Asymmetric topological password generation method and device based on tree-type graph lattice and medium

Abstract

The invention discloses an asymmetric topological password generation method and device based on tree grids and a medium, and relates to the technical field of information encryption. Obtaining a plurality of mutually different trees generated by a Chinese character graph to be encrypted or others; forming a tree graph network block base or a full-colored tree graph network block base by a plurality of different trees, and performing merging operation on the plurality of different trees to determine a tree graph grid; the merging operation is non-repeated edge vertex coincidence operation or edge connection operation, then obtaining a full-colored topological coding matrix of the tree-shaped graph lattice, and generating an asymmetric topological password according to the full-colored topological coding matrix. According to the method, the asymmetric topological password capable of resisting quantum computing and intelligent attack can be generated.

Description

Technical Field

[0001] The present invention relates to the field of information encryption technology, and in particular to a method, device and medium for generating an asymmetric topological password based on a tree grid. Background Art

[0002] With the rapid development of the Internet and communication technology, society has become increasingly information-based and intelligent. While more and more companies and individuals are enjoying the convenient on-demand services they provide, they are also facing more and more security attacks.

[0003] At present, in order to improve the security of data collection, storage and transmission, cryptographic technology is usually used to transform readable data into incomprehensible garbled code through encryption transformation, thereby protecting data. However, due to the rapid development of quantum computing and intelligent attacks, quantum computing and intelligent attacks may crack the passwords in traditional encryption algorithms, resulting in potential security threats to traditional encryption methods.

[0004] Therefore, there is an urgent need for a password generation method that can generate a password that is resistant to quantum computing and intelligent attacks. Summary of the invention

[0005] Based on this, it is necessary to provide a method, device and medium for generating an asymmetric topological password based on a tree grid to address the above technical problems. The method can generate an asymmetric topological password that is resistant to quantum computing and intelligent attacks.

[0006] The present invention adopts the following technical solutions:

[0007] The present invention provides an asymmetric topological password generation method based on a tree grid, comprising:

[0008] Acquire multiple mutually isomorphic trees generated by the Chinese character graph to be encrypted or other means; the multiple mutually isomorphic trees constitute a tree graph network block base or a fully colored tree graph network block base;

[0009] Perform a merging operation on multiple trees of different structures to determine the tree-type grid; the merging operation is a non-overlapping vertex overlap operation or an edge connection operation;

[0010] Get the full coloring topological encoding matrix of the tree grid, and generate an asymmetric topological password based on the full coloring topological encoding matrix.

[0011] Preferably, the definition of the tree graph network block base includes:

[0012] In multiple trees T1, T2, ..., T m In, if And when (i≠j), the tree T i Not identical to the tree T j, then T={T1,T2,...,T m} is the tree graph network block basis; where i, j∈[1,m].

[0013] Preferably, a plurality of mutually inhomogeneous trees are merged to determine a tree grid, including:

[0014] Get multiple mutually incompatible trees a1T1, a2T2, ..., amT m Full permutation of , we get multiple trees H1, H2, ..., H M ,

[0015] Perform the no-overlapping vertex overlap operation on the trees H1 and H2 to obtain the tree L1 = H1[·]H2;

[0016] Perform the no-overlapping vertex overlap operation on tree L1 and tree H3, and so on, to obtain tree L k =L k-1 [·]H k+1 (k∈[1,M-1]);

[0017] According to multiple non-overlapping vertex overlap operations, the tree is obtained

[0018] According to the tree L M-1 , determine the tree grid as

[0019] Preferably, the definition of the fully colored tree graph network block base includes:

[0020] If each tree T in the tree graph network block basis k Admit a set ordered graceful total coloring f k , and there is a node u k ∈V(T k ) coloring f k (u k )=0, then the network block basis of the set-ordered graceful fully colored tree graph is determined to be That is the fully colored tree graph network block basis; among them, And when (i≠j), the tree Different from tree

[0021] Preferably, a plurality of mutually inhomogeneous trees are merged to determine a tree grid, including:

[0022] Get multiple mutually isomorphic trees A full permutation of , we get multiple fully colored trees H1, H2, ..., H B ,

[0023] Apply the no-overlapping vertex overlap operation to the trees H1 and H2, and obtain the tree L1 = H1[·]H2; the tree L1 admits a full coloring F1, so that the overlapping vertex w1 = u1·u 2， The coloring of (u1∈V(H1), u2∈V(H2)) is F1(w1)=0, and there exists a coloring F1(z)=f1(z), (z∈V(H1)∪E(H1), z≠u1), and a coloring F1(t)=f1(t), (t∈V(H2)∪E(H2), t≠u2);

[0024] Perform the non-overlapping vertex overlap operation on tree L1 and tree H3, and so on to obtain the fully colored tree L k =L k-1 [·]H k+1 (k∈[1,B-1]); full coloring tree L k Admit a full coloring F k , so that the coincident vertex w k =u·u k+1 ,(u∈V(L k-1 ),u k+1 ∈V(H k+1 )) is colored as F k (w k )=0; and there is a coloring F k (z) = F k-1 (z), (z∈V(H k-1 )∪E(H k-1 ), z≠u), and coloring F k (t) = F k-1 (t), (t∈V(H k+1 )∪E(H k+1 ), t≠u k+1 );

[0025] According to multiple non-overlapping vertex overlap operations, the full coloring tree is obtained

[0026] According to the full coloring tree L B-1 , determine the tree grid as

[0027] Preferably, the fully colored tree graph network block base Merge multiple inhomogeneous trees to determine the tree grid, including:

[0028] Get multiple mutually isomorphic trees A full permutation of , we get multiple full coloring trees B1, B2, ..., B C ,

[0029] According to the edge connection operation, connect a vertex u1 of the full coloring tree B1 with a vertex u2 of the full coloring tree B2, and assign a color to the new edge u1u2 to obtain the full coloring tree

[0030] According to the edge connection operation, connect a vertex x1 of the full coloring tree Q1 with a vertex u3 of the full coloring tree B3, and assign color to the new edge x1u3, and so on, to obtain the full coloring tree

[0031] According to the full coloring tree Q C-1， Get the fully colored tree graph network block base A c Tree grid of

[0032] Preferably, the tree grid is an infinite set, and an asymmetric topological code is generated according to the full-color topological coding matrix, including:

[0033] Generate infinite topological digital strings according to the full-coloring topological coding matrix;

[0034] Each topological word string is determined as an asymmetric topological password.

[0035] Preferably, the asymmetric topological cryptography includes a public key topological signature, a private key topological signature, and a public key character string and a private key character string.

[0036] The present invention provides an asymmetric topological password generation device based on a tree-type grid, comprising:

[0037] An acquisition module is used to acquire a plurality of mutually inhomogeneous trees generated by a Chinese character graph to be encrypted or other means; the plurality of trees constitute a tree graph network block base or a fully colored tree graph network block base;

[0038] The operation module is used to merge multiple trees of different structures to determine the tree-shaped grid;

[0039] The generation module is used to obtain the full-color topological coding matrix of the tree grid and generate an asymmetric topological password based on the full-color topological coding matrix.

[0040] The present invention provides a computer-readable storage medium, which stores a computer program. When the computer program is executed by a processor, the asymmetric topological password generation method based on the tree grid is implemented.

[0041] The present invention provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the program, the above-mentioned tree-type grid-based asymmetric topological password generation method is implemented.

[0042] The above at least one technical solution adopted by the present invention can achieve the following beneficial effects:

[0043] The present invention uses a Chinese character graph to be encrypted or multiple other generated non-isomorphic trees to form a tree-shaped lattice, and generates an asymmetric topological cipher with the tree-shaped lattice. In the process of generating the asymmetric cipher, the technologies involved are three essentially different fields of "topological structure", "mathematical constraint" and "Chinese meaning of Chinese character graph", so that the asymmetric topological cipher has an anti-cracking function and can resist quantum computing and intelligent attacks. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] The drawings described herein are used to provide a further understanding of the present invention, and constitute a part of the present invention. The schematic embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation to the present invention. In the drawings:

[0045] Figure 1 A Chinese character graph "yong" provided by the present invention and its colored homomorphism graph;

[0046] Figure 2 Another Chinese character graph "yong" provided by the present invention and its colored homomorphism graph;

[0047] Figure 3 A schematic flow chart of a method for generating an asymmetric topological cipher based on a tree-shaped lattice provided by the present invention;

[0048] Figure 4 A schematic structural diagram of a self-similar network provided by the present invention;

[0049] Figure 5 A schematic diagram for explaining tree homomorphism provided by the present invention;

[0050] Figure 6 A schematic structural diagram for explaining linear connection operation provided by the present invention;

[0051] Figure 7 Another schematic structural diagram for explaining linear connection operation provided by the present invention;

[0052] Figure 8 A schematic diagram of asymmetric topological coding encryption provided by the present invention;

[0053] Fig. 9 A schematic diagram of a device for generating an asymmetric topological cipher based on a tree-shaped lattice provided by the present invention;

[0054] Fig.10 A schematic diagram of a computer device for implementing a method for generating an asymmetric topological cipher based on a tree-shaped lattice provided by the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0055] To make the objectives, technical solutions and advantages of the present invention clearer, the technical solutions of the present invention will be clearly and completely described below in conjunction with specific embodiments of the present invention and the corresponding drawings. Obviously, the described embodiments are only a part rather than all of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the scope of protection of the present invention.

