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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 朱樺(Huah Chu) | |
| dc.contributor.author | Tse-Chung Yang | en |
| dc.contributor.author | 楊策仲 | zh_TW |
| dc.date.accessioned | 2021-06-13T16:26:56Z | - |
| dc.date.available | 2005-07-22 | |
| dc.date.copyright | 2005-07-22 | |
| dc.date.issued | 2005 | |
| dc.date.submitted | 2005-07-15 | |
| dc.identifier.citation | [1] Y. Choie, E. Jeong, Isomorphism classes of elliptic and hyperelliptic curves over nite elds F(2g+1)n,
Finite Fields Appl., 10(2004), 583{614. [2] Y. Choie, D. Yun, Isomorphism classes of hyperelliptic curves of genus 2 over Fq, in: L.M. Batten, J. Seberry (Eds.), Information Security and Privacy, Lecture Notes in Computer Science 2384, Springer, Berlin, 2002, pp. 190{202. [3] Y. Deng, M. Liu, Isomorphism classes of hyperelliptic curves of genus 2 over nite elds with char- acteristic 2. Preprint. [4] Y. Deng, M. Liu, Isomorphism classes of hyperelliptic curves of genus 3 over nite elds. To appear in Finite Fields Appl. [5] L.H. Encinas, J.M. Masqu e, Isomorphism classes of hyperelliptic curves of genus 2 in characteristic 5, Tech. Rep. CORR2002-07, Centre For Applied Cryptographic Research, The University of Waterloo, Canada, 2002. Available at http://www.cacr.math.uwaterloo.ca/techreports/2002/corr2002-07.ps [6] L.H. Encinas, A.J. Menezes, J.M. Masqu e, Isomorphism classes of genus-2 hyperelliptic curves over nite elds, Appl. Algebra Engrg. Comm. Comput. 13(2002) 57{65. [7] William Fulton, Algebraic curves : an introduction to algebraic geometry / notes written with the collaboration of Richard Weiss, Benjamin, New York, 1969. [8] Nathan Jacobson, Basic algebra II, second edition. W. H. Freeman and Company, New York, 1989. [9] Y. Jeong,. Isomorphism classes of hyperelliptic curves of genus 3 over nite elds., Cryptology ePrint Archive. 2003/25/. [10] N. Koblitz, Hyperelliptic cryptosystems, J.Cryptology 1(1989) 139{150. [11] R. Lidl, H. Niederreiter, Introduction to nite elds and their applications, Cambridge University Press, Cambridge, 1994. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/38139 | - |
| dc.description.abstract | 在這篇論文裡,我們得到了有限體F_q上之超橢圓曲線在genus為4且特徵值等於2的同構類個數。我們得到了以下的公式:
N=2q^7+q^4-q^3 若2整除m N=2q^7+q^4-q^3+4q^2-4q+4 若6整除m N=2q^7+q^4-q^3+4q^2-4q+16 若2整除m,但若6不整除m ,其中q=2^m。這個結果可以被用在超橢圓函數密碼系統(HECC)之上。 | zh_TW |
| dc.description.abstract | In this thesis we will find the number of isomorphism classes of hyperelliptic curves of genus 4 over a finite field F_q with characteristic 2. We prove the formula of the number N of isomorphism classes as the following:
N=2q^7+q^4-q^3 if 2 divides m N=2q^7+q^4-q^3+4q^2-4q+4 if 6 divides m N=2q^7+q^4-q^3+4q^2-4q+16 if 2 divides m,but 6 does not divide m. These results can be used in the classification problems and the hyperelliptic curve cryptosystems. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-13T16:26:56Z (GMT). No. of bitstreams: 1 ntu-94-R91221020-1.pdf: 444012 bytes, checksum: 41f3173552445b2e900478fa1a359a10 (MD5) Previous issue date: 2005 | en |
| dc.description.tableofcontents | 中文摘要
Abstract 1.Introduction...........................1 2.g=2 2.1 |(R_g)_s| for g=2..................6 2.2 Fixed points ......................10 3.g=3 3.1 |(R_g)_s| for g=3..................19 3.2 Fixed points ......................24 4.g=4 4.1 |(R_g)_s| for g=4..................35 4.2 Fixed points ......................42 Appendix ................................69 Reference................................71 | |
| dc.language.iso | en | |
| dc.subject | 同構類 | zh_TW |
| dc.subject | 超橢圓曲線 | zh_TW |
| dc.subject | 超橢圓曲線密碼系統 | zh_TW |
| dc.subject | hyperelliptic curve cryptosystem | en |
| dc.subject | isomorphism classes | en |
| dc.subject | hyperelliptic curves | en |
| dc.title | 有限體上之超橢圓曲線的同構類 | zh_TW |
| dc.title | The Isomorphism Classes of
Hyperelliptic Curves over Finite Fields with Characteristic 2 | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 93-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 胡守仁,陳永秋,洪有情 | |
| dc.subject.keyword | 超橢圓曲線,超橢圓曲線密碼系統,同構類, | zh_TW |
| dc.subject.keyword | hyperelliptic curves,hyperelliptic curve cryptosystem,isomorphism classes, | en |
| dc.relation.page | 71 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2005-07-15 | |
| 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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