Same-origin signature methods, apparatus, devices, and media

Abstract

This invention provides a signature method, apparatus, device, and medium based on homogeneity, applicable to the field of computer technology. The method includes: for the private key to be processed, solving for the discrete logarithm associated with a first eccentricity point to obtain first homogeneous data, the first homogeneous data representing the mapping from an initial elliptic curve to an intermediate elliptic curve; performing embedding projection processing on the homogeneous data between two-dimensional Abelian clusters to obtain private key homogeneous data to determine the private key, the private key homogeneous data representing the mapping from the initial elliptic curve to a public key elliptic curve; solving for the discrete logarithm of the torsion group of a first smooth number associated with the public key elliptic curve to obtain third and fourth homogeneous data; signing the private key based on auxiliary homogeneous data generated from the third and fourth homogeneous data to obtain a target private key, and sending the target private key to a target terminal to perform information encryption operations on the target information.

Description

Technical Field

[0001] This invention relates to the field of computer technology, and more specifically to a signature method, apparatus, device, and medium based on same-origin signatures. Background Technology

[0002] Isogeny-based signatures are a cryptographic technique based on elliptic curve homology mappings, primarily used to construct digital signature schemes resistant to quantum attacks.

[0003] In related technologies, two-dimensional homologous computation is used to generate auxiliary homologous data to complete the signing of the private key. However, this method suffers from low computational efficiency when performing high-dimensional calculations, making it difficult to achieve efficient digital signatures. This results in poor real-time performance and stability of signature generation, compromising signature security. Furthermore, it leads to excessive resource consumption, reducing system processing efficiency and making it difficult to handle more complex signature data. Summary of the Invention

[0004] In view of the above problems, the present invention provides signature methods, apparatus, devices, media and program products based on same origin.

[0005] According to a first aspect of the present invention, a signature method based on homology is provided, comprising: for a private key to be processed, solving for the discrete logarithm associated with a first tortuosity point to obtain first homology data, wherein the first homology data represents the mapping from an initial elliptic curve to an intermediate elliptic curve, and the first tortuosity point is the tortuosity point of the initial elliptic curve on a first smooth number; performing embedding projection processing on the two-dimensional Abelian cluster homology data to obtain private key homology data to determine the private key, wherein the two-dimensional Abelian cluster homology is generated based on the first homology data, and the private key homology data represents the mapping from the initial elliptic curve to a public key elliptic curve; solving for the discrete logarithm of the tortuosity group of the first smooth number associated with the public key elliptic curve to obtain third homology data and fourth homology data, wherein the third homology data represents the mapping from the public key elliptic curve to a first transition elliptic curve, and the fourth homology data represents the mapping from the public key elliptic curve to a second transition elliptic curve; signing the private key according to auxiliary homology data generated from the third homology data and the fourth homology data to obtain a target private key, and sending the target private key to a target terminal to perform an information encryption operation on the target information.

[0006] According to an embodiment of the present invention, solving the discrete logarithm associated with the first torsion point to obtain first homologous data includes: decomposing a first smooth number in a first automorphism degree to determine a second automorphism degree, wherein the first automorphism degree is determined by the first smooth number and the second smooth number, and the first smooth number and the second smooth number are coprime; solving the discrete logarithm associated with the torsion point of the first elliptic curve on the first smooth number to obtain a first homologous kernel; and determining the mapping from the first elliptic curve to the second elliptic curve based on the second automorphism degree and the first homologous kernel to obtain the first homologous data.

[0007] According to an embodiment of the present invention, embedding projection processing is performed on two-dimensional Abelian inter-cluster homogeneous data to obtain private key homogeneous data, including: determining a first set of basis points on the tortuosity of the initial elliptic curve at the second smooth number; determining a first action data of the first set of basis points on the first homogeneous data; processing the first action data based on the double addition algorithm to generate two-dimensional Abelian inter-cluster homogeneous data; and performing embedding projection processing on the two-dimensional Abelian inter-cluster homogeneous data to obtain private key homogeneous data.

[0008] According to an embodiment of the present invention, solving for the discrete logarithm of the torsion group of a first smooth number associated with a public-key elliptic curve to obtain third and fourth homologous data includes: determining the degree of a third automorphism, wherein the degree of the third automorphism is determined by the first smooth number, the second smooth number, and the degree of the fourth automorphism associated with the response elliptic curve; determining a second basis set of the public-key elliptic curve at the torsion points of the first smooth number; solving for the discrete logarithm of the dual of the third automorphism in the second basis set to obtain the kernel of the third homologous data and the kernel of the fourth homologous data, wherein the dual of the third automorphism is associated with the public-key elliptic curve; and generating the third homologous data and the fourth homologous data respectively based on the kernel of the third homologous data and the kernel of the fourth homologous data.

[0009] According to an embodiment of the present invention, signing a private key based on auxiliary homogeneous data generated from third homogeneous data and fourth homogeneous data includes: determining a fifth homogeneous source based on the third and fourth homogeneous sources, wherein the fifth homogeneous source represents the homogeneous mapping from a first transitional elliptic curve to a second transitional elliptic curve; determining a third basis for the first transitional elliptic curve at the torsion point of a second smooth number; determining third action data of the third basis on the first transitional elliptic curve; processing the third action data based on a double addition algorithm to generate auxiliary two-dimensional Abelian cluster homogeneous data; performing embedding projection processing on the auxiliary two-dimensional Abelian cluster homogeneous data to obtain auxiliary homogeneous data; and signing the private key based on the auxiliary homogeneous data.

[0010] According to an embodiment of the present invention, the method further includes: selecting a third smoothing number less than the second smoothing number; determining a fourth set of bases for the initial elliptic curve at the deflection point of the third smoothing number; determining fourth action data of the fourth set of bases on the initial elliptic curve; and processing the fourth action data based on the double addition algorithm to generate committed homologous data, wherein the committed homologous data characterizes the mapping from the initial elliptic curve to the committed elliptic curve.

[0011] According to an embodiment of the present invention, the method further includes: selecting a number less than a first smoothness number as a target multiple value; determining a fifth basis of the committed elliptic curve at the deflection point of the first smoothness number; determining a fifth action data of the fifth basis on the committed elliptic curve; and processing the fifth action data and the target multiple value based on a double addition algorithm to generate response homogeneous data.

