Graphic Groups Towards Cryptographic Systems Resisting Classical and Quantum Computers

For building up new cryptographic systems of “resisting classical computers and quantum computers”, we introduce the every-zero mixed graphic group containing many every-zero graphic subgroups, and design a technique of encrypting networks by every-zero mixed graphic groups such that the encrypted networks form graphic group lattices. We show theoretical research for encrypting networks by every-zero mixed graphic groups, and provide particular graphic groups, such as planar graphic group, twin graphic group, dual coloring/labelling graphic group, matching graphic group, Topcode-matrix group and Topcode-string group. These groups are related many mathematical problems, in which some problems are NP-hard.

[1]  Chao Yang,et al.  Topological Graphic Passwords And Their Matchings Towards Cryptography , 2018, ArXiv.

[2]  Bing Yao,et al.  Exploring New Cryptographical Construction of Complex Network Data , 2016, 2016 IEEE First International Conference on Data Science in Cyberspace (DSC).

[3]  Hui Sun,et al.  Algebraic Groups for Construction of Topological Graphic Passwords in Cryptography , 2018, 2018 IEEE 3rd Advanced Information Technology, Electronic and Automation Control Conference (IAEAC).

[4]  Jin Xu,et al.  The key-models and their lock-models for designing new labellings of networks , 2016, 2016 IEEE Advanced Information Management, Communicates, Electronic and Automation Control Conference (IMCEC).

[5]  B. Yao,et al.  CONNECTIONS BETWEEN LABELLINGS OF TREES , 2017 .

[6]  Tanja Lange,et al.  Post-quantum cryptography , 2008, Nature.

[7]  Bing Yao,et al.  A Note on Strongly Graceful Trees , 2009, Ars Comb..

[8]  Bing Yao,et al.  Twin Odd-graceful Trees Towards Information Security , 2017 .

[9]  Xiangqian Zhou,et al.  A proof to the odd-gracefulness of all lobsters , 2012, Ars Comb..

[10]  Frank Harary,et al.  Graph Theory , 2016 .

[11]  Bing Yao,et al.  Matrices From Topological Graphic Coding of Network Security , 2019, 2019 IEEE 4th Advanced Information Technology, Electronic and Automation Control Conference (IAEAC).

[12]  Joseph A. Gallian,et al.  A Dynamic Survey of Graph Labeling , 2009, The Electronic Journal of Combinatorics.

[13]  Hui Sun,et al.  On coloring/labelling graphical groups for creating new graphical passwords , 2017, 2017 IEEE 2nd Information Technology, Networking, Electronic and Automation Control Conference (ITNEC).

[14]  B. Yao,et al.  New Algebraic Groups Produced By Graphical Passwords Based On Colorings And Labellings , 2017 .

[15]  W. Xiao.  Survey of Lattice-based Cryptography , 2014 .