[0056] The mathematical theory and computer technology of topological coding come from disciplines such as graph theory, combinatorial mathematics, linear algebra, number theory, set theory, algebra and abstract algebra, probability theory, and computer science.

[0057] As is well known, the discipline of graph theory has important research results in fields such as transportation systems, social networks, big data environments, the Internet of Things, power infrastructures, and biological neural networks, complex brain networks, network effectiveness and fault tolerance, and wireless sensor networks. The cycle structure of graph theory is applicable to the control systems of network distributed computing, and the path structure of graph theory is extremely helpful for designing simple and effective routing algorithms and designs. Social network analysis based on graph theory combines the relationships between individuals, "micro" networks with the "macro" structure of large-scale social systems.

[0058] The asymmetric topological encryption of topological coding is a new technology in the field of information encryption, mainly applied to open networks, involving key establishment, encryption technology, digital signatures, identity authentication, etc., and provides key technologies for identity verification, confidentiality, integrity, and non-repudiation. In the future era of quantum computers, the objective of the present invention is to generate asymmetric topological ciphers for resisting quantum computing or resisting intelligent attacks.

[0059] First, before explaining the method for generating an asymmetric topological cipher based on a tree-shaped lattice provided by the present invention, basic concepts and theorems will be explained.

[0060] Basic terms and notations:

[0061] The set of all non-negative integers is denoted as Z 0 ; the set of all positive integers is Z + =Z 0 \{0}. Let a, b, k, d, m, α, β ∈ Z 0 , for 0 ≤ a < b, the set of non-negative integers {a, a + 1,..., b} is abbreviated as [a, b]; when α and β are odd integers and α < β, the set of odd integers {α, α + 2,..., β} is denoted as [α, β] o . The number of elements in set S is denoted as |S|. Set S s，k，r，d ={k + rd, k + (r + 1)d,..., k + (r + s)d} is called a parameter set, where s, k, r, d ∈ Z0 .

[0062] If the vertex set of graph \(G\) is \(V(G)=X\cup Y\), and the intersection of the two vertex subsets such that for each edge \(uv\in E(G)\) of graph \(G\), the two endpoints \(u\) and \(v\) satisfy \(u\in X\) and \(v\in Y\), then \(G\) is called a bipartite graph. Let the bipartite graph \(G\) admit a \(W\)-constrained coloring \(f:S\rightarrow M\), where the set The set of colors of the elements of set \(S\) is denoted as \(f(S)=\{h(w):w\in S\}\), where the \(W\)-constraint consists of a mathematical constraint or a set of mathematical constraints. If the set of vertex colorings of graph \(G\) satisfies the set-ordered constraint \(\max\{f(x):x\in X\}=\max f(X)<\min f(Y)=\min\{f(y):y\in Y\}\), then this \(W\)-constrained coloring \(f\) is called a set-ordered \(W\)-constrained coloring of the bipartite graph \(G\). When \(S = V(G)\), \(f\) is called a vertex coloring of the bipartite graph \(G\); when \(S=V(G)\cup E(G)\), \(f\) is called a total coloring of the bipartite graph \(G\). If the colorings of any two vertices \(x\) and \(y\) of the bipartite graph \(G\) satisfy \(f(x)\neq f(y)\), then \(f\) is called a labeling of the bipartite graph \(G\).

[0063] Basic definitions and theorems:

[0064] Definition 1. The total-object coloring topological coding matrix is a \((p,q)\)-graph \(G\) that admits a total coloring \(f:V(G)\cup E(G)\to S\) thing , which corresponds to a \(3\times q\) order topological coding matrix

[0065]

[0066] where \(x\) j y j are the edges of the \((p,q)\)-graph \(G\), \(x\) j and \(y\) j are the endpoints of edge \(x\) j y j ; \(S\) thing =\(\{s_1,s_2,\cdots,s\) n \}\) is a set of \(n\) objects; such that the coloring of each edge \(x\) j y j and its endpoints \(x\) j and \(y\) j satisfies the constraints in a constraint set \(R(c_1,c_2,\cdots,c\) m ). In particular, the \((p,q)\)-graph \(G\) is called a total-coloring topological coding graph.

[0067] Note 1. If the elements of a matrix are all topological coding graphs, or all topological coding matrices, or all strings derived from topological coding matrices, we call this matrix a super-topological coding matrix.

[0068] Definition 2. Let the \((p,q)\)-graph \(G\) be a bipartite graph with \(V(G)=X\cup Y\), such that each edge \(xy\) of the graph \(G\) satisfies \(x\in X\) and \(y\in Y\), and the bipartite graph \(G\) admits a total coloring \(f:V(G)\cup E(G)\to[0,q]\). If (i) edge difference: each edge \(xy\) of the graph \(G\) satisfies \(f(xy) = |f(x)-f(y)|(x\in X,y\in Y)\); (ii) graceful edge - coloring set: \(f(E(Y))=\{1,2,\cdots,q\}=[1,q]\); (iii) set - order constraint: \(\max\{f(x):x\in X\}<\min\{f(y):y\in Y\}\). Then the total coloring \(f\) is called a set - ordered graceful total coloring.

[0069] For example, Figure 1 is the Chinese character graph "yong" and its colored - homomorphism graph. Figure 1 The Chinese character graph \(H\) of the character "yong" in is a total - colored topological - coding \((13,16)\) - graph, which admits a set - ordered graceful total coloring \(f\), and its total - colored topological - coding matrix is the following \(3\times16\) - order matrix

[0070]

[0071] In addition, the total - colored topological - coding matrix \(T\) of the Chinese character graph \(H\) of the character "yong" code (\(H,f\)) can derive the following topological digital strings:

[0072] \(s1 = 6178266399453588626713981291113103311141312101313141401151616160\);

[0073] \(t1 = 0616161511041413131012131411133013111921893176268853549936628716\);

[0074] \(s2 = 7816299366485581363279118619131410231113131231131416140015161610\);

[0075] \(t2 = 0161615100416141311321313111320141319168119723631855846639926178\)

[0076] to generate the key pairs \((s1,t1)\) and \((s2,t2)\), and each topological digital string has 63 bytes. The total - colored topological - coding matrix \(T\) code (\(H,f\)) can derive \((48)!\approx2\) 202A topological digital string with 63 bytes. Note that the digital strings t1 and t2 are not fully colored topological coding matrices T code (H, f)-derived topological digital strings, which are fully colored topological coding matrices T code The reverse order strings of the (H, f)-derived topological digital strings s1 and s2

[0077] As Figure 2 shown, the figure is another Chinese character figure "yong" and its colored homomorphic figure

[0078] Definition 3, Weighted graph homomorphism: Let graph G admit a full coloring f and graph H admit a full coloring h. If there exists a mapping F: V(H) → V(G) that satisfies the following constraint conditions: (i) For each edge uv ∈ E(H), there is an edge F(u)F(v) ∈ E(G) if and only if; (ii) For each vertex x ∈ V(H), f(F(x)) = h(x), and for each edge uv ∈ E(H), f(F(u)F(v)) = h(uv); then graph H is said to be weighted graph homomorphic to graph G, denoted as

[0079] If graph G and graph H only satisfy the above constraint condition (i), then graph H is said to be graph homomorphic to graph G, denoted as H → G

[0080] Definition 4, Non - multiple - edge vertex coincidence operation: Perform a non - multiple - edge vertex coincidence operation on two vertex - disjoint graphs G and T: Coincide a vertex u of graph G j with a vertex v of graph T j to form a vertex w j = u j ·v j (j ∈ [1, k]), such that the operation result G[· k T is a graph without multiple edges, and its number of edges satisfies |E(G[· k T)| = |E(G)| + |E|, and the number of vertices satisfies |V([· k )| = |V(G)| + |V| - k. In addition, for two vertices x and y of graph G, if their neighbor sets satisfy then these two vertices x and y can be coincided into a vertex z = x·y, and the resulting graph is denoted as G[x·y]. Obviously, the number of edges of these two graphs satisfies |E(G[x·y])| = |E(G)|, the number of vertices satisfies |V(G[x·y])| = |V(G)| - 1, and there is a graph homomorphism G → G[x●y]

[0081] Definition 5, Vertex tearing operation. If the degree |N ei (w)| of vertex w in a connected graph G is ≥ 2, then vertex w can be torn into k vertices w i (i ∈ [1, k]], 2 ≤ k ≤ N ei(w)|), the resulting graph is denoted by G∧ k w, so that the neighbor set of node w satisfies N ei (w) = N ei (w1)∪N ei (w2)∪…∪N ei (w k )as well as And the number of edges satisfies |E(G)|=|E(G∧ k w)|, the number of vertices satisfies |V(G)|=|V(G∧ k w)|-k+1, and the graph homomorphism G∧ k w→G.