[0012] A second aspect of the present invention provides a signature apparatus based on homology, comprising: a first obtaining module, configured to solve for a discrete logarithm associated with a first tortuosity point for a private key to be processed, thereby obtaining first homology data, wherein the first homology data represents a mapping from an initial elliptic curve to an intermediate elliptic curve, and wherein the first tortuosity point is a tortuosity point of the initial elliptic curve on a first smoothness number; and a second obtaining module, configured to perform embedding projection processing on the two-dimensional Abelian cluster homology data to obtain private key homology data to determine the private key, wherein the two-dimensional Abelian cluster homology is generated based on the first homology data, and the private key homology data represents... The system includes: an initial elliptic curve mapping to a public-key elliptic curve; a third module for solving the discrete logarithm of the torsion group of the first smooth number associated with the public-key elliptic curve, obtaining third and fourth homologous data, wherein the third homologous data represents the mapping from the public-key elliptic curve to the first transitional elliptic curve, and the fourth homologous data represents the mapping from the public-key elliptic curve to the second transitional elliptic curve; and a signature module for signing the private key based on auxiliary homologous data generated from the third and fourth homologous data, obtaining the target private key, and sending the target private key to the target terminal to perform information encryption operations on the target information.

[0013] A third aspect of the present invention provides an electronic device comprising: one or more processors; and a memory for storing one or more computer programs, wherein the one or more processors execute the one or more computer programs to implement the steps of the method described above.

[0014] A fourth aspect of the present invention also provides a computer-readable storage medium having a computer program or instructions stored thereon, wherein the computer program or instructions, when executed by a processor, implement the steps of the above-described method.

[0015] A fifth aspect of the present invention also provides a computer program product, including a computer program or instructions that, when executed by a processor, implement the steps of the above-described method.

[0016] According to an embodiment of the present invention, for the private key to be processed, the discrete logarithm associated with the first torsion point is solved to obtain first homologous data, which represents the mapping from the initial elliptic curve to the intermediate elliptic curve, wherein the first torsion point is the torsion point of the initial elliptic curve on the first smooth number; the two-dimensional Abelian cluster homologous data is subjected to embedding projection processing to obtain private key homologous data to determine the private key, wherein the two-dimensional Abelian cluster homologous data is generated based on the first homologous data, and the private key homologous data represents the mapping from the initial elliptic curve to the public key elliptic curve; the discrete logarithm of the torsion group of the first smooth number associated with the public key elliptic curve is solved to obtain third homologous data and fourth homologous data, wherein the third homologous data represents the mapping from the public key elliptic curve to the first transition elliptic curve, and the fourth homologous data represents the mapping from the public key elliptic curve to the second transition elliptic curve; the private key is signed according to the auxiliary homologous data generated by the third homologous data and the fourth homologous data to obtain the target private key, and the target private key is sent to the target terminal to perform information encryption operation on the target information. By using the deflection points of the first elliptic curve on the first smooth number to generate the first homogeneous data, the high resource consumption problem caused by high-dimensional data in related technologies is avoided, enabling rapid generation of the private key and ensuring the real-time performance and stability of the signature. Furthermore, the private key is signed based on auxiliary homogeneous data generated from the third and fourth homogeneous data, avoiding direct computation of the auxiliary homogeneous data, further improving the system's data processing efficiency, reducing system resource consumption, and lowering the system load. Attached Figure Description

[0017] The above-described features, other objects, and advantages of the present invention will become clearer from the following description of embodiments of the invention with reference to the accompanying drawings, in which:

[0018] Figure 1 The diagram illustrates application scenarios of a signature method, apparatus, device, medium, and program product based on the same source according to embodiments of the present invention.

[0019] Figure 2 A flowchart of a same-origin-based signature method according to an embodiment of the present invention is shown.

[0020] Figure 3 A schematic diagram of private key generation according to an embodiment of the present invention is shown.

[0021] Figure 4 A schematic diagram of assisted homology generation according to an embodiment of the present invention is shown.

[0022] Figure 5 A comparison chart of the calculated quantities according to an embodiment of the present invention is shown.

[0023] Figure 6A comparison chart of computational efficiency according to an embodiment of the present invention is shown.

[0024] Figure 7 A structural block diagram of a signature device based on same origin according to an embodiment of the present invention is shown.

[0025] Figure 8 A block diagram of an electronic device suitable for implementing a same-origin signature method according to an embodiment of the present invention is shown. Detailed Implementation

[0026] Hereinafter, embodiments of the present invention will be described with reference to the accompanying drawings. However, it should be understood that these descriptions are exemplary only and are not intended to limit the scope of the invention. In the following detailed description, numerous specific details are set forth to provide a thorough understanding of the embodiments of the invention for ease of explanation. However, it will be apparent that one or more embodiments may be practiced without these specific details. Furthermore, descriptions of well-known structures and techniques are omitted in the following description to avoid unnecessarily obscuring the concept of the invention.

[0027] The terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the invention. The terms “comprising,” “including,” etc., as used herein indicate the presence of the stated features, steps, operations, and / or components, but do not exclude the presence or addition of one or more other features, steps, operations, or components.

[0028] All terms used herein (including technical and scientific terms) have the meanings commonly understood by those skilled in the art, unless otherwise defined. It should be noted that the terms used herein are to be interpreted in a manner consistent with the context of this specification, and not in an idealized or overly rigid way.

[0029] When using expressions such as "at least one of A, B and C", they should generally be interpreted in accordance with the meaning that is commonly understood by those skilled in the art (e.g., "a system having at least one of A, B and C" should include, but is not limited to, a system having A alone, a system having B alone, a system having C alone, a system having A and B, a system having A and C, a system having B and C, and / or a system having A, B and C, etc.).

[0030] An embodiment of the present invention provides a signature method based on homology, comprising: for a private key to be processed, solving the discrete logarithm associated with a first torsion point to obtain first homology data, wherein the first homology data represents the mapping from an initial elliptic curve to an intermediate elliptic curve; performing embedding projection processing on the homology data between two-dimensional Abelian clusters to obtain private key homology data to determine the private key, wherein the private key homology data represents the mapping from the initial elliptic curve to a public key elliptic curve; solving the discrete logarithm of the torsion group of a first smooth number associated with the public key elliptic curve to obtain third homology data and fourth homology data; signing the private key based on auxiliary homology data generated from the third homology data and fourth homology data to obtain a target private key, and sending the target private key to a target terminal to perform information encryption operation on the target information.

[0031] Figure 1 The diagram illustrates application scenarios of a signature method, apparatus, device, medium, and program product based on the same source according to embodiments of the present invention.

[0032] like Figure 1 As shown, application scenario 100 according to this embodiment may include a first terminal device 101, a second terminal device 102, a third terminal device 103, a network 104, and a server 105. The network 104 serves as a medium for providing a communication link between the first terminal device 101, the second terminal device 102, the third terminal device 103, and the server 105. The network 104 may include various connection types, such as wired or wireless communication links, or fiber optic cables, etc.

