臺灣博碩士論文加值系統

這一篇論文主要討論在橢圓曲線上解log問題，我把M-O-V, Semave, 和Voloch的論文作重新的整理。
橢圓曲線上解log問題如下：E是一個在有限體F上的橢圓曲線，給曲線上任兩點有理點P, Q. 我們想算出是否有整數m滿足Q=[m]P.
如果P的order是n,且F的特徵值是p,我們分兩個部分討論
(1)n跟p互質
(2)n跟p不互質
並且我們比較出每個方法的優缺點。

In this master thesis, we talk about the discrete logarithm on an elliptic curve, and this is a reorganization of M-O-V's, Semaev's, and Voloch's papers.
Let E be an elliptic curve over a finite field F and char(F)=p,
the discrete logarithm problem on an elliptic curve is to compute an integer m such that Q=[m]P, where P and Q are rational points on E. If P has order n, we consider two cases:
(1)gcd(n,p)=1
(2)gcd(n,p) is not 1
Finally, we can use the Chinese remainder theorem to compute m

1. Introduction
2. Preliminaries of elliptic curve
3. Reducing Elliptic curve logarithm with gcd(n,q)=1
4. Evaluation of discrete logarithm in a group of p-torsion points of an elliptic curve in characteristic
5. Reducing elliptic curve logarithm with gcd(n,q) is not 1

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