[0082] Definition 6: Let graph G admit a total coloring f:V(G)∪E(G)→S s，k，r，d If the coloring of each edge uv∈E(G) satisfies f(uv)=|f(u)-f(v)|, then the edge coloring set f(E(G))=S q-1，k，0，d , and the vertex shader set Then the total coloring f is called a graceful (k, d)-total coloring of the graph G.

[0083] Theorem 1. Every tree T admits a graceful (k, d)-total coloring f. When (k, d) = (1, 1), f is a set-ordered graceful total coloring, and there is a coloring of node u∈V(T) with f(u) = 0; when (k, d) = (1, 2), f is a set-ordered odd graceful total coloring, and there is a coloring of node v∈V with f(v) = 0.

[0084]

[0085]

[0086] The technical solutions provided by various embodiments of the present invention are described in detail below in conjunction with the accompanying drawings.

[0087] Figure 3 The present invention is a schematic diagram of a method for generating an asymmetric topological password based on a tree grid, which specifically includes the following steps:

[0088] S301, obtaining a plurality of mutually isomorphic trees generated by a Chinese character graph to be encrypted or other means; the plurality of mutually isomorphic trees constitute a tree graph network block base or a fully colored tree graph network block base.

[0089] The definition of the tree graph network block base includes: in multiple trees T1, T2, ..., T m In, if And when (i≠j), the tree T i Not identical to tree T j , then {T1, T2, ..., Tm} is the tree graph network block basis; where i, j∈[1,m].

[0090] Preferably, the definition of the fully colored tree graph network block base includes:

[0091] If each tree T in the tree graph network block basis k Admit a set ordered graceful total coloring f k , and there is a node u k ∈V(T k ) coloring f k (u k )=0, then the network block basis of the set-ordered graceful fully colored tree graph is determined to be That is the fully colored tree graph network block basis; among them, And when (i≠j), the tree Different from tree

[0092] Definition 7: Tree-type network block base T = {T1, T2, ..., T m Each graph T in k (k∈[1,m]) is a tree where And when (i≠j), the tree T i Not identical to tree T j .

[0093] Definition 8: Fully colored tree graph network block basis. According to Theorem 1, every tree T in the tree graph network block basis T k Admit a set ordered graceful total coloring f k , and there is a node u k ∈V(T k ) coloring f k (u k )=0. To distinguish, we denote the network block basis of the set ordered graceful fully colored tree graph as It is called the fully colored tree graph network block basis, where And when (i≠j), the tree Different from tree

[0094] Note 2: Regarding Definition 7 and Definition 8, there is the following special tree graph network block base:

[0095] ①If |V(T i (t))|=|V(T j (t))|(or ), then we say that the graph network block basis T(t) (or the fully colored tree graph network block basis T c (t)) is v-homogeneous; ② If |E(T i(t))|=|E(T j (t))|(or ), then we say that the graph network block basis T(t) (or the fully colored tree graph network block basis T c (t)) is e-homogeneous; ③ If the diameter D(T i (t)) = D(T j (t))(or ), then we say that the graph network block basis T(t) (or the fully colored tree graph network block basis T c (t)) is the same diameter; ④ If the diameter D(T i (t))≠D(T j (t))(or Then the graph network block basis T(t) (or the fully colored tree graph network block basis T c (t)) are different in diameter; ⑤ If each graph network block T i (t)(or ) is equal to r, then the graph network block basis T(t) (or the fully colored tree graph network block basis T c (t)) is the longest r-aligned path; ⑥ If each graph network block T i (t)(or ) is a caterpillar tree, then the graph network block basis T(t) (or the fully colored tree graph network block basis T c (t)) is the caterpillar tree base; ⑦ If each graph network block T i (t)(or ) is a spider tree, then the graph network block basis T(t) (or the fully colored tree graph network block basis T c (t)) is the spider tree base.

[0096] It should be noted that there is no limitation on the type of Chinese character graph or other graphs, as long as multiple mutually isomorphic trees can be generated.

[0097] S302, performing a merging operation on a plurality of mutually incompatible trees to determine a tree-type grid; the merging operation is a non-overlapping vertex overlap operation or an edge connection operation.

[0098] The merging operation is an operation without overlapping edges and vertices. In an exemplary embodiment, a plurality of mutually incompatible trees are merged to determine a tree grid, including: obtaining a plurality of mutually incompatible trees a1T1, a2T2, ..., amT m Full permutation of , we get multiple trees H1, H2, ..., H M , Perform the no-overlapping-edge-vertex-coincidence operation on trees H1 and H2 to obtain tree L1 = H1[●]H2; perform the no-overlapping-edge-vertex-coincidence operation on trees L1 and H3, and so on to obtain tree L k =L k-1[·]H k+1 (k∈[1,M-1]); Based on multiple non-overlapping vertex overlap operations, we get the tree According to the tree L M-1 , determine the tree grid as

[0099] That is, Definition 9: Let trees H1, H2, ..., H M is a tree a1T1, a2T2, ..., a in the tree graph network block base T (Definition 7). m T m A full permutation of The non-overlapping edge vertex overlap operation is performed on the tree H1 and the tree H2. That is, a vertex of the tree H1 is overlapped with a vertex of the tree H2 to form a vertex, and the tree L1 = H1[·]H2 is obtained. Then, the non-overlapping edge vertex overlap operation is performed to obtain the tree L2 = L1[·]H3. In this way, the tree L k =L k-1 [·]H k+1 (k∈[1,M-1]), we remember the tree:

[0100]

[0101] The set represented by formula (4) is called a tree T-grid based on the tree graph network block base T.

[0102]

[0103] Note 3: Figure 4 is the tree obtained by the non-overlapping vertex operation in Definition 9. Note that is a set of trees. k =L k-1 [·]H k+1 (k∈[1,M-1]), there is at least |V(L k-1 )|×|V(H k+1 )|Tree and Tree k Similar trees, thus, operations Generate μ trees.

[0104]

[0105] In another exemplary embodiment, when the merging operation is a non-overlapping edge vertex overlap operation, a plurality of mutually incompatible trees are merged to determine a tree grid, including: obtaining a plurality of mutually incompatible trees A full permutation of , we get multiple fully colored trees H1, H2, ..., H B , Apply the no-overlapping-edge-vertex-coincidence operation to the trees H1 and H2, and obtain the tree L1=H1[·]H2; the tree L1 admits a total coloring F1, so that the coloring of the overlapping vertex w1=u1·u2, (u1∈V(H1), u2∈V(H2)) is F1(w1)=0, and there exists a coloring F1(z)=f1(z), (z∈V(H1)∪E(H1), z≠u1), and a coloring F1(t)=f1(t)(t∈V(H2)∪E(H2), t≠u2); apply the no-overlapping-edge-vertex-coincidence operation to the trees L1 and H3, and so on, to obtain the total colored tree L k =L k-1 [·]H k+1 (k∈[1,B-1]); full coloring tree L k Admit a full coloring F k , so that the coincident vertex w k =u·u k+1 ,(u∈V(L k-1 ),u k+1 ∈V(H k+1 )) is colored as F k (w k )=0; and there is a coloring F k (z) = F k-1 (z), (z∈V(H k-1 )∪E(H k-1 ), z≠u), and coloring F k (t) = F k-1 (t), (t∈V(H k+1 )∪E(H k+1 ), t≠u k+1 ); Based on multiple non-overlapping vertex overlap operations, a fully colored tree is obtained According to the full coloring tree L B-1 , determine the tree grid as

[0106] That is, Definition 10: Let trees H1, H2, ..., H B is a fully colored tree graph network block basis T c The tree in (Definition 8) A full permutation of Since the tree H i And tree H j The set of ordered graceful full coloring f i and f j , satisfying f i (u i )=0 and f j (u j)=0, then the no-overlapping-edge vertex overlap operation can be implemented, so that the vertex overlap graph L1=H1[·]H2 is a tree, which recognizes a total coloring F1, so that the coloring of the overlapping vertex w1=u1·u2(u1∈V(H1), u2∈V(H2)) is F1(w1)=0; and there is a coloring F1(z)=f1(z)(z∈V(H1)∪E(H1), z≠u1), and a coloring F1(t)=f1(t)(t∈V(H2)∪E(H2), t≠u2). In this way, we get the total coloring tree L k =L k-1 [·]H k+1 (k∈[1,B-1]), full coloring tree L k Admit a full coloring F k , so that the coincident vertex w k =u·u k+1 (u∈V(L k-1 ),u k+1 ∈V(H k+1 )) is colored as F k (w k )=0; and there is coloring F k (z) = F k-1 (z)(z∈V(H k-1 )∪E(H k-1 ), z≠u), and coloring F k (t) = F k-1 (t)(t∈V(H k+1 )∪E(H k+1 ), t≠u k+1 ). Remember the full coloring tree:

[0107]

[0108] Based on formula (6), we get the network block basis T based on the fully colored tree graph c The fully colored tree T c - TUG:

[0109]

[0110] In an exemplary embodiment, there is also a tree grid of a graph-generated tree base: after performing vertex tearing on a connected (p, q)-graph G, a tree set S consisting of all q mutually inhomogeneous trees with edges is obtained. plit (G). We start from the tree set S plit (G) Select the trees L1, L2, ..., L with q edges m To make a tree base, And when i≠j, the tree L i Not identical to the tree L jFor the sake of distinction, it is called the G-vertex tearing tree base, and is denoted as GT = {L1, L2, ..., L m}. Let the connected (p, q)-graph G admit a total coloring, then there is a total coloring G-vertex tearing tree base We obtain the tree GT-lattice based on the G-vertex-torn tree-based GT (Formula (8)) and the tree-based GT based on the G-vertex-torn tree-based GT c Fully colored tree GT c -Graph (formula (9)).