[0033] Users can use the first terminal device 101, the second terminal device 102, and the third terminal device 103 to interact with the server 105 via the network 104 to receive or send messages, etc. Various communication client applications can be installed on the first terminal device 101, the second terminal device 102, and the third terminal device 103, such as shopping applications, web browser applications, search applications, instant messaging tools, email clients, social media platform software, etc. (for example only).

[0034] The first terminal device 101, the second terminal device 102, and the third terminal device 103 can be various electronic devices with displays and support web browsing, including but not limited to smartphones, tablets, laptops, and desktop computers.

[0035] Server 105 can be a server that provides various services, such as a backend management server that supports websites browsed by users using the first terminal device 101, the second terminal device 102, and the third terminal device 103 (this is just an example). The backend management server can analyze and process data such as received user requests, and feed back the processing results (such as web pages, information, or data obtained or generated according to user requests) to the terminal devices.

[0036] It should be noted that the same-origin signature method provided in the embodiments of the present invention can generally be executed by server 105. Correspondingly, the same-origin signature device provided in the embodiments of the present invention can generally be located in server 105. The same-origin signature method provided in the embodiments of the present invention can also be executed by a server or server cluster that is different from server 105 and capable of communicating with the first terminal device 101, the second terminal device 102, the third terminal device 103, and / or server 105. Correspondingly, the same-origin signature device provided in the embodiments of the present invention can also be located in a server or server cluster that is different from server 105 and capable of communicating with the first terminal device 101, the second terminal device 102, the third terminal device 103, and / or server 105.

[0037] It should be understood that Figure 1 The number of terminal devices, networks, and servers in the system is only a limited number. Depending on implementation needs, there can be any number of terminal devices, networks, and servers.

[0038] The following will be based on Figure 1 The described scene, through Figures 2-6 The same-origin signature method of the present invention embodiments is described in detail.

[0039] Figure 2 A flowchart of a same-origin-based signature method according to an embodiment of the present invention is shown.

[0040] like Figure 2 As shown, the same-origin signature method in this embodiment includes operations S210 to S240.

[0041] In operation S210, for the private key to be processed, the discrete logarithm associated with the first torsion point is solved to obtain the first homologous data. The first homologous data represents the mapping from the initial elliptic curve to the intermediate elliptic curve, where the first torsion point is the torsion point of the initial elliptic curve on the first smooth number.

[0042] According to an embodiment of the present invention, for the private key to be processed, during the private key generation process, an initial elliptic curve is first determined. Supersingular elliptic curves (ECCs) utilize the mathematical properties of elliptic curves to perform operations such as encryption, signatures, and key exchange.

[0043] According to an embodiment of the present invention, when performing a mapping operation on an initial elliptic curve, it is necessary to determine prime numbers to assist the mapping operation, such as determining the degree of homologous mappings. In the present invention, a prime number of the form [missing information] is selected. prime numbers ,in As the first smooth number As the second smooth number, the first and second smooth numbers are coprime, and c is a constant.

[0044] According to an embodiment of the present invention, during the mapping operation on the initial elliptic curve, the first deflection point is the point on the initial elliptic curve at the first smoothing number. A class of points with special properties, for example, the first torsion point P, satisfying... , where O is the point at infinity of the initial elliptic curve.

[0045] According to an embodiment of the present invention, solving for the discrete logarithm associated with the first torsion point can be done by solving for any number of first torsion points, specifically the integer multiple by which one first torsion point maps to another, in order to determine the first homogeneous data based on the solution results. Thus, the initial elliptic curve is completed. to the middle elliptic curve The mapping.

[0046] According to an embodiment of the present invention, the intermediate elliptic curve is an elliptic curve generated by performing a mapping operation on the initial elliptic curve, and is used together with the initial elliptic curve to generate a private key.

[0047] In operation S220, the two-dimensional Abelian cluster homogeneous data is embedded and projected to obtain private key homogeneous data to determine the private key. The two-dimensional Abelian cluster homogeneity is generated based on the first homogeneous data, and the private key homogeneous data represents the mapping from the initial elliptic curve to the public key elliptic curve.

[0048] According to an embodiment of the present invention, two-dimensional Abelian cluster homogeneous data It can be from Starting from the initial elliptic curve and the intermediate elliptic curve Each subgroup constructs its own quotient homologous data, and then uses this constructed quotient homologous data to build a two-dimensional Abelian inter-cluster homologous data. .

[0049] According to an embodiment of the present invention, embedding projection processing is performed on two-dimensional Abelian cluster homogeneous data to obtain private key homogeneous data. , It's the private key. It is a public-key elliptic curve, in which, It is less than prime numbers, satisfy .

[0050] In operation S230, the discrete logarithm of the torsion group of the first smooth number associated with the public key elliptic curve is solved to obtain the third and fourth homologous data, wherein the third homologous data represents the mapping from the public key elliptic curve to the first transitional elliptic curve, and the fourth homologous data represents the mapping from the public key elliptic curve to the second transitional elliptic curve.

[0051] According to an embodiment of the present invention, the dual of the torsion group of the first smooth number associated with the public-key elliptic curve is solved, and the discrete logarithm is further solved based on the obtained dual, thereby generating two homologous data and a third homologous data. Fourth source data ,in, It is the first transition elliptic curve. It is the second transition elliptic curve.

[0052] In operation S240, the private key is signed based on the auxiliary source data generated from the third and fourth source data to obtain the target private key, and the target private key is sent to the target terminal to perform information encryption operation on the target information.

[0053] According to embodiments of the present invention, auxiliary homogeneous data can be generated based on the two-dimensional Abelian cluster homogeneity between the third and fourth homogeneous data. .

[0054] According to an embodiment of the present invention, the private key is signed based on auxiliary same-source data, and the signature is as follows: ,in, Representing an ideal, It is a set of bases generated during the process of generating auxiliary homologous data. To ensure consistent data source, In response to data from the same source.

[0055] According to an embodiment of the present invention, the target information includes at least one of transaction information, image information, and audio information.

