Asymmetric topological key manufacturing method based on odd graceful topological coding graph

Abstract

The invention discloses an asymmetric topological key manufacturing method based on an odd graceful topological coding graph. An asymmetric topological key is composed of two essentially different mathematical branches, namely a topological structure and a mathematical code. Wherein the theory of the topological structure is based on a graph theory and topology; the theory of mathematical coding is based on combinatorial mathematics, linear algebra, number theory, set theory, algebra, computer science and other subjects. Giving a coding mirror image from the odd topology to the odd topology, and a mirror image or inverse substitution operation from one odd topology (private key) to another odd topology (public key); establishing a odd extension graph group and a topological graph group signature thereof; a set ordered odd topology graph W-operation graph lattice is constructed by using topological coding point superposition operation and edge addition operation, and a topological graph lattice signature and infinite'one-time pad 'keys are obtained; a generic topological coding matrix and a Fibonacci key sequence are defined so as to be suitable for wider information security application scenarios.

Description

Technical Field

[0001] This invention belongs to the field of information encryption technology, specifically involving asymmetric key creation technology based on chiral topological coding graphs in graph theory, which is applicable to scenarios such as electronic document encryption and network security authentication. Background Technology

[0002] In the field of information encryption, traditional key systems face challenges in computational security and resistance to attacks. The development of disciplines such as topological coding, combinatorics, algebra, and graph theory has provided a theoretical foundation for new encryption technologies. Among these, long-standing unsolved public problems in graph theory, such as chiral graphs and the full coloring conjecture, have become important directions for constructing highly secure keys due to their close association with NP-complete or NP-class problems. In existing technologies, key systems spanning multiple branches of mathematics have attracted considerable attention due to their high decryption difficulty; however, further breakthroughs are still needed to efficiently combine topological structures and mathematical coding to achieve secure generation and authentication of asymmetric keys. Summary of the Invention

[0003] The purpose of this invention is to provide a method for generating asymmetric topological keys based on the Qiyou topological coding graph.

[0004] This invention uses the elegant topological coding graph of graph theory to create asymmetric topological keys. This is because asymmetric topological keys consist of two fundamentally different branches of mathematics: "topological structure" and "mathematical coding." The "topological structure" is used as an electronic topological signature, while the "mathematical coding" derives a topological number string to encrypt electronic documents.

[0005] This invention is a method for generating an asymmetric topological key based on a chimei topological coding graph. The specific steps are as follows: S1. Using the adjacency matrix and the fully encoded topological coding matrix of graph theory, input the odd topology graph (graph group) into the computer and derive the topological signature and topological digital string key; S2. It establishes a coded mirror image (public key) from the OddTop graph itself (private key) to itself, and a mirror image or inverse substitution from one OddTop graph (private key) to another OddTop graph (public key). It establishes OddTop graph group and set-ordered OddTop graph W-operation lattice, which can generate infinitely many asymmetric OddTop topological coding "one-time pad" encryption subsystems.

[0006] Asymmetric topological encryption addresses many long-standing conjectures and open problems in graph theory, making asymmetric topological keys provably secure. Asymmetric topological encryption generates various forms of topological signatures: public-key topological signatures, private-key topological signatures, one-to-one topological signatures, one-to-many topological signatures, and many-to-many topological signatures. These topological signatures are entirely different from the "digital signatures" of other encryption systems, making asymmetric topological encryption independent of other encryption systems.

[0007] Asymmetric topology encryption uses matrices to input the "topology structure" and "mathematical codes" into a computer. It requires little space, is computationally fast, and can output very long topology strings (public key and private key topology strings) for encrypting and decrypting electronic documents. Asymmetric topology encryption generates various graph groups and lattices, enabling it to perform overall network encryption and generate an infinite number of "one-time pad" keys.

[0008] The topology coding technique of this invention is not only practical and convenient, but also computationally secure and provably secure. Attached Figure Description

[0009] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0010] Figure 1 It is a unique topological coding diagram T Matching the connection graph with one's own twin, Figure 2 This is a diagram of the general algorithm-I. Detailed Implementation

[0011] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0012] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0013] Table 1 lists the terms and symbols commonly used in this invention:

