此篇論文主要在講述離散對數問題 (discrete logarithm problem)的解。在密碼學中，離散對數問題是一個擁有廣泛應用的研究主題，有許多系統，安全性便是建立在解離散對數問題的難題上。文中首先介紹離散對數問題與密碼學中關係，進一步說明嬰步巨步演算法、波立格-赫爾曼演算法以及指數計算法等三種解離散對數問題的方法，最後呈現使用 MATLAB 語言實現這些算法程式的計算結果並比較計算時間的多寡。 In this thesis, we are concerned to calculate discrete logarithm problem. In cryptography, the discrete logarithm problem is a research topic with a wide range of applications. There are many systems that security is built on the difficulty of solving discrete logarithm problems.First, we introduce the relationship between discrete logarithm problem and cryptography. And explain three methods for solving discrete logarithm problems. Baby-Step Giant-step methods, Pohlig-Hellman Algorithm and Index calculus methods. Finally, the calculation results and the calculation time of these algorithm are implemented using the MATLAB to compared.
