Global ETD Search

1	Analýza algoritmu SQUFOF / Analysis of the SQUFOF algoritm Langer, Lukáš January 2016 (has links) This thesis deals with collecting facts and making the complete analysis of SQUFOF algorithm. In the beginning you can find a short hystorical re- view and then it continues with desribing how the binary quadratic forms, which represents the number N, continued fractions of √ N, ideals in the ring Z( √ N) and lattices in Q( √ N) are related. This thesis offers the tools usable to switch between these structures and finally it uses these tools to show, how the algorithm SQUFOF works. 1
2	Square Forms Factoring with Sieves Clinton W Bradford (10732485) 05 May 2021 (has links) Square Form Factoring is an <i>O</i>(<i>N</i><sup>1/4</sup>) factoring algorithm developed by D. Shanks using certain properties of quadratic forms. Central to the original algorithm is an iterative search for a square form. We propose a new subexponential-time algorithm called SQUFOF2, based on ideas of D. Shanks and R. de Vogelaire, which replaces the iterative search with a sieve, similar to the Quadratic Sieve. Algebra and Number Theory factoring factoring algorithms subexponential factoring algorithms quadratic forms SQUFOF SQUFOF2 Square Forms Factoring square forms integral binary quadratic forms indefinite quadratic forms polynomial sieves quadratic sieve infrastructure distance