Non-associative public-key cryptography
This work addresses the need for more flexible cryptographic schemes by extending public-key cryptography to non-associative settings, which is an incremental advancement over non-commutative approaches.
The authors tackled the problem of generalizing public-key cryptography to non-associative algebraic structures by introducing a generalized Anshel-Anshel-Goldfeld key establishment protocol for magmas, resulting in the foundation of non-associative public-key cryptography with concrete realizations using f-conjugacy in groups and shifted conjugacy in braid groups.
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.