https://scholars.lib.ntu.edu.tw/handle/123456789/29927
Title: | 有限體上之超橢圓曲線的同構類 The Isomorphism Classes of Hyperelliptic Curves over Finite Fields with Characteristic 2 |
Authors: | 楊策仲 Yang, Tse-Chung |
Keywords: | 超橢圓曲線;超橢圓曲線密碼系統;同構類;hyperelliptic curves;hyperelliptic curve cryptosystem;isomorphism classes | Issue Date: | 2005 | 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。 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. |
URI: | http://ntur.lib.ntu.edu.tw//handle/246246/59477 | Other Identifiers: | en-US |
Appears in Collections: | 數學系 |
File | Description | Size | Format | |
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ntu-94-R91221020-1.pdf | 23.53 kB | Adobe PDF | View/Open |
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