Abstract:
In this paper, we discuss the properties of making a deterministic algorithm suitable to generate a pseudo random sequence of numbers: high value of Kolmogorov-Sinai entropy, high dimensionality of the parent dynamical system, and very large period of the generated sequence. We propose the chaotic coupled map lattices as a pseudo random number generator. We show what chaotic features of the coupled map lattices are useful for generating pseudo random numbers and investigate numerically which of them survive in the discrete state version of the map. To evaluate the randomness of the bit sequences generated by the RNGs, the NIST suite tests were performed. The proposed RNGs can be used in many applications requiring random bit sequences and also in the design of secure cryptosystems.

Abstract:
In recent years, information security essential in various arenas like internet communication, multimedia systems, medical imaging, tele-medicine and military communication. However, most of them faced with some problems such as the lack of robustness and security. In this letter, after reviewing the main points of the chaotic trigonometric maps and the coupled map lattices, we introduce the scheme of chaos-based image encryption based on coupled map lat tices. The scheme decreases periodic effect of the ergodic dynamical systems in the chaos-based image encryption. To evaluate the security of the encrypted image of this scheme, the key space analysis, the correlation of two adjacent pixels and differential attack were performed. This scheme tries to improve the problem of failure of encryption such as small key space and level of security.

Abstract:
In this paper, after reviewing the main points of Haar wavelet transform and chaotic trigonometric maps, we introduce a new perspective of Haar wavelet transform. The essential idea of the paper is given linearity properties of the scaling function of the Haar wavelet. With regard to applications of Haar wavelet transform in image processing, we introduce chaotic trigonometric Haar wavelet transform to encrypt the plain images. In addition, the encrypted images based on a proposed algorithm were made. To evaluate the security of the encrypted images, the key space analysis, the correlation coefficient analysis and differential attack were performed. Here, the chaotic trigonometric Haar wavelet transform tries to improve the problem of failure of encryption such as small key space and level of security.

Abstract:
Cryptography is always very important in data origin authentications, entity authentication, data integrity and confidentiality. In recent years, a variety of chaotic cryptographic schemes have been proposed. These schemes has typical structure which performed the permutation and the diffusion stages, alternatively. The random number generators are intransitive in cryptographic schemes and be used in the diffusion functions of the image encryption for diffused pixels of plain image. In this paper, we propose a chaotic encryption scheme based on pseudorandom bit padding that the bits be generated by a novel logistic pseudorandom image algorithm. To evaluate the security of the cipher image of this scheme, the key space analysis, the correlation of two adjacent pixels and differential attack were performed. This scheme tries to improve the problem of failure of encryption such as small key space and level of security.

Abstract:
In this paper, after reviewing the main points of image encryption and threshold function, we introduce the methods of chaotic image encryption based on pseudorandom bit padding that the bits be generated by the novel generalized threshold function (segmentation and self-similarity) methods. These methods decrease periodic effect of the ergodic dynamical systems in randomness of the chaotic image encryption. The essential idea of this paper is that given threshold functions of the ergodic dynamical systems. To evaluate the security of the cipher image of this scheme, the key space analysis, the correlation of two adjacent pixels and differential attack were performed. This scheme tries to improve the problem of failure of encryption such as small key space and level of security.

Abstract:
Cryptography is always very important in data origin authentications, entity authentication, data integrity and confidentiality. In recent years, a variety of chaotic cryptographic schemes have been proposed. These schemes have typical structure which performed the permutation and the diffusion stages, alternatively. The random number generators are intransitive in cryptographic schemes and be used in the diffusion functions of the image encryption for diffused pixels of plain image. In this paper, we propose a chaotic encryption scheme based on pseudorandom bit padding that the bits be generated by a novel logistic pseudorandom image algorithm. To evaluate the security of the cipher image of this scheme, the key space analysis, the correlation of two adjacent pixels and differential attack were performed. This scheme tries to improve the problem of failure of encryption such as small key space and level of security.

Abstract:
By cross-coupling two logistic maps a novel method is proposed for the public key steganography in JPEG image. Chaotic maps entail high complexity in the used algorithm for embedding secret data in a medium. In this paper, discrete cross- coupled chaotic maps are used to specifying the location of the different parts of the secret data in the image. Modifying JPEG format during compressing and decompressing, and also using public key enhanced difficulty of the algorithm. Simulation results show that in addition to excessive capacity, this method has high robustness and resistance against hackers and can be applicable in secret communication. Also the PSNR value is high compared to the other works.

Abstract:
By means of a binary visibility graph, we present a novel method to study random binary sequences. The behavior of the some topological properties of the binary visibility graph, such as the degree distribution, the clustering coefficient, and the mean path length have been investigated. Several examples are then provided to show that the numerical simulations confirm the accuracy of the theorems for finite random binary sequences. Finally, in this paper we propose, for the first time, three topological properties of the binary visibility graph as a randomness criteria.

Abstract:
Chaos transition, as an important topic, has become an active research subject in non-linear science. By considering a Dicke Hamiltonian coupled to a bath of harmonic oscillator, we have been able to introduce a logistic map with quantum corrections. Some basic dynamical properties, such as Lyapunov exponents and bifurcation diagram of the model are studied. we show that in this model, the transition from integrable motion to periodic, chaotic and hyperchaotic as the control parameter $r$ is increased.

Abstract:
We introduce an interesting hierarchy of rational order chaotic maps that posses an invariant measure. In contrast to the previously introduced hierarchy of chaotic maps \cite{J1,J2,J3,J4,J5}, with merely entropy production, the rational order chaotic maps can simultaneously produce and consume entropy . We compute the Kolmogorov-Sinai entropy of theses maps analytically and also their Lyapunov exponent numerically, where that obtained numerical results support the analytical calculations.