Graph Set-colorings And Hypergraphs In Topological Coding
Bing Yao, Fei Ma

TL;DR
This paper explores set-colorings of graphs and hypergraphs to enhance topological coding for quantum-resistant cryptography, introducing new graph-theoretic techniques and structures for secure communication.
Contribution
It introduces novel set-coloring methods for hypergraphs and their applications in topological coding, with potential for cryptographic algorithms resistant to quantum attacks.
Findings
Hypergraph set-colorings reflect complex set intersections.
Connected graphs can be represented as intersected-graphs of hypergraphs.
Various graph lattices and hypernetwork structures are constructed.
Abstract
In order to make more complex number-based strings from topological coding for defending against the intelligent attacks equipped with quantum computing and providing effective protection technology for the age of quantum computing, we will introduce set-colored graphs admitting set-colorings that has been considerable cryptanalytic significance, and especially related with hypergraphs. We use the set-coloring of graphs to reflect the intersection of elements, and add other constraint requirements to express more connections between sets (as hyperedges). Since we try to find some easy and effective techniques based on graph theory for practical application, we use intersected-graphs admitting set-colorings defined on hyperedge sets to observe topological structures of hypergraphs, string-type Topcode-matrix, set-type Topcode-matrix, graph-type Topcode-matrix, hypergraph-type…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsGraph Labeling and Dimension Problems · Quantum Computing Algorithms and Architecture · graph theory and CDMA systems
