Welcome to the resource topic for 2001/094
Title:
Slope packings and coverings, and generic algorithms for the discrete logarithm problem
Authors: M. Chateauneuf, A. C. H. Ling, D. R. Stinson
Abstract:We consider the set of slopes of lines formed by
joining all pairs of points in some subset S of a
Desarguesian affine plane of prime order, p.
If all the slopes are distinct and non-infinite, we have a
slope packing;
if every possible non-infinite slope occurs, then we have
a slope covering. We review and unify some results on these problems
that can be derived from the study of Sidon sets and sum covers.
Then we report some
computational results we have obtained for small values of p.
Finally, we
point out some connections between slope packings and coverings
and generic algorithms for the discrete logarithm problem in prime
order (sub)groups. Our results provide a combinatorial
characterization
of such algorithms, in the sense that any generic algorithm
implies the
existence of a certain slope packing or covering, and conversely.
ePrint: https://eprint.iacr.org/2001/094
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