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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:135下載:12
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  • 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.

    Abstract i Contents ii 1 Introduction 1 2 Classical Image Encryption 2 2.1 RSA Cryptosystem 2 2.2 Implementation Results 3 3 Quantum Algorithms for Breaking Classical Cryptosystems 7 3.1 Preliminaries 7 3.1.1 Qubits 7 3.1.2 Quantum Gates 9 3.2 Grover's Algorithm 10 3.3 Shor's Algorithm 12 4 Quantum Images Encryption 18 4.1 A Novel Enhanced Quantum Representation of Digital Images 19 4.1.1 Quantum Image Preparation 19 4.1.2 Computational Complexity of Preparing NEQR 22 4.2 Image Encryption Based on Quantum Random Image 22 4.2.1 Procedures of Encryption and Decryption 22 4.2.2 Computational Complexity of Quantum Image Encryption 24 4.3 Statistical Analysis 26 4.3.1 Information Entropy 26 4.3.2 Spatial Frequency 27 5 Conclusion 29 Reference 30

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