Non-associative key establishment for left distributive systems
Arkadius Kalka, Mina Teicher
TL;DR
This paper introduces non-associative key exchange protocols tailored for left distributive systems, utilizing generalized shifted conjugacy in braid groups, and identifies a new group-theoretic problem called the subgroup conjugacy coset problem.
Contribution
It presents novel non-associative key establishment protocols for left distributive systems and introduces the subgroup conjugacy coset problem based on braid group instantiations.
Findings
Protocols applicable to all left self-distributive systems
Introduction of the subgroup conjugacy coset problem
Connection to generalized shifted conjugacy in braid groups
Abstract
We construct non-associative key establishment protocols for all left self-distributive (LD), multi-LD-, and other left distributive systems. Instantiations of these protocols using generalized shifted conjugacy in braid groups lead to instances of a natural and apparently new group-theoretic problem, which we call the (subgroup) conjugacy coset problem.
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