[0056] According to an embodiment of the present invention, for the private key to be processed, the discrete logarithm associated with the first torsion point is solved to obtain first homologous data, which represents the mapping from the initial elliptic curve to the intermediate elliptic curve, wherein the first torsion point is the torsion point of the initial elliptic curve on the first smooth number; the two-dimensional Abelian cluster homologous data is subjected to embedding projection processing to obtain private key homologous data to determine the private key, wherein the two-dimensional Abelian cluster homologous data is generated based on the first homologous data, and the private key homologous data represents the mapping from the initial elliptic curve to the public key elliptic curve; the discrete logarithm of the torsion group of the first smooth number associated with the public key elliptic curve is solved to obtain third homologous data and fourth homologous data, wherein the third homologous data represents the mapping from the public key elliptic curve to the first transition elliptic curve, and the fourth homologous data represents the mapping from the public key elliptic curve to the second transition elliptic curve; the private key is signed according to the auxiliary homologous data generated by the third homologous data and the fourth homologous data to obtain the target private key, and the target private key is sent to the target terminal to perform information encryption operation on the target information. By using the deflection point of the initial elliptic curve on the first smooth number to generate the first homogeneous data, the high resource consumption problem caused by high-dimensional data in related technologies is avoided, and the private key is generated quickly. In addition, the private key is signed based on the auxiliary homogeneous data generated by the third and fourth homogeneous data, avoiding the direct calculation of the auxiliary homogeneous data, which further improves the data processing efficiency of the system, reduces the system's resource consumption, and reduces the system's load.

[0057] According to an embodiment of the present invention, solving the discrete logarithm associated with the first torsion point to obtain first homologous data includes: decomposing a first smooth number in a first automorphism degree to determine a second automorphism degree, wherein the first automorphism degree is determined by the first smooth number and the second smooth number, and the first smooth number and the second smooth number are coprime; solving the discrete logarithm associated with the torsion point of the first elliptic curve on the first smooth number to obtain a first homologous kernel; and determining the mapping from the first elliptic curve to the second elliptic curve based on the second automorphism degree and the first homologous kernel to obtain the first homologous data.

[0058] According to an embodiment of the present invention, for an elliptic curve defined on a finite field, its automorphic ring is the set of all homomorphic mappings from the elliptic curve to itself, which form a ring under an additive group structure, wherein the degree of the automorphism usually refers to the degree of a particular automorphism in the automorphic ring.

[0059] According to an embodiment of the present invention, the first self-homo degree can be expressed as: .

[0060] According to an embodiment of the present invention, utilizing exist The data on the action at the deflection point and the discrete logarithm were obtained by solving. The number of times is Homologous kernels, i.e., the first homologous kernel, are then used to calculate the homology of this part based on the first homologous kernel, and then backtrack to obtain the kernel from the first homologous kernel. Departure, number of times First source data Determine the mapping from the initial elliptic curve to the intermediate elliptic curve.

[0061] in, For the first automorphism of the initial elliptic curve, the action data can be a characterization How to The matrix data mapping the torsion point on the first smoothness number to other points in the matrix. This represents the second automorphism order.

[0062] According to embodiments of the present invention, by calculating the first source data based on the first smoothness number, the computational complexity can be reduced, the processing efficiency of the system in the process of calculating the first source data can be improved, and the burden on the system can be reduced. At the same time, due to the improved computational efficiency of the first source data, the signature generation process is faster and more stable, and the obtained signature is secure.

[0063] According to an embodiment of the present invention, embedding projection processing is performed on two-dimensional Abelian inter-cluster homogeneous data to obtain private key homogeneous data, including: determining a first set of basis points on the tortuosity of the initial elliptic curve at the second smooth number; determining a first action data of the first set of basis points on the first homogeneous data; processing the first action data based on the double addition algorithm to generate two-dimensional Abelian inter-cluster homogeneous data; and performing embedding projection processing on the two-dimensional Abelian inter-cluster homogeneous data to obtain private key homogeneous data.

[0064] According to an embodiment of the present invention, a first set of bases for the initial elliptic curve at the deflection point of the second smoothness number is determined, and a first action data of the first set of bases on the first source data is determined to obtain its position on the first source data. A set of bases The first action data on, among which, On The set of torsion points can all be represented as The first role of data representation is how to... Mapped to The matrix data of other points on the graph.

[0065] Figure 3 A schematic diagram of private key generation according to an embodiment of the present invention is shown.

[0066] like Figure 3 As shown, by calculating the homogeneous data among two-dimensional Abelian clusters Then, private key source data is obtained through embedding and projection. .

[0067] According to an embodiment of the present invention, the first action data is processed based on a double addition algorithm, from... Departure from The generated kernel generates corresponding two-dimensional Abelian inter-cluster homogeneous data. .

[0068] According to an embodiment of the present invention, embedding projection processing is performed on two-dimensional Abelian cluster homogeneous data to obtain private key homogeneous data. .

[0069] According to embodiments of the present invention, in the private key generation process, the present invention only needs to utilize... The calculation of two-dimensional homology and one-dimensional homology is performed, compared to the calculation in related technologies. The two-dimensional homology improves efficiency, enabling faster private key generation and thus faster signing, thus enhancing the real-time performance and security of signatures.

[0070] According to an embodiment of the present invention, solving for the discrete logarithm of the torsion group of a first smooth number associated with a public-key elliptic curve to obtain third and fourth homologous data includes: determining the degree of a third automorphism, wherein the degree of the third automorphism is determined by the first smooth number, the second smooth number, and the degree of the fourth automorphism associated with the response elliptic curve; determining a second basis set of the public-key elliptic curve at the torsion points of the first smooth number; solving for the discrete logarithm of the dual of the third automorphism in the second basis set to obtain the kernel of the third homologous data and the kernel of the fourth homologous data, wherein the dual of the third automorphism is associated with the public-key elliptic curve; and generating the third homologous data and the fourth homologous data respectively based on the kernel of the third homologous data and the kernel of the fourth homologous data.

[0071] According to an embodiment of the present invention, the third self-homogeneous state The third automorphism order can be expressed as ,in It is the fourth automorphism degree of the homomorphic data corresponding to the response elliptic curve.

[0072] According to an embodiment of the present invention, by calculation and The duality in A set of bases Using the image below to solve the discrete logarithm, we obtain two common source data points and a third common source data point. Fourth source data The kernels, namely the kernels of the third and fourth homologous data, can be used to calculate the kernels of the third and fourth homologous data to obtain the third and fourth homologous data.

[0073] According to an embodiment of the present invention, the determination of the third and fourth automorphism times is performed using the first and second smoothing numbers, thereby reducing computational complexity, improving system processing efficiency, reducing system resource consumption, and ensuring stability in the signature generation process.

