Drinfeld modules and their application to factor polynomials

[摘要] ENGLISH ABSTRACT:Major works done in Function Field Arithmetic show a strong analogy betweenthe ring of integers Z and the ring of polynomials over aniteeld Fq[T]. Whilean algorithm has been discovered to factor integers using elliptic curves, thediscovery of Drinfeld modules, which are analogous to elliptic curves, made itpossible to exhibit an algorithm for factorising polynomials in the ring Fq[T].In this thesis, we introduce the notion of Drinfeld modules, then we demonstratethe analogy between Drinfeld modules and Elliptic curves. Finally, wepresent an algorithm for factoring polynomials over aniteeld using Drinfeldmodules.

[发布机构] Stellenbosch University