On the computation of discrete logarithms in finite prime fields [Elektronische Ressource] / von Damian Weber

On the Computationof Discrete Logarithmsin Finite Prime FieldsDissertationzur Erlangung des GradesDoktor der Ingenieurwissenschaften (Dr.–Ing.)der Technischen Fakult¨atder Universit¨at des SaarlandesvonDamian WeberSaarbrucken¨1997Tag des Kolloquiums: 30.10.1997Dekan: Prof. Dr.–Ing. Alexander KochGutachter:Prof. Dr. Johannes BuchmannProf. Ph. D. Raimund SeidelIAcknowledgementsTo write a thesis on discrete logarithms has been a very demanding and a highlyfascinating challenge.First of all, I would like to thank my thesis supervisor, Prof. Dr. Johannes Buch-mann, who approved of my proposal to consider the practicability of the asympto-tically fastest discrete logarithm algorithm for finite prime fields, the NFS, and whogave me the chance to join his research group at the university of Saarbrucken.¨Many thanks to the members of this research group for their support and assis-tance; especially to Thomas Denny who has been able to solve bigger and biggermatrix equations and who shared his experience with the quadratic sieve factoringalgorithm. I am also very grateful to Thomas Papanikolaou for his generosity ininvesting plenty of his time in answering questions about integer arithmetic andC++ internals. Thank you as well to him and Susanne Wetzel for proofreading themanuscript. Furthermore, I would like to thank Dr. Jo¨rg Zayer for providing manyimplementation tricks and details of the NFS factoring algorithm.Special thanks are due to Dr.