N元有向圖之研究

Abstract

在這篇論文中, 我們描述了一個植基在 N 元有向圖(n-ary directed graph)上的密碼系統。為了實作這套系統, 我們會遭遇到一些問題, 所以 本篇論文討論了一些 N元有向圖的性質。首先, N 元有向圖的最小化過程 跟有限狀態機(finite state machine)的最小化過程非常類似, 所以我們 提到了有限狀態機的最小化過程, 並且描述了 N元有向圖的最小化過程 。 N 元有向圖經過最小化後才可避免系統因儲存了太多多餘的資料而浪 費空間。在這篇論文中我們也介紹了一個特殊的 N元有向圖以及它的最小 化過程。最後, 我們介紹了一個 N元有向圖的表格表示法。表格表示法是 一個簡單的方法。另外, 我們也討論了一些關於表格表示法的特殊情形。 In this thesis, we describe a cryptosystem based on n-ary directed graphs. In order to implement this cryptosystem, we discuss some properties of an n-ary directed graph. First of all, we discuss the minimization of an n-ary directed graph which is very similar to a finite state machine, so we refer a way to minimize a finite state machine while minimizing an n- ary directed graph. A special n-ary directed graph, an isolated n-ary directed graph, is also discussed. Finally, we describe the tabular representation of an n-ary directed graph. It is a simple way to represent an n-ary directed graph. We describe some special cases of tabular representation in the final section of this thesis.