by Chan Hing Che. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2000. / Includes bibliographical references (leaves 59-[61]). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Background --- p.8 / Chapter 2.1 --- Abstract Algebra --- p.8 / Chapter 2.1.1 --- Group --- p.9 / Chapter 2.1.2 --- Ring --- p.10 / Chapter 2.1.3 --- Field --- p.11 / Chapter 2.1.4 --- Useful Theorems in Number Theory --- p.12 / Chapter 2.2 --- Discrete Logarithm --- p.13 / Chapter 2.3 --- Solving Discrete Logarithm --- p.14 / Chapter 2.3.1 --- Exhaustive Search --- p.14 / Chapter 2.3.2 --- Baby Step Giant Step --- p.15 / Chapter 2.3.3 --- Pollard's rho --- p.16 / Chapter 2.3.4 --- Pohlig-Hellman --- p.18 / Chapter 2.3.5 --- Index Calculus --- p.23 / Chapter 3 --- Forging ElGamal Signature --- p.26 / Chapter 3.1 --- ElGamal Signature Scheme --- p.26 / Chapter 3.2 --- ElGamal signature without hash function --- p.29 / Chapter 3.3 --- Security of ElGamal signature scheme --- p.32 / Chapter 3.4 --- Bleichenbacher's Attack --- p.34 / Chapter 3.4.1 --- Constructing trapdoor --- p.36 / Chapter 3.5 --- Extension to Bleichenbacher's attack --- p.37 / Chapter 3.5.1 --- Attack on variation 3 --- p.38 / Chapter 3.5.2 --- Attack on variation 5 --- p.39 / Chapter 3.5.3 --- Attack on variation 6 --- p.39 / Chapter 3.6 --- Digital Signature Standard(DSS) --- p.40 / Chapter 4 --- Quadratic Field Sieve --- p.47 / Chapter 4.1 --- Quadratic Field --- p.47 / Chapter 4.1.1 --- Integers of Quadratic Field --- p.48 / Chapter 4.1.2 --- Primes in Quadratic Field --- p.49 / Chapter 4.2 --- Number Field Sieve --- p.50 / Chapter 4.3 --- Solving Sparse Linear Equations Over Finite Fields --- p.53 / Chapter 4.3.1 --- Lanczos and conjugate gradient methods --- p.53 / Chapter 4.3.2 --- Structured Gaussian Elimination --- p.54 / Chapter 4.3.3 --- Wiedemann Algorithm --- p.55 / Chapter 5 --- Conclusion --- p.57 / Bibliography --- p.59
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_323057 |
| Date | January 2000 |
| Contributors | Chan, Hing Che., 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, viii, 59, [2] leaves : ill. ; 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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