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We construct new non-associative key establishment protocols for all leftself-distributive (LD), multi-LD-, and mutual LD-systems. The hardness of theseprotocols relies on variations of the (simultaneous) iterated LD-problem andits generalizations. We discuss instantiations of these protocols usinggeneralized shifted conjugacy in braid groups and their quotients, LD-conjugacyand $f$-symmetric conjugacy in groups. We suggest parameter choices forinstantiations in braid groups, symmetric groups and several matrix groups.

Iterated LD-Problem in non-associative key establishment