An unconditional improvement to the running time of the quadratic Frobenius test

Abstract

In a 2006 paper, Damgård and Frandsen designed a faster version of the Quadratic Frobenius Test. This test assumes the Extended Riemann Hypothesis in order to find small nonresidues, which allow construction of quadratic extensions with faster arithmetic. In this paper, I describe a version of the test using small nonresidues, without assuming any unproven hypothesis.