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.     

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 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.     

Extended substitution–diffusion based image cipher using chaotic standard map

This paper proposes an extended substitution–diffusion based image cipher using chaotic standard map [1] and linear feedback shift register to overcome the weakness of previous technique by adding nonlinearity. The first stage consists of row and column rotation and permutation which is controlled by the pseudo-random sequences which is generated by standard chaotic map and linear feedback shift register, second stage further diffusion and confusion is obtained in the horizontal and vertical pixels by mixing the properties of the horizontally and vertically adjacent pixels, respectively, with the help of chaotic standard map. The number of rounds in both stage are controlled by combination of pseudo-random sequence and original image. The performance is evaluated from various types of analysis such as entropy analysis, difference analysis, statistical analysis, key sensitivity analysis, key space analysis and speed analysis. The experimental results illustrate that performance of this is highly secured and fast.     

Cryptography using multiple one-dimensional chaotic maps

Recently, Pareek et al. [Phys. Lett. A 309 (2003) 75] have developed a symmetric key block cipher algorithm using a one-dimensional chaotic map. In this paper, we propose a symmetric key block cipher algorithm in which multiple one-dimensional chaotic maps are used instead of a one-dimensional chaotic map. However, we also use an external secret key of variable length (maximum 128-bits) as used by Pareek et al. In the present cryptosystem, plaintext is divided into groups of variable length (i.e. number of blocks in each group is different) and these are encrypted sequentially by using randomly chosen chaotic map from a set of chaotic maps. For block-by-block encryption of variable length group, number of iterations and initial condition for the chaotic maps depend on the randomly chosen session key and encryption of previous block of plaintext, respectively. The whole process of encryption/decryption is governed by two dynamic tables, which are updated time to time during the encryption/decryption process. Simulation results show that the proposed cryptosystem requires less time to encrypt the plaintext as compared to the existing chaotic cryptosystems and further produces the ciphertext having flat distribution of same size as the plaintext.     

A new cryptosystem based on chaotic map and operations algebraic

Based on the study of some existing chaotic encryption algorithms, a new block cipher is proposed. The proposed cipher encrypts 128-bit plaintext to 128-bit ciphertext blocks, using a 128-bit key K and the initial value x₀ and the control parameter mu of logistic map. It consists of an initial permutation and eight computationally identical rounds followed by an output transformation. Round r uses a 128-bit roundkey K^(r) to transform a 128-bit input C^(r-1), which is fed to the next round. The output after round 8 enters the output transformation to produce the final ciphertext. All roundkeys are derived from K and a 128-bit random binary sequence generated from a chaotic map. Analysis shows that the proposed block cipher does not suffer from the flaws of pure chaotic cryptosystems and possesses high security.     

Improvement of cryptosystem based on iterating chaotic map

In this letter we demonstrate that the improvement of cryptosystem based on iterating chaotic map proposed by Yong in 2007 are weak and this cryptosystem can be easily broken using chosen plaintext attack. Then, we give novel improvements to the proposed chaotic cryptosystem. We choose image as plaintext, some experimental tests like sensitivity on initial condition and correlation between two adjacent pixels are presented to show the performances of the new cryptosystem.     

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.     

Cryptanalysis of a chaos block cipher for wireless sensor network

Based on the analysis of a chaos block cipher for wireless sensor network (WSN), it is found that there is a fatal flaw in its security because the number of rounds is too small and the calculation precision of round function is too short. The scheme could be cryptanalyzed by utilizing differential cryptanalysis theory. First, the third round key is recovered by chosen plaintext attack according to the characteristics of the round function. Then, the second round key can be deduced from the relationship of the sub-keys between the second and the third rounds. Based on the above successful attacks, the first round key could also be broken by brute-force attack. Finally, by employing the characteristics of Feistel structure, the fourth round key could also be obtained. Since all round keys have been cryptanalyzed, the plaintext can then be decrypted. The encryption scheme is proven to be insecure consequently.     

A new color image cryptosystem via hyperchaos synchronization

This paper proposes a novel color image cryptosystem based on synchronization of two different six-dimensional hyperchaotic systems. In the transmitter end, we apply the drive system to generate the diffusion matrices and scrambling ones, which are used to change the image pixel value and position, respectively. Thus the ciphered image is obtained. In the receiver, synchronization of two nonidentical hyperchaotic systems can be achieved by designing the appropriate controllers. The response system is employed to yield the corresponding diffusion matrices and scrambling ones using the same generation method in the encryption algorithm. Then the cipher-image can be decrypted by the decryption algorithm, which is similar to that of the encryption process but in the reversed order. The experimental results show that the presented image cryptosystem has high security and can resist noise and crop attacks.     

Chaotic map based key agreement with/out clock synchronization

In order to address Bergamo et al.’s attack, Xiao et al. proposed a key agreement protocol using chaotic maps. Han then presented three attacks on Xiao et al.’s protocol. To enhance the security of key agreement based on chaotic maps, Chang et al. proposed a new key agreement using passphrase, which works in clock synchronization environment. However, their protocol still has some issues: one is its passphrase is not easy to remember and much longer than password; the second one is it cannot resist guessing attack if the constructed passphrase is easy to remember and also has already existed in some rational dictionaries; the third one is it cannot work without clock synchronization. In this paper, we will present two different key agreement protocols, which can resist guessing attack. The first one works in clock synchronization environment. The second one can work without clock synchronization. They both use authenticated password for secure communications. The protocols are secure against replaying attacks and a shared session key can be established.     

