Public Key Exchange Using Matrices Over Group Rings
This addresses secure communication for users needing efficient key exchange, but it appears incremental as it adapts an existing paradigm with a new mathematical structure.
The paper tackles the problem of public key exchange by proposing a protocol similar to Diffie-Hellman but using small matrices over group rings of symmetric groups, resulting in efficient computation for legitimate parties, with security analyzed via DDH and CDH problems.
We offer a public key exchange protocol in the spirit of Diffie-Hellman, but we use (small) matrices over a group ring of a (small) symmetric group as the platform. This "nested structure" of the platform makes computation very efficient for legitimate parties. We discuss security of this scheme by addressing the Decision Diffie-Hellman (DDH) and Computational Diffie-Hellman (CDH) problems for our platform.