Non-associative public-key cryptography

TL;DR

This paper introduces a new framework for non-associative public-key cryptography based on a generalized key establishment protocol for magmas, expanding the scope beyond traditional associative and non-commutative cryptography.

Contribution

It develops a generalized AAG-KEP for magmas, establishing the foundation for non-associative PKC and providing concrete realizations using group-theoretic concepts.

Findings

Identification of left selfdistributive systems in the generalized AAG-KEP

Concrete realizations using f-conjugacy and shifted conjugacy in groups

Discussion of advantages over classical braid group-based schemes

Abstract

We introduce a generalized Anshel-Anshel-Goldfeld (AAG) key establishment protocol (KEP) for magmas. This leads to the foundation of non-associative public-key cryptography (PKC), generalizing the concept of non-commutative PKC. We show that left selfdistributive systems appear in a natural special case of a generalized AAG-KEP for magmas, and we propose, among others instances, concrete realizations using $f$-conjugacy in groups and shifted conjugacy in braid groups. We discuss the advantages of our schemes compared with the classical AAG-KEP based on conjugacy in braid groups.