A fast image encryption and authentication scheme based on chaotic maps

In recent years, a variety of chaos-based image cryptosystems have been proposed. The key used for encryption/decryption is usually independent of the plain-image. To achieve a satisfactory level of security, at least two overall rounds of the substitution-diffusion process are required so that a change in any pixels of the plain-image spreads over the whole cipher-image. Moreover, the receiver is not able to determine whether the decrypted image is exactly the one sent. In this paper, a fast image encryption and authentication scheme is proposed. In particular, a keyed hash function is introduced to generate a 128-bit hash value from both the plain-image and the secret hash keys. The hash value plays the role of the key for encryption and decryption while the secret hash keys are used to authenticate the decrypted image. Simulation results show that satisfactory security performance is achieved in only one overall round. The speed efficiency is thus improved.     

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.     

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.     

Air traverse time in grain bins

To maintain the quality of cereal grains during storage, it is necessary to keep the grain cool and free from insects, and typical methods for dealing with these problems are considered in this paper. In particular the insect population is controlled by fumigating the grain bed with carbon dioxide gas and the grain is cooled by forcing ambient air through the bed. In both problems, the equations which describe the physical processes contain a mixture of advection and diffusion or conduction terms. This paper explores the relationship between traverse time and heat and mass transfer and gains an insight into the grain storage processes that are controlled by forced convection. When heat and mass transport is dominated by the advection terms, the equations are simplified by changing variables from the (x,y) space coordinates to (ψ,τ), where ψ is the stream function for the problem and the traverse time τ at a point in the storage bin is the time taken for the air to travel to the point from the inlet duct. The conditions are described for the equations to be independent of ψ, with the main condition being that the derivatives of the metrics g₁₁, g₁₂ and g₂₂ with respect to ψ are small enough. If the equations are independent of ψ then the dependent variable (concentration or temperature) will be constant on lines of constant traverse time τ. This relationship between traverse time and the cooling or fumigation pattern can be used in the design of storage bins since it implies that the best outlet surface is a line of constant τ.     

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.     

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 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.     

Cryptosystems in automorphism groups of group rings of Abelian groups

We introduce a new class of public-key cryptosystems generalizing ElGamal cryptosystems to automorphism groups of group rings of Abelian groups. A scheme of the basic variant of such a cryptosystem is presented and some types of attacks to it are considered. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 13, No. 3, pp. 157–164, 2007.     

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 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.     

An improved chaotic cryptosystem with external key

In recent years, external key was introduced to chaotic cryptography by Pareek et al. and find its application in several discrete chaotic cryptosystems. The first part of this paper is devoted to the analysis of their essential weaknesses as well as some redundancies that contribute little to the security of those cryptosystems. Then, an improved scheme with all existing deficiencies and redundancies eliminated, is proposed. Theoretic analysis and numerical simulation both verify its superiority and security.     

How to Mask the Structure of Codes for a Cryptographic Use

In this paper we show how to strengthen public-key cryptosystems against known attacks, together with the reduction of the public-key. We use properties of subcodes to mask the structure of the codes used by the conceiver of the system. We propose new parameters for the cryptosystems and even a modified Niederreiter cryptosystem in the case of Gabidulin codes, with a public-key size of less than 4000 bits.Communicated by: P. WildAMS Classification: 11T71     

Analysis and improvement of a hash-based image encryption algorithm

The security of digital image attracts much attention recently. A hash-based digital image encryption algorithm has been proposed in Ref. [1]. But both the theoretical analysis and computer simulation show the characteristic of diffusion is too weak to resist Chosen Plaintext Attack and Known Plaintext Attack. Besides, one bit difference of the plain pixel will lead to only one corresponding bit change of the cipher pixel. In our improved algorithm, coupled with self-adaptive algorithm, only one pixel difference of the plain-image will cause changes of almost all the pixels in the cipher-image (NPCR > 98.77%), and the unified average changing intensity is high (UACI > 30.96%). Both theoretical analysis and computer simulation indicate that the improved algorithm can overcome these flaws and maintain all the merits of the original one.     

On non-Abelian homomorphic public-key cryptosystems

An important problem of modern cryptography concerns secret public-key computations in algebraic structures. We construct homomorphic cryptosystems, which are (secret) epimorphisms f : G H, where G and H are (publically known) groups and H is finite. A letter of a message to be encrypted is an element h H, while its encryption is an element g G such that f(g) = h. A homomorphic cryptosystem allows one to perform computations (in the group G) with encrypted information (without knowing the original message over H).In this paper, homomorphic cryptosystems are constructed for the first time for non-Abelian groups H (earlier, homomorphic cryptosystems were known only in the Abelian case). In fact, we present such a system for any (fixed) solvable group H. Bibliography: 24 titles.Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 293, 2002, pp. 39–58.This revised version was published online in April 2005 with a corrected cover date and article title.     

How to Choose Secret Parameters for RSA-Type Cryptosystems over Elliptic Curves

Recently, and contrary to the common belief, Rivest and Silverman argued that the use of strong primes is unnecessary in the RSA cryptosystem. This paper analyzes how valid this assertion is for RSA-type cryptosystems over elliptic curves. The analysis is more difficult because the underlying groups are not always cyclic. Previous papers suggested the use of strong primes in order to prevent factoring attacks and cycling attacks. In this paper, we only focus on cycling attacks because for both RSA and its elliptic curve-based analogues, the length of the RSA-modulus n is typically the same. Therefore, a factoring attack will succeed with equal probability against all RSA-type cryptosystems. We also prove that cycling attacks reduce to find fixed points, and derive a factorization algorithm which (most probably) completely breaks RSA-type systems over elliptic curves if a fixed point is found.     

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.     

G-Perfect nonlinear functions

Perfect nonlinear functions are used to construct DES-like cryptosystems that are resistant to differential attacks. We present generalized DES-like cryptosystems where the XOR operation is replaced by a general group action. The new cryptosystems, when combined with G-perfect nonlinear functions (similar to classical perfect nonlinear functions with one XOR replaced by a general group action), allow us to construct systems resistant to modified differential attacks. The more general setting enables robust cryptosystems with parameters that would not be possible in the classical setting. We construct several examples of G-perfect nonlinear functions, both -valued and -valued. Our final constructions demonstrate G-perfect nonlinear planar permutations (from to itself), thus providing an alternative implementation to current uses of almost perfect nonlinear functions.      

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.