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完整後設資料紀錄
DC 欄位 | 值 | 語言 |
---|---|---|
dc.contributor.advisor | 陳君明 | |
dc.contributor.author | Chien-Yeo Chiang | en |
dc.contributor.author | 江前佑 | zh_TW |
dc.date.accessioned | 2021-05-20T20:47:20Z | - |
dc.date.available | 2008-07-14 | |
dc.date.available | 2021-05-20T20:47:20Z | - |
dc.date.copyright | 2008-07-14 | |
dc.date.issued | 2008 | |
dc.date.submitted | 2008-07-07 | |
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dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/9885 | - |
dc.description.abstract | 現今許多密碼系統的安全性, 是以橢圓曲線離散對數問題(ECDLP) 的困難度為基礎。這些密碼系統的安全性, 通常取決於曲線的選擇。在這篇論文中, 我們對現在針對橢圓曲線離散對數問題的攻擊法做一個整理, 找出弱曲線的條件, 也提出一些安全曲線應該有的條件。另外, 我們也會討論一些其他的攻擊法, 這些攻擊法對ECDLP 是失敗的。 | zh_TW |
dc.description.abstract | The elliptic curve discrete logarithm problem (ECDLP) forms the basis of numerous cryptosystems today. The security of these cryptosystems usually depends on the choice of curves. In this thesis, we give a summary of recent attacks on the ECDLP, find the criteria of weak curves, and suggest the conditions that a secure curve should have. We will also discuss some attacks which works on the DLP but may fail to the ECDLP. | en |
dc.description.provenance | Made available in DSpace on 2021-05-20T20:47:20Z (GMT). No. of bitstreams: 1 ntu-97-R94221032-1.pdf: 524854 bytes, checksum: e72ab8bbf789e2808eb6a1d46e8e421d (MD5) Previous issue date: 2008 | en |
dc.description.tableofcontents | Contents
口試委員會審定書i 致謝ii Abstract in Chinese iii Abstract in English iv 1 Introduction 1 2 General Attacks on the ECDLP 4 2.1 Baby Step, Giant Step . . . . . . . . . . . . . . . . . 4 2.2 The Pollard Method. . . . . . . . . . . . . . . . . . . 5 2.2.1 Pollard’s ρ Method. . . . . . . . . . . . . . . . . 5 2.2.2 Pollard’s λ Method. . . . . . . . . . . . . . . . . 9 2.3 Pohlig-Hellman Attack. . . . . . . . . . . . . . . . . 11 3 Isomorphism Attacks on the ECDLP 15 3.1 Attacks on Anomalous Curves. . . . . . . . . . . . . . 15 3.1.1 Smart’s Method. . . . . . . . . . . . . . . . . . . 15 3.1.2 Semaev’s Method . . . . . . . . . . . . . . . . . . 18 3.2 MOV Attack . . . . . . . . . . . . . . . . . . . . . . 22 3.3 Tate Pairing Attack. . . . . . . . . . . . . . . . . . 26 3.4 Weil Descent . . . . . . . . . . . . . . . . . . . . . 29 4 Other Attacks 33 4.1 Index Calculus on the ECDLP. . . . . . . . . . . . . . 33 4.2 Xedni Calculus on the ECDLP. . . . . . . . . . . . . . 36 4.3 Semaev’s Summation Polynomials. . . . . . . . . . . . 44 4.4 Further Results. . . . . . . . . . . . . . . . . . . . 47 5 Conclusions 50 References 52 A Computation of the Parings 57 | |
dc.language.iso | en | |
dc.title | 橢圓曲線密碼系統之曲線安全性研究 | zh_TW |
dc.title | The Security of Curves for Elliptic Curve Cryptosystems | en |
dc.type | Thesis | |
dc.date.schoolyear | 96-2 | |
dc.description.degree | 碩士 | |
dc.contributor.oralexamcommittee | 陳其誠,黃柏嶧,鄭振牟,楊柏因 | |
dc.subject.keyword | 橢圓曲線密碼學,橢圓曲線離散對數,弱曲線,索引演算,離散對數。, | zh_TW |
dc.subject.keyword | ECC,ECDLP,weak curve,index calculus,DLP., | en |
dc.relation.page | 60 | |
dc.rights.note | 同意授權(全球公開) | |
dc.date.accepted | 2008-07-07 | |
dc.contributor.author-college | 理學院 | zh_TW |
dc.contributor.author-dept | 數學研究所 | zh_TW |
顯示於系所單位: | 數學系 |
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