[0111]

[0112] Definition 11. Since every tree L k ∈S plit (G) Graph Homomorphism and Connected (p, q)-Graph G, i.e. L k →G, or G→ split L k . For a connected graph H, if there is a graph homomorphism L k →H, then the connected (p, q)-graph G is said to be isomorphic to the graph H, denoted by G→ split L k →H.

[0113] Note 4: Figure 5 Give two examples of tree isomorphism G→ that explain Definition 11. split T→H and G→ split T→L. It is worth noting that graph G is not isomorphic to graphs H and L, and their vertex tearing trees are also not isomorphic to each other, and there is G→ split G1, H → split H1, L → split L1.

[0114] Theorem 2. According to Definition 11, if every tree L k ∈S plit (G) satisfies G→ split L k →H, each tree T k ∈S plit (H) satisfies H→ split T k →G, then graph G and graph H are isomorphic, that is,

[0115] Question 1: The complete graph K8 can be torn into a tree with 29 vertices. Determine the tree set S plit (K8) is difficult because it involves the NP-complete problem of subgraph isomorphism.

[0116] Question 2: Let the connected (p, q)-graph G kAfter the vertex tearing operation, the tree set of all q vertices is S plit (G k ), let G1 = even graph K 1，q-1 , find a connected (p, q)-graph group L = {G1, G2, ..., G n}, so that the union of the tree set A tree containing all q vertices, and making n reach the minimum, where S plit (G1) = {K 1，q-1 Determine all connected (p, q)-graph groups like the connected (p, q)-graph group L.

[0117] Therefore, when the merge operation is an edge connection operation, the fully colored tree graph network block base Merge multiple isomorphic trees to determine the tree grid, including: obtaining multiple isomorphic trees A full permutation of , we get multiple full coloring trees B1, B2, ..., B C , According to the edge connection operation, connect a vertex of the full coloring tree B1 with a vertex u2 of the full coloring tree B2, and assign a color to the new edge u1u2 to obtain the full coloring tree According to the edge connection operation, connect a vertex x1 of the full coloring tree Q1 with a vertex u3 of the full coloring tree B3, and assign color to the new edge x1u3, and so on, to obtain the full coloring tree According to the full coloring tree Q C-1 , get the full colored tree graph network block base A c Tree grid of

[0118] Specifically, the edge connection operation tree grid: fully colored tree graph network block base Every fully colored graph of is a tree, And when i≠j, the tree Different from tree See Definition 8. Fully Colored Tree Graph Network Block Basis A c Tree in A full permutation of is B1, B2, ..., B C ,in

[0119] Use an edge to connect a vertex u1 of the full coloring tree B1 with a vertex u2 of the full coloring tree B2, and assign a color to the new edge u1u2 to obtain another full coloring tree Next, connect a vertex x1 of the fully - colored tree Q1 to a vertex u3 of the fully - colored tree B3 with an edge, and assign a coloring to the new edge x1u3, thus obtaining another fully - colored tree By using this edge - connection operation, we obtain the fully - colored tree Briefly denoted as:

[0120]

[0121] We obtain the linear - connection operation tree - type A based on the fully - colored tree - type graph network block base A c of c - graph lattice

[0122]

[0123] Figure 6 and Figure 7 Give an example of the linear - connection operation of the tree

[0124] According to the above description, it can be determined that the above - mentioned tree - type graph lattice is a structured representation and calculation, with structured behavior

[0125] S303. Obtain the fully - colored topological coding matrix of the tree - type graph lattice, and generate an asymmetric topological cipher according to the fully - colored topological coding matrix

[0126] Perform full - coloring on the tree - type graph lattice. According to the fully - colored tree - type graph lattice, determine the fully - colored topological coding matrix. In an exemplary embodiment, the tree - type graph lattice is an infinite set. According to the fully - colored topological coding matrix, generate an asymmetric topological cipher, including: generating an infinite number of topological digital strings according to the fully - colored topological coding matrix; determining each topological digital string as an asymmetric topological cipher. Among them, the asymmetric topological cipher includes a public - key topological signature, a private - key topological signature, as well as a public - key string and a private - key string

[0127] The present invention not only has practicality and convenience, but also has computational security and provable security. It enables the practical algorithm designed by the present invention not to need to prove its computational security and provable security every time. This is because asymmetric topological encryption can generate a public - key topological signature, a private - key topological signature, as well as a public - key string and a private - key string. Among them, the topological signature is similar to the digital signature of asymmetric encryption, and has multiple functions such as identity authentication and file encryption, as well as zero - knowledge applications

[0128] As a topological signature for identity authentication: For example Figure 1 the fully - colored topological coding matrix of the Chinese character graph H of the character "yong" in code (H, f) is the matrix T in formula (2), where the Chinese character graph H admits an ordered graceful full - coloring f, and for each k ∈ [1, 10], the vertex - torn graph Yk → H such that each vertex tears the graph Y k 's total coloring topological coding matrix T code (Y k , f k ) = T code (H, f), where each vertex tears the graph Y k admits a set-ordered graceful total coloring f k (k ∈ [1, 10]). It can be observed that Figure 1 has a bidirectional graph homomorphism

[0129] Theorem 3: A total coloring topological coding matrix can correspond to multiple non-isomorphic total coloring graphs.

[0130] Figure 1 In the "used" Chinese character graph H in, the adjacent matrix A(H) is a 13×13 symmetric matrix, and each vertex tears the graph Y k 's adjacent matrix A(Y k ) has an order greater than 13.

[0131] Theorem 4: Any two adjacent matrices A(H) and A′(H) of a graph H are similar, that is, there exists an invertible matrix P such that A′(H) = PA(H)P -1 .

[0132] Under matrix similarity operations, the graph H and its adjacent matrix A(H) are in one-to-one correspondence. Using this property in the field of information security, the total coloring graph H is used as the "topological signature" for identity authentication, where "topological structure and mathematical constraints" are the two basic elements that make up the "topological signature". Generally speaking, it is the two basic elements of the topological structure of graph H and the coloring admitted by graph H. The mathematical constraints are determined by the total coloring topological coding matrix T code (H, f), and the topological structure is determined by the adjacent matrix A(H). However, a total coloring topological coding matrix can correspond to multiple non-isomorphic graphs, and the digital string derived from this total coloring topological coding matrix is used to encrypt files. The topological properties of the adjacent matrix and the total coloring topological coding matrix and their association with NP-class problems bring an unbearable time overhead for attacking and breaking non-symmetric topological ciphers.

[0133] Verifying the "topological signature" requires verifying "topological structure and mathematical constraints". Since the topological structure is associated with the subgraph isomorphism NP-complete problem and the mathematical constraints are associated with topological coding, the "topological signature" contains NP-complete problems and sharp-P-hard problems. Therefore, it is impossible to attack and break the topological signature within an effective time overhead. Figure 8 is a schematic diagram of non-symmetric topological coding encryption and can be explained by Figure 8 the non-symmetric topological encryption technology of the present invention.

[0134] In addition, using a fully colored Chinese character graph as a topological signature adds a new deciphering difficulty for the attacker, namely, requiring that the topological structure of the topological signature can be torn into meaningful Chinese character graph statements by vertices. For example, the Chinese character image "If everyone is fair, the world will be peaceful" in Figure 5 also has the following sentence arrangement: 1) If people are good and fair, the world will be peaceful; 2) If everyone is good, the world will be fair; 3) If people are good and fair, the world will be peaceful; 4) If people are fair, the world will be good and peaceful; 5) If the world is fair, people are good and peaceful; 6) If the world is peaceful, people are good and fair; 7) If everyone is fair, the world will be peaceful; 8) If the world is peaceful, everyone is fair; 9) If people are good and fair, the world will be peaceful; 10) If everyone is fair, the world will be good and peaceful; 11) If people are good and fair, the world will be peaceful; 12) If the world is peaceful, people are good and fair; 13) If everyone is fair, the world will be too good; 14) If people in the world are too good, everyone will be fair; 15) If people are fair, people in the world are too good; 16) If people in the world are fair, everyone is too good; 17) If people in the world are too good, everyone will be fair.

