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研究生： 王資猛
Wang, Tzu-Meng
論文名稱： 基於中國餘氏定理和原根的影像分享及還原
Image Sharing and Recovering with Chinese Remainder Theorem and Primitive Roots
指導教授： 陳朝欽
Chen, Chaur-Chin
口試委員: 張隆紋
Chang, Long-Wen
黃仲陵
Huang, Chung-Lin
學位類別： 碩士
Master
系所名稱： 電機資訊學院 - 資訊工程學系
Computer Science
論文出版年： 2020
畢業學年度： 108
語文別： 中文
論文頁數： 26
中文關鍵詞： 影像處理 、影像分享 、密碼學
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    • 隨著越來越多的信息在網路上傳遞，確保重要資訊的安全變得越來越重要。有許多算法是設計來提高重要資訊的安全性。其中之一就是影像分享，這種方法相當知名並且在提高資訊安全上非常有用。大多數影像分享方法是在（k，n）為門檻值的前提下運行。將秘密影像分割成n個子影像，而在得到k個子影像後便可以還原秘密圖片。
    我們通過在編碼過程中應用原根來擴展（k，n）為門檻的影像分享方法。我們提出的方法提高了秘密影像的安全性。由於攻擊者不知道在編碼階段使用了哪個主根或使用了多少個主根，因此攻擊者很難完整的重建秘密影像。這個方法的實驗結果也收錄在論文中。

    Today, more and more messages are passed on the internet and keeping critical information safe has become more and more important. Many schemes are designed to improve the security of important messages. Among them, image sharing is a well-known and useful method to achieve such a goal. Most image sharing methods apply (k,n)-threshold to their secret image embedding algorithms. The secret image is divided into n shadow images and we can reconstruct the original image by collecting k out of n shadows.
    We extend the (k,n)-threshold image sharing method by applying primitive roots in the encoding process. Our proposed method improves the security of secret images. Since the attackers do not know which primitive roots or how many primitive roots are used during the encoding phase, it is difficult for them to obtain a fully reconstructed image. Experiments for our proposed method are provided in this thesis.

    Chapter 1 Introduction………………………………………………………….1 Chapter 2 Background…………………………………………………………..3 2.1 Shamir secret sharing scheme [Sham1979]……………………………………..3 2.2 Chinese Remainder Theorem [Web01]…………………………………………4 2.3 Mignotte Secret Sharing [Mign1983]………………………………………......6 2.4 Image Sharing based on Mignotte's Secret Sharing [Shyu2008]………….........7 2.5 Asmuth and Bloom Based Secret Sharing Scheme [Ulut2009]………………...9 Chapter 3 Proposed Image sharing methods…………………………………12 3.1 Encryption Algorithm…………………………………………………………13 3.2 Decryption Algorithm…………………………………………………………15 3.3 Discussion……………………………………………………………………..16 Chapter 4 Experiment Results…………………………………………………….17 4.1 Experiment Results by the Proposed Algorithm………………………………17 4.2 Comparison of Experiment Results on Images Lenna, Peppers, Baboon..........18 4.3 Experiment Results Between Using A Single Primitive Root and Multiple Primitive Roots………………………………………………………………...21 Chapter 5 Conclusion…………………………………………………………………………………………..24 References…………………………………………………………………………...25

    [Sham1979] A. Shamir, "How to share a secret," Communications of the ACM, Vol.22, No. 11, 612-613, 1979.
    [Mign1983] M. Mignotte, “How to share a secret,” in T. Beth, editor, Lecture Notes in Computer Science, Vol. 149, 371-375, 1983.
    [Blak1979] G.R. Blakley, “Safeguarding cryptographic keys,” Proceedings of the National Computer Conference, American Federation of Information Proceeding Societies, Vol. 48, 313-317, 1979.
    [Asmu1983] C. Asmuth and J. Bloom, “A Modular Approach to Key Safeguarding,” IEEE Trans. on Information Theory, Vol. 29, No. 2, 208-210, 1983.

    [Chen2005] C.C. Chen, W.Y. Fu, and C.C. Chen, “A Geometry-Based Secret Image Sharing Approach,” Proceedings of Image and Vision Computing, 428-431, Dunedin, Otago, New Zealand, 2005.

    [Shyu2008] S.J. Shyu and Y.R. Chen, "Threshold secret image sharing by Chinese Remainder Theorem," IEEE Asia-Pacific Services Computing Conference, 1332-1337, 2008.
    [Ulut2009] M. Ulutas, V.V. Nabiyev, and G. Ulutas, "A New Secret Image Sharing Technique Based on Asmuth Bloom's Scheme." Application of Information and Communication Technologies, 1-5, 2009.
    [Web01] https://en.wikipedia.org/wiki/Lagrange_polynomial, last access on February 25, 2020.
    [Web02] https://en.wikipedia.org/wiki/Shamir%27s_Secret_Sharing, last access on February 25, 2020.
    [Web03] https://en.wikipedia.org/wiki/Chinese_remainder_theorem, last access on February 25, 2020.
    [Web04] https://en.wikipedia.org/wiki/Secret_sharing_using_the_Chinese_remainder_theorem, last access on February 25,2020

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