A method for constructing a minimal linear code, a secret sharing method and a secret sharing system

Abstract

The present application belongs to the technical field of information security and coding theory, and provides a minimal linear code construction method, a secret sharing method and a secret sharing system, comprising: first defining a trace function in a finite field, constructing a two-to-one mapping, a vector Boolean function with a finite discrete value of Walsh spectrum, and then defining a code word set based on the function, embedding the output of the trace function into a linear code generation expression to generate a minimal linear code with a weight set and a support without strict inclusion; then using the dual code to establish a one-to-one correspondence between the participants and the dual code coordinates, the minimal code word support and the minimum access structure, embed the secret generation share distribution, and the participants meeting the conditions restore the secret through linear combination. The system contains four functional modules, which are suitable for distributed storage, blockchain key management and other scenes, and realize safe, efficient and expandable secret sharing. The present application can improve the security, efficiency and flexibility of secret sharing, and is suitable for multiple scenes and easy to expand.

Description

Technical Field

[0001] This invention belongs to the field of information security and coding theory technology, and provides a method for constructing minimal linear codes, a secret sharing method, and a secret sharing system. Background Technology

[0002] Secret sharing technology, as one of the core technologies in the field of information security, involves splitting the original secret into several shares and distributing them to different participants. The original secret can only be recovered when a set of participants meeting preset access conditions collaborate. This effectively solves the security risks of centralized secret storage and the problem of secret loss due to single-node failures. With the development of distributed systems, blockchain, and other technologies, traditional threshold secret sharing schemes based on polynomial interpolation, due to their fixed access structure and support for verification by only threshold-based participant sets, are no longer suitable for the flexible access control requirements in complex scenarios. Therefore, secret sharing methods based on linear codes have emerged and become the mainstream technical approach in the current secret sharing field.

[0003] The core principle of the secret sharing method based on linear codes is as follows: Utilizing the algebraic structure properties of linear codes and their dual codes, secret information is mapped into linear codeword components and distributed to participants. The minimum access structure for secret sharing is characterized by the support set of the smallest codeword in the dual code. When the coordinate supports corresponding to the participant sets satisfy predetermined conditions, secret recovery can be achieved through linear combination. This technical approach breaks through the fixed structure limitations of traditional threshold schemes, supports the design of general access structures, and has significant advantages in access control flexibility. Therefore, it has been widely studied and attempted to be applied to key management scenarios in large-scale distributed systems.

[0004] However, existing secret sharing methods based on linear codes still suffer from many key technical defects in practical applications, which restrict their security, practicality, and scalability. These defects are specifically reflected in the following aspects: Existing schemes often directly use ordinary linear codes as the basic coding structure. The non-zero codeword support set of ordinary linear codes is prone to strict inclusion relationships, which cannot satisfy the minimumity criterion. Consequently, the support set of the smallest codeword in the dual code cannot establish a unique correspondence with the minimum access structure of secret sharing. The non-minimal access set may participate in secret recovery, which seriously reduces the security of the secret sharing scheme at the access structure level and the consistency of the secret recovery result.

[0005] The secret recovery process of existing schemes can only rely on the minimum codeword set of the dual code for post-event judgment. However, this set is prone to mixing in non-minimal codewords, resulting in non-unique secret recovery paths and ambiguous judgment conditions. When participants collude or engage in abnormal behavior, it is difficult to guarantee that only the legal minimum access structure can recover the secret, and the system has weak anti-attack capabilities.

[0006] Following the traditional threshold secret sharing design approach, the linear code has fixed parameters, making it difficult to adapt to the actual needs of dynamic changes in access policies and flexible expansion of participant scale in scenarios such as distributed storage and blockchain key management, resulting in significant limitations in engineering deployment.

[0007] Existing linear code constructions are mostly based on scalar Boolean functions, which cannot systematically construct linear codes that balance minimization and computational efficiency. Some schemes require extensive post-processing and judgment of the generated codewords to meet the minimization requirement, which further increases computational complexity and is not suitable for application scenarios with limited computing resources or a large number of participants. Summary of the Invention

