On the implementation of AKS-class primality tests

Algorithms of the new “cyclotomic AKS class” determine rigorously and in polynomial time whether an input integer is prime. Herein are discussed implementation issues, with a focus on techniques such as asymptotically fast polynomial manipulations, the possible use of floating-point arithmetic, and special powering ladders. We implemented various of the ideas herein on an Apple G4, Mac OS X system, and report performance for one particular AKS variant. We note two performance issues: a) although single-precision vector floats were not employed in this test implementation, double-precision float performance was quite impressive (we quantify this), and b) there are many additional ways to invoke vectorization, if one so desires, for further speedups. * Advanced Computation Group, Apple Computer ** University of Maryland College Park