Using shifted conjugacy in braid-based cryptography

Patrick Dehornoy (1)

1 LMNO - Laboratoire de Mathématiques Nicolas Oresme

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.

Mots clés: cryptography; self-distributive operation; braid group; Fiat-Shamir scheme; Laver table

Domaines: Cryptographie et sécurité [cs.CR]

Patrick Dehornoy. Using shifted conjugacy in braid-based cryptography. 2006. ⟨hal-00095575⟩