[0074] According to an embodiment of the present invention, signing a private key based on auxiliary homogeneous data generated from third homogeneous data and fourth homogeneous data includes: determining a fifth homogeneous source based on the third and fourth homogeneous sources, wherein the fifth homogeneous source represents the homogeneous mapping from a first transitional elliptic curve to a second transitional elliptic curve; determining a third basis for the first transitional elliptic curve at the torsion point of a second smooth number; determining third action data of the third basis on the first transitional elliptic curve; processing the third action data based on a double addition algorithm to generate auxiliary two-dimensional Abelian cluster homogeneous data; performing embedding projection processing on the auxiliary two-dimensional Abelian cluster homogeneous data to obtain auxiliary homogeneous data; and signing the private key based on the auxiliary homogeneous data.

[0075] According to an embodiment of the present invention, a fifth source data is determined based on the third and fourth source data, namely... .

[0076] According to an embodiment of the present invention, it is further possible to obtain from arrive The number of times is homology and in The third group of bases The third function data above, calculated by The generated kernels are used to generate the corresponding auxiliary two-dimensional Abelian clusters for homology. .

[0077] Figure 4 A schematic diagram of assisted homology generation according to an embodiment of the present invention is shown.

[0078] According to an embodiment of the present invention, embedding projection processing is performed on auxiliary two-dimensional Abelian cluster homogeneous data to obtain homogeneous data. Furthermore, such as Figure 4 As shown, through The parallelogram relationship between them can be calculated from The number of departures is q's auxiliary homogeneous data. .

[0079] According to an embodiment of the present invention, auxiliary homogeneous data is obtained by calculating push-out and pull-back. Instead of calculating directly This can improve the efficiency of obtaining auxiliary source data, thereby reducing the system burden, improving the system's processing efficiency, and making signature generation real-time and stable.

[0080] According to an embodiment of the present invention, the method further includes: selecting a third smoothing number less than the second smoothing number; determining a fourth set of bases for the initial elliptic curve at the deflection point of the third smoothing number; determining fourth action data of the fourth set of bases on the initial elliptic curve; and processing the fourth action data based on the double addition algorithm to generate committed homologous data, wherein the committed homologous data characterizes the mapping from the initial elliptic curve to the committed elliptic curve.

[0081] According to an embodiment of the present invention, a random number less than The number N is used as the third smooth number.

[0082] According to an embodiment of the present invention, the set of torsion points on the initial elliptic curve, i.e., the fourth basis, is determined based on the third smoothness number N, and the fourth action data of the fourth basis on the initial elliptic curve is determined. Based on the double addition algorithm, the fourth action data and the associated discrete logarithm are calculated and solved to obtain the committed homogeneous data. , For commitment elliptic curves.

[0083] According to an embodiment of the present invention, the method further includes: selecting a number less than a first smoothness number as a target multiple value; determining a fifth basis of the committed elliptic curve at the deflection point of the first smoothness number; determining a fifth action data of the fifth basis on the committed elliptic curve; and processing the fifth action data and the target multiple value based on a double addition algorithm to generate response homogeneous data.

[0084] According to an embodiment of the present invention, a value between 0 and... The number x between these two values ​​is used as the target multiple value.

[0085] According to an embodiment of the present invention, for The fifth group of bases their choice The generated subgroup is used as the kernel to compute a response from homogeneous data. , In response to elliptic curves.

[0086] According to an embodiment of the present invention, a comparison is made with SQIsign2D-East of the related technology to obtain the acceleration ratio.

[0087] Specifically, this invention modifies the private key generation part of the original SQIsign2D-East signature, changing it to find a key that has been used a certain number of times. self-homogeneous Then calculate the self-homogeneous middle By reverting back from some of the same source data, we can obtain a result from... The number of departures is Same source data .

[0088] By calculating the homology data among two-dimensional Abel clusters Then, private key source data is obtained through embedding and projection. .

[0089] Furthermore, the calculation part of the auxiliary homomorphic data was modified to calculate the self-homogeneous data. The number of times is ,in This represents the number of responses to data from the same source. This is calculated... and The duality in A set of bases The image below shows two data points from the same source. , .

[0090] Thus, from arrive The number of times is Same source data At this point, by calculating the homogeneous data between two-dimensional Abelian clusters... Then, homogeneous data is obtained through embedding and projection. This leads to the acquisition of auxiliary homologous data. .

[0091] According to embodiments of the present invention, by adding a one-dimensional homology component to the self-homogeneous form, the number of times and the number of high-dimensional homology operations need to be calculated are reduced, thereby improving signature efficiency. During private key generation, the present invention only needs to calculate one... Two-dimensional homology and one-dimensional homology, compared with the calculation in SQIsign2D-East The two-dimensional homology calculation is twice as efficient. During the signature process, this invention only requires calculating one auxiliary homology. Two-dimensional homology and two one-dimensional homology, compared to the calculation of one in SQIsign2D-East. Two-dimensional homology and a The efficiency of two-dimensional homology calculations is more than doubled. During the verification process, efficiency is improved by reducing one-dimensional homology calculations in the actual code. Furthermore, this increased efficiency enables faster signing, enhancing both the security and real-time performance of the signature.

[0092] Figure 5A comparison chart of the calculated quantities according to an embodiment of the present invention is shown; Figure 6 A comparison chart of computational efficiency according to an embodiment of the present invention is shown.

[0093] like Figure 5 As shown, this illustrates the number of homologous signatures of different types that need to be calculated in different signature methods. It can be seen that the present invention requires relatively fewer calculations compared to related technologies such as SQIsign2D-East, SQIsign2D-West, and PRISM-sig. Furthermore, as... Figure 6 As shown, the computational efficiency in different signature scenarios (e.g., NIST-I, NIST-III, NIST-V) is illustrated. The last column represents the acceleration percentage. It can be seen that, compared to related technologies, this invention accelerates private key generation and signing by approximately 100%, while verification also shows a slight acceleration. Furthermore, this invention also achieved good results in the Julia test.

[0094] Based on the above-described same-origin signature method, this invention also provides a same-origin signature apparatus. The following will be combined with... Figure 7 The device is described in detail.

[0095] Figure 7 A structural block diagram of a signature device based on same origin according to an embodiment of the present invention is shown.

[0096] like Figure 7 As shown, the signature-based device 900 of this embodiment includes a first obtaining module 910, a second obtaining module 920, a third obtaining module 930, and a signature module 940.

[0097] The first obtaining module 910 is used to solve the discrete logarithm associated with the first torsion point for the private key to be processed, and obtain the first homogeneous data. The first homogeneous data represents the mapping from the initial elliptic curve to the intermediate elliptic curve, wherein the first torsion point is the torsion point of the initial elliptic curve on the first smoothness number. In one embodiment, the first obtaining module 910 can be used to perform the operation S210 described above, which will not be repeated here.

