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XTR is a general method that can be applied to 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 posed in [4], concerning the size of XTR-like representations of elements(More)
The design of a computational facility for finite fields that allows complete freedom in the manner in which fields are constructed, is complicated by the fact that a field of fixed isomorphism type K may be constructed in many different ways. It is desirable that the user be able to perform simultaneous computations in different versions of K in such a way(More)
We review the well-known relation between Lucas sequences and exponentiation. This leads to the observation that certain public-key cryptosystems that are based on the use of Lucas sequences have some elementary properties their re-inventors were apparently not aware of. In particular, we present a chosen-message forgery for 'LUC' (cf. [21; 25]), and we(More)
MAGMA is a new software system for computational algebra, number theory and geometry whose design is centred on the concept of algebraic structure (magma). The use of algebraic structure as a design paradigm provides a natural strong typing mechanism. Further, structures and their morphisms appear in the language as first class objects. Standard(More)