[0014] This invention designs the following universal algorithm for "one-to-one" asymmetric topological keys - I: Step-I-1: A uses an encoded topology graph. G Adjacency matrix of edge points of 1 A E ( G 1) Export the public key topology signature string S pub and private key topology signature string S priA then uses this encoded topology map. G 1-bit fully encoded topological encoding matrix Export the public key topology string N pub and private key topology number string N pri ; Step-I-2: Person A will use the public key topological signature string S pub and public key topology string N pub Send it to my mobile communication user B; Step-I-3: B uses the public key to topologically analyze the digital string N. pub Encrypted plaintext F Receive ciphertext D 1. Then use the public key topological signature string S pub Encrypted ciphertext D 1. Obtain ciphertext with two layers of protection. D 2; Step 1-4: B puts the ciphertext... D 2. Given to A;

[0015] Step I-5: A uses his private key to topologically sign the string S. pri Decryption text D 2. Adjacent matrix of edge points Topology signature authentication A knows that the ciphertext was sent by B, completes the topological identity authentication, and then A receives the ciphertext. D 1; Step-I-6: A uses the private key to topologically analyze the digital string N. pri Decryption text D 1. After full encoding topological coding matrix Topological number string After authentication, the data authenticity was verified, and Party A finally obtained the plaintext. F .

[0016] A graphical representation of the general algorithm-I is shown in Figure 2 The following is given: A fully encoded topological encoding matrix. Corresponding to a graph set with multiple encoded topological graphs This makes the encoded topological graph homomorphic. G k -G Established. For example, Figure 1 Encoding topology diagram G 1-bit fully encoded topological encoding matrix The corresponding encoding topology graph set G rape T code It contains 5 coding topologies G1, G2, G3, G4, and G5, of which 4 are homomorphic. .

[0017] This invention designs the following general algorithm for "one-to-many" asymmetric topological keys - II: Step II-1: Use the coding topology diagram. G Adjacency matrix of edge points A E ( G Corresponding encoding topology graph set The edge adjacency matrix A in E (G K (A uses an edge-point adjacency matrix). A E ( G Export the private key topology signature string S arpi A uses the edge-point adjacency matrix A E (G K Export the public key topology signature string. ;

[0018] Step II-2: Use the coding topology diagram. G Fully encoded topological encoding matrix Export the public key topology string N pub (K) and private key topology string ; Step II-3: A transfers the public key topological signature string S. pub {K} and the public key topological string N pub (K) Distributed to its own communication user B ; Step II-4: A uses its private key to topologically sign the string S. pri Encrypted plaintext F This yields encrypted text with a single layer of protection. D 1; A then uses his private key to topologically analyze the number string N. pri (K) to encrypt ciphertext D 1. Obtain ciphertext with double protection; Step II-5: A presents the ciphertext D 2( k ) to be sent to B ; Step II-6, B Upon receiving the ciphertext, first use your own public key to topologically sign the string S. pub {K} is used to decrypt the ciphertext. D 2( k Due to the homomorphism of the encoded topology graph. The edge-adjacent matrix is ​​homomorphic. right Certification, B- k Knowing this cipher D 2(k The ) is sent by A to himself (to ensure identity authentication), thus completing the topological identity authentication, B- k Obtain ciphertext with one layer of protection D 1; Step-II-7, B Then use the public key topological number string N pub (K) to decrypt the ciphertext D 1. When the fully encoded topological encoding matrix pass After certification, B- k Obtain plaintext F .

[0019] Note 2: (i) General Algorithm-II forms a “one-to-many asymmetric topological key”.

[0020] (ii) In the general algorithms-I and-II of asymmetric topological encryption, it is possible to achieve "non-public asymmetric topological keys".

[0021] (iii) "One-time key". In equation (1), the edge adjacency matrix A E (G1) 8*8 Can export (64)!=1268869321858841641034333893351614808028655161745 45192198801894375214704230400000000000000(>2 295 ) A topological signature topological number string. Let A be the edge adjacency matrix. E (G) p*p If it is of order p*p, then the adjacency matrix A of the edge points is... E (G) p*p Exportable ( p 2 )! A topological number string. Online reports estimate the number of stars in the universe to be 3.10 22 ~2 74 There are approximately 10 atoms in the solar system. 57 ~2 189 There are 10 atoms. We can say that the adjacency matrix A of edge points... E (G1) 8*8 The number of topological signature strings that can be exported is 10 times the number of atoms in the solar system. 57 (»2 189 ) is much larger.

[0022] (iv) In graph theory, some graph structure problems related to NP-class problems include: cliques, feedback sets, vertex cover problems, graph isomorphism, Hamiltonian path problems, graph coloring, and graph planarity.