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.     

Dynamic visual cryptography based on chaotic oscillations

Dynamic visual cryptography scheme based on chaotic oscillations is proposed in this paper. Special computational algorithms are required for hiding the secret image in the cover moiré grating, but the decryption of the secret is completely visual. The secret image is leaked in the form of time-averaged geometric moiré fringes when the cover image is oscillated by a chaotic law. The relationship among the standard deviation of the stochastic time variable, the pitch of the moiré grating and the pixel size ensuring visual decryption of the secret is derived. The parameters of these chaotic oscillations must be carefully preselected before the secret image is leaked from the cover image. Several computational experiments are used to illustrate the functionality and the applicability of the proposed image hiding technique.     

An improved chaos-based secure communication technique using a novel encryption function with an embedded cipher key

In this paper, a secure communication technique, using a chaotic system with a single adjustable parameter and a single observable time series, is proposed. The chosen chaotic system, which is a variant of the famous Rikitake model, has a special structure for which the adjustable parameter appears in the dynamic equation of the observable time series. This particular structure is used to build a synchronization-based state observer that is decoupled from the adaptive parameter identifier. A local Lyapunov function is used to design the parameter identifier, with an adjustable convergence rate that guarantees the stability of the overall system. A two-channel transmission method is used to exemplify the suggested technique where the secret message is encoded using a nonlinear function of both the chaotic states and the adjustable parameter of the chaotic system that acts as a secret key. Simulations show that, at the receiver, the signal can be efficiently retrieved only if the secret key is known, even when both the receiver and the transmitter are in perfect synchronization. The proposed technique is demonstrated to have improved security and privacy against intruders, when compared to other techniques reported in the literature, while being simple to implement using both analog and digital hardware. In addition, the chosen chaotic system is shown to be flexible in accommodating the transmission of signals with variable bandwidths, which promotes the superiority and versatility of the suggested secure communication technique.     

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.     

Breaking a modified substitution–diffusion image cipher based on chaotic standard and logistic maps

Recently, an image encryption scheme based on chaotic standard and logistic maps was proposed by Patidar et al. It was later reported by Rhouma et al. that an equivalent secret key can be reconstructed with only one known/chosen-plaintext and the corresponding ciphertext. Patidar et al. soon modified the original scheme and claimed that the modified scheme is secure against Rhouma et al.’s attack. In this paper, we point out that the modified scheme is still insecure against the same known/chosen-plaintext attack. In addition, some other security defects existing in both the original and the modified schemes are also reported.     

Control of chaotic vibration in automotive wiper systems

Chaotic vibration has been identified in the automotive wiper system at certain wiping speeds. This irregular vibration not only decreases the wiping efficiency, but also degrades the driving comfort. The purpose of this paper is to propose a new approach to stabilize the chaotic vibration in the wiper system. The key is to employ the extended time-delay feedback control in such a way that the applied voltage of the wiper motor is online adjusted according to its armature current feedback. Based on a practical wiper system, it is verified that the proposed approach can successfully stabilize the chaotic vibration, and provide a wide range of wiping speeds.     

Cryptosystem using chaotic keys

According to Kerchoff's principle, the secrecy of a cryptosystem must reside entirely on the secret keys. In this paper, a new cryptosystem is presented and one of its secret keys is generated by a chaotic map, we call it chaotic key. Some experimental results are given and the security of our cryptosystem is discussed.     

Cryptanalysis of Two McEliece Cryptosystems Based on Quasi-Cyclic Codes

We cryptanalyse here two variants of the McEliece cryptosystem based on quasi-cyclic codes. Both aim at reducing the key size by restricting the public and secret generator matrices to be in quasi-cyclic form. The first variant considers subcodes of a primitive BCH code. The aforementioned constraint on the public and secret keys implies to choose very structured permutations. We prove that this variant is not secure by producing many linear equations that the entries of the secret permutation matrix have to satisfy by using the fact that the secret code is a subcode of a known BCH code. This attack has been implemented and in all experiments we have performed the solution space of the linear system was of dimension one and revealed the permutation matrix. The other variant uses quasi-cyclic low density parity-check (LDPC) codes. This scheme was devised to be immune against general attacks working for McEliece type cryptosystems based on LDPC codes by choosing in the McEliece scheme more general one-to-one mappings than permutation matrices. We suggest here a structural attack exploiting the quasi-cyclic structure of the code and a certain weakness in the choice of the linear transformations that hide the generator matrix of the code. This cryptanalysis adopts a polynomial-oriented approach and basically consists in searching for two polynomials of low weight such that their product is a public polynomial. Our analysis shows that with high probability a parity-check matrix of a punctured version of the secret code can be recovered with time complexity O(n ³) where n is the length of the considered code. The complete reconstruction of the secret parity-check matrix of the quasi-cyclic LDPC codes requires the search of codewords of low weight which can be done with about 2³⁷ operations for the specific parameters proposed.