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研究生： 馮鼎軒
Feng, Ting-Hsuan
論文名稱： RSA 上的低解密指數攻擊法
Attacks on RSA with Low-Exponet Private Key
指導教授： 柯文峰
Ke, Wen-Fong
學位類別： 碩士
Master
系所名稱： 理學院 - 數學系應用數學碩博士班
Department of Mathematics
論文出版年： 2014
畢業學年度： 102
語文別： 英文
論文頁數： 18
中文關鍵詞： RSA 、低解密指數
外文關鍵詞： RSA, Low-exponent
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    • 我們討論RSA 密碼體系在低指數私鑰時的安全性。首先介紹
    RSA 的定義與加解密方式。接著是本篇的第一種攻擊法Wiener’s
    Attack 的運作。以Wiener’s Attack 作為啟發，第二個要介紹的是
    Dan Boneh & Glenn Durfee 所提出的改良，他們將Wiener 的結果
    加以優化。Dan Boneh & Glenn Durfee 同時也提出一個新的RSA 攻
    擊法。而在最後的小節裡，會給出一些建議以避免這些低指數攻擊法。

    We discuss the security of RSA cryptosystem with low-exponent pri-
    vate key. Firstly, we give a brief de nition for RSA. Sencondly, we
    show how does Wiener's Attack work. An improvement of the result of
    Wiener's Attack is given by Dan Boneh & Glenn Durfee in 2000. They
    propose a di erent view for RSA cryptosystem. Some suggestions for
    avoiding these attacks are include in the last section.

    1. Introduction 1 2. Cryptosystem and RSA 1 2.1. Cryptosystem 1 2.2. RSA 2 3. Wiener Theorem and his Attack 2 3.1. Continued Fraction 3 3.2. Wiener’s theorem and attack 4 4. The Idea of Dan Boneh & Glenn Durfee 5 5. Lattices and their properties 6 5.1. Lattices 6 5.2. Determinant and Properties 7 5.3. LLL-reduced 9 6. Lattice attacks 9 7. Using the Chinese remainder theorem to avoid attacks 15 8. Conclusions 16 Appendix A. LLL basis reduction algorithm 17 References 18

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