簡易檢索 / 詳目顯示
| 研究生： |
汪柏立 Wang, Bo-Li |
|---|---|
| 論文名稱： |
密碼學及其相關的演算法和一種基於量子隨機圖像的加密方法 Cryptography and Its Related Algorithms and An Encryption Method Based on Quantum Random Images |
| 指導教授： |
陳建隆
Chern, Jann-Long |
| 口試委員： |
陳建隆
Chern, Jann-Long 黃志煒 Huang, Chi-Wei 陳志有 Chen, Zi-You 林政宏 Lin, Zheng-Hong |
| 口試日期： | 2022/08/12 |
| 學位類別： |
碩士 Master |
| 系所名稱： |
數學系 Department of Mathematics |
| 論文出版年： | 2022 |
| 畢業學年度： | 110 |
| 語文別： | 英文 |
| 論文頁數： | 31 |
| 中文關鍵詞： | RSA演算法 、亂數生成器 、量子演算法 、Grover 演算法 、Shor 演算法 、數位影 像的量子表示法 、量子隨機影像 |
| 英文關鍵詞： | RSA algorithm, Random Number Generator, Quantum Algorithm, Grover’s Algorithm, Shor’sAlgorithm, Quantum Representation of Images, Quantum Random Image |
| 研究方法: | 實驗設計法 |
| DOI URL： | http://doi.org/10.6345/NTNU202201761 |
| 論文種類： | 學術論文 |
| 相關次數： | 點閱：99 下載：12 |
| 分享至: |
| 查詢本校圖書館目錄 查詢臺灣博碩士論文知識加值系統 勘誤回報 |
在這篇論文中，我們首先展示了一種傳統加密影像的方法。我們利用了亂數生成器來重
新排列像素，並使用 RSA 演算法加密影像。同時我們說明量子電腦是如何破解傳統的密碼系統，然後介紹廣為人知用來破解傳統密碼系統的量子演算法，也就是 Grover 演算法與 Shor 演算法。最後，我們引入了數位影像的量子表示法。並藉由這個概念來表示隨機生成的影像。此外，我們進一步利用此隨機影像進行加密。因為該提出的方法具有大量的密鑰，所以可以抵抗暴力破解法。
In this thesis, we initially highlight a traditional method for encrypting images. We
rearrange the pixels using a random number generator and encrypt the image using the RSA algorithm. At the same time, we illustrate how quantum computers can crack traditional cryptosystems, and introduce the well known quantum algorithms used to crack traditional cryptosystems, namely Grover's algorithm and Shor's algorithm. Finally, we introduce quantum representations of digital images and use this concept to represent a randomly generated image. Furthermore, we utilize this random image for encryption. This proposed method has a comprehensive number of keys, so it is resistant to brute-force attack.
[1] Jeffery Hoffstein, Jill Pipher, Joseph H. Silverman, An Introduction to Mathematical Cryptography. Springer Science + Business Media, 2008.
[2] Christof Paar, Jan Pelzl, Understanding Cryptography. Springer-Verlag Berlin Heidelberg, 2009.
[3] Grover Lov, A fast quantum mechanical algorithm for database search. 1996, 212-219.
[4] Peter W. Shor, Algorithms for Quantum Computation: Discrete Logarithms and Factoring. IEEE Computer Society Press, 1994, 124–134.
[5] Artur Ekert, Richard Jozsa, Quantum computation and Shor’s factoring algorithm, Rev. Mod. Phys, 1996, 733-753.
[6] Michael A. Nielsen, Issac L. Chuang. Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge: Cambridge University Press, 2010.
[7] Wolfgang Scherer, Mathematics of Quantum Computing. Springer Link, 2019.
[8] Jian zhi S, Shen W. Qiong L. A novel quantum representation of color digital images, Springer Science + Business Media, 2016.
[9] Yi Z, Kai L, Yinghui G, Mo W, NEQR: a novel enhanced quantum representation of digital images. Springer Science + Business Media, 2013, 2833–2860.
[10] Fei Y, Salvador E. Venegas-Andraca, Quantum Image Processing. Springer,2020
[11] Jian W, Ya-Cong G, Lei H, Ji-Qiang L, Quantum Image Encryption Algorithm Based on Quantum Key Image. Springer Science + Business Media, 2018, 308-322.
[12] Li-Yi Hsu, Quantum secret-sharing protocol based on Grover’s algorithm. PHYSICAL REVIEW A, 2003.
[13] Mark Hillery, Vladim´ırBuˇzek, Andr´e Berthiaume, Quantum SecretSharing. Phys. Rev. A, 1998.
[14] Arti Chamoli, C. M. Bhandari, Grover’s algorithm based multi-qubit secret sharing scheme. 2007.
[15] Thomas Lawson, Odd orders in Shor’s factoring algorithm. SpringerLink, 1999.
[16] Yuchen W, Zixuan H, Barry C. Sander, Sabre Kais, Qudits and High-Dimensional Quantum Computing. Frontiers in Physics, 2020.
[17] 溫巧燕. 郭奮卓. 朱甫臣. 量子保密通信協議的設計與分析. 科學出版社. 2009. [18] Shuta L, James T. Kwok, Yaonan W, Combination of images with diverse focuses using the spatial frequency. Information Fusion, 2001, 169-176.
[19] Fei Yan, Yiming Guo, Abdullah M. Iliyasu, and Huamin Yang, Flexible Representation and Manipulation of Audio Signals on Quantum Computers. Theoretical Computer Science, 2018, 71-85.
[20] Shahrokh Heidari, Mosayeb Naseri, Koji Nagata, International Journal of Theoretical Physics, 2019, 3908-3926.
