function for the eigenfunctions is described. These characteristics define the relaxation properties and decay of correlations in discrete dynamical systems.     

On variational expressions for quantum relative entropies

Distance measures between quantum states like the trace distance and the fidelity can naturally be defined by optimizing a classical distance measure over all measurement statistics that can be obtained from the respective quantum states. In contrast, Petz showed that the measured relative entropy, defined as a maximization of the Kullback–Leibler divergence over projective measurement statistics, is strictly smaller than Umegaki’s quantum relative entropy whenever the states do not commute. We extend this result in two ways. First, we show that Petz’ conclusion remains true if we allow general positive operator-valued measures. Second, we extend the result to Rényi relative entropies and show that for non-commuting states the sandwiched Rényi relative entropy is strictly larger than the measured Rényi relative entropy for \(\alpha \in (\frac{1}{2}, \infty )\) and strictly smaller for \(\alpha \in [0,\frac{1}{2})\). The latter statement provides counterexamples for the data processing inequality of the sandwiched Rényi relative entropy for \(\alpha < \frac{1}{2}\). Our main tool is a new variational expression for the measured Rényi relative entropy, which we further exploit to show that certain lower bounds on quantum conditional mutual information are superadditive.     

Some Properties of the kth-partial Rényi Entropy

The kth-partial Rényi entropies for both classical and quantum cases are defined and some properties of them are given. Also, we study the stability of kth-partial Rényi entropy for two states which satisfy majorization condition.     

Beam propagation factor based on the Rényi entropy

A beam width measure based on Rényi entropy was introduced by Luis [Opt. Lett31, 3644 (2006)]. That one-dimensional analysis was limited to beam profiles with rectangular symmetry. In this Letter, we derive a general Rényi beam width measure that accounts for the diffraction properties of beams with profiles of arbitrary symmetry. We also show that the square of this measure has a quadratic dependence as a function of the propagation coordinate, so that it can be applied to propagation through arbitrary ABCD paraxial systems. The Rényi beam propagation factor, here introduced, is discussed in examples where the M(2) factor seems to have a limited effectiveness in describing the beam spreading.