Development of an enhanced scatter search algorithm using discrete chaotic Arnold’s cat map

Solving optimization problems is an ever-growing subject with an enormous number of algorithms. Examples of such algorithms are Scatter Search (SS) and genetic algorithms. Modifying and improving of algorithms can be done by adding diversity and guidance to them. Chaotic maps are quite sensitive to the initial point, which means even a very slight change in the value of the initial point would result in a dramatic change of the sequence produced by the chaotic map Arnold's Cat Map. Arnold's Cat Map is a chaotic map technique that provides long non-repetitive random-like sequences. Chaotic maps play an important role in improving evolutionary optimization algorithms and meta-heuristics by avoiding local optima and speeding up the convergence. This paper proposes an implementation of the scatter search algorithm with travelling salesman as a case study, then implements and compares the developed hyper Scatter Arnold's Cat Map Search (SACMS) method against the traditional Scatter Search Algorithm. SACMS is a hyper Scatter Search Algorithm with Arnold's Cat Map Chaotic Algorithm. Scatter Arnold's Cat Map Search shows promising results by decreasing the number of iterations required by the Scatter Search Algorithm to get an optimal solution(s). Travelling Salesman Problem, which is a popular and well-known optimization example, is implemented in this paper to demonstrate the results of the modified algorithm Scatter Arnold's Cat Map Search (SACMS). Implementation of both algorithms is done with the same parameters: population size, number of cities, maximum number of iterations, reference set size, etc. The results show improvement by the modified algorithm in terms of the number of iterations required by SS with an iteration reduction of 10–46 % and improvements in time to obtain solutions with 65 % time reduction

Crypto-Watermarking Algorithm Using Weber’s Law and AES: A View to Transfer Safe Medical Image

We propose a novel method for medical image watermarking in the DCT domain using the AES encryption algorithm. First, we decompose the original medical image into subblocks of 8 × 8. Besides, we apply the DCT and the quantization, respectively, to each subblock. However, in the DCT domain, an adequate choice of the DCT coefficients according to the quantization table in the middle frequencies band is performed. After that, we embed the patient’s data into the corresponding medical image. The insertion step is carried out just after the quantization phase. To increase the robustness, we encrypt the watermarked medical images by using the AES algorithm based on chaotic technique. Arnold’s cat map is used to shuffle the pixel values, and a chaotic Henon map is utilized to generate an aleatory sequence for the AES algorithm. The shuffled watermarked image is encrypted using the modified AES algorithm. The constant of Weber is used to choose the suitable visibility factor for embedding a watermark with high robustness. To control identification, after application of attacks, we use the serial turbo code for correction of the watermark to recover the data inserted. The average peak signal-to-noise ratio (PSNR) of the medical images obtained is 61,7769 dB. Experimental results demonstrate the robustness of the proposed schema against various types of attacks.

A Hyperbolic Arnold's Cat Map-Based System for Multimedia Data Encryption

Cryptography is one of the most used techniques to secure data since antiquity. It has been largely improved by introducing several mathematical concepts. This paper proposes a new asymmetric cryptography approach using combined Arnold's cat map with hyperbolic function and Chebyshev chaotic map for audio and image encryption. The proposed scheme uses Chebyshev map for public and secrete keys generation and the same equation with Arnold's cat map for encryption and decryption. Hyperbolic functions are also introduced replacing regular integer values in Arnold's map. The results show a good and promising efficiency as well as the theoretical discussion. Several future possible improvements are presented in the conclusion.

X-Ray Images Encryption Analysis Using Arnold's Cat Map and Bose Chaudhuri Hocquenghem Codes

In the medical world, a digital medical image is a requirement for image sharing in which the confidential data of the patient should be protected from unauthorized access. This study proposes a technique that can preserve image confidentiality using image encryption. This approach converts the original image into another shape that can not be visually interpreted, so unauthorized parties can not see an image's substance. This research proposes a method of X-Ray images encryption based on Arnold's Cat Map and Bose Chaudhuri Hocquenghem by shuffling coordinates from the original pixel into new coordinates. The Bose Chaudhuri Hocquenghem encoding scheme strengthens Arnold's cat map encryption by detecting and fixing bits of an image pixel value error. This study comprises results checked by giving the X-Ray or rontgen image noise with distinct variances. These algorithms are supposed to provide decrypted images with high accuracy and are more resistant to attack. Our result showed that the system using Bose Chaudhuri Hocquenghem codes has a better Peak Signal-to-Noise Ratio result equal to infinity and Bit Error Rate, equivalent to 0 at a more significant variance of each form of noise than the process using Arnold's Cat Map codes only. The Brute Force Attack for Bose Chaudhuri Hocquenghem takes 2.86 × 1058 years, while Arnold's Cat Map takes 3.9 × 1011 years, so the Bose Chaudhuri Hocquenghem code is more resistant to Brute Force Attack than the Arnold's Cat Map method.