[0135] When the topological structure of a topological signature has tens of thousands of vertices, its vertices are torn into meaningful Chinese character graph statements, so that this Chinese character graph statement is exactly the user's key. It is not difficult to imagine that it is impossible to tear the topological signature into Chinese character graph statements within an effective time overhead. Therefore, there are: the topological coding graph is easy to store and fast to calculate; data compressibility; data resistance to modification; data irreversibility; topological signature. It can realize the overall key management of local area networks and communities; the length and number of generated digital strings can meet the needs of practical applications. It has the potential to resist quantum computing and become a member of the post-quantum cryptography family.

[0136] Exponential total coloring: Theorem 5. A tree T with diameter D(T) (≥3) admits at least β graceful (k, d)-total colorings, 2 of which m-1 ≤β≤2 m+2 , and m+1=[D(T) / 2].

[0137] Algorithmic proof: Initialize, assume T1 is a tree with diameter D(T1) ≥ 3, L eaf (T1) is the set of leaves of tree T1. Remove all leaves of tree T1 and get another tree T2 = T1-L eaf (T1). In this way, we get tree T i+1 =T i -L eaf (T i )(i∈[1,m]), and the tree T m+1 is a star tree whose vertex set is V(T m+1 )={x}∪{x j :j∈[1,n]}, the edge set is E(T m+1 )={xx j:j∈[1,n]}.

[0138] Step 1: For non-negative integers k and d, we define the star tree T m+1 Define a graceful (k, d)-total coloring f m+1 For example: (i) f m+1 (x) = 0, f m+1 (x j ) = k + (j-1) d; (ii) f m+1 (xx j )=f m+1 (x j )-f m+1 (x)(j∈[1,n]).

[0139] Step 2: Note that for each tree T i It is for the tree i+1 Add leaf set L eaf (T i ) in the leaves, that is, T i =T i+1 +L eaf (T i ). According to Theorem 1, the tree T i Admit a graceful (k, d)-total coloring f i , and is from the tree T i+1 A graceful (k, d)-total coloring of i+1 The derived graceful (k, d)-full coloring f i .

[0140] Step 3. By induction, the tree T1 admits a graceful (k, d)-total coloring f1.

[0141] Step 4: Because each tree T i There are at least 2 leaves, which is the number of leaves |L eaf (T i )|≥2(i∈[1,m]). Since each tree T i+1 =T i -L eaf (T i )(i∈[1,m-1]) of the vertex set V(T i+1 )=X i+1 ∪Y i+1 satisfy |X i+1 |≥2 and |Y i+1 |≥2, we assert that tree T1 admits at least 2 m-1 distinct graceful (k, d)-total colorings.

[0142] The proof of this theorem is complete.

[0143] Definition 12: A connected (p, q)-graph G admits a fully distinct index λ:V(G)∪E(G)→[1, p+q], such that the total coloring set λ(V(G)∪E(G))=[1, p+q], i.e., for any two elements w, z∈V(G)∪E(G), there is always λ(w)≠λ(z). Define the inverse of the fully distinct index λ to be λ -1 (w)=p+q-λ(w)(w∈V(G)∪E(G)), that is, there is λ -1 (w)+λ(w)=p+q.

[0144] Theorem 6. Let P ine (G) is the set of all mutually distinct labels of a connected (p, q)-graph G, then |P ine (G)| is an even number.

[0145] Question: Obviously, any fully distinct labeling of a connected (p, q)-graph G is a fully distinguishable labeling, that is, for any two elements w, z∈V(G)∪E(G), there is always a coloring set of elements adjacent to w, z that satisfies C(w)≠C(z). When G is a complete graph with p vertices K p When the complete graph K p The number of all distinct labelings of the spanning tree of is

[0146]

[0147] Key making technology:

[0148] ⑴One-to-one: Fully colored topological encoding matrix T code (H, f) derives (3q)! Topological digital strings, each topological digital string s corresponds to its own reverse string t, forming a digital string matching (s, t). ⑵ One-to-many: (i) Parameter one-to-many. Since the positive integers k and d can be infinite, the exponentially graceful (k, d)-total coloring in Theorem 5 also has infinite keys. For a positive integer k (as a private key), you can take an infinite number of positive integers d (as a public key), thus forming a pair of infinite key groups. It is also a "one-time one-pad" key pair or key group; (ii) A private key is torn into multiple public keys. In the tree-type T-graph grid L based on the tree graph network block base T (Definition 7) tree (Z 0 [·]T), give the figure Then we can use W-constrained full coloring F and split the graph H into trees a1T1, a2T2, …, a m T m , each tree T k Let us admit a total coloring f derived from a W-constrained total coloring F. k . The full coloring topological encoding matrix T code (H, F)(private key) and the fully colored topological encoding matrix Tcode (H k , f k ) (public key) to form a one-to-many key group. ⑶ According to Definition 12, the fully distinct labels λ (private key) of the connected (p, q)-graph G and its inverse λ -1 (public key) forms a key matching pair, that is, there is λ -1 (w)+λ(w)=p+q. Fully colored topological encoding matrix T code (G,λ) derives (3q)! private keys, which are matched by the fully colored topological encoding matrix T code (G,λ -1 ) derive (3q)! public keys. (4) In the "Algorithm implementation of partial Wi-constrained labeling" of Theorem 9, an algorithm for matching pair labels is given.

[0149] PRKPUK - Question:

[0150] Based on the tree-like T-grid of the tree-like network block base T, we propose the following PRKPUK-problem (Private-keydudespublic-keysproblem):

[0151] Decipher a topological digital string s=s1s2…s n (s i ∈[0,9]), the following steps are required:

[0152] ⑴Write the topological digital string s as s*=A1A2…A 3q , where the digital segment A k =b k，1 b k，2 …b k，q(k) (k∈[1,3q]), such that every number s i Only in one number segment A k Appears in, not in any other digital segment A j Appears in (k≠j).

[0153] ⑵ Find a fully colored topological encoding matrix T based on the digital string s* code , find a graph H that admits a W-constrained total coloring F, and the total coloring topological encoding matrix T code (H, F) = T code , so that T code (H, F) just derives the number string s*.

[0154] ⑶ The full coloring topology encoding matrix T code (H, F) is decomposed into a small full-coloring topological encoding matrix T code (H k , f k)(k∈[1,M]), where

[0155] ⑷ Based on the small full coloring topological encoding matrix T code (H k , f k )(k∈[1,M]), find trees H1,H2,…,H M .

[0156] ⑸ Perform vertex tearing operation on graph H to obtain trees H1, H2, ..., H M , so that these trees are exactly the trees a1T1, a2T2, …, a m T m , thus determining the tree graph network block base T = {T1, T2, ..., T m}, or a tree graph network block base with special constraints (see Note 2).

[0157] ⑹ Full coloring topological encoding matrix T code (H, F) The derived topological digital string (private key) contains all small fully colored topological encoding matrices T code (H k , f k )The topological digital string (public key) derived from .

[0158] ⑺Based on the tree diagram network block base T and operation Write out the tree T-grid L tree (Z 0 [·]T).

[0159] PRKPUK-Complexity of the problem:

[0160] ⑴ There is no polynomial algorithm to write the topological digital string s as s*=A1A2…A 3q ⑵ A fully colored topological encoding matrix T code It can correspond to more than two mutually isomorphic topological coding graphs. Determining the graph H that accepts W-constraint full coloring F will encounter the NP-complete problem of subgraph isomorphism. ⑶ It is known that there are thousands of full colorings, and finding a special W-constraint is a terrible computer task. ⑷ If it is known that it is a certain type of W-constraint full coloring, however, finding all W-constraint full colorings accepted by graph H is a shar-P-hard problem. ⑸ If the full coloring topological coding matrix T code (H, F) is determined and decomposed into a small full-coloring topological encoding matrix T code (H k , f k )(k∈[1,M]) has no polynomial algorithm, and every small total coloring topological encoding matrix T code (H k , f k) is a tree k ⑹ Find the tree graph network block basis T = {T1, T2, ..., T m}, or a tree graph network block basis with special constraints (see Note 2), so that each tree T k The fully colored topological encoding matrix of (k∈[1,m]) is exactly some T code (H k , f k ). ⑺Vertex tearing graph H to trees H1, H2, …, H M We will encounter: (i) subgraph isomorphism is an NP-complete problem; (ii) when the number of vertices in graph H is huge, the tearing work is exponential; (iii) making the trees H1, H2, ..., H M It is the tree a1T1, a2T2, ..., a m T m (iv) such that the trees H1, H2, ..., H M It is a meaningful group of Chinese characters.

[0161] Based on the complexity of the PRKPUK-problem, the original topological coding graph and its fully colored topological coding matrix cannot be found from the topological digital string, that is, irreversibility holds, thus proving the computational security and provable security of the technology of the present invention. At the same time, the practical algorithm using the method of the present invention does not need to prove its own computational security and provable security.

