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.     

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 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.     

A chaotic block cipher algorithm for image cryptosystems

Recently, many scholars have proposed chaotic cryptosystems in order to promote communication security. However, there are a number of major problems detected in some of those schemes such as weakness against differential attack, slow performance speed, and unacceptable data expansion. In this paper, we introduce a new chaotic block cipher scheme for image cryptosystems that encrypts block of bits rather than block of pixels. It encrypts 256-bits of plainimage to 256-bits of cipherimage within eight 32-bit registers. The scheme employs the cryptographic primitive operations and a non-linear transformation function within encryption operation, and adopts round keys for encryption using a chaotic system. The new scheme is able to encrypt large size of images with superior performance speed than other schemes. The security analysis of the new scheme confirms a high security level and fairly uniform distribution.     

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 improved key agreement protocol based on chaos

Cryptography based on chaos theory has developed fast in the past few years, but most of the researches focus on secret key cryptography. There are few public key encryption algorithms and cryptographic protocols based on chaos, which are also of great importance for network security. We introduce an enhanced key agreement protocol based on Chebyshev chaotic map. Utilizing the semi-group property of Chebyshev polynomials, the proposed key exchange algorithm works like Diffie–Hellman algorithm. The improved protocol overcomes the drawbacks of several previously proposed chaotic key agreement protocols. Both analytical and experimental results show that it is effective and secure.     

Synchronized hybrid chaotic generators: Application to real-time wireless speech encryption

In this paper, a new stream key generator Hybrid Discrete Continuous Chaotic System (HDCCS) based on continuous and discrete chaotic systems is proposed. Our solution provides an easy and robust chaos synchronization while decrease the degradation due to finite precision during a digital implementation. Real-time application to wireless speech encryption effectively hides the original signal. Statistical security analysis for the proposed cryptosystem against cryptanalysis attacks, from a strict cryptographic viewpoint, are presented. These results verify and prove that the proposed speech cryptosystem is highly secure and has a very powerful diffusion and confusion mechanisms widely used in conventional cryptography.     

A new substitution–diffusion based image cipher using chaotic standard and logistic maps

In this paper, we propose a new loss-less symmetric image cipher based on the widely used substitution–diffusion architecture which utilizes chaotic standard and logistic maps. It is specifically designed for the coloured images, which are 3D arrays of data streams. The initial condition, system parameter of the chaotic standard map and number of iterations together constitute the secret key of the algorithm. The first round of substitution/confusion is achieved with the help of intermediate XORing keys calculated from the secret key. Then two rounds of diffusion namely the horizontal and vertical diffusions are completed by mixing the properties of horizontally and vertically adjacent pixels, respectively. In the fourth round, a robust substitution/confusion is accomplished by generating an intermediate chaotic key stream (CKS) image in a novel manner with the help of chaotic standard and logistic maps. The security and performance of the proposed image encryption technique has been analyzed thoroughly using various statistical analysis, key sensitivity analysis, differential analysis, key space analysis, speed analysis, etc. Results of the various types of analysis are encouraging and suggest that the proposed image encryption technique is able to manage the trade offs between the security and speed and hence suitable for the real-time secure image and video communication applications.     

Fixed-time synchronization of a reaction-diffusion BAM neural network with distributed delay and its application to image encryption

In this paper, the fixed-time synchronization of reaction-diffusion BAM neural networks is investigated, where both discrete and distributed delays are taken into account. Combining Lyapunov stability theory and several integral inequalities, fixed-time synchronization criteria are established. Through sensitivity analysis, we find the key controller parameters that have a great influence on the maximum settling time. Using the chaotic sequences generated by the neural network, the color image can be encrypted by the Arnold Cat Map and the pixel diffusion. Experiments show that the image encryption algorithm designed in this paper has good properties of security and anti-attacking, which meets the requirements for the secure transmission of image information.     

Identifying attributes and insecurity of a public-channel key exchange protocol using chaos synchronization

Klein et al. proposed a key exchange protocol using chaos synchronization. The first protocol comprises two parties with chaotic dynamics that are mutually coupled and undergo a synchronization process, at the end of which they can use their identical dynamical state as an encryption key. From cryptographic point of view, their key exchange protocol is a key agreement protocol. Klein et al. claimed that their key agreement can be carried out over a public channel. In order to increase the key space and decrease the precision of the calculation, they made an extension of the system to a network of N Lorenz equations. In this paper, we will provide a cryptanalysis of their key agreement protocol. We will first point out some weaknesses, and then show that their protocol is not secure against several attacks including impersonation attack.     

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.     

