A novel image encryption scheme based on spatial chaos map

In recent years, the chaos-based cryptographic algorithms have suggested some new and efficient ways to develop secure image encryption techniques, but the drawbacks of small key space and weak security in one-dimensional chaotic cryptosystems are obvious. In this paper, spatial chaos system are used for high degree security image encryption while its speed is acceptable. The proposed algorithm is described in detail. The basic idea is to encrypt the image in space with spatial chaos map pixel by pixel, and then the pixels are confused in multiple directions of space. Using this method one cycle, the image becomes indistinguishable in space due to inherent properties of spatial chaotic systems. Several experimental results, key sensitivity tests, key space analysis, and statistical analysis show that the approach for image cryptosystems provides an efficient and secure way for real time image encryption and transmission from the cryptographic viewpoint.     

Design of an image encryption scheme based on a multiple chaotic map

In order to solve the problem that chaos is degenerated in limited computer precision and Cat map is the small key space, this paper presents a chaotic map based on topological conjugacy and the chaotic characteristics are proved by Devaney definition. In order to produce a large key space, a Cat map named block Cat map is also designed for permutation process based on multiple-dimensional chaotic maps. The image encryption algorithm is based on permutation–substitution, and each key is controlled by different chaotic maps. The entropy analysis, differential analysis, weak-keys analysis, statistical analysis, cipher random analysis, and cipher sensibility analysis depending on key and plaintext are introduced to test the security of the new image encryption scheme. Through the comparison to the proposed scheme with AES, DES and Logistic encryption methods, we come to the conclusion that the image encryption method solves the problem of low precision of one dimensional chaotic function and has higher speed and higher security.     

An image encryption scheme using reverse 2-dimensional chaotic map and dependent diffusion

In recent years, a variety of chaos-based image cryptosystems have been studied. Most of them adopt the traditional confusion–diffusion architecture, which is considered insecure upon chosen/known plain-image attacks. In this paper, a nonlinear traverse on the plain-image using dependent diffusion and reverse cat map is proposed to replace the traditional linear traverse performed in the confusion phase. Two cryptosystems are designed and are implemented by software means. Simulation results and numerical analysis justify their high efficiency and sufficient strength.     

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.     

Cryptanalysis of an image encryption scheme based on a new total shuffling algorithm

Chaotic systems have been broadly exploited through the last two decades to build encryption methods. Recently, two new image encryption schemes have been proposed, where the encryption process involves a permutation operation and an XOR-like transformation of the shuffled pixels, which are controlled by three chaotic systems. This paper discusses some defects of the schemes and how to break them with a chosen-plaintext attack.     

A chaotic image encryption scheme owning temp-value feedback

Many round-based chaotic image encryption algorithms employ the permutation–diffusion structure. This structure has been found insecure when the iteration round is equal to one and the secret permutation of some existing schemes can be recovered even a higher round is adopted. In this paper, we present a single round permutation–diffusion chaotic cipher for gray image, in which some temp-value feedback mechanisms are introduced to resist the known attacks. Specifically, we firstly embed the plaintext feedback technique in the permutation process to develop different permutation sequences for different plain-images and then employ plaintext/ciphertext feedback for diffusion to generate equivalent secret key dynamically. Experimental results show that the new scheme owns large key space and can resist the differential attack. It is also efficient.     

On the security analysis of an image scrambling encryption of pixel bit and its improved scheme based on self-correlation encryption

An image scrambling encryption scheme for pixel bits was presented by Ye [Ye GD. Image scrambling encryption algorithm of pixel bit based on chaos map. Pattern Recognit Lett 2010;31:347-54], which can be seen as one kind of typical binary image scrambling encryption considering from the bit-plain of size M × (8N). However, recently, some defects existing in the original image encryption scheme, i.e., Ye’s scheme, have been observed by Li and Lo [Li CQ, Lo KT. Optimal quantitative cryptanalysis of permutation-only multimedia ciphers against plaintext attacks. Signal Process 2011;91:949-54]. In the attack proposed by Li and Lo at least 3 + ⌈log₂(MN)⌉ plain images of size M × N are used to reveal the permutation matrix W = [w(i, k)] (i ∈ {1, 2, … , M}; k ∈ {1, 2, … , 8N}) which can be applied to recover the exact plain image. In the current paper, at first, one type of special plain image/cipher image is used to analyze the security weakness of the original image scrambling scheme under study. The final encryption vectors TM and TN or the decryption vectors TM′ and TN′ are revealed completely according to our attack. To demonstrate the performance of our attack, a quantified comparison is drawn between our attack and the attack proposed by Li and Lo. Compared with Li and Lo’s attack, our attack is more efficient in the general conditions. In particular, when the sizes of images satisfy the condition M = N or M ? 8N, the number of the used plain images/cipher images is at most 9, which is sharply less than 3 + ⌈log₂(MN)⌉ when M and N are of large size. To overcome the weaknesses of the original scheme, in this paper, an improved image scrambling encryption scheme is proposed. In the improved scheme, the idea of the “self-correlation” method is used to resist the chosen-plaintext attack/known-plaintext attack. The corresponding simulations and analyses illustrate that the improved encryption method has good cryptographic properties, and can overcome the weakness of the original image encryption scheme. Finally, farther improvement is briefly presented for the future work.     

Efficient quantum homomorphic encryption scheme with flexible evaluators and its simulation

Designs, Codes and Cryptography - Quantum homomorphic encryption (QHE) allows computation on encrypted data by employing the principles of quantum mechanics. Usually, only one evaluator is chosen...     