[0098] The second obtaining module 920 is used to perform embedding projection processing on the two-dimensional Abelian cluster homogeneous data to obtain private key homogeneous data, thereby determining the private key. The two-dimensional Abelian cluster homogeneity is generated based on the first homogeneous data, and the private key homogeneous data represents the mapping from the initial elliptic curve to the public key elliptic curve. In one embodiment, the second obtaining module 920 can be used to perform the operation S220 described above, which will not be repeated here.

[0099] The third obtaining module 930 is used to solve for the discrete logarithm of the torsion group of the first smooth number associated with the public-key elliptic curve, obtaining third and fourth homologous data. The third homologous data represents the mapping from the public-key elliptic curve to the first transitional elliptic curve, and the fourth homologous data represents the mapping from the public-key elliptic curve to the second transitional elliptic curve. In one embodiment, the third obtaining module 930 can be used to perform the operation S230 described above, which will not be repeated here.

[0100] The signature module 940 is used to sign the private key based on auxiliary same-source data generated from the third and fourth same-source data to obtain the target private key, and then send the target private key to the target terminal to perform information encryption operations on the target information. In one embodiment, the signature module 940 can be used to perform the operation S240 described above, which will not be repeated here.

[0101] According to an embodiment of the present invention, for the private key to be processed, the discrete logarithm associated with the first torsion point is solved to obtain first homologous data. The first homologous data represents the mapping from the first elliptic curve to the second elliptic curve, wherein the first torsion point is the torsion point of the first elliptic curve on the first smooth number. Embedding projection processing is performed on the two-dimensional Abelian cluster homologous data to obtain private key homologous data, thereby determining the private key. The discrete logarithm of the torsion group of the first smooth number associated with the public key elliptic curve is solved to obtain third and fourth homologous data. Based on the auxiliary homologous data generated from the third and fourth homologous data, the private key is signed to obtain the target private key, and the target private key is sent to the target terminal to perform information encryption operations on the target information. Since the first homologous data is generated by using the torsion point of the first elliptic curve on the first smooth number, the high resource consumption problem caused by high-dimensional data in related technologies is avoided, achieving rapid private key generation. Furthermore, signing the private key based on the auxiliary homologous data generated from the third and fourth homologous data avoids directly calculating the auxiliary homologous data, further improving the system's data processing efficiency.

[0102] According to embodiments of the present invention, any plurality of modules among the first obtaining module 910, the second obtaining module 920, the third obtaining module 930, and the signature module 940 may be combined into one module, or any one of these modules may be split into multiple modules. Alternatively, at least part of the functionality of one or more of these modules may be combined with at least part of the functionality of other modules and implemented in one module. According to embodiments of the present invention, at least one of the first obtaining module 910, the second obtaining module 920, the third obtaining module 930, and the signature module 940 may be at least partially implemented as hardware circuitry, such as a field-programmable gate array (FPGA), a programmable logic array (PLA), a system-on-a-chip, a system-on-a-substrate, a system-on-package, an application-specific integrated circuit (ASIC), or any other reasonable means of integrating or packaging the circuitry, or implemented in software, hardware, or firmware, or in any one of the three implementation methods, or in a suitable combination of any of them. Alternatively, at least one of the first obtaining module 910, the second obtaining module 920, the third obtaining module 930, and the signature module 940 may be implemented at least partially as a computer program module, which can perform corresponding functions when the computer program module is run.

[0103] According to an embodiment of the present invention, the first obtaining module 910 includes a first determining submodule, a first obtaining submodule, and a second determining submodule.

[0104] The first determining submodule is used to decompose the first smooth number in the first automorphism order and determine the second automorphism order, wherein the first automorphism order is determined by the first smooth number and the second smooth number, and the first smooth number and the second smooth number are coprime.

[0105] The first submodule is used to solve the discrete logarithm associated with the torsion point of the initial elliptic curve on the first smooth number, and to obtain the first homologous kernel.

[0106] The second determining submodule is used to determine the mapping from the initial elliptic curve to the intermediate elliptic curve based on the second automorphism degree and the first homologous kernel, so as to obtain the first homologous data.

[0107] According to an embodiment of the present invention, the second obtaining module 920 includes a third determining submodule, a fourth determining submodule, a first processing submodule, and a second processing submodule.

[0108] The third determination submodule is used to determine the first set of bases for the initial elliptic curve at the torsion point of the second smooth number.

[0109] The fourth determination submodule is used to determine the first action data of the first set of bases on the first source data.

[0110] The first processing submodule is used to process the first action data based on the double addition algorithm to generate two-dimensional Abelian cluster homogeneous data.

[0111] The second processing submodule is used to perform embedding projection processing on the two-dimensional Abel cluster homogeneous data to obtain private key homogeneous data.

[0112] According to an embodiment of the present invention, the third obtaining module 930 includes a fifth determining submodule, a sixth determining submodule, a second obtaining submodule, and a first generating submodule.

[0113] The fifth determination submodule is used to determine the third automorphism degree, wherein the third automorphism degree is determined by the first smoothing number, the second smoothing number and the fourth automorphism degree associated with the response elliptic curve, wherein the response elliptic curve is obtained based on the initial elliptic curve.

[0114] The sixth determination submodule is used to determine the second set of bases for the public key elliptic curve at the tortuosity of the first smooth number.

[0115] The second submodule is used to solve the discrete logarithm of the dual of the third automorphism in the second set of bases to obtain the kernel of the third homologous data and the kernel of the fourth homologous data, wherein the dual of the third automorphism is associated with the public key elliptic curve.

[0116] The first generation submodule is used to generate third and fourth source data based on the kernels of the third and fourth source data, respectively.

[0117] According to an embodiment of the present invention, the signature module 940 includes a seventh determining submodule, an eighth determining submodule, a ninth determining submodule, a second generating submodule, a third obtaining submodule, and a signature submodule.

[0118] The seventh determination submodule is used to determine the fifth homology based on the third and fourth homology, whereby the fifth homology represents the homology mapping from the first transition elliptic curve to the second transition elliptic curve.

[0119] The eighth determination submodule is used to determine the third set of bases for the first transition elliptic curve at the torsion point of the second smooth number.

[0120] The ninth determination submodule is used to determine the third action data of the third set of bases on the committed elliptic curve.

[0121] The second generation submodule is used to process the third action data based on the double addition algorithm to generate auxiliary two-dimensional Abelian cluster homogeneous data.

[0122] The third submodule is used to perform embedding projection processing on the auxiliary two-dimensional Abelian cluster homogeneous data to obtain auxiliary homogeneous data.

