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 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 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.     

One-Time Pad as a nonlinear dynamical system

The One-Time Pad (OTP) is the only known unbreakable cipher, proved mathematically by Shannon in 1949. In spite of several practical drawbacks of using the OTP, it continues to be used in quantum cryptography, DNA cryptography and even in classical cryptography when the highest form of security is desired (other popular algorithms like RSA, ECC, AES are not even proven to be computationally secure). In this work, we prove that the OTP encryption and decryption is equivalent to finding the initial condition on a pair of binary maps (Bernoulli shift). The binary map belongs to a family of 1D nonlinear chaotic and ergodic dynamical systems known as Generalized Luröth Series (GLS). Having established these interesting connections, we construct other perfect secrecy systems on the GLS that are equivalent to the One-Time Pad, generalizing for larger alphabets. We further show that OTP encryption is related to Randomized Arithmetic Coding – a scheme for joint compression and encryption.     

Image encryption using chaotic coupled map lattices with time-varying delays

In this paper, a novel image encryption scheme using coupled map lattices (CML) with time delay is proposed. By employing discretized tent map to shuffle the positions of image pixels and then using delayed coupled map lattices (DCML) to confuse the relationship between the plain-image and the cipher-image, image encryption algorithms with permutation-diffusion structure are introduced in detail. In the process of generating keystream, the time-varying delay is also embedded in our proposed scheme to enhance the security. Theoretical analysis and computer experiments confirm that the new algorithm possesses high security for practical image encryption.     

Pseudo random number generator based on quantum chaotic map

For many years dissipative quantum maps were widely used as informative models of quantum chaos. In this paper, a new scheme for generating good pseudo-random numbers (PRNG), based on quantum logistic map is proposed. Note that the PRNG merely relies on the equations used in the quantum chaotic map. The algorithm is not complex, which does not impose high requirement on computer hardware and thus computation speed is fast. In order to face the challenge of using the proposed PRNG in quantum cryptography and other practical applications, the proposed PRNG is subjected to statistical tests using well-known test suites such as NIST, DIEHARD, ENT and TestU01. The results of the statistical tests were promising, as the proposed PRNG successfully passed all these tests. Moreover, the degree of non-periodicity of the chaotic sequences of the quantum map is investigated through the Scale index technique. The obtained result shows that, the sequence is more non-periodic. From these results it can be concluded that, the new scheme can generate a high percentage of usable pseudo-random numbers for simulation and other applications in scientific computing.     

Chaotic secure content-based hidden transmission of biometric templates

The large-scale proliferation of biometric verification systems creates a demand for effective and reliable security and privacy of its data. Like passwords and PIN codes, biometric data is also not secret and if it is compromised, the integrity of the whole verification system could be at high risk. To address these issues, this paper presents a novel chaotic secure content-based hidden transmission scheme of biometric data. Encryption and data hiding techniques are used to improve the security and secrecy of the transmitted templates. Secret keys are generated by the biometric image and used as the parameter value and initial condition of the chaotic map, and each transaction session has different secret keys to protect from the attacks. Two chaotic maps are incorporated for the encryption to resolve the finite word length effect and to improve the system’s resistance against attacks. Encryption is applied on the biometric templates before hiding into the cover/host images to make them secure, and then templates are hidden into the cover image. Experimental results show that the security, performance, and accuracy of the presented scheme are encouraging comparable with other methods found in the current literature.     

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.     

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.     

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.     

Lattice-based completely non-malleable public-key encryption in the standard model

An encryption scheme is non-malleable if giving an encryption of a message to an adversary does not increase its chances of producing an encryption of a related message (under a given public key). Fischlin introduced a stronger notion, known as complete non-malleability, which requires attackers to have negligible advantage, even if they are allowed to transform the public key under which the related message is encrypted. Ventre and Visconti later proposed a comparison-based definition of this security notion, which is more in line with the well-studied definitions proposed by Bellare et al. The authors also provide additional feasibility results by proposing two constructions of completely non-malleable schemes, one in the common reference string model using non-interactive zero-knowledge proofs, and another using interactive encryption schemes. Therefore, the only previously known completely non-malleable (and non-interactive) scheme in the standard model, is quite inefficient as it relies on generic NIZK approach. They left the existence of efficient schemes in the common reference string model as an open problem. Recently, two efficient public-key encryption schemes have been proposed by Libert and Yung, and Barbosa and Farshim, both of them are based on pairing identity-based encryption. At ACISP 2011, Sepahi et al. proposed a method to achieve completely non-malleable encryption in the public-key setting using lattices but there is no security proof for the proposed scheme. In this paper we review the mentioned scheme and provide its security proof in the standard model. Our study shows that Sepahi’s scheme will remain secure even for post-quantum world since there are currently no known quantum algorithms for solving lattice problems that perform significantly better than the best known classical (i.e., non-quantum) algorithms.     

