博碩士論文 86221008 完整後設資料紀錄

DC 欄位 語言
DC.contributor數學系zh_TW
DC.creator黃博峙zh_TW
DC.creatorBo-Chih Huangen_US
dc.date.accessioned2000-7-18T07:39:07Z
dc.date.available2000-7-18T07:39:07Z
dc.date.issued2000
dc.identifier.urihttp://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.descriptionNational Central Universityen_US
dc.description.abstractThe 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.subjectFactoring Integeren_US
DC.subjectPrimality Testen_US
DC.subjectCryptographyen_US
DC.subjectDiscrete Logarithm Problemen_US
DC.subjectElliptic Curveen_US
DC.title數論在密碼學上的應用zh_TW
dc.language.isozh-TWzh-TW
DC.titleNumber Theory in Cryptography - a General Surveyen_US
DC.type博碩士論文zh_TW
DC.typethesisen_US
DC.publisherNational Central Universityen_US

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