基于参数自适应控制的分数阶离散logistic映射同步

讨论了分数阶离散混沌系统驱动系统和相应系统都是相同混沌映射、但是参数不同时的同步问题,采用了参数自适应算法实现了分数阶离散logistic映射的同步,并且给出了同步的充分条件.     

An improved model averaging scheme for logistic regression

Recently, penalized regression methods have attracted much attention in the statistical literature. In this article, we argue that such methods can be improved for the purposes of prediction by utilizing model averaging ideas. We propose a new algorithm that combines penalized regression with model averaging for improved prediction. We also discuss the issue of model selection versus model averaging and propose a diagnostic based on the notion of generalized degrees of freedom. The proposed methods are studied using both simulated and real data.     

Delayed q-deformed logistic map

The delay logistic map with two types of q-deformations: Tsallis and Quantum-group type are studied. The stability of the logistic map and its bifurcation scheme is analyzed as a function of the deformation and delay parameters. Chaos is suppressed in a certain region of deformation and delay parameter space. By introducing delay, the steady state in one type of deformation is maintained while chaotic behavior is recovered in another type.     

Efficient image or video encryption based on spatiotemporal chaos system

In this paper, an efficient image/video encryption scheme is constructed based on spatiotemporal chaos system. The chaotic lattices are used to generate pseudorandom sequences and then encrypt image blocks one by one. By iterating chaotic maps for certain times, the generated pseudorandom sequences obtain high initial-value sensitivity and good randomness. The pseudorandom-bits in each lattice are used to encrypt the Direct Current coefficient (DC) and the signs of the Alternating Current coefficients (ACs). Theoretical analysis and experimental results show that the scheme has good cryptographic security and perceptual security, and it does not affect the compression efficiency apparently. These properties make the scheme a suitable choice for practical applications.     

An efficient diffusion approach for chaos-based image encryption

One of the existing chaos-based image cryptosystems is composed of alternative substitution and diffusion stages. A multi-dimensional chaotic map is usually employed in the substitution stage for image pixel permutation while a one-dimensional (1D) chaotic map is used for diffusion purpose. As the latter usually involves real number arithmetic operations, the overall encryption speed is limited by the diffusion stage. In this paper, we propose a more efficient diffusion mechanism using simple table lookup and swapping techniques as a light-weight replacement of the 1D chaotic map iteration. Simulation results show that at a similar security level, the proposed cryptosystem needs about one-third the encryption time of a similar cryptosystem. The effective acceleration of chaos-based image cryptosystems is thus achieved.     

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.     

Short-term cascaded hydroelectric system scheduling based on chaotic particle swarm optimization using improved logistic map

In order to solve the model of short-term cascaded hydroelectric system scheduling, a novel chaotic particle swarm optimization (CPSO) algorithm using improved logistic map is introduced, which uses the water discharge as the decision variables combined with the death penalty function. According to the principle of maximum power generation, the proposed approach makes use of the ergodicity, symmetry and stochastic property of improved logistic chaotic map for enhancing the performance of particle swarm optimization (PSO) algorithm. The new hybrid method has been examined and tested on two test functions and a practical cascaded hydroelectric system. The experimental results show that the effectiveness and robustness of the proposed CPSO algorithm in comparison with other traditional algorithms.     

An efficient third-order scheme for BSDEs based on nonequidistant difference scheme

Numerical Algorithms - In this paper, we propose an efficient third-order numerical scheme for backward stochastic differential equations(BSDEs). We use 3-point Gauss-Hermite quadrature rule for...     

On a coupled logistic map with large strength

In this paper, a class of diffusive coupled logistic map with large strength is considered. Depending on the parameter of the logistic family and the strength of coupling, we show the existence of a forward invariant curve which determines, in some sense, the boundary of the set whose points have unbounded orbit.     

Reflections on the security proofs of Boneh-Franklin identity-based encryption scheme

In this paper, we first review the existing proofs of the Boneh-Franklin identity-based encryption scheme (BF-IBE for short), and show how to admit a new proof by slightly modifying the specifications of the hash functions of the original BF-IBE. Compared with prior proofs, our new proof provides a tighter security reduction and minimizes the use of random oracles, thus indicates BF-IBE has better provable security with our new choices of hash functions. The techniques developed in our proof can also be applied to improving security analysis of some other IBE schemes. As an independent technical contribution, we also give a rigorous proof of the Fujisaki-Okamoto (FO) transformation in the case of CPA-to-CCA, which demonstrates the efficiency of the FO-transformation (CPA-to-CCA), in terms of the tightness of security reduction, has long been underestimated. This result can remarkably benefit the security proofs of encryption schemes using the FO-transformation for CPA-to-CCA enhancement.     

基于Arnold变换的图像逆置乱算法

针对Arnold变换的周期依赖于图像的阶数这一特性,提出了一种反变换算法.该算法通过分析加密图像任一点处两坐标分量间关系,得到原图像相应点的坐标,从而实现图像的解密.该反变换也可作为图像置乱的正变换,相应的反变换就是Arnold变换.在此基础上,把二维反变换算法推广到m维的情形.实验结果表明,对于已应用Arnold变换进行预处理的置乱图像,在无须计算原图像变换周期的前提下可快速实现图像的逆置乱,该过程具有确定性,其迭代次数与预处理置乱次数相等.