Khalil, Antoine (2002) Application of sieve methods to factorization and the discrete logarithm problem. Masters thesis, Concordia University.
Factoring large numbers and computing discrete logarithms are presumed to be hard problems. No polynomial time solution for those problem has yet been found. Those problems have many significant applications, particularly in cryptography. Several cryptosystems base their security on their supposed difficulty. In this thesis we present some of the algorithms to solve these two problems. We mainly explore sieving as a tool for that purpose. Among other material we describe the Quadratic Sieve and the Number Field Sieve as they apply to factoring. We finally sketch how the Number Field Sieve can be applied to compute discrete logarithms.
|Divisions:||Concordia University > Faculty of Arts and Science > Mathematics and Statistics|
|Item Type:||Thesis (Masters)|
|Pagination:||vi, 70 leaves ; 29 cm.|
|Degree Name:||Theses (M.Sc.)|
|Program:||Mathematics and Statistics|
|Thesis Supervisor(s):||Ford, David|
|Deposited By:||Concordia University Libraries|
|Deposited On:||27 Aug 2009 17:22|
|Last Modified:||08 Dec 2010 15:23|
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