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Article Citation - WoS: 5Citation - Scopus: 5An Unrestricted Arnold's Cat Map Transformation(Springer, 2024) Turan, Mehmet; Goekcay, Erhan; Tora, HakanThe Arnold's Cat Map (ACM) is one of the chaotic transformations, which is utilized by numerous scrambling and encryption algorithms in Information Security. Traditionally, the ACM is used in image scrambling whereby repeated application of the ACM matrix, any image can be scrambled. The transformation obtained by the ACM matrix is periodic; therefore, the original image can be reconstructed using the scrambled image whenever the elements of the matrix, hence the key, is known. The transformation matrices in all the chaotic maps employing ACM has limitations on the choice of the free parameters which generally require the area-preserving property of the matrix used in transformation, that is, the determinant of the transformation matrix to be +/- 1.\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\pm 1.$$\end{document} This reduces the number of possible set of keys which leads to discovering the ACM matrix in encryption algorithms using the brute-force method. Additionally, the period obtained is small which also causes the faster discovery of the original image by repeated application of the matrix. These two parameters are important in a brute-force attack to find out the original image from a scrambled one. The objective of the present study is to increase the key space of the ACM matrix, hence increase the security of the scrambling process and make a brute-force attack more difficult. It is proved mathematically that area-preserving property of the traditional matrix is not required for the matrix to be used in scrambling process. Removing the restriction enlarges the maximum possible key space and, in many cases, increases the period as well. Additionally, it is supplied experimentally that, in scrambling images, the new ACM matrix is equivalent or better compared to the traditional one with longer periods. Consequently, the encryption techniques with ACM become more robust compared to the traditional ones. The new ACM matrix is compatible with all algorithms that utilized the original matrix. In this novel contribution, we proved that the traditional enforcement of the determinant of the ACM matrix to be one is redundant and can be removed.Article Citation - Scopus: 1Two-Stage Feature Generator for Handwritten Digit Classification(Mdpi, 2023) Pirim, M. Altinay Gunler; Tora, Hakan; Oztoprak, Kasim; Butun, IsmailIn this paper, a novel feature generator framework is proposed for handwritten digit classification. The proposed framework includes a two-stage cascaded feature generator. The first stage is based on principal component analysis (PCA), which generates projected data on principal components as features. The second one is constructed by a partially trained neural network (PTNN), which uses projected data as inputs and generates hidden layer outputs as features. The features obtained from the PCA and PTNN-based feature generator are tested on the MNIST and USPS datasets designed for handwritten digit sets. Minimum distance classifier (MDC) and support vector machine (SVM) methods are exploited as classifiers for the obtained features in association with this framework. The performance evaluation results show that the proposed framework outperforms the state-of-the-art techniques and achieves accuracies of 99.9815% and 99.9863% on the MNIST and USPS datasets, respectively. The results also show that the proposed framework achieves almost perfect accuracies, even with significantly small training data sizes.Article Citation - WoS: 13Citation - Scopus: 19A Generalized Arnold's Cat Map Transformation for Image Scrambling(Springer, 2022) Tora, Hakan; Gokcay, Erhan; Turan, Mehmet; Buker, MohamedThis study presents a new approach to generate the transformation matrix for Arnold's Cat Map (ACM). Matrices of standard and modified ACM are well known by many users. Since the structure of the possible matrices is known, one can easily select one of them and use it to recover the image with several trials. However, the proposed method generates a larger set of transform matrices. Thus, one will have difficulty in estimating the transform matrix used for scrambling. There is no fixed structure for our matrix as in standard or modified ACM, making it much harder for the transform matrix to be discovered. It is possible to use different type, order and number of operations to generate the transform matrix. The quality of the shuffling process and the strength against brute-force attacks of the proposed method is tested on several benchmark images.