[0023] A method for creating asymmetric topological keys based on Chimei topological coding graphs: Self-to-self mirror encoding: Full encoding based on vertex-edge mirroring: (p,q)-graph G Recognizing the elegant code of the odd Then the (p,q)-graph G The recognition of a point-edge mirror full encoding (point-edge inversion substitution full odd elegant encoding) s And satisfy: (3) This invention recognizes the elegant encoding of all odd numbers. (p,q)-graph G Use this as the private key, and then fully encode the mirror image of the acknowledged point edge. s - Picture G Using the public key, we obtain the vertex-edge mirror key matching pair.

[0024] Note that... .

[0025] The Qiyou topological coding graph L1 is an even graph, and its fully coded topological coding matrix is:

[0026] Clearly, the fully encoded topological encoding matrix The private key topological string derived from (see equation (2)) is different from the fully encoded topological encoding matrix T. code (L1,s1) 3*10 (See equation (4) for the public key topology string. However, they can all be authenticated using algorithm (3).

[0027] Homomorphic keys for the Qiyou topological coding graph atlas: Due to the fully encoded topological coding matrix The corresponding set of fully encoded topological graphs G rap (T) code (This satisfies) that each fully encoded topology graph The graph is homomorphic to the fully encoded topology. G That is, H>G In other words, the diagram G Sign the private key, each fully encoded topology graph Signing with public keys, graph homomorphism H>GThis refers to topological authentication of the signing key. For example, Figure 1 The topological coding graph in the graph satisfies graph homomorphism. .

[0028] Now let's create the following W-constraint diagram: The set-ordered odd-beautiful topological coding graph is a point-coincidence operation graph. From the basis H of the set-ordered odd-beautiful topological coding graph... A unique and beautiful topological coding diagram H k , recorded as .set up It is a unique topological coding diagram A permutation of vertices is obtained by using the operation of vertex coincidence of ordered odd numbers in a set, resulting in a vertex coincidence graph with the labels of ordered odd numbers in the set. .gather (5) This is a set-ordered odd-graceful graph vertex-coinciding graphic lattice based on the base H of the set-ordered odd-graceful topologically encoded graph.

[0030] This invention yields the following twin set-ordered odd-graceful graph graphic lattice. (6).

[0031] Edge addition operations on an ordered odd-beautiful topologically encoded graph basis: 1. Algorithm for edge addition operation of ordered odd sets Initialization: Let , Note each code It is an odd number, and has .

[0032] make , Each code It is an even number, and has Create a new code. F as follows: Step 2-1: , , Formula

[0033] Step 2-1: Note and .

[0034] Then there is ,make ,as well as

[0035] Then there is an edge encoding set. .

[0036] because, , Edge missing coding .

[0037] Step 2-2: Note and .

[0038] make ,as well as , Then there is an edge encoding set. .

[0039] because,

[0040] Edge missing coding .

[0041] Step 2-3: Note and .

[0042] make ,as well as

[0043] Then there is Obtain the edge encoding set. .

[0044] because , Edge missing coding .

[0045] Step 2-4: Note and .

[0046] make ,make ,as well as .

[0047] Obtain the edge encoding set .

[0048] because , Edge missing coding

[0049] Step 2-5: Note and . ,make ,as well as .

[0050] Step 3: Add edges By completing the missing edge encodings indicated in the previous steps, a connected dual graph is obtained. T = It acknowledges the ordered and elegant labels of sets. F And there is an edge coding set , where m+1+.

[0051] The above steps yield an ordered, odd, and beautifully labeled set of recognition. F Connected dual graph T = The operation is called the set-ordered odd-graceful edge-adding operation, also known as the W-constraint edge-adding operation.

[0052] The ordered odd-beautiful topological coding graph basis H can generate m A set-ordered odd-odd topological coding graph based on edge addition operation.

[0053] 2. Add edge operations to the ordered odd-beautiful topologically encoded graph. Take from the basis H of the ordered odd-beautiful topologically encoded graph... b k ( Z 0 A unique and beautiful topological coding diagram H K , recorded as .set up It is a unique topological coding diagram A permutation of a set is obtained by adding edges to ordered odd vertices, resulting in an edge-addition graph that recognizes the ordered odd vertices of the set. .gather (9) This is a set-ordered odd-graceful graph edge-adding graphic lattice based on the base H of the set-ordered odd-graceful topologically encoded graph.

[0055] 3. Let It is an ordered odd-beautiful topological coding graph base The twin base, the unique topological encoding graph of each pk vertex. With each rK A uniquely beautiful topologically encoded graph with 10 vertices Construct a vertex coincidence graph The number of vertices in the vertex-coincident graph Gk is The vertex-coincident graph GK has A graph with overlapping edges and vertices, Gk, acknowledges an ordered twin set with a uniquely beautiful encoding. .

