57 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
Conjugacy in Artin groups and applications to the classification of surfaces
We show thatthe double reversing algorithm proposed by dehornoy for solving
the word problem in the braid group can also be used to recognize the
conjugates of powers of the generators in an Artin group of spherical type. The
proof uses a characterization of these powers in terms of their fractional
decomposition. This algorithm could have potential applications to braid-based
cryptography; it also provides a fast method for testing a necessary condition
in the classification of surfaces in algebraic geometry
On an authentication scheme based on the Root Problem in the braid group
Lal and Chaturvedi proposed two authentication schemes based on the
difficulty of the Root Problem in the braid group. We point out that the first
scheme is not really as secure as the Root Problem, and describe an efficient
way to crack it. The attack works for any group.Comment: This paper has been withdrawn by the author. One of the claims is
incorrect as written. We are working on correcting and generalizing it. This
will be published in another pape
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