Mohammad Ghebleh

An image encryption scheme based on irregularly decimated chaotic maps

Abstract An image encryption scheme provides means for securely transmitting images over public channels. In this work, we propose a robust shuffling–masking image encryption scheme based on chaotic maps. The shuffling phase permutes square blocks of bytes using a 3-dimensional chaotic cat map coupled with a zigzag scanning procedure. The masking phase then scrambles b -byte blocks of the shuffled image with combined outputs of three 1-dimensional chaotic skew tent maps, in such a way that the masking of every block is influenced by all previously masked blocks. Empirical results show that while the suggested scheme has good running speed, it generates ciphered images that exhibit (i) random-like behavior, (ii) almost flat histograms, (iii) almost no adjacent pixel correlation, (iv) information entropy close to the ideal theoretical value. Furthermore, this scheme has a large key space, strong sensitivity to the secret key, and is robust against differential attacks. On the basis of these results, this scheme can be regarded as secure and reliable scheme for use in secure communication applications.

A blind chaos-based watermarking technique

This paper presents a robust blind frequency domain watermarking scheme based on chaotic maps. The proposed scheme embeds a black and white watermark logo in the midband components of a host image according to a discrete wavelet transform. Each watermark bit is embedded into a small submatrix of selected second level subbands of an image resulting from iterated applications of a two-dimensional discrete wavelet transform. This scheme embeds two copies of the watermark using two different methods, in two different subbands of the image. At the cost of embedding capacity, this results in improving the security and robustness of the watermarking scheme. Experimental results demonstrate that the suggested scheme provides imperceptibility and robustness against image processing attacks such as JPEG compression, low-pass filtering, median filtering, Gaussian noise, scaling, rotating, cropping, histogram equalization, and gamma correction. Experimental results also show superior robustness of the suggested scheme over existing algorithms with a similar approach. Copyright

A novel image encryption algorithm based on piecewise linear chaotic maps and least squares approximation

In this paper, we propose a novel image encryption algorithm based on chaotic maps and least squares approximations. The proposed algorithm consists of two main phases, which are applied sequentially in several rounds, namely a shuffling phase and a masking phase. Both phases are based on 1–dimensional piecewise linear chaotic maps and act on the rows/columns of the input plain image. Least squares approximations are used to strengthen the security of the proposed algorithm by providing strong mixing between the rows/columns of the image. Simulation results show that the proposed image encryption algorithm is robust against common statistical and security attacks. We present thorough comparison of the proposed algorithm with some existing image encryption algorithms.

A novel secret image sharing scheme using large primes

A secret image sharing scheme is any method of distributing shares of a secret image amongst a set of peers, such that the secret may be revealed only with participation of all members of a qualified set of peers. Following Shamir’s (t, n)–threshold scheme, we propose a novel lossy/lossless secret image sharing scheme, that improves existing schemes in terms of security and performance. As opposed to the usual convention of representing a digital image by a collection of 8–bit integer values, we consider 8b–bit values where b is a positive integer. This approach accommodates a larger finite field, which in turn produces a less intrusive secret image sharing scheme. Extensive empirical results are presented to demonstrate the efficiency and robustness of the proposed scheme.

An efficient (t,n)–threshold secret image sharing scheme

We propose a novel (t,n)–threshold secret image sharing scheme based on Shamir’s polynomial interpolation paradigm. The proposed scheme is a derivative of Thien and Lin’s (Computers & Graphics 26(5):765–770, [13]) and some of its variants by ensuring less intrusive changes in the secret image. This is achieved by cyclically shifting the bits of the secret image, thus allowing a modification in the least significant bit to have a large effect on the values used in computation of shadow images. Statistical tests and simulations are presented to show the efficiency and robustness of the proposed scheme, in particular good randomness of shadow images, little correlation between adjacent pixels, and high entropy. Competence of the proposed scheme is further demonstrated by means of comparison with existing schemes.

A concurrent key exchange protocol based on commuting matrices

In this paper, we suggest a cryptographic protocol for symmetric key exchange based on a set of m commutative square singular matrices of dimension n×n. The suggested scheme provides a concurrent technique for users of symmetric‐key cipher systems to securely exchange their private keys over public channels. This protocol is shown to possess a high level of security based on the algorithms parameters. We also present a scheme for generating pseudorandom numbers from a single chaotic map for use in various applications, in particular, the suggested key exchange protocol.Copyright

A variant of Baptista's encryption scheme

The idea of employing chaotic maps in building encryption schemes has attracted the attention of many researchers since the late 1980s. In 1998, M.S. Baptista proposed an elegant encryption scheme based on a one-dimensional chaotic map. Many variants of this scheme have been proposed. Baptistas scheme and some of its variants have been subjected to cryptanalytic attacks such as the one-time pad attack and the entropy attack. We propose a variant of Baptistas encryption scheme based on two coupled one-dimensional chaotic maps, which also employs mixing, that is, every character in the ciphertext depends on all preceding plaintext characters. Our proposed scheme overcomes the aforementioned attacks. Empirical results show that this idea improves the performance of the scheme. Baptistas approach generates a ciphertext, which is generally larger than the plaintext, but the distribution of the ciphertext symbols allows compression. Simulation results verify that our proposed scheme accommodates better compression rates than the original scheme. Copyright