Random Generation Topology Coding Technique in Asymmetric Topology Encryption

Jing Su () and Bing Yao
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Jing Su: College of Computing Science and Technology, Xi’an University of Science and Technology, NO.58 Yanta Middle Road, Xi’an 710054, China
Bing Yao: College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China

Mathematics, 2024, vol. 12, issue 17, 1-10

Abstract: The security of traditional public key cryptography algorithms depends on the difficulty of the underlying mathematical problems. Asymmetric topological encryption is a graph-dependent encryption algorithm produced to resist attacks by quantum computers on these mathematical problems. The security of this encryption algorithm depends on two types of NP-complete problems: subgraph isomorphism and graph coloring. Topological coding technology refers to the technology of generating key strings or topology signature strings through topological coding graphs. We take odd-graceful labeling and set-ordered odd-graceful labeling as limiting functions, and propose two kinds of topological coding generation technique, which we call the random leaf-adding operation and randomly adding edge-removing operation. Through these two techniques, graphs of the same scale and larger scales can be generated with the same type of labeling so as to derive more number strings, expand the key space, and analyze the topology and property of the generated graphs.

Keywords: topological coding; graph labeling; graph coloring; set-ordered odd-graceful labeling (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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