| 000 | 07255nam a22002657a 4500 | ||
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| 008 | 201210b2024 a|||f bm|| 00| 0 eng d | ||
| 024 | 7 |
_a0000-0003-2997-272X _2ORCID |
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| 040 |
_aEG-CaNU _cEG-CaNU |
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| 041 | 0 |
_aeng _beng |
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| 082 | _a610 | ||
| 100 | 0 |
_aBishoy Kamal Gad Sharobim _93652 |
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| 245 | 1 |
_aSECRET IMAGE SHARING APPROACHES USING NUMBER THEORY AND CHAOTIC SYSTEMS _c/Bishoy Kamal Gad Sharobim |
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| 260 | _c2024 | ||
| 300 |
_a 180p. _bill. _c21 cm. |
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| 500 | _3Supervisor: Heba Kamal Aslan | ||
| 502 | _aThesis (M.A.)—Nile University, Egypt, 2024 . | ||
| 504 | _a"Includes bibliographical references" | ||
| 505 | 0 | _aContents: Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VII List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . XII List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . XVII List of Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . XXI List of Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . XXII 1. Introduction 1 1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Problem Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3 Contributions Summary . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.4 Thesis Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2. Background and Survey 4 2.1 Evaluation Criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2 Chaotic Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2.1 Numerical Solvers Overview . . . . . . . . . . . . . . . . . . . 9 2.2.2 Chaotic Generators Simulation . . . . . . . . . . . . . . . . . 11 2.2.3 PRNGs Results and Tests . . . . . . . . . . . . . . . . . . . . 15 2.2.4 Fractional-Order Rossler System . . . . . . . . . . . . . . . . 19 2.2.5 Generalized Tent Map . . . . . . . . . . . . . . . . . . . . . . 20 2.2.6 Generalized Arnold Transform . . . . . . . . . . . . . . . . . . 27 2.3 Number Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 2.3.1 The Divisibility . . . . . . . . . . . . . . . . . . . . . . . . . . 27 2.3.2 Congruences . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 2.3.3 Euler’s Theorem . . . . . . . . . . . . . . . . . . . . . . . . . 39 2.3.4 Cryptographic Applications of Basic Number Theory . . . . . 41 2.4 Secure Hash Algorithm: SHA-256 . . . . . . . . . . . . . . . . . . . . 44 2.5 Secret Sharing Literature . . . . . . . . . . . . . . . . . . . . . . . . . 47 2.5.1 VSS Approaches . . . . . . . . . . . . . . . . . . . . . . . . . 49 2.5.2 SIS Using Polynomial Interpolation . . . . . . . . . . . . . . . 52 2.5.3 XOR-Based MSIS . . . . . . . . . . . . . . . . . . . . . . . . 54 3. Number Theory Based Secret Image Sharing 56 3.1 A (k, n)-Secret Image Sharing With Steganography Using Generalized Tent Map . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 3.1.1 Proposed System . . . . . . . . . . . . . . . . . . . . . . . . . 56 3.1.2 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . 58 3.2 An Efficient Multi-Secret Image Sharing System Based on Chinese Remainder Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 3.2.1 Proposed System . . . . . . . . . . . . . . . . . . . . . . . . . 67 3.2.2 Security Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 74 IV 3.2.3 Performance Analysis . . . . . . . . . . . . . . . . . . . . . . 80 3.2.4 Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 3.3 A Unified System for Encryption and Multi-Secret Image Sharing Using S-box and CRT . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 3.3.1 Proposed System . . . . . . . . . . . . . . . . . . . . . . . . . 83 3.3.2 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . 86 4. Chaos Based Secret Image Sharing 97 4.1 Different Designs of Chaos-Based Secret Image Sharing Systems . . . 97 4.1.1 The VSS System . . . . . . . . . . . . . . . . . . . . . . . . . 98 4.1.2 The First SIS System . . . . . . . . . . . . . . . . . . . . . . 100 4.1.3 The Second SIS System . . . . . . . . . . . . . . . . . . . . . 102 4.1.4 Results and Comparisons . . . . . . . . . . . . . . . . . . . . 103 4.2 Multi-Secret Image Sharing Using Fractional-Order Rossler System . 111 4.2.1 Proposed MSIS System . . . . . . . . . . . . . . . . . . . . . 112 4.2.2 Security Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 116 4.2.3 Comparisons . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 4.3 Progressive Multi-Secret Sharing of Color Images Using Lorenz Chaotic System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 4.3.1 Proposed MSIS system . . . . . . . . . . . . . . . . . . . . . . 127 4.3.2 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . 129 4.3.3 Comparisons . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 5. Conclusions and Future Work 141 5.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 5.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 | |
| 520 | 3 | _aAbstract: Securing the transmission of secret information is important. When sending a secret image to mutually suspicious receivers, they must be together to recover the image. Secret Image Sharing (SIS) provides this feature by sending meaningless shares 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, 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 number theory concepts, such as polynomial interpolation, and Chinese Remainder Theorem (CRT), and various chaotic systems, such as Lorenz and Rossler systems as Pseudo-Random Number Generator (PRNG). In this research, several tests have shown good randomness of the different PRNGs. The proposed approaches worked 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 were also introduced with good results, including statistical tests such as Root Mean Square Error (RMSE), correlation, entropy, and the National Institute of Standards 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 key sensitivity tests and performance analysis, where the systems used long sensitive system keys. Keywords: Chaos theory, Number theory, Pseudo-Random Number Generator (PRNG), Secret Image Sharing (SIS), Visual Secret Sharing (VSS) | |
| 546 | _aText in English, abstracts in English and Arabic | ||
| 650 | 4 |
_aInformatics-IFM _9266 |
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| 655 | 7 |
_2NULIB _aDissertation, Academic _9187 |
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| 690 |
_aInformatics-IFM _9266 |
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| 942 |
_2ddc _cTH |
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| 999 |
_c10997 _d10997 |
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