[0056] Twin set-ordered odd-graceful graph edge-adding graphic lattice (10) 4. Let It is an ordered odd-beautiful topological coding graph base The mirror base. Similarly, the image set-ordered odd-graceful graph edge-adding graphic lattice. , (11).

[0057] Twin matching join operation based on Chimei topological coding graph: The twin-matching join operation of the Qiyou topological coding graph can construct a variety of topological coding graphs. Figure 1 Give the Qiyou topology coding diagram T An example of a connection that matches its own twin. Similarly, the Chimei topological coding graph. T Connect it with its own twin mirror image to form a new topological coding graph.

[0058] This invention constructs a self-to-self encoding mirroring mechanism and a mirroring or reverse substitution system from one graph (private key) to another graph (public key), defines a novel topological matrix—the pan-topological encoding matrix—suitable for a wider range of application scenarios, and proposes a set of ordered odd-beautiful topological encoding graphs W-operational lattices (including... , By generating more "one-time pad" keys through graph group topological signatures and graph lattice topological signatures, and by using topological coding point coincidence operation and edge addition operation to derive new objects such as point coincidence operation Fibonacci key sequence and edge addition operation Fibonacci key sequence, an asymmetric topological key production system that is both innovative and practical has been formed.

[0059] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the systems disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the descriptions are relatively simple; relevant parts can be referred to the method section.

[0060] The above are merely preferred embodiments of the present invention, and the scope of protection of the present invention is not limited to the above embodiments. All technical solutions falling within the scope of the present invention's concept are within the scope of protection of the present invention. It should be noted that for those skilled in the art, any improvements and modifications made without departing from the principle of the present invention should be considered within the scope of protection of the present invention.

Claims

1. A method for generating an asymmetric topological key based on a chimeric topological coding graph, characterized in that, The specific steps are as follows: S1. Using the adjacency matrix and the fully encoded topological coding matrix of graph theory, input the odd topology graph (graph group) into the computer and derive the topological signature and topological digital string key; S2. It establishes a coded mirror image (public key) from the OddTop graph itself (private key) to itself, and a mirror image or inverse substitution from one OddTop graph (private key) to another OddTop graph (public key). It establishes the OddTop graph group and the set-ordered OddTop graph W-operation lattice, which can generate infinitely many asymmetric OddTop topological coding "one-time pad" encryption subsystems.

2. The method for generating an asymmetric topological key based on a chimeric topological coding graph according to claim 1, characterized in that: Each oddtopic graph (private key) has its own twin matching set (public key set); each oddtopic graph (private key) has its own mirror topology encoding graph (public key).

3. The method for generating an asymmetric topological key based on a chimeric topological coding graph according to claim 1, characterized in that: Topological encoding point coincidence operation and edge addition operation: After the topological encoding point coincidence operation, the result of a set of odd topology graphs with disjoint vertices is an odd topology graph; after the topological encoding edge addition operation, the result of a set of odd topology graphs with disjoint vertices is still an odd topology graph.

4. The method for generating an asymmetric topological key based on a chimeric topological coding graph according to claim 1, characterized in that: The adjacency matrix and the fully encoded topological encoding matrix are used. The odd topological graph and its adjacency matrix are in one-to-one correspondence under matrix similarity operations, so they are used as topological signatures. The fully encoded topological encoding matrix of the odd topological graph corresponds to a set of graphs, each of which is an odd topological graph. Its fully encoded topological encoding matrix is ​​equivalent to the fully encoded topological encoding matrix of the odd topological graph, so it is used to derive the topological number string of the encrypted file. A general topological encoding matrix is ​​defined to be applicable to a wider range of application scenarios.

5. The method for generating an asymmetric topological key based on a chimeric topological coding graph according to claim 1, characterized in that: The Qitop graph group is a set of graphs based on finite modulo Abelian additive operations. Any two Qitop graphs are isomorphic and are mainly used for overall encryption of local area networks. The Qitop graph group derives its twin matching graph group and mirror topology-coded graph group. The Qituo graph group derives a fully encoded topological encoding matrix group, which in turn derives a topological number string group.

6. The method for generating an asymmetric topological key based on a chimeric topological coding graph according to claim 1, characterized in that: W-operation lattices of set-ordered odd topology graphs, where W-operations are vertex coincidence operations and edge addition operations; based on set-ordered odd topology graphs... , mirror base , twin base of The operation grid is , and Each graph in the W-operation lattice is a set of ordered odd topology graphs, resulting in infinitely many lattice topological signatures and infinitely many "one-time pad" keys, which are in turn infinitely many asymmetric odd topology coding encryption subsystems.

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