[0123] The signature submodule is used to sign the private key based on auxiliary same-source data.

[0124] According to an embodiment of the present invention, the signature device 900 based on the same source further includes a first selection module, a first determination module, a second determination module, and a first generation module.

[0125] The first selection module is used to select a third smooth number that is less than the second smooth number.

[0126] The first determining module is used to determine the fourth set of bases for the initial elliptic curve at the deflection point of the third smoothness number.

[0127] The second determining module is used to determine the fourth action data of the fourth set of bases on the initial elliptic curve.

[0128] The first generation module is used to process the fourth action data based on the double addition algorithm to generate committed homogeneous data, which represents the mapping from the initial elliptic curve to the committed elliptic curve.

[0129] According to an embodiment of the present invention, the signature device 900 based on the same source further includes a second selection module, a third determination module, a fourth determination module, and a second generation module.

[0130] The second selection module is used to select a number less than the first smooth number as the target multiple value.

[0131] The third determining module is used to determine the fifth set of bases for the committed elliptic curve at the torsion point of the first smoothness number.

[0132] The fourth determination module is used to determine the fifth action data of the fifth set of bases on the committed elliptic curve.

[0133] The second generation module is used to process the fifth action data and the target multiple value based on the double addition algorithm to generate response source data.

[0134] Figure 8 A block diagram of an electronic device suitable for implementing a same-origin signature method according to an embodiment of the present invention is shown.

[0135] like Figure 8As shown, an electronic device 1000 according to an embodiment of the present invention includes a processor 1001, which can perform various appropriate actions and processes according to a program stored in a read-only memory (ROM) 1002 or a program loaded from a storage portion 1008 into a random access memory (RAM) 1003. The processor 1001 may include, for example, a general-purpose microprocessor (e.g., a CPU), an instruction set processor and / or an associated chipset and / or a special-purpose microprocessor (e.g., an application-specific integrated circuit (ASIC)), etc. The processor 1001 may also include onboard memory for caching purposes. The processor 1001 may include a single processing unit or multiple processing units for performing different actions of the method flow according to an embodiment of the present invention.

[0136] RAM 1003 stores various programs and data required for the operation of electronic device 1000. Processor 1001, ROM 1002, and RAM 1003 are interconnected via bus 1004. Processor 1001 executes various operations of the method flow according to embodiments of the present invention by executing programs in ROM 1002 and / or RAM 1003. It should be noted that the programs may also be stored in one or more memories other than ROM 1002 and RAM 1003. Processor 1001 may also execute various operations of the method flow according to embodiments of the present invention by executing programs stored in said one or more memories.

[0137] According to an embodiment of the present invention, the electronic device 1000 may further include an input / output (I / O) interface 1005, which is also connected to a bus 1004. The electronic device 1000 may also include one or more of the following components connected to the input / output (I / O) interface 1005: an input section 1006 including a keyboard, mouse, etc.; an output section 1007 including a cathode ray tube (CRT), liquid crystal display (LCD), etc., and a speaker, etc.; a storage section 1008 including a hard disk, etc.; and a communication section 1009 including a network interface card such as a LAN card, modem, etc. The communication section 1009 performs communication processing via a network such as the Internet. A drive 1010 is also connected to the input / output (I / O) interface 1005 as needed. A removable medium 1011, such as a disk, optical disk, magneto-optical disk, semiconductor memory, etc., is installed on the drive 1010 as needed so that computer programs read from it can be installed into the storage section 1008 as needed.

[0138] The present invention also provides a computer-readable storage medium, which may be included in the device / apparatus / system described in the above embodiments; or it may exist independently and not assembled into the device / apparatus / system. The computer-readable storage medium carries one or more programs, which, when executed, implement the method according to the embodiments of the present invention.

[0139] According to embodiments of the present invention, a computer-readable storage medium may be a non-volatile computer-readable storage medium, such as including, but not limited to: portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination thereof. In the present invention, a computer-readable storage medium may be any tangible medium containing or storing a program that can be used by or in conjunction with an instruction execution system, apparatus, or device. For example, according to embodiments of the present invention, a computer-readable storage medium may include ROM 1002 and / or RAM 1003 and / or one or more memories other than ROM 1002 and RAM 1003 described above.

[0140] Embodiments of the present invention also include a computer program product comprising a computer program containing program code for performing the methods shown in the flowchart. When the computer program product is run on a computer system, the program code is used to enable the computer system to implement the same-origin signature method provided in the embodiments of the present invention.

[0141] When the computer program is executed by the processor 1001, it performs the functions defined in the system / apparatus of this invention. According to embodiments of the invention, the systems, apparatuses, modules, units, etc., described above can be implemented by computer program modules.

[0142] In one embodiment, the computer program may rely on a tangible storage medium such as an optical storage device or a magnetic storage device. In another embodiment, the computer program may also be transmitted and distributed in the form of signals over a network medium, and may be downloaded and installed via the communication section 1009, and / or installed from a removable medium 1011. The program code contained in the computer program can be transmitted using any suitable network medium, including but not limited to: wireless, wired, etc., or any suitable combination thereof.

[0143] In such an embodiment, the computer program can be downloaded and installed from a network via the communication section 1009, and / or installed from the removable medium 1011. When the computer program is executed by the processor 1001, it performs the functions defined in the system of this embodiment of the invention. According to embodiments of the invention, the systems, devices, apparatuses, modules, units, etc., described above can be implemented by computer program modules.

[0144] According to embodiments of the present invention, program code for executing the computer programs provided in the embodiments of the present invention can be written in any combination of one or more programming languages. Specifically, these computational programs can be implemented using high-level procedural and / or object-oriented programming languages, and / or assembly / machine languages. Programming languages ​​include, but are not limited to, languages ​​such as Java, C++, Python, "C", or similar programming languages. The program code can be executed entirely on the user's computing device, partially on the user's device, partially on a remote computing device, or entirely on a remote computing device or server. In cases involving remote computing devices, the remote computing device can be connected to the user's computing device via any type of network, including a local area network (LAN) or a wide area network (WAN), or it can be connected to an external computing device (e.g., via the Internet using an Internet service provider).

[0145] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of the present invention. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of code containing one or more executable instructions for implementing a specified logical function. It should also be noted that in some alternative implementations, the functions indicated in the blocks may occur in a different order than those indicated in the drawings. For example, two consecutively indicated blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in a block diagram or flowchart, and combinations of blocks in a block diagram or flowchart, may be implemented using a dedicated hardware-based system that performs the specified function or operation, or using a combination of dedicated hardware and computer instructions.