[0008] To address the aforementioned technical problems, this invention provides a method for constructing minimal linear codes, comprising: A coding system is established over a finite field, the trace function is defined, and the structure of the vector Boolean function, the dimension of the input and output space, and the range of free parameters for constructing the linear code are determined according to the application scenario. The parameter constraints of the target linear code, such as the code length, dimension, and minimum distance, are set. Based on the structure, input-output space dimension, and free parameter range of the vector Boolean function, a vector Boolean function with a two-to-one mapping characteristic is constructed. This allows different input elements in the domain of the vector Boolean function to be mapped to the same output value in pairs according to a predetermined rule. Consequently, the Walsh spectrum of the vector Boolean function takes only a finite number of discrete values. Then, the output of the vector Boolean function is mapped to a binary symbol through the trace function. The binary symbol retains the frequency domain controllable characteristics of the vector Boolean function. Binary symbols are embedded into the generative expression of linear codes according to parameter constraints. A codeword set is defined according to the generative expression. Minimal linear codes that satisfy the minimumity criterion are selected from the codeword set. The minimumity criterion is that the support sets of different non-zero codewords have no strict inclusion relationship.

[0009] Furthermore, the Walsh spectral distribution characteristics of the vector Boolean function directly determine the codeword weight distribution characteristics of the induced linear code.

[0010] Furthermore, the minimal linear code is a three-weighted or five-weighted linear code.

[0011] Furthermore, the codeword set is as follows: In the formula, n is a positive integer, It is a two-to-one function. For trace function, It is a finite field.

[0012] Furthermore, the construction method that guarantees the minimality of linear codes is as follows: By applying dual constraints on the mapping and frequency domain characteristics of the vector Boolean function, a vector Boolean function with a two-to-one mapping characteristic and a Walsh spectrum that takes only a finite number of discrete values ​​is selected. This function is then embedded into the linear code generation expression after being mapped by the trace function. This ensures that the linear code satisfies the minimumity criterion during the construction stage, eliminating the need for post-processing and complex judgment of the generated codeword set. From the source of the coding structure, it guarantees that the support set of non-zero codewords of the linear code has no strict inclusion relationship.

[0013] This invention also provides a secret sharing method, which constructs a dual code implementation of a minimal linear code, comprising the following steps: Establish a one-to-one correspondence between each participant in the secret sharing system and a coordinate position of the dual code.

[0014] The secret to be shared is embedded in the codeword generation process of the dual code, and the codeword component at the corresponding coordinate position in the dual code is distributed as a secret share to the corresponding participant.

[0015] The support set of the smallest codewords in the dual code is used as the minimum access structure for secret sharing. The secret recovery condition is satisfied only when the coordinate support corresponding to the participant set covers the support set of a certain smallest codeword.

[0016] The set of participants that meet the secret recovery conditions performs a linear combination operation on their respective secret shares to recover the original secret; the set of participants that do not meet the secret recovery conditions cannot recover the original secret because they cannot form a valid dual code support relationship.

[0017] Furthermore, the support of the minimal codeword in the dual code of the minimal linear code is unique, so that the support set of the minimal codeword of the dual code forms a strict one-to-one correspondence with the minimum access structure of secret sharing, and the operation of the secret sharing process depends only on linear operations and trace operations on a finite field.

[0018] Furthermore, by adjusting the construction parameters of the vector Boolean function or the finite field... Based on the scale, generate secret sharing schemes with different access structures to achieve dynamic configuration of general access structures.

[0019] The present invention also provides a secret sharing system, comprising functional modules that work in sequence and in coordination: The vector Boolean function generation module is used to construct vector Boolean functions with two-to-one mapping properties and Walsh spectra taking finite discrete values, and to map their outputs to binary symbols through trace functions. A linear code encoding module is used to generate a minimal linear code that satisfies the minimality criterion based on the vector Boolean function, and to solve for the dual code of the minimal linear code; The secret share distribution module is used to establish the correspondence between participants and the coordinate positions of the dual code, embed the secret to be shared into the dual code generation process, and complete the distribution of secret shares. The secret recovery module is used to determine whether the participant set meets the secret recovery conditions, and to perform a linear combination operation on the secret share of the participant set that meets the conditions to recover the original secret.

[0020] The technical solution provided by this invention has the following advantages compared with the prior art: 1. This invention introduces a vector Boolean function with a two-to-one mapping property and utilizes its Walsh spectrum to take finite discrete values ​​to constrain the codeword weight distribution of the linear code during the construction stage. This ensures that the weights of the non-zero codewords in the generated linear code are concentrated within a finite range of values, thereby avoiding strict inclusion relationships between different codeword support sets and ensuring that the resulting linear code naturally satisfies the minimumity criterion. This guarantees a stable one-to-one correspondence between the support set of the minimal codewords of the dual code and the minimum access structure in the secret sharing scheme, improving the security and consistency of the secret sharing scheme at the access structure level.