[0162] Asymmetric topological encryption technology has the following advantages:

[0163] ① Topological coding graphs involve two or more mathematical disciplines. The two basic elements that make up a topological coding graph are "topological structure" and "mathematical constraints". Among them, "mathematical constraints" come from theories of multiple branches of mathematics and computer science techniques; "topological structure" is neither an ordinary geometric graph nor a picture, but a colored graph in graph theory (often called a topological coding graph). To destroy the "asymmetric topological key", an AI attack with quantum computing needs to constantly switch from one mathematical field to another. In addition, the number of topological structures and mathematical constraints is huge, and there is no logical relationship reasoning between them, which makes it impossible for an AI attack with quantum computing to successfully decipher the "asymmetric topological key" within an effective time cost.

[0164] ② The topological coding graph is represented by a common matrix. The topological coding graph is input into the computer through various algebraic matrices and calculated to generate the key required for actual encryption applications. When the number of vertices of the topological coding graph is large, calculating the adjacent matrix of the topological coding graph requires greater computing power and massive storage space.

[0165] ③ Topological coding graphs have a huge number of topological structures. In graph theory, the number of graphs is huge and the configuration is complex. There is no polynomial algorithm that can draw all mutually incompatible graphs with a specified number of vertices. The number of graphs with 23 vertices and 24 vertices is n. 23 、n 24 They are as follows:

[0166] n 23 =559946939699792080597976380819462179812276348458981632≈2 179 ;

[0167] n 24 =195704906302078447922174862416726256004122075267063365754368≈2 197 .

[0168] Among them, the estimated number of stars in the universe is 3×10 22 ~2 74 , the number of atoms in the solar system is about 10 57 ~2 189 atoms. That is, the number of graphs with 24 vertices is n 24 10 more than the number of atoms in the solar system 57 (≈2 189 ) is much larger. However, finding and determining a graph will encounter the NP-complete problem of subgraph isomorphism.

[0169] ④ Topologically coded graphs have a large number of labeling and coloring. In the field of graph theory, there are not only a large number of graph colorings and graph notations, but also new graph colorings and graph notations are generated every day. Even for a graph G and a special type of coloring, finding all the coloring schemes of the graph G for this special type of coloring is a sharp-P-hard problem.

[0170] ⑤ Topological coding graphs can achieve asymmetric diversity. Under the structural operation and coloring of the graph, it can be achieved that: one public key topological signature corresponds to multiple private key topological signatures, multiple public key topological signatures correspond to a single private key topological signature, and multiple public key topological signatures correspond to multiple private key topological signatures.

[0171] ⑥Easy to create topological coding graph keys. The fully colored topological coding matrix T of the topological coding graph G with q edges code (G, f) is a 3×q-order matrix, which can be easily obtained from the matrix T code (G, f) leads to (3q)! different topological digital strings. The tree graph allows dozens of graph numbers and graph colorings, and various matching colorings of these colorings can produce multiple topological signature key pairs.

[0172] ⑦ The digital string generated by the topological coding map is irreversible. The topological coding matrix in the topological coding map can quickly generate a topological digital string. However, the topological digital string has no association with the topological structure. One topological digital string can correspond to multiple topological coding maps. It is extremely difficult to reconstruct the original topological coding map. In other words, the topological digital string is irreversible.

[0173] ⑧ Computational security and provable security. In asymmetric topological encryption technology, there are a large number of unresolved problems and mathematical conjectures, such as the graceful tree conjecture, edge magic total coloring conjecture, odd graceful tree conjecture, total coloring conjecture, vertex coloring conjecture, uniform total coloring conjecture, etc. Among them, many conjectures and unresolved problems are related to NP-type problems. "Topological structure" and "mathematical constraints" prove the computational security and provable security of the method of the present invention.

[0174] Establish a key management center for the local area network (community): Establish an asymmetric topology key management center (ATKMC) with the following functions: (1) ATKMC does not require users in the network to learn various key production technologies, especially the key production technologies that are changing with each passing day, which prevents leaks and increases the security and confidentiality of privacy. (2) ATKMC provides network users with topological signature key pairs and string key pairs produced with the latest technology, putting destroyers in a difficult situation of continuous learning and increasing costs. (3) ATKMC can produce keys that are different for each person and reflect personalization. For example, it can produce literary key pairs and Chinese character topological signatures for users who use Chinese. (4) ATKMC can be miniaturized and become private key management software for individual users of the network. (5) Non-user parties in the network do not need to place their public keys and secret keys on a public platform, or transmit public keys and secret keys to the communication party through public channels. Every communication between the two users is protected by ATKMC, so that decryption requires attacking the key under the topological structure. The attacker must switch and search in different mathematical fields, which cannot form an effective attack, and its benefits are far less than its cost. ⑹ After the user obtains the key sent by ATKMC, he can communicate directly and safely without the help of a third party. ⑺ATKMC performs overall key management work such as key registration, key production, key distribution, key use, key authentication, key revocation, and key update for users in the community and local area network. ⑻ATKMC can use graph groups and grids to encrypt the community and local area network as a whole, which is one of the advantages of asymmetric topological encryption. ⑼ATKMC tailors overall encryption for different groups and communities, so that users of each group and community can adopt encryption technologies such as blockchain.

[0175] Strength of asymmetric topological keys: The strength of asymmetric topological keys has the following basic indicators: ① The length of the asymmetric topological key; ② The mathematical constraint set R (c1, c2, ..., c m ) dimension n; ③ the topological structure of the asymmetric topological key; ④ the topological structure of the asymmetric topological key can be torn into meaningful Chinese character graph sentences by vertices; ⑤ the cardinality of the graph space for constructing the asymmetric topological key is at least 2e=2 200 , the number of vertices and edges of the graph is not less than 50.

[0176] The present invention is based on the tree graph network block base T (Definition 7) of the full color tree T-grid, based on the tree graph network block base T c (Definition 8) The fully colored tree T c - Grid, Tree GT-Grid based on Vertex-Torn Tree-Based GT, and Network Block-Based A based on Fully Colored Tree-Based Graph c The linear connection operation tree type A c -The graph is structured knowledge, structured behavior, structured representation and structured computation. The following gives their combined generalization properties.

[0177] Tree grid of graph network framework: Let F(n) be a set of connected graph network frameworks G with no more than n vertices, T = {T1, T2, ..., T m} is a tree graph network block base, where each graph T k (k∈[1,m]) is a tree. We have a tree-like F(n)-T-graph grid based on the tree-like graph network block base T and the connected graph network frame set F(n):

[0178]

[0179] Graph network block basis homomorphism: A graph network block basis T = {T1, T2, ..., T m} is homomorphic to another non-tree graph network block base H = {H1, H2, ..., H m}, if there is a graph network block homomorphism T k →H k (k∈[1,m]), then a graph network block basis homomorphism is defined, namely T→H.

[0180] Theorem 7. If the graph network block basis T = {T1, T2, ..., T m} Homomorphic to non-tree graph network block basis H = {H1, H2, ..., H m}, then the F(n)-T-lattice is isomorphic to the F(n)-H-lattice, that is,

[0181] L(F(n)[●]T)→L(F(n)[●]H) (14)

[0182] Combination generalization of dynamic tree grid:

[0183] Theorem 8: Let the dynamic tree graph network block base T(t) = {T1(t), T2(t), ..., T m Every tree T in (t)}(t∈[a,b]) k (t) Acknowledge a W i (t)-Constrained Coloring And there is a shading transformation Here the coloring f k It's a tree k (t)∈T(t) is a set of ordered and gracefully labeled numbers. We have a recognition that W i (t)-constrained colored tree graph network block basis, denoted as T(W i , t) = {T1(W i , t), T2(W i , t),…,T m (W i , t)}(t∈[a,b]), and obtain the following tree-based network block basis T(W i , t) of the tree grid:

[0184] Since the tree grid L tree (Z 0 [·η]T(W i , t)) of the tree graph network block base T(W i , t) is the shading transformation The result is the following two tree grid transformations:

[0185] L tree (Z 0 [·η]T(W i , t)) = θ i [L tree (Z 0 [·η]T(t))] (15)

[0186] Theorem 9. Let T be a tree of p nodes, (X, Y) be a bipartition of the set V of nodes of the tree T, and integers k ≥ 1 and d ≥ 1. If the tree T admits a set of ordered graceful full labeling, then the tree T admits every W below i- Constraint labels: Graceful label, Set-ordered graceful label, Graceful intersection total set label, Graceful group label. Odd-graceful label, Set-ordered odd-graceful label, Edge-odd-graceful intersection total label, Odd-graceful intersection total set label, Odd-graceful group label, Perfect odd-graceful label. Elegant label, Odd-elegant label η satisfies η(x)+η(y)≤2p - 3(xy∈E). 6C-label, Odd-6C-label, Parity-separable 6C-label. Edge-magic total label, Super edge-magic total label, Super set-ordered edge-magic total label, Edge-magic total graceful label, Loose edge-magic total label. Odd edge-magic matching label, Edge-difference graceful magic matching label, Edge-difference odd edge-magic matching label. Mirror label, Harmonious mirror label, (k, d)-harmonious mirror label. Difference-sum label, Happy-sum label. Super happy label α satisfies maxα(X)<minα(Y). Super edge-magic total label γ satisfies maxγ(X)<minγ(Y), and |X| + 2p + 1 is the magic constant. Super (|X| + p + 3, 2)-edge anti-magic total label θ satisfies maxθ(X)<minθ(Y). (k, d)-graceful label β satisfies β(x)<β(y)–k + d(x∈X, y∈Y). (k, d)-arithmetic label φ satisfies maxφ(x)<minφ(y)–k + d·|X|(x∈X, y∈Y). (k, d)-edge anti-magic total label. (k, d)-harmonious label ξ satisfies maxξ(X)<minξ(Y\{y0}), ξ(y0)=0. Twin (k, d)-label, Twin Fibonacci-type icon label, Twin odd-graceful label.

