by Li King Hung. / Thesis submitted in: July, 1998. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1999. / Includes bibliographical references (leaves 54-56). / Abstract also in Chinese. / Chapter 1 --- Description of the Number Field Sieve --- p.6 / Chapter 1.1 --- Introduction --- p.6 / Chapter 1.2 --- Outline of the algorithm --- p.8 / Chapter 2 --- Algebraic knowledge --- p.17 / Chapter 2.1 --- Factorization of an ideal over the class of ideals --- p.17 / Chapter 2.2 --- Existence of the square roots of an element in the ring of algebraic integers --- p.26 / Chapter 3 --- Run time analysis and Practical result --- p.31 / Chapter 3.1 --- Relation between sieving over X and finding the linear dependencies --- p.32 / Chapter 3.2 --- Relation between the size of a factor base and finding the linear dependencies --- p.34 / Chapter 3.3 --- Practical consideration --- p.36 / Chapter 4 --- Improvement of the algorithm --- p.38 / Chapter 4.1 --- Quadratic characters --- p.38 / Chapter 4.2 --- Finding the square root --- p.40 / Chapter 4.3 --- Solving the linear system of equation --- p.42 / Chapter 4.4 --- Reusing the computation --- p.47 / Chapter 4.5 --- Using more general purpose data --- p.50 / Chapter 4.6 --- Examples --- p.51 / Chapter 4.6.1 --- "A 18-digit example,761260375069630873" --- p.52 / Chapter 4.6.2 --- "A 23-digit example, 16504377514594481520559" --- p.52 / Bibliography
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_322419 |
| Date | January 1999 |
| Contributors | Li, King Hung., Chinese University of Hong Kong Graduate School. Division of Mathematics. |
| Source Sets | The Chinese University of Hong Kong |
| Language | English, Chinese |
| Detected Language | English |
| Type | Text, bibliography |
| Format | print, 56 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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