Afshin Akhshani

A symmetric image encryption scheme based on combination of nonlinear chaotic maps

Abstract During the recent years several chaotic image encryption algorithms have been proposed, but most of them encountered some drawbacks such as small key space, low speed, lack of robustness and low security. In this paper, we have proposed an image algorithm based on the combination of a one-dimensional polynomial chaotic map and a piecewise nonlinear chaotic map. Theoretical analysis and computer simulations, both confirm that the new algorithm possesses high security, robust fast encryption speed for practical image encryption and solves the problem of small key space.

A novel parallel hash function based on 3D chaotic map

As the core of cryptography, hash function is one of the basic techniques for information security. During the last few years, considerable effort has been devoted to research on chaos-based hash functions. Nevertheless, the corresponding analysis of them lag far behind. In this paper, a new efficient scheme for parallel hash function based on high-dimensional chaotic map is proposed. In the proposed scheme, the confusion as well as the diffusion effect is enhanced significantly by utilizing two nonlinear coupling parameters. Theoretical and experimental results indicate that the proposed scheme can satisfy all performance requirements of hash function such as desired statistical properties and strong collision resistance. At the same time, the proposed scheme can keep the parallel merit and message sensitivity with high potential to be adopted for network security.

Image encryption based on the Jacobian elliptic maps

An image encryption algorithm based chaotic Jacobian elliptic maps is presented.The proposed scheme is subjected to some security analyses as well as statistical tests suites.Security analysis and simulation results indicate that the scheme possesses high security. In this paper, a novel image encryption algorithm based on the Jacobian elliptic maps is presented. To illustrate the effectiveness of the proposed scheme, some security analyses are presented. It can be concluded that, the proposed image encryption technique can be applied for practical applications. Although the Jacobian elliptic maps presented in this paper aim at image encryption, it is not just limited to this experience and can be directly applied in other information security fields such as video encryption.

CHAOTIC CRYPTOGRAPHIC SCHEME BASED ON COMPOSITION MAPS

In recent years, a growing number of cryptosystems based on chaos have been proposed. But most of them have encountered many problems such as small key space and weak security. In the present paper, a new kind of chaotic cryptosystem based on Composition of Trigonometric Chaotic Maps is proposed. These maps which are defined as ratios of polynomials of degree N, have interesting properties such as invariant measure, ergodicity, variable chaotic region with respect to the control parameters and ability to construct composition form of maps. We have used a composition of chaotic map to shuffle the position of image pixels. Another composition of chaotic map is used in diffusion process. According to the performed analysis, the introduced algorithm can satisfy the required performances such as high level security, large key space and the acceptable encryption speed.

A novel dynamic model of pseudo random number generator

An interesting hierarchy of random number generators is introduced in this paper based on the review of random numbers characteristics and chaotic functions theory. The main objective of this paper is to produce an ergodic dynamical system which can be implemented in random number generators. In order to check the efficacy of pseudo random number generators based on this map, we have carried out certain statistical tests on a series of numbers obtained from the introduced hierarchy. The results of the tests were promising, as the hierarchy passed the tests satisfactorily, and offers a great capability to be employed in a pseudo random number generator.

A new image encryption algorithm based on one-dimensional polynomial chaotic maps

In recent years, a growing number of cryptosystems based on chaos have been proposed, however, most of them encounter with some problems such as: low level of security and small key space. Chaotic maps have good properties such as ergodicity, sensitivity to initial conditions and control parameters, etc. Due to these features, they are good candidate for information encryption. In this paper, encryption based on the Polynomial Chaotic Maps (PCMs) is proposed. The theoretic and simulation results state that the proposed algorithm has many properties such as high speed and large key space and high security. Therefore it is suitable for practical use in the secure communications.

PSEUDO RANDOM NUMBER GENERATOR BASED ON SYNCHRONIZED CHAOTIC MAPS

In this paper, a hierarchy of coupled maps in synchronized state is introduced. Then some discussions about the individual properties of these chaotic maps are presented, from a dynamical systems viewpoint. Also, one of these chaotic map is used as a Nonlinear Pseudo Random Generator (NPRNG). This paper addresses the chaotic features of this map which are useful for generating nonlinear pseudo random numbers. Results of the analysis and extensive tests such as the NIST, DIEHARD and ENT test suites indicate that the NPRNG exhibits good statistical randomness properties.

DNA in a Dissipative Environment: A Charge Transfer Approach

Conductivity properties of DNA molecule is investigated in a simple, chemically specific approach, that is intimately related to the Su–Schrieffer–Heeger (SSH) model. In the SSH model, the non-diagonal matrix element dependent on intersite displacements is considered and there is a coupling between the charge and lattice deformation along DNA helix. In order to study the evolution of the electrical current flowing through DNA in the presence of external electrical field, the electrical current is directly extracted from the dynamical equations. Ranges of electrical field and hopping constant value are estimated using MLE approach. The model is studied by means of I–V characteristic diagrams and the environmental effects is conducted through a phonon bath using different lengths of DNA. The NDR and quasi-Ohmic regions are observed.

A NOVEL SCHEME FOR IMAGE ENCRYPTION BASED ON A SYNCHRONIZED COUPLED MAP

This paper investigates properties of synchronization of trigonometric coupled maps. These maps have some advantages, such as an invariant measure, ergodicity and the possibility of Kolmogorov–Sinai (KS) entropy calculation. Moreover, an encryption algorithm based on a synchronized coupled map is suggested and described in detail. Also, some security analyses are presented to illustrate the effectiveness of the proposed scheme. The cryptosystems speed is analyzed as well. Results of the various types of analysis are encouraging and it can be concluded that the proposed image encryption technique is a suitable choice for practical applications.

Random Maps with Parameter-Dependent Probabilities

The random map model is a deterministic dynamical system in a finite phase space with n points. A map that establishes the dynamics of the system is constructed by randomly choosing, for every point, another one as its image. In this paper, a hierarchy of random maps with parameter-dependent probabilities is introduced. Then some discussion is presented about the properties of the invariant measure corresponding to random maps. Also, the Kolmogorov–Sinai (KS) entropy of the random maps is calculated analytically using the invariant measure. Simulation results indicate that the proposed random dynamical system is more complex than the standard logistic map.