[0187] Part W of Theorem 9 i - Algorithm implementation of constraint labels:

[0188] Initialization. Let the tree T have p nodes, and (X, Y) be the bipartite partition of the node set V(T) of the tree T, X = {x1, x2, …, x s}, Y = {y1, y2, …, y t}(s + t = p); Suppose the tree T admits a set-ordered graceful total label f, then maxf(X)<minf(Y), and f(x k y r ) = f(y r )–f(x k )∈f(E(T)) = [1, p–1]. Without loss of generality, assume:

[0189] 0 = f(x1)<f(x2)<…<f(x s ) = s<s + 1 = f(y1)<f(y2)<…<f(y t ) = p–1 (16)

[0190] W-constraint label algorithm 1. Odd-graceful label: Step - 1 - 1. Let F odd(x k )=2f(x k )(k∈[1,s]),F odd (y r )=2f(y r )–1(r∈[1,t]), then maxF odd (X) <minF odd (Y). Step-1-2. Let F odd (x k y r )=F odd (y r )–F odd (x k )(x k y r ∈E(T)). Step-1-3. Because F odd (x k y r )=2f(x k y r )–1, then F odd (E(T)) = {1, 3, ..., 2p-1}. Step-1-4. Return the set-ordered odd-graceful label F of the tree T odd , and the set ordered graceful full label f ​​forms a matching pair label (f, F odd ).

[0191] W-constrained labeling algorithm 2, I-happiness difference magic labeling: Step-2-1. Let F fd (x k )=f(x s–k+1 )(k∈[1,s]),F fd (y r )=f(y r )(r∈[1,t]). Then maxF fd (X) <minF fd (Y). Step-2-2. Let F fd (x k y r )=f(x k y r )(x k y r ∈E(T)). Step-2-3. Then we have ||F fd (x k )+F fd (y r )|–F fd (x k y r )|=f(x s–k+1 )+f(y r )–f(x ky r )=f(x s–k+1 )+f(y r )–[f(y r )–f(x k )]=f(x s–k+1 )+f(x k ) = s. Step-2-4. Return the set of ordered I-happiness difference magic label F of tree T fd .

[0192] W-constrained labeling algorithm 3, edge magic full labeling: Step-3-1. Let F em (x k )=f(x k )(k∈[1,s]),F em (y r )=f(y t–r+1 )(r∈[1,t]). Then maxF em (X) <minF em (Y). Step-3-2. Let F em (x k y r )=f(x k y r )(x k y r ∈E(T)). Step-3-3. Because F em (x k )+F em (y r )+F em (x k y r )=f(x k )+f(y t–r+1 )+f(x k y r )=f(x k )+f(y t–r+1 )+[f(y r )–f(x k )]=f(y t–r+1 )+f(y r ) = s + p – 1. Step-3-4. Return the magic full label F of the set ordered edges of the tree T em .

[0193] W-constrained labeling algorithm 4, edge magic matching full labeling: Step-4-1. Let F emm (x k )=2p–f(x k )(k∈[1,s]),F emm (y r )=2p–f(y r)(r∈[1,t]). Then maxF emm (Y) <minF emm (X). Step-4-2. Let F emm (x k y r )=2p–f(x k y r )(x k y r ∈E(T)). Step-4-3. Then we have F emm (x k )+F emm (y r )+F emm (x k y r )=6p-[f(x k )+f(y t–r+1 )+f(x k y r )]=6p-[f(y t–r+1 )+f(y r )] = 5p-s + 1. Step-4-4. There is F em (w)+F emm (w) = 2p(w∈V(T)∪E(T)), forming a matching label (F em , F emm ). Step-4-5. Return the set of ordered edge magic matching full label F of tree T emm .

[0194] W-constrained labeling algorithm 5, edge difference magic full labeling: Step-5-1. Let F ed (x k )=f(x k )(k∈[1,s]),F ed (y r )=f(y r )(r∈[1,t]). Then maxF ed (X) <minF ed (Y). Step-5-2. Let F ed (x k y r )=f(x s–k+1 y t–r+1 )(x k y r ∈E(T), k∈[1,s], r∈[1,t]). Step-5-3. Then for each edge x k y r ∈E(T), there is F ed (x k )-F ed (yr )|+F ed (x k y r )=[f(y r )–f(x k )]+f(x s–k+1 y t–r+1 )=[f(y r )–f(x k )]+p-1-f(x k y r ) = p-1. Step-5-4. Return the set ordered edge difference magic full label F of the tree T ed .

[0195] W-constrained labeling algorithm 6, II-happiness difference magic full labeling: Step-6-1. Let L ed (x k )=pf(x k )(k∈[1,s]),L ed (y r )=pf(y r )(r∈[1,t]). Then maxL ed (Y) <minL ed (X). Step-6-2. Let L ed (x k y r )=f(x s–k+1 y t–r+1 )(x k y r ∈E(T), k∈[1,s], r∈[1,t]). Step-6-3. Then for each edge x k y r ∈E(T), we have |L ed (x k )-L ed (y r )|+L ed (x k y r )=[f(y r )–f(x k )]+f(x s–k+1 y t–r+1 )=[f(y r )–f(x k )]+p-1-f(x k y r ) = p-1. Step-6-4. Return the set of tree T in order II-happy magic full label L ed .

[0196] W-constrained labeling algorithm 7, odd-even separable 6C-full labeling: Step-7-1. Let Ioe6 (x k )=2f(x k )-1(k∈[1,s]),I ed (y r )=2f(y r )-1(r∈[1,t]). Then maxI oe6 (X) <minI oe6 (Y). Step-7-2. Let I oe6 (x k y r )=2f(x k y r )(x k y r ∈E(T)). Step-7-3. Then for each edge x k y r ∈E(T), let L oe6 (x k y r )=I oe6 (x s–k+1 y t–r+1 )(x k y r ∈E(T), k∈[1,s], r∈[1,t]), and L oe6 (w) = I oe6 (w)(w∈V(T)). Step-7-4. Return the set of tree T that is even-odd separable 6C-full label L oe6 .

[0197] W-constrained labeling algorithm 8, odd-even separable 6C-full labeling (matching): Step-8-1. Using the odd-even separable 6C-full labeling L of the tree T of Algorithm 7 oe6 Step-8-2. Let M oe6 (w) = 2p - L oe6 (w)(w∈V(T)). Then maxM oe6 (Y) <minM oe6 (X). Step-8-3. Let M oe6 (x k y r )=L oe6 (x k y r )-1(x k y r ∈E(T)). Step-8-4. Return the set of tree T that is ordered even-odd separable 6C-full label M oe6 , and odd-even separable 6C-full-number matching pairs (L oe6 , M oe6 ).

[0198] W-constrained labeling algorithm 9, parameter class full labeling parameters: Step-9-1. Let P ara (x r )=d×f(x r )(r∈[1,s]),P ara (y r )=k+d×[f(y r )-1](r∈[1,t]). When k≥1, then maxP ara (X) <minP ara (Y). Step-9-2. Let P ara (x k y r )=P ara (y r )-P ara (x k )=k+d×[f(x k y r )-1](x k y r ∈E(T)). Step-9-3. Then for each edge x k y r ∈E(T), there is P ara (E(T)) = {k, k+d, k+2d, ..., k+(p-1)d}. Step-9-4. Return the set of ordered and graceful (k, d)-full label P of tree T ara .

[0199] Theorem 10. Let the tree T admit a set-ordered graceful full label f, then the full labels of the W-constrained labeling algorithm k (k∈[1,8]) can be logically inferred from each other. The full labels of each W-constrained labeling algorithm k (k∈[1,8]) can form a (k,d)-full label.

[0200] Note 5: The set of trees T is ordered and graceful (k, d)-all-labeled can be transformed into other W of T i -Constraint (k, d) - Full label.

[0201] The present invention establishes a special tree graph network block base, a tree grid, a tree grid of a graph-generated tree grid, an edge-connected computing tree grid, a fully colored tree graph network block base A c The linear connection operation tree type A c - Grid. Defined all mutually distinct labels and calculated the complete graph K p The total unique labeling and number U of the spanning tree of tree (K p)(See formula (12)). Designing a private key to be torn into multiple public keys leads to the PRKPUK-problem. Based on the graph network block-based homomorphism and grid transformation, Theorems 8 and 9 give the grid homomorphism, grid relational reasoning and their combination generalization, thus exploring the relational reasoning of intelligent evolution and structured intelligent technology.