[0021] 2. This invention, through the algebraic structure of vector Boolean functions and their Walsh spectral characteristics, can guarantee that the linear code satisfies the minimum condition during the construction stage, without the need for additional codeword selection or complex judgment, thereby significantly reducing the computational complexity of the construction process and improving the algorithm efficiency.

[0022] 3. The secret sharing scheme constructed in this invention mainly relies on linear operations and trace operations on finite fields to generate and restore secret shares, avoiding the complex polynomial interpolation and reconstruction calculations in traditional threshold secret sharing schemes, so that the secret sharing system can still maintain high operating efficiency in environments with a large number of participants or limited computing resources.

[0023] 4. This invention utilizes the support set of minimal codewords in the dual code of minimal linear codes to characterize the minimum access structure in the secret sharing scheme. This access structure is naturally determined by the algebraic structure of the linear code and does not depend on fixed threshold parameters. By adjusting the construction parameters of the vector Boolean function or the size of the finite field, secret sharing schemes with different access structures can be flexibly generated, thereby adapting to diverse access control requirements in complex application scenarios.

[0024] 5. This invention modularizes the vector Boolean function generation, linear code construction, secret share distribution, and secret recovery process, making the entire system structure clear and simple to implement. It can be easily deployed in practical application environments such as distributed storage systems and blockchain key management systems, and has good engineering scalability and practical value.

[0025] Other advantages, objectives and features of the present invention will become apparent in part from the following description, and in part from those skilled in the art through study and practice of the invention. Detailed Implementation

[0026] The following detailed description is based on a specific embodiment, but it should be understood that the scope of protection of the present invention is not limited to the specific embodiment.

[0027] This invention provides a method for constructing minimal linear codes, comprising: In a finite field Establish an encoding system and define the trace function. At the same time, based on the application scenario, the structure of the vector Boolean function, the dimension of the input and output space, and the range of free parameters for constructing the linear code are determined, and the parameter constraints of the target linear code, such as the code length, dimension, and minimum distance are set.

[0028] Based on the structure, input-output space dimension, and free parameter range of the vector Boolean function, a vector Boolean function with a two-to-one mapping characteristic is constructed. This allows different input elements in the domain of the vector Boolean function to be paired and mapped to the same output value according to a predetermined rule. Consequently, the Walsh spectrum of the vector Boolean function takes only a finite number of discrete values. The output of the vector Boolean function is then mapped to binary symbols through the trace function, which preserves the frequency-domain controlled characteristics of the vector Boolean function. It is important to note that the Walsh spectrum reflects the correlation between the vector Boolean function and the linear function. The limited range of its values ​​implies that the function output has a highly structured distribution characteristic overall. The Walsh spectrum characteristics of the vector Boolean function directly affect the weight distribution of the codewords it induces in the Hamming space.

[0029] Binary symbols are embedded into the generative expression of linear codes according to parameter constraints. A codeword set is defined according to the generative expression. Minimal linear codes that satisfy the minimumity criterion are selected from the codeword set. The minimumity criterion is that the support sets of different non-zero codewords have no strict inclusion relationship.

[0030] Furthermore, the Walsh spectral distribution characteristics of the vector Boolean function induce the codeword weight distribution characteristics of the generated linear code.

[0031] Furthermore, the minimal linear code is a three-weighted or five-weighted linear code, which provides a stable and unique minimum access structure basis for subsequently constructing a secret sharing scheme using its dual code.

[0032] Furthermore, the codeword set is as follows: In the formula, n is a positive integer, It is a two-to-one function. For trace function, It is a finite field.

[0033] Furthermore, the construction method that guarantees the minimality of linear codes is as follows: By applying dual constraints on the mapping and frequency domain characteristics of the vector Boolean function, a vector Boolean function with a two-to-one mapping characteristic and a Walsh spectrum that takes only a finite number of discrete values ​​is selected. This function is then embedded into the linear code generation expression after being mapped by the trace function. This ensures that the linear code satisfies the minimumity criterion during the construction stage, eliminating the need for post-processing and complex judgment of the generated codeword set. From the source of the coding structure, it guarantees that the support set of non-zero codewords of the linear code has no strict inclusion relationship.

[0034] This invention also provides a secret sharing method, which constructs a dual code implementation of a minimal linear code, comprising the following steps: Establish a one-to-one correspondence between each participant in the secret sharing system and a coordinate position of the dual code.