[0146] Those skilled in the art will understand that the features described in the various embodiments of the present invention can be combined and / or combined in various ways, even if such combinations or combinations are not explicitly described in the present invention. In particular, the features described in the various embodiments of the present invention can be combined and / or combined in various ways without departing from the spirit and teachings of the present invention. All such combinations and / or combinations fall within the scope of the present invention.

[0147] The embodiments of the present invention have been described above. However, these embodiments are merely illustrative and not intended to limit the scope of the invention. Although various embodiments have been described above, this does not mean that the measures in the various embodiments cannot be used advantageously in combination. Various substitutions and modifications can be made by those skilled in the art without departing from the scope of the invention, and all such substitutions and modifications should fall within the scope of the invention.

Claims

1. A homology-based signature method, characterized in that, The method comprises: solving a discrete logarithm associated with a first flex point to obtain first homology data, the first homology data representing a mapping of an initial elliptic curve to an intermediate elliptic curve, wherein the first flex point is a flex point of the initial elliptic curve on a first smooth number; embedding projection processing on two-dimensional Abelian inter-cluster homology data to obtain private key homology data to determine a private key, wherein the two-dimensional Abelian inter-cluster homology is generated based on the first homology data, and the private key homology data represents a mapping of the initial elliptic curve to a public key elliptic curve; solving a discrete logarithm of a flex group of the first smooth number associated with the public key elliptic curve to obtain third homology data and fourth homology data, wherein the third homology data represents a mapping of the public key elliptic curve to a first over elliptic curve, and the fourth homology represents a mapping of the public key elliptic curve to a second over elliptic curve; signing the private key according to auxiliary homology data generated by the third homology data and the fourth homology data to obtain a target private key, and sending the target private key to a target terminal to perform information encryption operation on target information.

2. The method of claim 1, wherein, The solving of the discrete logarithm associated with the first flex point to obtain the first homology data comprises: decomposing the first smooth number in a first endomorphism frequency to determine a second endomorphism frequency, the first endomorphism frequency being determined by the first smooth number and a second smooth number, wherein the first smooth number and the second smooth number are relatively prime; solving a discrete logarithm associated with a flex point of the initial elliptic curve on the first smooth number to obtain a first homology core; determining the mapping of the initial elliptic curve to the intermediate elliptic curve according to the second endomorphism frequency and the first homology core to obtain the first homology data.

3. The method of claim 2, wherein, The embedding projection processing on the two-dimensional Abelian inter-cluster homology data to obtain the private key homology data comprises: determining a first group of bases of the flex point of the initial elliptic curve on the second smooth number; determining first action data of the first group of bases on the first homology data; processing the first action data based on a double-addition algorithm to generate the two-dimensional Abelian inter-cluster homology data; embedding projection processing on the two-dimensional Abelian inter-cluster homology data to obtain the private key homology data.

4. The method of claim 2, wherein, The solving of the discrete logarithm of the flex group of the first smooth number associated with the public key elliptic curve to obtain the third homology data and the fourth homology data comprises: determining a third endomorphism frequency, wherein the third endomorphism frequency is determined by the first smooth number, the second smooth number, and a fourth endomorphism frequency associated with a response elliptic curve, wherein the response elliptic curve is obtained based on the initial elliptic curve; determining a second group of bases of the flex point of the public key elliptic curve on the first smooth number; solving a discrete logarithm of a dual of a third endomorphism on the second group of bases to obtain a core of the third homology data and a core of the fourth homology data, wherein the dual of the third endomorphism is associated with the public key elliptic curve; The third homology data and the fourth homology data are respectively generated according to the nucleus of the third homology data and the nucleus of the fourth homology data.

5. The method of claim 2, wherein, The private key is signed according to the auxiliary homology data generated from the third homology data and the fourth homology data. A fifth homology is determined according to the third homology and the fourth homology, and the fifth homology represents a homology mapping of the first over-elliptic curve to the second over-elliptic curve. A third group of bases of the first over-elliptic curve at the torsion point of the second smooth number is determined. Third action data of the third group of bases on the first over-elliptic curve is determined. The third action data is processed based on a double-addition algorithm to generate auxiliary two-dimensional Abelian inter-cluster homology data. The auxiliary two-dimensional Abelian inter-cluster homology data is subjected to embedding projection processing to obtain the auxiliary homology data. The private key is signed based on the auxiliary homology data.

6. The method of claim 2, wherein, The method further comprises: A third smooth number smaller than the second smooth number is selected. A fourth group of bases of the initial elliptic curve at the torsion point of the third smooth number is determined. Fourth action data of the fourth group of bases on the initial elliptic curve is determined. The fourth action data is processed based on a double-addition algorithm to generate commitment homology data representing a mapping of the initial elliptic curve to a commitment elliptic curve.

7. The method of claim 6, wherein, The method further comprises: A number smaller than the first smooth number is selected as a target multiple value. A fifth group of bases of the commitment elliptic curve at the torsion point of the first smooth number is determined. Fifth action data of the fifth group of bases on the commitment elliptic curve is determined. The fifth action data and the target multiple value are processed based on a double-addition algorithm to generate response homology data.

8. A homology-based signature device, characterized in that, The device comprises: A first obtaining module is configured to solve a discrete logarithm of a first torsion point associated with a discrete logarithm for a private key to be processed to obtain first homology data representing a mapping of an initial elliptic curve to an intermediate elliptic curve, wherein the first torsion point is a torsion point of the initial elliptic curve on a first smooth number. A second obtaining module is configured to perform embedding projection processing on two-dimensional Abelian inter-cluster homology data to obtain private key homology data to determine a private key, wherein the two-dimensional Abelian inter-cluster homology is generated based on the first homology data, and the private key homology data represents a mapping of the initial elliptic curve to a public key elliptic curve. A third obtaining module is configured to solve a discrete logarithm of a torsion group of the first smooth number associated with the public key elliptic curve to obtain third homology data and fourth homology data, wherein the third homology data represents a mapping of the public key elliptic curve to a first over-elliptic curve, and the fourth homology represents a mapping of the public key elliptic curve to a second over-elliptic curve. A signing module is configured to sign the private key according to auxiliary homology data generated from the third homology data and the fourth homology data to obtain a target private key, and send the target private key to a target terminal to perform an information encryption operation on target information.

9. An electronic device, comprising: one or more processors; a memory for storing one or more computer programs, characterized in that the one or more processors execute the one or more computer programs to implement the steps of the method according to any one of claims 1-7.

10. A computer readable storage medium having stored thereon a computer program or instructions, characterized in that, the computer program or instructions, when executed by a processor, implement the steps of the method according to any one of claims 1-7.

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