朱樺臺灣大學：數學研究所楊策仲Yang, Tse-ChungTse-ChungYang2007-11-282018-06-282007-11-282018-06-282005http://ntur.lib.ntu.edu.tw//handle/246246/59477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.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................................71444012 bytesapplication/pdfen-US超橢圓曲線超橢圓曲線密碼系統同構類hyperelliptic curveshyperelliptic curve cryptosystemisomorphism classesthesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/59477/1/ntu-94-R91221020-1.pdf