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.     

Inner-product encryption under standard assumptions

Predicate encryption is a generalized notion for public key encryption that enables one to encrypt attributes as well as a message. In this paper, we present a new inner-product encryption (IPE) scheme, as a specialized predicate encryption scheme, whose security relies on the well-known Decision Bilinear Diffie-Hellman (BDH) and Decision Linear assumptions. Our IPE scheme uses prime order groups equipped with a bilinear map and works in both symmetric and asymmetric bilinear maps. Our result is the first construction of IPE under the standard assumptions. Prior to our work, all IPE schemes known to date require non-standard assumptions to prove security, and moreover some of them use composite-order groups. To achieve our goal, we introduce a novel technique for attribute-hiding, which may be of independent interest.     

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 new compound mode of confusion and diffusion for block encryption of image based on chaos

A block encryption for image using combination of confusion and diffusion is proposed in this paper. In this encryption, a new compound mode is proposed. Baker map is used to generate a pseudo-random sequence, and several one-dimension chaotic maps are dynamically selected to encrypt blocks of image, in the order of the pseudo-random sequence generated by Baker map. Different with other combined encryptions, the algorithm of this encryption does not confusion original image directly, but generate a pseudo-random, which is used as a route for diffusion, combines pixels to block randomly and arrays them. When diffusion is executing, for mutual diffusion of pixels, the confusion is working by the pseudo-random order of route, the combination is deep-seated.     

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 cryptosystem based on elementary cellular automata

Based on elementary cellular automata, a new image encryption algorithm is proposed in this paper. In this algorithm, a special kind of periodic boundary cellular automata with unity attractors is used. From the viewpoint of security, the number of cellular automata attractor states are changed with respect to the encrypted image, and different key streams are used to encrypt different plain images. The cellular neural network with chaotic properties is used as the generator of a pseudo-random key stream. Theoretical analysis and experimental results have both confirmed that the proposed algorithm possesses high security level and good performances against differential and statistical attacks. The comparison with other existing schemes is given, which shows the superiority of the proposal scheme.     

Comments on “arithmetic coding as a non-linear dynamical system”

Nagaraj et al. [1], [2] present a skewed-non-linear generalized Luroth Series (s-nGLS) framework. S-nGLS uses non-linear maps for GLS to introduce a security parameter a which is used to build a keyspace for image or data encryption. The map introduces non-linearity to the system to add an “encryption key parameter”. The skew is added to achieve optimal compression efficiency. s-nGLS used as such for joint encryption and compression is a weak candidate, as explained in this communication. First, we show how the framework is vulnerable to known plaintext based attacks and that a key of size 256 bits can be broken within 1000 trials. Next, we demonstrate that the proposed non-linearity exponentially increases the hardware complexity of design. We also discover that s-nGlS cannot be implemented as such for large bitstreams. Finally, we demonstrate how correlation of key parameter with compression performance leads to further key vulnerabilities.     

Cryptanalyzing a nonlinear chaotic algorithm (NCA) for image encryption

This paper describes the security weakness of a recently proposed image encryption algorithm based on a logistic-like new chaotic map. We show that the chaotic map’s distribution is far from ideal, thus making it a bad candidate as a pseudo-random stream generator. As a consequence, the images encrypted with this algorithm are shown to be breakable through different attacks of variable complexity.     

A novel keyed parallel hashing scheme based on a new chaotic system

Hash functions play important role in the information security era. Although there are different methods to design these functions, in recent years chaos theory has emerged as a strong solution in this area. Chaotic hash functions use one-dimensional maps such as logistic and tent, or employ complex multi-dimensional maps which are typically insecure or slow and most of them has been successfully attacked. In this paper, we propose a new chaotic system and employ it to design a secure and fast hash function. The improved security factor has roots in the hyper sensitivity of the proposed chaotic map while properties like speed and security can be parameterized. On the other hand, the proposed hash function has a dynamic random array of functions and can be implemented by a parallel architecture. This data-level parallel architecture makes it fast to generate the hash value. Statistical simulations show success of the proposed hashing scheme. Cryptanalysis of proposed function, such as key sensitivity, meet-in-the-middle attack, collision, preimage resistance and high level attacks, proves security of the proposed function.