[0035] The secret to be shared is embedded in the codeword generation process of the dual code, and the codeword component at the corresponding coordinate position in the dual code is distributed as a secret share to the corresponding participant.

[0036] The support set of the smallest codewords in the dual code is used as the minimum access structure for secret sharing. The secret recovery condition is satisfied only when the coordinate support corresponding to the participant set covers the support set of a certain smallest codeword.

[0037] The set of participants that meet the secret recovery conditions performs a linear combination operation on their respective secret shares to recover the original secret; the set of participants that do not meet the secret recovery conditions cannot recover the original secret because they cannot form a valid dual code support relationship.

[0038] Furthermore, the support of the minimal codeword in the dual code of the minimal linear code is unique, so that the support set of the minimal codeword of the dual code forms a strict one-to-one correspondence with the minimum access structure of secret sharing, and the operation of the secret sharing process depends only on linear operations and trace operations on a finite field.

[0039] Furthermore, by adjusting the construction parameters of the vector Boolean function or the finite field... Based on the scale, generate secret sharing schemes with different access structures to achieve dynamic configuration of general access structures.

[0040] The present invention also provides a secret sharing system, comprising functional modules that work in sequence and in coordination: The vector Boolean function generation module is used to construct vector Boolean functions with two-to-one mapping properties and Walsh spectra taking finite discrete values, and to map their outputs to binary symbols through trace functions. A linear code encoding module is used to generate a minimal linear code that satisfies the minimality criterion based on the vector Boolean function, and to solve for the dual code of the minimal linear code; The secret share distribution module is used to establish the correspondence between participants and the coordinate positions of the dual code, embed the secret to be shared into the dual code generation process, and complete the distribution of secret shares. The secret recovery module is used to determine whether the participant set meets the secret recovery conditions, and to perform a linear combination operation on the secret share of the participant set that meets the conditions to recover the original secret.

[0041] Example By selecting a vector Boolean function that satisfies the two-to-one mapping property, a minimal linear code is constructed, and the dual code of this minimal linear code is further used to realize a secret sharing scheme.

[0042] 1. System parameters and configuration environment settings.

[0043] In this embodiment, the positive integer parameters are selected as follows: set up and define Constructing a finite field In implementation, primitive polynomials can be used: Generate the finite field and denote it. Let be the primitive element of this finite field.

[0044] Define from extended field to base domain The trace function is: ; 2. The specific construction of a two-to-one vector Boolean function.

[0045] In this embodiment, a vector Boolean function of the following form is selected: in: , parameter The following algebraic constraints must be satisfied: Right now: Under the above parameter conditions, the vector Boolean function exist This forms a two-to-one mapping function, meaning that, except for the zero element, any output value is obtained by mapping exactly two different input elements.

[0046] Furthermore, calculations verify that the Walsh spectrum of this vector Boolean function takes only a finite number of discrete values, exhibiting a five-valued distribution.

[0047] 3. Generation of minimal linear codes.

[0048] Based on the above two-to-one vector Boolean function Constructing binary linear codes Its codeword set is defined as: The linear code obtained by this construction method has the following defined parameters: Code length: Code dimension: Due to vector Boolean functions The Walsh spectrum takes only a finite number of discrete values, and the non-zero codeword weights of the generated linear code are concentrated within a finite number of values.

[0049] Under the aforementioned weight distribution conditions, the support sets of different non-zero codewords do not have a strict inclusion relationship, and the linear code satisfies the minimumity criterion, thus constituting a minimum linear code.

[0050] 4. Secret sharing implementation of dual codes of minimal linear codes.

[0051] Using the above minimal linear codes dual codes The specific implementation process of constructing a secret sharing scheme is as follows.

[0052] (1) Participant mapping.

[0053] Suppose the secret-sharing system contains 255 participants, denoted as: Each participant and its dual code There is a one-to-one correspondence between the coordinates and the positions.

[0054] (2) Distribution of secret shares.

[0055] Suppose the secret to be shared is a one-bit piece of information: In dual codes During the code generation process, the secret As one of the generation parameters, the dual codeword is generated: And the first Each coordinate component As a secret share, it is distributed to the corresponding participants. .

[0056] (3) Determine the minimum access structure.

[0057] Dual Codes The smallest codeword in the secret sharing scheme has its non-zero coordinate position forming the minimum access structure.

[0058] For example, in this embodiment, the support set of a very small codeword in the dual code is: .

