Using shifted conjugacy in braid-based cryptography
Patrick Dehornoy
Abstract
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.
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