請用此 Handle URI 來引用此文件：
http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/9430完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 陳君明(Jiun-Ming Chen) | |
| dc.contributor.author | Tzh-Huan Lin | en |
| dc.contributor.author | 林子桓 | zh_TW |
| dc.date.accessioned | 2021-05-20T20:22:15Z | - |
| dc.date.available | 2009-02-10 | |
| dc.date.available | 2021-05-20T20:22:15Z | - |
| dc.date.copyright | 2009-02-10 | |
| dc.date.issued | 2009 | |
| dc.date.submitted | 2009-01-23 | |
| dc.identifier.citation | [1] I.F. Blake, G. Seroussi and N.P. Smart. Elliptic curve in cryptography. volume 265 of London Mathematical Society Lecture Note Series. CambridgeUniversity Press, Cambridge, 2000.
[2] R. Lercier. Computing isogenies in F2n, ANTS-II: Algorithmic Number Theory, Lecture Notes Computation Science, vol. 1122, Springer-Verlag, 1996, p. 197-212 [3] A. J. Menezes. Elliptic curve public key cryptosystems. Springer, 1993 [4] A. Meneze, S. Vanstone and T. Okamoto. Reducing elliptic curve logarithms to logarithms in a finite field. IEEE Transactions on Information Theory, 39:1639-1646, 1993 [5] V. Mueller. Ein Algorithmus zur Bestimmung der Punktzahl elliptischer Kurvenueber endlichen Koerpern der Charackteristik groesser drei, Ph.D. Thesis, Universitaet des Saarlandes, 1995 [6] R. Schoof. Counting points on elliptic curves over finite fields. Journal de théorie des nombres de Bordeaux,7 no. 7 (1995), p. 219-254 [7] Shamus Software. Multiprecision Integer and Rational Arithmetic C/C++ Library. http://www.shamus.ie/ [8] F. Vercauteren. The SEA algorithm in characteristic 2. Preprint, 2000. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/9430 | - |
| dc.description.abstract | 目前尋找安全橢圓曲線的最好方法為群秩計算法 (Point-counting Method)。Schoof-Elkies-Atkin 演算法 (SEA 演算法) 為質數體上計算橢圓曲線群秩最有效率的演算法。Lercier 提出了計算二元體上同源的方法，使得 SEA 演算法也可應用基於二元體的橢圓取線上。這篇論文我們將依據 Lercier 提出的方法實作 SEA 演算法，用它來計算美國國家標準和技術研究院 (NIST) 推薦的十條曲線的群秩並觀察其效率。 | zh_TW |
| dc.description.abstract | The best suggested way to find secure elliptic curves is point-counting. So far Schoof-Elkies-Atkin algorithm (SEA algorithm) is the most efficient point-counting algorithm for elliptic curves over prime fields. Lercier proposed an algorithm to compute isogenies in GF(2^n) such that SEA algorithm can be used for binary case. In this thesis we will follow Lericier's approach to implement SEA algorithm computing the order of an elliptic curve over binary fields. | en |
| dc.description.provenance | Made available in DSpace on 2021-05-20T20:22:15Z (GMT). No. of bitstreams: 1 ntu-98-R94221002-1.pdf: 330275 bytes, checksum: 3474666da5462a3351469b00bc7d0aa1 (MD5) Previous issue date: 2009 | en |
| dc.description.tableofcontents | Contents
Acknowledgements i Abstract in Chinese ii Abstract in English iii 1 Introduction 1 2 Mathematical Backgrounds 3 3 SEA Algorithm 8 3.1 Schoof's Algorithm. . . . . . . . . . . . . . 8 3.2 Modular Polynomials . . . . . . . . . . . . . . 10 3.3 SEA Algorithm. . . . . . . . . . . . . . . . . . 12 4 Implementation of SEA Algorithm 20 4.1 Computing Modular Polynomials. . . . . . . . . . 20 4.2 Computing Isogenies. . . . . . . . . . . . . . 23 5 Experimental Results 27 5 Conclusions 28 References 29 A Source Code with Explanation 30 A.1 Some Preprocessors. . . . . . . . . . . . . . 30 A.2 Computing Isogenies . . . . . . . . . . . . . . 40 A.3 Computing Isogenies for Koblitz Curves. . . . . . . . . . . . . 49 B Experimental Data 54 B.1 NIST Binary Curves. . . . . . . . . . . . . . 54 B.2 NIST Koblitz Curves . . . . . . . . . . . . . . 64 | |
| dc.language.iso | en | |
| dc.title | 計算二元體上橢圓曲線群之群秩：SEA演算法的實作 | zh_TW |
| dc.title | Implementations of SEA Algorithm Counting the Orders of Elliptic Curve Groups over Binary Fields | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 97-1 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 賴溪松(Chi-Sung Laih),楊柏因(Bo-Yin Yang) | |
| dc.subject.keyword | 橢圓曲線,群秩,SEA 演算法,Schoof 演算法,Elkies 質數,Atkin 質數, | zh_TW |
| dc.subject.keyword | elliptic curve,group order,SEA algorithm,Schoof algorithm,Elkies prime,Atkin prime, | en |
| dc.relation.page | 73 | |
| dc.rights.note | 同意授權(全球公開) | |
| dc.date.accepted | 2009-01-23 | |
| 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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