Knot-based Key Exchange protocol

Silvia Sconza; Arno Wildi

Paper 2024/471

Knot-based Key Exchange protocol

Silvia Sconza

, University of Zurich

Arno Wildi

, University of Zurich

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.

Note: New complexification method in Subsection 2.1.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Preprint.
Keywords: Generalised Diffie-Hellman Key Exchange Public Key Cryptography Knot Theory Finite type Invariants Semigroup Action
Contact author(s): silvia sconza @ math uzh ch
arno wildi @ math uzh ch
History: 2024-09-22: last of 2 revisions; 2024-03-20: received; See all versions
Short URL: https://ia.cr/2024/471
License: CC BY

BibTeX

@misc{cryptoeprint:2024/471,
      author = {Silvia Sconza and Arno Wildi},
      title = {Knot-based Key Exchange protocol},
      howpublished = {Cryptology {ePrint} Archive, Paper 2024/471},
      year = {2024},
      url = {https://eprint.iacr.org/2024/471}
}