Generating polynomials for number field sieve

Title: Generating polynomials for number field sieve Author: Anežka Pejlová Department: Department of Algebra Supervisor: prof. RNDr. Aleš Drápal, CSc., DSc., Department of Algebra Abstract: The topic of this thesis is mainly focused on Kleinjung algorithm for generating polynomials within the General Number Field Sieve, which is the most efficient factorization algorithm nowadays. Commonly used consecu- tions are explained with respect to the fact whether they can be rigorously proven or they are based only on heuristic assumptions. Another contribution of this thesis is the attached implementation of Kleinjung algorithm develo- ped as a part of the Number Field Sieve project led by the Department of Algebra. The appropriateness of some heuristics used in the theory beyond the Kleinjung algorithm is supported by empirical data obtained from this implementation. Keywords: Number field sieve, Kleinjung algorith