Theoretical Techniques For Set-colorings,graphial Groups And Labellings In Topsnut-graphical Passwords

Keys and locks are early-used mechanical devices used to protect personal prop-erty or privacy.With the improvement of economy,money,the most intuitive symbol of personal wealth,1s no longer stored in a box of gold eoins in a bank,but in a string of numbers in a financial account.So,how to protect this kind of money?Traditional keys and locks clearly fail to do it because of their natural physical properties,so the password becomes a new " Key and lock".Nowadays,the most widely used password is the form of the text-based passwords based on," letters+digits+punctuation ".At the end of last centtury,Blonder put for-ward graphic password.With the rapid development of computer technology,graphic cryptography has been commonly used in network and various electronic devices.Two-dimensional code and fingerprint unlock are examples of successful application of graphic cryptography.Topsnut-graphical passwords(abbreviated as Topsnut-gpws),which are referred to below,is based on the thought of "topological structure plus number theory "proposed by Wang et al.If we restrict the construction of Topsnut-gpws in the field of mathematics,it is exactly the object of this thesis,Topsnut-gpws.But if we restrict its construction in other non-matiematical fields,such as music,chemistry,literature,cooking and so on,it is ealled a pan-Topsnut-gpws(abbreviated as PTopsnut-gpws).Topsnut-gpws will be applieable to a wider range of people,and it will be possible for everyone to have their own personalized password.In addition,Topsnut-gpws are stored in the form of matrix in the computer,and the operations on them simple addition and subtraction operations and module operation,so it takes up less storage space of the computer and the operation speed is faster.In the basic research of graphical theory,it is always a difficult problem to find all the non-isomorphic graphs with fixed vertices.The number of graphs of 23 vertices is about 2179 and the number of graphs of 24 vertices is 2197.There are many conjectures on labelling,such Graceful Tree Conjecture.Besides,at least 200 labellings have been proposed.All of these show that a large number of Topsnut-gpws' spaces existed,which can satisfy the demand of cryptography.In this thesis,we mainly explore the Topsnut-gpws from the following four parts:(1)The basic techniques and methods of Topsnut-gpws are mainly introduced in this thesis,such as the method of set-ordered transformation and the method of adding leaves.(2)Set-coloring is applied in Topsnut-gpws.A general set-coloring construction method is introduced.(3)The graphical group theory in Topsnut-gpws establishes the relation between the graphical theory and Algebra.(4)Based on the equivalence relations between several kinds of labellings of trees,this part mainly introduces the equivalence relations between some labellings of general trees and perfect matching trees.Exploring the equivalence relations can help people to establish the relationship between two different things and can strengthen.Deepen peopled understanding and acquaintance of them.