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Fast irreducibility testing for XTR using a gaussian normal basis of low complexity
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XTR is a general methodthat can be appliedto discrete logarithm based cryptosystems in extension fields of degree six, providing a compact representation of the elements involved. In this paper we present a precise formulation of the Brouwer-Pellikaan-Verheul conjecture, originally posedin [4], concerning the size of XTR-like representations of elements in extension fields of arbitrary degree. If true this conjecture wouldpro vide even more compact representations of elements than XTR in extension fields of degree thirty. We test the conjecture by experiment, showing that in fact it is unlikely that such a compact representation of elements can be achieved in extension fields of degree thirty.