Secure communication using low dimensional topological elements

TL;DR

This paper explores the use of low-dimensional topological objects like knots and braids for secure communication, leveraging their resilience to deformations to improve cryptographic protocols.

Contribution

It introduces a novel challenge-response protocol utilizing framed links and braids for authentication in secure communication systems.

Findings

Demonstrated how topological elements can encode information securely.

Showed the resilience of topological objects under deformations enhances security.

Provided illustrative examples of the protocol in practice.

Abstract

Low-dimensional topological objects, such as knots and braids, have become prevalent in multiple areas of physics, such as fluid dynamics, optics, and quantum information processing. Such objects also now play a role in cryptography, where a framed knot can store encoded information using its braid representation for communications purposes. The greater resilience of low-dimensional topological elements under deformations allows them to be employed as a reliable framework for information exchange. Here, we introduce a challenge-response protocol as an application of this construction for authentication. We provide illustrative examples of both procedures showing how framed links and braids may help to enhance secure communication.