Paper 2024/471 Original: eprint.iacr.org/2024/471 ↗

A Knot-based Key Exchange protocol

Abstract

We propose a new key exchange protocol based on the Generalised Diffie-Hellman Key Exchange. In the latter, instead of using a group action, we consider a semigroup action. In our proposal, the semigroup is the set of oriented knots in $\mathbb{S}^3$ with the operation of connected sum. As a semigroup action, we choose the action of the semigroup on itself through the connected sum. For the protocol to work, we need to use knot invariants, which allow us to create the shared secret key starting from the same knot represented in two different ways. In particular, we use finite type invariants. The security of the protocol is guaranteed by the hardness of decomposing knots in the semigroup.