[0202] The present invention designs a tree grid encryption system based on a tree graph network block base and a fully colored tree graph network block base, which generates an infinite number of asymmetric topological keys and topological signatures, so that the tree grid has combinatorial generalization in structured knowledge and structured behavior. The present invention uses Chinese character graphs to form a tree grid encryption technology, involving three essentially different fields of "topological structure", "mathematical constraints" and "Chinese meaning of Chinese character graphs", so that the topological signature has an anti-AI decryption function. The topological signature of the patent of the present invention is diverse, and the topological structure of the topological signature involves the NP-complete problem of subgraph isomorphism. The exponential coloring of the tree in the tree grid is given, and the tree grid and the parameter fully colored topological coding matrix derive a "one-time one-key" topological digital string. The practical algorithm designed using the technology of the present invention does not need to be proved to have computational security and provable security every time.

[0203] When applying the asymmetric topological password generation method based on tree grid provided by the present invention, it is not necessary to Figure 1 The steps are executed in the order shown. The specific execution order of the steps can be determined according to needs, and the present invention does not limit this.

[0204] The above is a tree-based asymmetric topological password generation method provided by one or more embodiments of the present invention. Based on the same idea, the present invention also provides a corresponding tree-based asymmetric topological password generation device, such as Fig. 9 shown.

[0205] Fig. 9 A schematic diagram of an asymmetric topological password generation device based on a tree grid provided by the present invention, the device 900 includes:

[0206] The acquisition module 901 is used to acquire a plurality of mutually inhomogeneous trees generated by the Chinese character graph to be encrypted or other means; the plurality of trees constitute a tree graph network block base or a fully colored tree graph network block base;

[0207] The operation module 902 is used to perform a merging operation on multiple trees of different structures to determine a tree-type grid;

[0208] The generation module 903 is used to obtain the full-coloring topological coding matrix of the tree-type grid, and generate an asymmetric topological password based on the full-coloring topological coding matrix.

[0209] For the specific limitations of the asymmetric topological password generation device based on tree-type grids, please refer to the limitations of the asymmetric topological password generation method based on tree-type grids above, which will not be repeated here. Each module in the above-mentioned asymmetric topological password generation device based on tree-type grids can be implemented in whole or in part by software, hardware and a combination thereof. The above-mentioned modules can be embedded in or independent of the processor in the computer device in the form of hardware, or can be stored in the memory of the computer device in the form of software, so that the processor can call and execute the operations corresponding to the above modules.

[0210] The present invention also provides a computer-readable storage medium, which stores a computer program, which can be used to execute the above Figure 3 The provided asymmetric topological password generation method based on tree grid.

[0211] The present invention also provides Fig.10 The structural diagram of the computer device shown in FIG. Fig.10 As shown in the figure, at the hardware level, the computer device includes a processor, an internal bus, a network interface, a memory, and a non-volatile memory, and may also include other hardware required for the business. The processor reads the corresponding computer program from the non-volatile memory into the memory and then runs it to achieve the above Figure 3 The provided asymmetric topological password generation method based on tree grid.

[0212] Those of ordinary skill in the art can understand that all or part of the processes in the above-mentioned embodiment methods can be completed by instructing the relevant hardware through a computer program, and the computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above-mentioned methods. Among them, any reference to memory, storage, database or other media used in the embodiments provided by the present invention can include at least one of non-volatile and volatile memory. Non-volatile memory may include read-only memory (ROM), magnetic tape, floppy disk, flash memory or optical memory, etc. Volatile memory may include random access memory (RAM) or external cache memory. As an illustration and not limitation, RAM can be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM).

[0213] The technical features of the above embodiments may be arbitrarily combined. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of the present invention.

Claims

1. A method for generating an asymmetric topological password based on a tree grid, characterized in that: The method comprises: Acquire multiple mutually isomorphic trees generated by the Chinese character graph to be encrypted or other means; the multiple mutually isomorphic trees constitute a tree graph network block base or a fully colored tree graph network block base; Performing a merging operation on the multiple mutually inhomogeneous trees to determine a tree-type grid; the merging operation is a non-overlapping vertex overlap operation or an edge connection operation; A full-coloring topological coding matrix of the tree grid is obtained, and an asymmetric topological password is generated according to the full-coloring topological coding matrix.

2. The method according to claim 1, characterized in that The definition of the tree graph network block base includes: In multiple trees T1, T2, ..., T m In, if And when (i≠j), the tree T i Not identical to tree T j , then T={T1,T2,...,T m } is the tree graph network block basis; where i, j∈[1,m].

3. The method according to claim 2, characterized in that Performing a merging operation on the multiple mutually inhomogeneous trees to determine a tree-type grid includes: Obtain the multiple mutually incompatible trees a1T1, a2T2, ..., amT m Full permutation of , we get multiple trees H1, H2, ..., H M , Perform the no-overlapping vertex overlap operation on the trees H1 and H2 to obtain the tree L1 = H1[·]H2; The tree L1 and the tree H3 are subjected to the no-overlapping vertex overlap operation, and so on, the tree L k =L k-1 [·]H k+1 (k∈[1,M-1]); According to multiple non-overlapping vertex overlap operations, the tree is obtained According to the tree L M-1 , determine the tree grid as 4. The method according to claim 2, characterized in that: The definition of the fully colored tree graph network block base includes: If each tree T in the tree graph network block base k Admit a set ordered graceful total coloring f k , and there is a node u k ∈V(T k ) coloring f k (u k )=0, then the network block basis of the set-ordered graceful fully colored tree graph is determined to be That is the fully colored tree graph network block basis; among them, And when (i≠j), the tree T i c Different from tree 5. The method according to claim 4, characterized in that Performing a merging operation on the multiple mutually inhomogeneous trees to determine a tree-type grid includes: Get multiple mutually isomorphic trees A full permutation of , we get multiple fully colored trees H1, H2, ..., H B , Perform the no-overlapping vertex overlap operation on the tree H1 and the tree H2 to obtain the tree L1 = H1[·]H2; the tree L1 admits a full coloring F1, so that the overlapped vertex w1 = u1·u 2， The coloring of (u1∈V(H1), u2∈V(H2)) is F1(w1)=0, and there exists a coloring F1(z)=f1(z), (z∈V(H1)∪E(H1), z≠u1), and a coloring F1(t)=f1(t), (t∈V(H2)∪E(H2), t≠u2); The tree L1 and the tree H3 are subjected to the no-overlapping vertex overlap operation, and so on, to obtain the fully colored tree L k =L k-1 [·]H k+1 (k∈[1,B-1]); full coloring tree L k Admit a full coloring F k , so that the coincident vertex w k =u·u k+1 ,(u∈V(L k-1 ),u k+1 ∈V(H k+1 )) is colored as F k (w k )=0; and there is a coloring F k (z) = F k-1 (z), (z∈V(H k-1 )∪E(H k-1 ), z≠u), and coloring F k (t) = F k-1 (t), (t∈V(H k+1 )∪E(H k+1 ), t≠u k+1 ); According to multiple non-overlapping vertex overlap operations, the full coloring tree is obtained According to the full coloring tree L B-1 , determine the tree grid as 6. The method according to claim 4, characterized in that The fully colored tree graph network block base Performing a merging operation on the multiple mutually inhomogeneous trees to determine a tree-type grid includes: Get multiple mutually isomorphic trees A full permutation of , we get multiple full coloring trees B1, B2, ..., B C , According to the edge connection operation, connect a vertex u1 of the full coloring tree B1 with a vertex u2 of the full coloring tree B2, and assign a color to the new edge u1u2 to obtain the full coloring tree According to the edge connection operation, connect a vertex x1 of the full coloring tree Q1 with a vertex u3 of the full coloring tree B3, and assign color to the new edge x1u3, and so on, to obtain the full coloring tree According to the full coloring tree Q C-1 , get the full colored tree graph network block base A c Tree grid of 7. The method according to claim 1, characterized in that The tree grid is an infinite set, and the asymmetric topological code is generated according to the full-coloring topological coding matrix, including: According to the full-coloring topological coding matrix, an infinite number of topological digital strings are generated; Each topological word character string is determined as the asymmetric topological password.

8. The method according to claim 1, characterized in that The asymmetric topological cipher includes a public key topological signature, a private key topological signature, a public key character string, and a private key character string.

9. A device for generating an asymmetric topological password based on a tree grid, characterized in that: include: An acquisition module, used for acquiring a plurality of mutually isomorphic trees generated by a Chinese character graph to be encrypted or other means; The plurality of trees constitute a tree graph network block base or a fully colored tree graph network block base; The operation module is used to merge multiple trees of different structures to determine the tree-shaped grid; A generation module is used to obtain a fully colored topological coding matrix of a tree-type grid, and generate an asymmetric topological password based on the fully colored topological coding matrix.

10. A computer-readable storage medium, characterized in that: The storage medium stores a computer program, and when the computer program is executed by a processor, the method according to any one of claims 1 to 8 is implemented.

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