### 博碩士論文 86221008 完整後設資料紀錄

 DC 欄位 值 語言 DC.contributor 數學系 zh_TW DC.creator 黃博峙 zh_TW DC.creator Bo-Chih Huang en_US dc.date.accessioned 2000-7-18T07:39:07Z dc.date.available 2000-7-18T07:39:07Z dc.date.issued 2000 dc.identifier.uri http://ir.lib.ncu.edu.tw:88/thesis/view_etd.asp?URN=86221008 dc.contributor.department 數學系 zh_TW DC.description 國立中央大學 zh_TW DC.description National Central University en_US dc.description.abstract The purpose of this thesis is to make a general survey of the development of cryptography and to discuss the mathematical background of cryptography. We first introduce the RSA cryptosystem which is based on the difficulty of factoring a large integer, and other cryptosystems based on the problem in number theory so called discrete logarithm problem. Then we describe some methods which can determine whether or not a given integer is a prime number and methods of efficient factoring large composite integers, and some methods of solving discrete logarithm problem on finite fields. In the second half of this thesis, we present some basic properties of elliptic curves and introduce a factorization method which is based on properties of elliptic curves over finite fields. Some elliptic curve cryptosystems will be introduced. In the final section of this thesis, we discuss some methods of counting the number of rational points on the elliptic curve over finite fields. en_US DC.subject 橢圓曲線 zh_TW DC.subject 離散對數 zh_TW DC.subject 整數分解 zh_TW DC.subject 質數檢定 zh_TW DC.subject 密碼學 zh_TW DC.subject Factoring Integer en_US DC.subject Primality Test en_US DC.subject Cryptography en_US DC.subject Discrete Logarithm Problem en_US DC.subject Elliptic Curve en_US DC.title 數論在密碼學上的應用 zh_TW dc.language.iso zh-TW zh-TW DC.title Number Theory in Cryptography - a General Survey en_US DC.type 博碩士論文 zh_TW DC.type thesis en_US DC.publisher National Central University en_US