[0059] The above set of participants constitutes a minimal access structure.

[0060] 4. Secret Recovery Process When the participant set contains the complete support set described above, each participant submits their share of the secret, and the original secret can be recovered through linear combination. .

[0061] When the set of participants does not contain any complete minimal support set, the secret information cannot be recovered because a valid dual code support relationship cannot be formed.

[0062] The present invention has at least the following significant technical effects, the mechanism of which is as follows: 1. Ensure the uniqueness and strictness of the minimum access structure from the source of the encoding structure. This invention introduces a vector Boolean function with controlled Walsh spectrum distribution characteristics to constrain the codeword weight distribution of the linear code during the construction stage, so that the non-zero codeword weights of the obtained linear code are concentrated within a finite range of values.

[0063] Under this weight distribution, it is difficult for the support sets of different non-zero codewords to form a strict inclusion relationship, thus structurally satisfying the minimumity criterion. Therefore, any non-zero codeword in the constructed linear code is a minimum codeword, and a one-to-one correspondence can be established between the support set of the minimum codewords in its dual code and the minimum access structure in the secret sharing scheme.

[0064] This structural constraint eliminates the possibility of non-minimal access sets participating in secret recovery from a mathematical perspective, significantly improving the security and consistency of secret sharing schemes at the access structure level.

[0065] 2. Avoid post-event screening and complex judgments, and improve the stability of the secret sharing scheme. In existing secret sharing schemes based on linear codes, the linear codes are usually constructed first, and then their smallest codewords are selected by traversal or judgment. Since there may be supporting and containing relationships between codewords, it is easy to cause redundancy or non-uniqueness of secret recovery paths.

[0066] This invention, through the algebraic structure of vector Boolean functions and their Walsh spectral characteristics, ensures that the resulting linear code satisfies the minimum requirement during the encoding construction stage, without the need for additional screening or complex judgment of the codeword set.

[0067] Therefore, the process of determining the minimum access structure in the secret sharing scheme is more stable, avoiding security risks introduced by the uncertainty of the codeword structure, and improving the overall reliability and predictability of the system.

[0068] 3. Reduce the computational complexity of the secret distribution and recovery process. The vector Boolean function and trace function combination construction method adopted in this invention makes the secret sharing process mainly rely on linear operations and trace operations on a finite field, avoiding the complex polynomial interpolation and reconstruction calculations in traditional threshold secret sharing schemes.

[0069] Meanwhile, since the dual code of the minimal linear code has a clear and unique minimum access structure, the secret recovery process can be completed by simply performing linear combination operations.

[0070] This inherent mechanism enables the invention to significantly reduce computational complexity while ensuring security, making it particularly suitable for application scenarios with a large number of participants or limited computing resources.

[0071] 4. Supports general access structures, improving the flexibility of access control. This invention utilizes the support set of minimal codewords in the dual code of minimal linear codes to characterize the minimum access structure in secret sharing. This access structure does not depend on fixed threshold parameters, but is naturally determined by the algebraic structure of the linear codes.

[0072] Therefore, by adjusting the construction parameters of the vector Boolean function or the size of the finite field, secret sharing schemes with different access structures can be flexibly generated, breaking through the limitations of the traditional threshold secret sharing schemes, which have a single access structure and insufficient scalability.

[0073] This feature enables the present invention to be adapted to complex application environments with diverse access policy requirements, such as distributed storage and blockchain key management.

[0074] 5. Improve the scalability of the project and the feasibility of system implementation. Because the method described in this invention has good modularity in mathematical structure, the construction of vector Boolean functions, linear code encoding, secret share distribution and secret recovery process can be encapsulated as independent functional modules.

[0075] This modular structure facilitates implementation in practical engineering through software, hardware, or a combination of both, and can be easily deployed in server clusters, blockchain nodes, or distributed storage systems.

[0076] Therefore, this invention not only has strict security guarantees in theory, but also has good scalability and practical value in engineering implementation.

[0077] It should be noted that any parts not disclosed or specifically described in this invention are existing technology or conventional configurations, and their specific structures and working principles will not be elaborated further. In this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes that element.

[0078] Although embodiments of the present invention have been disclosed above, they are not limited to the applications listed in the specification and embodiments. It can be applied to various fields suitable for the present invention. Other modifications can be readily implemented by those skilled in the art. Therefore, the present invention is not limited to the specific details without departing from the general concept defined by the claims and their equivalents.