Cycle detection for secure chaos-based encryption

Digital generators of chaos present several limitations that affect the vulnerability of chaotic encryption systems, among the most important are degraded probability distribution and short cycle lengths. Periodic perturbations of the chaotic parameter and/or state variable have been employed to deal with these limitations, although blindfold; the periodicity of the perturbation is set up during the initialization process without reference to the cycle length of the chaotic map under consideration. For best results, the periodicity of the perturbation must be close to the actual cycle length. So far, it is analytically impossible and numerically impractical (for real-time applications) to have a priori information of the cycle length. In this work we propose an on-the-fly detection and quantification of the chaotic cycle length to eliminate short cycles (which make cryptosystems vulnerable to attacks) and maximize the strength of long cycles by perturbing the system at the right time. Our proposal consists of two algorithms: (1) Unrestricted Search Algorithm (USA), which tracks down the cycle without any assumption or restriction on the digital chaotic trajectory, and (2) Ergodic Search Algorithm (ESA), which assumes ergodic trajectories to reduce the cycle search space, without this being a necessary requirement for the analyzed trajectory. USA and ESA are intended to increase the security of chaotic encryption systems without compromising their performance. Furthermore, they can be employed for the development of new chaotic-map independent encryption systems, where a full knowledge of the map is not required.     

A modified method of a class of recently presented cryptosystems

In this paper, a modified method of a class of recently proposed cryptosystems is presented. As a remedy, the piecewise linear chaotic map (PLCM) which has a uniform distribution is adopted in our method. The experimental results demonstrate that the application of PLCM can not only ensure the feasibility but also promote the encryption speed of these cryptosystems. Moreover, a new design of dynamical look-up table is used as an efficient way to ensure the security of our cryptosystem.     

A novel image encryption algorithm using chaos and reversible cellular automata

In this paper, a novel image encryption scheme is proposed based on reversible cellular automata (RCA) combining chaos. In this algorithm, an intertwining logistic map with complex behavior and periodic boundary reversible cellular automata are used. We split each pixel of image into units of 4 bits, then adopt pseudorandom key stream generated by the intertwining logistic map to permute these units in confusion stage. And in diffusion stage, two-dimensional reversible cellular automata which are discrete dynamical systems are applied to iterate many rounds to achieve diffusion on bit-level, in which we only consider the higher 4 bits in a pixel because the higher 4 bits carry almost the information of an image. Theoretical analysis and experimental results demonstrate the proposed algorithm achieves a high security level and processes good performance against common attacks like differential attack and statistical attack. This algorithm belongs to the class of symmetric systems.     

A method for image encryption based on fractional-order hyperchaotic systems

By using sequences generated from fractional-order hyperchaotic systems, a color image encryption scheme is investigated. Firstly, a plain image, which is known to users in advance, is chosen as a secret key to confuse the original image. Then, the confused image is encrypted by the sequences generated from the fractional-order hyperchaotic systems. With this simple encryption method, we can get an encrypted image that is fully scrambled and diused. For chaos-based image cryptosystems, this encryption scheme enhances the security and improves the eectiveness. Furthermore, the cryptosystem resists the dierential attack. Experiments show that the algorithm is suitable for image encryption, and some statistical tests are provided to show the high security in the end     

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.     

On enumeration of polynomial equivalence classes and their application to MPKC

The Isomorphism of Polynomials (IP) is one of the most fundamental problems in multivariate public key cryptography (MPKC). In this paper, we introduce a new framework to study the counting problem associated to IP. Namely, we present tools of finite geometry allowing to investigate the counting problem associated to IP. Precisely, we focus on enumerating or estimating the number of isomorphism equivalence classes of homogeneous quadratic polynomial systems. These problems are equivalent to finding the scale of the key space of a multivariate cryptosystem and the total number of different multivariate cryptographic schemes respectively, which might impact the security and the potential capability of MPKC. We also consider their applications in the analysis of a specific multivariate public key cryptosystem. Our results not only answer how many cryptographic schemes can be derived from monomials and how big the key space is for a fixed scheme, but also show that quite many HFE cryptosystems are equivalent to a Matsumoto–Imai scheme.     

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.     

Steganographic algorithm based on a chaotic map

In this paper, we suggest a new steganographic spatial domain algorithm based on a single chaotic map. Unlike most existing steganographic algorithms, the proposed algorithm uses one chaotic map to determine the pixel position of the host color image, the channel (red, green or blue) and the bit position of the targeted value in which a sensitive information bit can be hidden. Furthermore, this algorithm can be regarded as a variable-sized embedding algorithm. Experimental results demonstrate that this algorithm can defeat many existing steganalytic attacks. In comparison with existing steganographic spatial domain based algorithms, the suggested algorithm is shown to have some advantages over existing ones, namely, larger key space and a higher level of security against some existing attacks.     

GLS coding based security solution to JPEG with the structure of aggregated compression and encryption

There exists close relation among chaos, coding and cryptography. All the three can be combined into a whole as aggregated chaos-based coding and cryptography (ATC) to compress and encrypt data simultaneously. In particular, image data own high redundancy and wide transmission and thereby it is well worth doing research on ATC for image, which is very helpful to real application.JPEG with high compression ratio has not provided security. If JPEG is incorporated into powerful cryptographic features, its application can be further extended. For this reason, in this paper, GLS coding as a special form of ATC, which attains synchronous compression and encryption, is used to modify JPEG and fill its gap. An image is first initialized using DCT, quantization and run-length coding in turn, just as JPEG. Then, it is encoded and encrypted simultaneously by utilizing GLS coding and binary keystream resulting from the chaotic generator. Results demonstrate that our scheme can not only achieve good compression performance but also resist known/chosen-plaintext attacks efficiently.