1,518 research outputs found
New Signature Scheme Using Conjugacy Problem
We propose a new digital signature scheme based on a
non-commutative group where the conjugacy search problem is hard
and the conjugacy decision problem is feasible. We implement our
signature scheme in the braid groups and prove that an existential
forgery of the implementation under no message attack
gives a solution to a variation of conjugacy search problem. Then
we discuss performance of our scheme under suggested parameters
Group theory in cryptography
This paper is a guide for the pure mathematician who would like to know more
about cryptography based on group theory. The paper gives a brief overview of
the subject, and provides pointers to good textbooks, key research papers and
recent survey papers in the area.Comment: 25 pages References updated, and a few extra references added. Minor
typographical changes. To appear in Proceedings of Groups St Andrews 2009 in
Bath, U
Local models of Shimura varieties, I. Geometry and combinatorics
We survey the theory of local models of Shimura varieties. In particular, we
discuss their definition and illustrate it by examples. We give an overview of
the results on their geometry and combinatorics obtained in the last 15 years.
We also exhibit their connections to other classes of algebraic varieties such
as nilpotent orbit closures, affine Schubert varieties, quiver Grassmannians
and wonderful completions of symmetric spaces.Comment: 86 pages, small corrections and improvements, to appear in the
"Handbook of Moduli
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