A generalized Arnold's Cat Map transformation for image scrambling

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2022

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Springer

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Mathematics
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The Atılım University Department of Mathematics was founded in 2000 and it offers education in English. The Department offers students the opportunity to obtain a certificate in Mathematical Finance or Cryptography, aside from their undergraduate diploma. Our students may obtain a diploma secondary to their diploma in Mathematics with the Double-Major Program; as well as a certificate in their minor alongside their diploma in Mathematics through the Minor Program. Our graduates may pursue a career in academics at universities, as well as be hired in sectors such as finance, education, banking, and informatics. Our Department has been accredited by the evaluation and accreditation organization FEDEK for a duration of 5 years (until September 30th, 2025), the maximum FEDEK accreditation period achievable. Our Department is globally and nationally among the leading Mathematics departments with a program that suits international standards and a qualified academic staff; even more so for the last five years with our rankings in the field rankings of URAP, THE, USNEWS and WEBOFMETRIC.
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Department of Software Engineering was founded in 2005 as the first department in Ankara in Software Engineering. The recent developments in current technologies such as Artificial Intelligence, Machine Learning, Big Data, and Blockchains, have placed Software Engineering among the top professions of today, and the future. The academic and research activities in the department are pursued with qualified faculty at Undergraduate, Graduate and Doctorate Degree levels. Our University is one of the two universities offering a Doctorate-level program in this field. In addition to focusing on the basic phases of software (analysis, design, development, testing) and relevant methodologies in detail, our department offers education in various areas of expertise, such as Object-oriented Analysis and Design, Human-Computer Interaction, Software Quality Assurance, Software Requirement Engineering, Software Design and Architecture, Software Project Management, Software Testing and Model-Driven Software Development. The curriculum of our Department is catered to graduate individuals who are prepared to take part in any phase of software development of large-scale software in line with the requirements of the software sector. Department of Software Engineering is accredited by MÜDEK (Association for Evaluation and Accreditation of Engineering Programs) until September 30th, 2021, and has been granted the EUR-ACE label that is valid in Europe. This label provides our graduates with a vital head-start to be admitted to graduate-level programs, and into working environments in European Union countries. The Big Data and Cloud Computing Laboratory, as well as MobiLab where mobile applications are developed, SimLAB, the simulation laboratory for Medical Computing, and software education laboratories of the department are equipped with various software tools and hardware to enable our students to use state-of-the-art software technologies. Our graduates are employed in software and R&D companies (Technoparks), national/international institutions developing or utilizing software technologies (such as banks, healthcare institutions, the Information Technologies departments of private and public institutions, telecommunication companies, TÜİK, SPK, BDDK, EPDK, RK, or universities), and research institutions such TÜBİTAK.
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Abstract

This 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.

Description

Tora, Hakan/0000-0002-0427-483X; Turan, Mehmet/0000-0002-1718-3902; Gokcay, Erhan/0000-0002-4220-199X
ORCID
Tora, Hakan ORCID logo
Turan, Mehmet ORCID logo
Gokcay, Erhan ORCID logo

Keywords

Image scrambling, Arnold's Cat Map, Information security, Transformation matrix, Chaotic maps

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7

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Q2

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Q2

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Volume

81

Issue

22

Start Page

31349

End Page

31362

URI

https://doi.org/10.1007/s11042-022-11985-2
 https://hdl.handle.net/20.500.14411/1840

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