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http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/51245完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 陳君明(Jiun-Ming Chen) | |
| dc.contributor.author | Ricardo Pontaza | en |
| dc.contributor.author | 龐德沙 | zh_TW |
| dc.date.accessioned | 2021-06-15T13:28:25Z | - |
| dc.date.available | 2016-03-08 | |
| dc.date.copyright | 2016-03-08 | |
| dc.date.issued | 2016 | |
| dc.date.submitted | 2016-02-09 | |
| dc.identifier.citation | [Apostol(1971)] T. M. Apostol. Some properties of completely multiplicative arithmetical functions.
American Mathematical Monthly, 78(3)((3)):266–271, March 1971. [Cohen(1993)] Henri Cohen. A Course in Computational Algebraic Number Theory. Springer-Verlag, New York, 1993. [Engel(1976)] Arthur Engel. Problem-Solving Strategies. Springer-Verlag, New York, 1976. [Hlawka et al.(1991)Hlawka, Schoibengeier, and Taschner] Edmund Hlawka, Johannes Schoibengeier, and Rudolf Taschner. Geometric and Analytic Number Theory. Springer- Verlag, New York, 1991. [Niven and Zuckerman(1976)] Ivan Niven and Herbert Zuckerman. Introduction to Number Theory. Wiley, New York, 1976. [Paar and Pelzl(2010)] Christof Paar and Jan Pelzl. Understanding Cryptography. Springer-Verlag, New York, 2010. [Papadimitriou(1995)] Christos H. Papadimitriou. Computational Complexity. Addison Wesley Longman, Reading, Massachusetts, 1995. [Sipser(2006)] Michael Sipser. Introduction to the Theory of Computation. Thomson Course Technology, Boston, 2006. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/51245 | - |
| dc.description.abstract | This thesis introduces the concept of p-vectors and p-arrays, which are algebraic constructions based on multiplicative arithmetic functions and prime numbers. With these concepts we construct several algebraic structures which allows us also to make a proposal for a public key encryption protocol. This public key encryption protocol, which we call p-array public key encryption protocol is a public-private key encryption system that allows the users to encrypt and decrypt messages of vectorial structure whose components are non negative integers upperly bounded. Along this work we present several of the theorems and lemmas that allow us to make the proof of correctness of the aforedmentioned protocol, and also to discuss some of the attacks that could potentially provide information of the private key to anyone performing them on the proposed algorithm. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-15T13:28:25Z (GMT). No. of bitstreams: 1 ntu-105-R03221027-1.pdf: 426309 bytes, checksum: 290e35e5b8479d44ae51bf591c78e0c0 (MD5) Previous issue date: 2016 | en |
| dc.description.tableofcontents | 口試委員會審定書 . . . . . .iii
Acknowledgements . . . . . . v Abstract . . . . . . vii List of Symbols . . . . . . xi Introduction . . . . . . xiii 1 On p-vectors and algebraic structures . . . . . . 1 1.1 Basic concepts . . . . . .1 1.2 p-vectors . . . . . .1 1.3 Operations over Fp and some useful properties . . . . . .2 1.3.1 Componentwise sum . . . . . .2 1.3.2 Componentwise multiplication . . . . . .3 1.3.3 Convoluted multiplication . . . . . .4 2 On p-cuts and p-arrays . . . . . . 7 2.1 Definitions . . . . . .7 2.2 p-cuts and multiplicative functions . . . . . .8 2.3 p-arrays . . . . . .10 2.3.1 Existence of p-arrays . . . . . .11 2.3.2 Operations . . . . . .12 2.3.3 Identity and inverses . . . . . .14 2.3.4 p-arrays over finite fields . . . . . .19 2.3.5 Normalization . . . . . .22 3 On p-arrays and cryptographic protocols . . . . . . 25 3.1 Preliminary theorems . . . . . .25 3.2 p-array public key encryption . . . . . .29 3.3 Proof of correctness . . . . . .33 3.4 Examples . . . . . .37 3.5 Security . . . . . .42 Bibliography . . . . . . 49 | |
| dc.language.iso | en | |
| dc.subject | 陣列 | zh_TW |
| dc.subject | 向量 | zh_TW |
| dc.subject | 密碼協定 | zh_TW |
| dc.subject | 向量 | zh_TW |
| dc.subject | 陣列 | zh_TW |
| dc.subject | 密碼協定 | zh_TW |
| dc.subject | ring | en |
| dc.subject | ring | en |
| dc.subject | field | en |
| dc.subject | cryptography | en |
| dc.subject | public key | en |
| dc.subject | private key | en |
| dc.subject | lattice | en |
| dc.subject | encryption | en |
| dc.subject | decryption | en |
| dc.subject | encryption | en |
| dc.subject | decryption | en |
| dc.subject | array | en |
| dc.subject | vector | en |
| dc.subject | arithmetic function | en |
| dc.subject | algebra | en |
| dc.subject | field | en |
| dc.subject | cryptography | en |
| dc.subject | public key | en |
| dc.subject | private key | en |
| dc.subject | lattice | en |
| dc.subject | array | en |
| dc.subject | vector | en |
| dc.subject | arithmetic function | en |
| dc.subject | algebra | en |
| dc.title | "p-向量, p-陣列與密碼協定" | zh_TW |
| dc.title | On p-vectors, p-arrays and cryptographic protocols | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 104-1 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 鄭振牟(Chen-Mou Cheng),謝致仁(Jyh-Ren Shieh),呂育道(Yuh-Dauh Lyuu) | |
| dc.subject.keyword | 向量,陣列,密碼協定, | zh_TW |
| dc.subject.keyword | array,vector,arithmetic function,algebra,ring,field,cryptography,public key,private key,lattice,encryption,decryption, | en |
| dc.relation.page | 49 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2016-02-13 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 數學研究所 | zh_TW |
| 顯示於系所單位： | 數學系 | |
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