MARC details
| 000 -LEADER |
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| fixed length control field |
07255nam a22002657a 4500 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
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| fixed length control field |
201210b2024 a|||f bm|| 00| 0 eng d |
| 024 7# - Author Identifier |
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| Standard number or code |
0000-0003-2997-272X |
| Source of number or code |
ORCID |
| 040 ## - CATALOGING SOURCE |
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| Original cataloging agency |
EG-CaNU |
| Transcribing agency |
EG-CaNU |
| 041 0# - Language Code |
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| Language code of text |
eng |
| Language code of abstract |
eng |
| 082 ## - DEWEY DECIMAL CLASSIFICATION NUMBER |
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| Classification number |
610 |
| 100 0# - MAIN ENTRY--PERSONAL NAME |
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| Personal name |
Bishoy Kamal Gad Sharobim |
| 245 1# - TITLE STATEMENT |
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| Title |
SECRET IMAGE SHARING APPROACHES USING NUMBER THEORY AND CHAOTIC SYSTEMS |
| Statement of responsibility, etc. |
/Bishoy Kamal Gad Sharobim |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. |
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| Date of publication, distribution, etc. |
2024 |
| 300 ## - PHYSICAL DESCRIPTION |
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| Extent |
180p. |
| Other physical details |
ill. |
| Dimensions |
21 cm. |
| 500 ## - GENERAL NOTE |
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| Materials specified |
Supervisor: Heba Kamal Aslan |
| 502 ## - Dissertation Note |
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| Dissertation type |
Thesis (M.A.)—Nile University, Egypt, 2024 . |
| 504 ## - Bibliography |
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| Bibliography |
"Includes bibliographical references" |
| 505 0# - Contents |
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| Formatted contents note |
Contents:<br/>Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VII<br/>List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . XII<br/>List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . XVII<br/>List of Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . XXI<br/>List of Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . XXII<br/>1. Introduction 1<br/>1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1<br/>1.2 Problem Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2<br/>1.3 Contributions Summary . . . . . . . . . . . . . . . . . . . . . . . . . 2<br/>1.4 Thesis Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3<br/>2. Background and Survey 4<br/>2.1 Evaluation Criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4<br/>2.2 Chaotic Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7<br/>2.2.1 Numerical Solvers Overview . . . . . . . . . . . . . . . . . . . 9<br/>2.2.2 Chaotic Generators Simulation . . . . . . . . . . . . . . . . . 11<br/>2.2.3 PRNGs Results and Tests . . . . . . . . . . . . . . . . . . . . 15<br/>2.2.4 Fractional-Order Rossler System . . . . . . . . . . . . . . . . 19<br/>2.2.5 Generalized Tent Map . . . . . . . . . . . . . . . . . . . . . . 20<br/>2.2.6 Generalized Arnold Transform . . . . . . . . . . . . . . . . . . 27<br/>2.3 Number Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27<br/>2.3.1 The Divisibility . . . . . . . . . . . . . . . . . . . . . . . . . . 27<br/>2.3.2 Congruences . . . . . . . . . . . . . . . . . . . . . . . . . . . 34<br/>2.3.3 Euler’s Theorem . . . . . . . . . . . . . . . . . . . . . . . . . 39<br/>2.3.4 Cryptographic Applications of Basic Number Theory . . . . . 41<br/>2.4 Secure Hash Algorithm: SHA-256 . . . . . . . . . . . . . . . . . . . . 44<br/>2.5 Secret Sharing Literature . . . . . . . . . . . . . . . . . . . . . . . . . 47<br/>2.5.1 VSS Approaches . . . . . . . . . . . . . . . . . . . . . . . . . 49<br/>2.5.2 SIS Using Polynomial Interpolation . . . . . . . . . . . . . . . 52<br/>2.5.3 XOR-Based MSIS . . . . . . . . . . . . . . . . . . . . . . . . 54<br/>3. Number Theory Based Secret Image Sharing 56<br/>3.1 A (k, n)-Secret Image Sharing With Steganography Using Generalized<br/>Tent Map . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56<br/>3.1.1 Proposed System . . . . . . . . . . . . . . . . . . . . . . . . . 56<br/>3.1.2 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . 58<br/>3.2 An Efficient Multi-Secret Image Sharing System Based on Chinese<br/>Remainder Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . 66<br/>3.2.1 Proposed System . . . . . . . . . . . . . . . . . . . . . . . . . 67<br/>3.2.2 Security Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 74<br/>IV<br/>3.2.3 Performance Analysis . . . . . . . . . . . . . . . . . . . . . . 80<br/>3.2.4 Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81<br/>3.3 A Unified System for Encryption and Multi-Secret Image Sharing Using S-box and CRT . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82<br/>3.3.1 Proposed System . . . . . . . . . . . . . . . . . . . . . . . . . 83<br/>3.3.2 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . 86<br/>4. Chaos Based Secret Image Sharing 97<br/>4.1 Different Designs of Chaos-Based Secret Image Sharing Systems . . . 97<br/>4.1.1 The VSS System . . . . . . . . . . . . . . . . . . . . . . . . . 98<br/>4.1.2 The First SIS System . . . . . . . . . . . . . . . . . . . . . . 100<br/>4.1.3 The Second SIS System . . . . . . . . . . . . . . . . . . . . . 102<br/>4.1.4 Results and Comparisons . . . . . . . . . . . . . . . . . . . . 103<br/>4.2 Multi-Secret Image Sharing Using Fractional-Order Rossler System . 111<br/>4.2.1 Proposed MSIS System . . . . . . . . . . . . . . . . . . . . . 112<br/>4.2.2 Security Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 116<br/>4.2.3 Comparisons . . . . . . . . . . . . . . . . . . . . . . . . . . . 120<br/>4.3 Progressive Multi-Secret Sharing of Color Images Using Lorenz Chaotic<br/>System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123<br/>4.3.1 Proposed MSIS system . . . . . . . . . . . . . . . . . . . . . . 127<br/>4.3.2 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . 129<br/>4.3.3 Comparisons . . . . . . . . . . . . . . . . . . . . . . . . . . . 135<br/>5. Conclusions and Future Work 141<br/>5.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141<br/>5.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144<br/>References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 |
| 520 3# - Abstract |
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| Abstract |
Abstract:<br/>Securing the transmission of secret information is important. When sending a<br/>secret image to mutually suspicious receivers, they must be together to recover the<br/>image. Secret Image Sharing (SIS) provides this feature by sending meaningless shares<br/>to n participants, and k or more shares must be available to recover the secret image, where k ≤ n. Furthermore, Multi-Secret Image Sharing (MSIS) was introduced,<br/>where multiple images are simultaneously shared instead of only one image. This research proposed different, simple, and efficient approaches for SIS and MSIS using the<br/>number theory concepts, such as polynomial interpolation, and Chinese Remainder<br/>Theorem (CRT), and various chaotic systems, such as Lorenz and Rossler systems<br/>as Pseudo-Random Number Generator (PRNG). In this research, several tests have<br/>shown good randomness of the different PRNGs. The proposed approaches worked<br/>on sharing any number or type of images, such as binary, grayscale, and color images, with lossless recovery. Security analysis and comparisons with related literature<br/>were also introduced with good results, including statistical tests such as Root Mean<br/>Square Error (RMSE), correlation, entropy, and the National Institute of Standards<br/>and Technology (NIST) SP-800-22 test suite. In addition, they passed several attacks, such as differential attacks, noise and crop attacks, and other tests, such as<br/>key sensitivity tests and performance analysis, where the systems used long sensitive<br/>system keys.<br/>Keywords: Chaos theory, Number theory, Pseudo-Random Number Generator<br/>(PRNG), Secret Image Sharing (SIS), Visual Secret Sharing (VSS) |
| 546 ## - Language Note |
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| Language Note |
Text in English, abstracts in English and Arabic |
| 650 #4 - Subject |
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| Subject |
Informatics-IFM |
| 655 #7 - Index Term-Genre/Form |
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| Source of term |
NULIB |
| focus term |
Dissertation, Academic |
| 690 ## - Subject |
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| School |
Informatics-IFM |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) |
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| Source of classification or shelving scheme |
Dewey Decimal Classification |
| Koha item type |
Thesis |
| 650 #4 - Subject |
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| -- |
266 |
| 655 #7 - Index Term-Genre/Form |
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187 |
| 690 ## - Subject |
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| -- |
266 |