43 research outputs found
Using shifted conjugacy in braid-based cryptography
Conjugacy is not the only possible primitive for designing braid-based
protocols. To illustrate this principle, we describe a Fiat--Shamir-style
authentication protocol that be can be implemented using any binary operation
that satisfies the left self-distributive law. Conjugation is an example of
such an operation, but there are other examples, in particular the shifted
conjugation on Artin's braid group B\_oo, and the finite Laver tables. In both
cases, the underlying structures have a high combinatorial complexity, and they
lead to difficult problems
Iterated LD-Problem in non-associative key establishment
We construct new non-associative key establishment protocols for all left
self-distributive (LD), multi-LD-, and mutual LD-systems. The hardness of these
protocols relies on variations of the (simultaneous) iterated LD-problem and
its generalizations. We discuss instantiations of these protocols using
generalized shifted conjugacy in braid groups and their quotients, LD-conjugacy
and -symmetric conjugacy in groups. We suggest parameter choices for
instantiations in braid groups, symmetric groups and several matrix groups.Comment: 30 pages, 5 figures. arXiv admin note: substantial text overlap with
arXiv:1305.440
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