Fast Modular Composition in any Characteristic

We give an algorithm for modular composition of degree n univariate polynomials over a finite field Fq requiring n1+o(1) log1+o(1) q bit operations; this had earlier been achieved in characteristic no(1) by Umans (2008). As an application, we obtain a randomized algorithm for factoring degree n polynomials over Fq requiring

• Type: Conference
• Year: 2008
• Where: FOCS
• Authors: Kiran S. Kedlaya, Christopher Umans
• Keywords: FOCS 2008, Modular Composition, Theoretical Computer Science, Univariate Polynomials, finite field Fq