Iterated LD-Problem in non-associative key establishment
This work addresses cryptographic security for key establishment in non-associative algebraic structures, but it appears incremental as it builds on existing LD-system concepts without claiming broad breakthroughs.
The authors tackled the problem of constructing secure key establishment protocols by introducing new non-associative protocols based on left self-distributive systems, with hardness relying on variations of the iterated LD-problem. They provided instantiations using braid groups, symmetric groups, and matrix groups, suggesting parameter choices for implementation.
We construct new non-associative key establishment protocols for all left self-distributive (LD), multi-LD-, and mutual LD-systems. The hardness of these protocols relies on variations of the (simultaneous) iterated LD-problem and its generalizations. We discuss instantiations of these protocols using generalized shifted conjugacy in braid groups and their quotients, LD-conjugacy and $f$-symmetric conjugacy in groups. We suggest parameter choices for instantiations in braid groups, symmetric groups and several matrix groups.