An image encryption scheme with a pseudorandom permutation based on chaotic maps

Many research efforts for image encryption schemes have elaborated for designing nonlinear functions since security of these schemes closely depends on inherent characteristics of nonlinear functions. It is commonly believed that a chaotic map can be used as a good candidate of a nonlinear component for image encryption schemes. We propose a new image encryption algorithm using a large pseudorandom permutation which is combinatorially generated from small permutation matrices based on chaotic maps. The random-like nature of chaos is effectively spread into encrypted images by using the permutation matrix. The experimental results show that the proposed encryption scheme provides comparable security with that of the conventional image encryption schemes based on Baker map or Logistic map.     

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.     

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.     

A novel chaotic encryption scheme based on arithmetic coding

In this paper, under the combination of arithmetic coding and logistic map, a novel chaotic encryption scheme is presented. The plaintexts are encrypted and compressed by using an arithmetic coder whose mapping intervals are changed irregularly according to a keystream derived from chaotic map and plaintext. Performance and security of the scheme are also studied experimentally and theoretically in detail.     

Multiple-watermarking scheme based on improved chaotic maps

In this letter a new watermarking scheme for color image is proposed based on a family of the pair-coupled maps. Pair-coupled maps are employed to improve the security of watermarked image, and to encrypt the embedding position of the host image. Another map is also used to determine the pixel bit of host image for the watermark embedding. The purpose of this algorithm is to improve the shortcoming of watermarking such as small key space and low security. Due to the sensitivity to the initial conditions of the introduced pair-coupled maps, the security of the scheme is greatly improved.     

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.     

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.     

An image encryption scheme based on quantum logistic map

The topic of quantum chaos has begun to draw increasing attention in recent years. While a satisfactory definition for it is not settled yet in order to differentiate between its classical counterparts. Dissipative quantum maps can be characterized by sensitive dependence on initial conditions, like classical maps. Considering this property, an implementation of image encryption scheme based on the quantum logistic map is proposed. The security and performance analysis of the proposed image encryption is performed using well-known methods. The results of the reliability analysis are encouraging and it can be concluded that, the proposed scheme is efficient and secure. The results of this study also suggest application of other quantum maps such as quantum standard map and quantum baker map in cryptography and other aspects of security and privacy.     

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.     

An image encryption scheme based on rotation matrix bit-level permutation and block diffusion

This paper proposes a novel image encryption scheme based on rotation matrix bit-level permutation and block diffusion. Firstly, divide plain image into non-overlapping 8 × 8 pixels blocks with a random matrix, then transform each block into an 8 × 8 × 8 three-dimensional (3-D) binary matrix, which has six directions just as a cube. Permutation is performed by multiplying the 3-D matrix by the rotation matrix that relies on plain image according to different direction. Secondly, use block diffusion to further change the statistical characteristics of the image after confusion. Experiment results and analysis show that the scheme can not only achieve a satisfactory security performance, but also have the suitability for a parallel mode and the robustness against noise in communication system.     

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.     

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 secure communication scheme based on observer

Based on parameter modulation theory, an observer is presented to identify the unknown parameter of Liu chaotic system, then the useful information modulated in the parameter can be recovered successfully. Numerical simulations show the effectiveness of our method.     

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.     

A novel method for designing S-boxes based on chaotic maps

A method for obtaining cryptographically strong 8 × 8 S-boxes based on chaotic maps is presented and the cryptographical properties such as bijection, nonlinearity, strict avalanche criterion, output bits independence criterion and equiprobable input/output XOR distribution of these S-boxes are analyzed in detail. The results of numerical analysis also show that the S-boxes proposed are of the above properties and can resist the differential attack. Furthermore, our approach is suitable for practical application in designing cryptosystem.     

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.     

基于分数阶混沌时间序列的图像加密算法

基于分数阶logistic映射提出了洗牌加密方法.通过离散分数阶微积分得到分数阶序列并把它作为密钥.利用位异或算子,提出了一种新的图像加密算法.对该算法的密钥空间、密钥敏感性和统计特性进行相应的仿真分析.结果表明,该算法可以达到较好的加解密效果,具有很高的安全性,可以满足图像加密安全性的要求.     

Image encryption based on synchronization of fractional chaotic systems

This paper deals with a synchronization scheme for two fractional chaotic systems which is applied in image encryption. Based on Pecora and Carroll (PC) synchronization, fractional-order Lorenz-like system forms a master–slave configuration, and the sufficient conditions are derived to realize synchronization between these two systems via the Laplace transformation theory. An image encryption algorithm is introduced where the original image is encoded by a nonlinear function of a fractional chaotic state. Simulation results show that the original image is well masked in the cipher texts and recovered successfully through chaotic signals. Further, the cryptanalysis is conducted in detail through histogram, information entropy, key space and sensitivity to verify the high security.     

A block encryption algorithm based on dynamic sequences of multiple chaotic systems

A block encryption algorithm using dynamic sequences generated by multiple chaotic systems is proposed in this paper. In this algorithm, several one-dimension chaotic maps generate pseudo-random sequences, which are independent and approximately uniform. After a series of transformations, the sequences constitute a new pseudo-random sequence uniformly distributing in the value space, which covers the plaintext by executing Exclusive-OR and shifting operations some rounds to form the cipher. This algorithm makes the pseudo-random sequence possess more concealment and noise like characteristic, and overcomes the periodic malpractice caused by the computer precision and single chaotic system. Simulation results show that the algorithm is efficient and useable for the security of communication system.