# An Unconditional Improvement to the Running Time of the Quadratic Frobenius Test

## TL;DR

This paper presents a new version of the Quadratic Frobenius Test that operates unconditionally, removing the reliance on the Extended Riemann Hypothesis, and achieves faster running times.

## Contribution

It introduces an unconditional variant of the Quadratic Frobenius Test that maintains efficiency without assuming unproven hypotheses.

## Key findings

- The new test is faster than previous versions under the same conditions.
- It eliminates the need for the Extended Riemann Hypothesis in the test's construction.
- The approach uses small nonresidues to improve arithmetic speed.

## Abstract

In a 2006 paper, Damg{\aa}rd 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.