Wong, Chun Kuen. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2002. / Includes bibliographical references (leaves 43-45). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Origin of The First Digital Signature Scheme --- p.2 / Chapter 1.2 --- On the security of digital signature schemes --- p.3 / Chapter 1.3 --- Organization of the Thesis --- p.4 / Chapter 2 --- Mathematical Background --- p.6 / Chapter 2.1 --- Divisibility --- p.6 / Chapter 2.2 --- Prime --- p.7 / Chapter 2.3 --- Modular arithmetic --- p.7 / Chapter 2.4 --- Congruence --- p.7 / Chapter 2.5 --- Greatest Common Divisor --- p.7 / Chapter 2.6 --- Integers modulo n --- p.8 / Chapter 2.7 --- Inverse --- p.8 / Chapter 2.8 --- Division in Zn --- p.8 / Chapter 2.9 --- Order of element --- p.8 / Chapter 2.10 --- Euclidean Algorithm --- p.9 / Chapter 2.11 --- Extended Euclidean Algorithm --- p.9 / Chapter 2.12 --- Chinese Remainder Theorem --- p.10 / Chapter 2.13 --- Relatively Prime --- p.10 / Chapter 2.14 --- Euler Totient Function --- p.10 / Chapter 2.15 --- Fermat's Little Theorem --- p.11 / Chapter 2.16 --- Euler's Theorem --- p.11 / Chapter 2.17 --- Square root --- p.12 / Chapter 2.18 --- Quadratic residue --- p.12 / Chapter 2.19 --- Legendre Symbol --- p.13 / Chapter 2.20 --- Jacobi Symbol --- p.14 / Chapter 2.21 --- Blum Integer --- p.15 / Chapter 2.22 --- The Factoring Problem --- p.16 / Chapter 2.23 --- The Discrete Logarithm Problem --- p.17 / Chapter 2.24 --- One-way Hash Function --- p.17 / Chapter 3 --- Survey of digital signature schemes --- p.19 / Chapter 3.1 --- The RSA signature scheme --- p.19 / Chapter 3.1.1 --- Key generation in the RSA signature scheme --- p.20 / Chapter 3.1.2 --- Signature generation in the RSA signature scheme --- p.20 / Chapter 3.1.3 --- Signature verification in the RSA signature scheme --- p.20 / Chapter 3.1.4 --- On the security of the RSA signature scheme --- p.21 / Chapter 3.2 --- The ElGamal signature scheme --- p.22 / Chapter 3.2.1 --- Key generation in the ElGamal signature scheme --- p.23 / Chapter 3.2.2 --- Signature generation in the ElGamal signature scheme --- p.23 / Chapter 3.2.3 --- Signature verification in the ElGamal signature scheme --- p.23 / Chapter 3.2.4 --- On the security of the ElGamal signature scheme --- p.24 / Chapter 3.3 --- The Schnorr signature scheme --- p.26 / Chapter 3.3.1 --- Key generation in the Schnorr signature scheme --- p.26 / Chapter 3.3.2 --- Signature generation in the Schnorr signature scheme --- p.26 / Chapter 3.3.3 --- Signature verification in the Schnorr signature scheme --- p.27 / Chapter 3.3.4 --- Discussion --- p.27 / Chapter 3.4 --- Digital signature schemes based on both the factoring and discrete logarithm problems --- p.27 / Chapter 3.4.1 --- The Brickell-McCurley signature scheme --- p.28 / Chapter 3.4.2 --- The Okamoto signature scheme --- p.29 / Chapter 3.4.3 --- The Harn signature scheme --- p.30 / Chapter 3.4.4 --- The Shao signature scheme --- p.30 / Chapter 3.4.5 --- The W. He signature scheme --- p.31 / Chapter 4 --- Cryptanalysis of the digital signature scheme of W. He --- p.32 / Chapter 4.1 --- The Digital Signature Scheme of W. He --- p.33 / Chapter 4.1.1 --- System setup in the W. He Digital Signature Scheme --- p.33 / Chapter 4.1.2 --- Key generation in the W. He Digital Signature Scheme --- p.34 / Chapter 4.1.3 --- Signature generation in the W. He Digital Signature Scheme --- p.34 / Chapter 4.1.4 --- Signature verification in the W. He Digital Signature Scheme --- p.34 / Chapter 4.2 --- Cryptanalysis of the digital signature scheme of W. He --- p.35 / Chapter 4.2.1 --- Theorems on the security of the digital signature scheme of W. He --- p.35 / Chapter 4.2.2 --- Signature Forgery in the digital signature scheme of W. He --- p.37 / Chapter 4.2.3 --- Remedy --- p.40 / Chapter 5 --- Conclusions --- p.41 / Bibliography --- p.43
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_323962 |
| Date | January 2002 |
| Contributors | Wong, Chun Kuen., Chinese University of Hong Kong Graduate School. Division of Information Engineering. |
| Source Sets | The Chinese University of Hong Kong |
| Language | English, Chinese |
| Detected Language | English |
| Type | Text, bibliography |
| Format | print, ix, 45 leaves ; 30 cm. |
| Rights | Use of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/) |
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