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In a 2006 paper, Damg{\aa}rd and Frandsen designed a faster version of theQuadratic Frobenius Test. This test assumes the Extended Riemann Hypothesis inorder to find small nonresidues, which allow construction of quadraticextensions with faster arithmetic. In this paper, I describe a version of thetest using small nonresidues, without assuming any unproven hypothesis.

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