Looking beyond xtr

Abstract

XTR is a general methodthat can be appliedto discrete logarithmbased cryptosystems in extension fields of degree six, providing acompact representation of the elements involved. In this paper we presenta precise formulation of the Brouwer-Pellikaan-Verheul conjecture, originallyposedin [4], concerning the size of XTR-like representations ofelements in extension fields of arbitrary degree. If true this conjecturewouldpro vide even more compact representations of elements than XTRin extension fields of degree thirty. We test the conjecture by experiment,showing that in fact it is unlikely that such a compact representation ofelements can be achieved in extension fields of degree thirty.