Exploring Relationship Between Traditional Lattices and Graph Lattices of Topological Coding

It is known that there are no polynomial quantum algorithms to solve some lattice difficult problems. Uncolored graphic lattice and colored graphic lattice are the products of multidisciplinary intersection inspired by lattice theory. A uncolored graphic lattice or a colored graphic lattice in topol...

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Autor principal:	ZHANG Mingjun, YANG Sihua, YAO Bing
Formato:	article
Lenguaje:	ZH
Publicado:	Journal of Computer Engineering and Applications Beijing Co., Ltd., Science Press 2021
Materias:	lattice graphic lattice total coloring graceful labelling topological coding network security Electronic computers. Computer science QA75.5-76.95
Acceso en línea:	https://doaj.org/article/0866fc81c35e4941a683c184197f100f
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id	oai:doaj.org-article:0866fc81c35e4941a683c184197f100f
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spelling	oai:doaj.org-article:0866fc81c35e4941a683c184197f100f2021-11-10T08:23:45ZExploring Relationship Between Traditional Lattices and Graph Lattices of Topological Coding10.3778/j.issn.1673-9418.20100721673-9418https://doaj.org/article/0866fc81c35e4941a683c184197f100f2021-11-01T00:00:00Zhttp://fcst.ceaj.org/CN/abstract/abstract2956.shtmlhttps://doaj.org/toc/1673-9418It is known that there are no polynomial quantum algorithms to solve some lattice difficult problems. Uncolored graphic lattice and colored graphic lattice are the products of multidisciplinary intersection inspired by lattice theory. A uncolored graphic lattice or a colored graphic lattice in topological coding is based on some graph operations and a set of disjoint connected graphs or disjoint connected colored graphs. Based on password authentication or digital file encryption, this paper introduces the number-based string topological authentication problem, and gives an asymmetric encryption system by topological coding. Topological coding can form an asymmetric encryption system with one public key corresponding to two or more private keys and, more public keys corresponding to more private keys. Topology authentication in topology coding requires two different fields of mathematical knowledge and can produce exponential level algorithm. Based on the edge-joining operation and vertex-coinciding operation of graphs, the existence of colored graphic lattice admitting graceful total colorings is shown, and graphic lattice and F-graphic lattice are established with infinite elements closed to graceful total coloring. Topological vectors for special coloring graphs are defined, and a connection between graphic lattice and non-negative integer traditional lattice is built up to provide a feasible technique for quantum resistance calculation, since there is no polynomial algorithm for solving number-based strings up to now. Because graph isomorphism problem is NP-hard, topological coding lattice has the function of resisting supercomputer and quantum computer.ZHANG Mingjun, YANG Sihua, YAO BingJournal of Computer Engineering and Applications Beijing Co., Ltd., Science Pressarticlelatticegraphic latticetotal coloringgraceful labellingtopological codingnetwork securityElectronic computers. Computer scienceQA75.5-76.95ZHJisuanji kexue yu tansuo, Vol 15, Iss 11, Pp 2171-2183 (2021)
institution	DOAJ
collection	DOAJ
language	ZH
topic	lattice graphic lattice total coloring graceful labelling topological coding network security Electronic computers. Computer science QA75.5-76.95
spellingShingle	lattice graphic lattice total coloring graceful labelling topological coding network security Electronic computers. Computer science QA75.5-76.95 ZHANG Mingjun, YANG Sihua, YAO Bing Exploring Relationship Between Traditional Lattices and Graph Lattices of Topological Coding
description	It is known that there are no polynomial quantum algorithms to solve some lattice difficult problems. Uncolored graphic lattice and colored graphic lattice are the products of multidisciplinary intersection inspired by lattice theory. A uncolored graphic lattice or a colored graphic lattice in topological coding is based on some graph operations and a set of disjoint connected graphs or disjoint connected colored graphs. Based on password authentication or digital file encryption, this paper introduces the number-based string topological authentication problem, and gives an asymmetric encryption system by topological coding. Topological coding can form an asymmetric encryption system with one public key corresponding to two or more private keys and, more public keys corresponding to more private keys. Topology authentication in topology coding requires two different fields of mathematical knowledge and can produce exponential level algorithm. Based on the edge-joining operation and vertex-coinciding operation of graphs, the existence of colored graphic lattice admitting graceful total colorings is shown, and graphic lattice and F-graphic lattice are established with infinite elements closed to graceful total coloring. Topological vectors for special coloring graphs are defined, and a connection between graphic lattice and non-negative integer traditional lattice is built up to provide a feasible technique for quantum resistance calculation, since there is no polynomial algorithm for solving number-based strings up to now. Because graph isomorphism problem is NP-hard, topological coding lattice has the function of resisting supercomputer and quantum computer.
format	article
author	ZHANG Mingjun, YANG Sihua, YAO Bing
author_facet	ZHANG Mingjun, YANG Sihua, YAO Bing
author_sort	ZHANG Mingjun, YANG Sihua, YAO Bing
title	Exploring Relationship Between Traditional Lattices and Graph Lattices of Topological Coding
title_short	Exploring Relationship Between Traditional Lattices and Graph Lattices of Topological Coding
title_full	Exploring Relationship Between Traditional Lattices and Graph Lattices of Topological Coding
title_fullStr	Exploring Relationship Between Traditional Lattices and Graph Lattices of Topological Coding
title_full_unstemmed	Exploring Relationship Between Traditional Lattices and Graph Lattices of Topological Coding
title_sort	exploring relationship between traditional lattices and graph lattices of topological coding
publisher	Journal of Computer Engineering and Applications Beijing Co., Ltd., Science Press
publishDate	2021
url	https://doaj.org/article/0866fc81c35e4941a683c184197f100f
work_keys_str_mv	AT zhangmingjunyangsihuayaobing exploringrelationshipbetweentraditionallatticesandgraphlatticesoftopologicalcoding
_version_	1718440345943932928

Exploring Relationship Between Traditional Lattices and Graph Lattices of Topological Coding

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