Claims

1. A method for constructing a minimal linear code, characterized in that, include: A coding system is established over a finite field, the trace function is defined, and the structure of the vector Boolean function, the dimension of the input and output space, and the range of free parameters for constructing the linear code are determined according to the application scenario. The parameter constraints of the target linear code, such as the code length, dimension, and minimum distance, are set. Based on the structure, input-output space dimension, and free parameter range of the vector Boolean function, a vector Boolean function with a two-to-one mapping characteristic is constructed. This allows different input elements in the domain of the vector Boolean function to be mapped to the same output value in pairs according to a predetermined rule. Consequently, the Walsh spectrum of the vector Boolean function takes only a finite number of discrete values. Then, the output of the vector Boolean function is mapped to a binary symbol through the trace function. The binary symbol retains the frequency domain controllable characteristics of the vector Boolean function. Binary symbols are embedded into the generative expression of linear codes according to parameter constraints. A codeword set is defined according to the generative expression. Minimal linear codes that satisfy the minimumity criterion are selected from the codeword set. The minimumity criterion is that the support sets of different non-zero codewords have no strict inclusion relationship.

2. The method for constructing a minimal linear code according to claim 1, characterized in that, The codeword weight distribution characteristics of the linear code induced by the Walsh spectral distribution characteristics of the vector Boolean function.

3. The method for constructing a minimal linear code according to claim 1, characterized in that, The minimal linear code is a three-weighted or five-weighted linear code.

4. The method for constructing a minimal linear code according to claim 1, characterized in that, The codeword set for: In the formula, n is a positive integer, It is a two-to-one function. For trace function, It is a finite field.

5. The method for constructing a minimal linear code according to claim 1, characterized in that, The method for constructing a linear code that guarantees its minimality is as follows: By applying dual constraints on the mapping and frequency domain characteristics of the vector Boolean function, a vector Boolean function with a two-to-one mapping characteristic and a Walsh spectrum that takes only a finite number of discrete values ​​is selected. This function is then embedded into the linear code generation expression after being mapped by the trace function. This ensures that the linear code satisfies the minimumity criterion during the construction stage, eliminating the need for post-processing and complex judgment of the generated codeword set. From the source of the coding structure, it guarantees that the support set of non-zero codewords of the linear code has no strict inclusion relationship.

6. A method for sharing secrets, characterized in that, The dual code of a minimal linear code constructed using any one of the minimal linear code construction methods according to claims 1 to 5 includes the following steps: Establish a one-to-one correspondence between each participant in the secret sharing system and a coordinate position of the dual code; The codeword generation process embeds the secret to be shared into the dual code, and the codeword component at the corresponding coordinate position in the dual code is distributed as a secret share to the corresponding participant. The support set of the smallest codewords in the dual code is used as the minimum access structure for secret sharing. The secret recovery condition is satisfied only when the coordinate support corresponding to the participant set covers the support set of a certain smallest codeword. The set of participants that meet the secret recovery conditions performs a linear combination operation on their respective secret shares to recover the original secret; the set of participants that do not meet the secret recovery conditions cannot recover the original secret because they cannot form a valid dual code support relationship.

7. A secret sharing method according to claim 6, characterized in that, The support of the minimal codeword in the dual code of the minimal linear code is unique, so that the support set of the minimal codeword of the dual code forms a strict one-to-one correspondence with the minimum access structure of secret sharing, and the operation of the secret sharing process depends only on linear operation and trace operation on a finite field.

8. A secret sharing method according to claim 6, characterized in that, By adjusting the construction parameters of the vector Boolean function or the finite field Based on the scale, generate secret sharing schemes with different access structures to achieve dynamic configuration of general access structures.

9. A secret sharing system, characterized in that, For implementing a secret sharing method according to any one of claims 6 to 8, the system includes functional modules that work in sequence and collaboratively: The vector Boolean function generation module is used to construct vector Boolean functions with two-to-one mapping properties and Walsh spectra taking finite discrete values, and to map their outputs to binary symbols through trace functions. A linear code encoding module is used to generate a minimal linear code that satisfies the minimality criterion based on the vector Boolean function, and to solve for the dual code of the minimal linear code; The secret share distribution module is used to establish the correspondence between participants and the coordinate positions of the dual code, embed the secret to be shared into the dual code generation process, and complete the distribution of secret shares. The secret recovery module is used to determine whether the participant set meets the secret recovery conditions, and to perform a linear combination operation on the secret share of the participant set that meets the conditions to recover the original secret.

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