Secret sharing method and device based on conditional symmetric bivariate polynomial, and medium

Abstract

The invention discloses a secret sharing method and device based on a conditional symmetric bivariate polynomial, and a medium. The method comprises the following steps: constructing a cryptographic algorithm conditional bivariate polynomial; distributing a unique identity label for each participant, and calculating an identity characteristic value based on the identity label; based on the identity feature value, generating a corresponding secret share for each participant and distributing the secret share; when the two participants need to generate a shared key, the two participants calculate conditional functions based on respective identity feature values; according to the output value of the conditional function, the symmetric computational logic or the asymmetric computational logic is dynamically selected, and the two participants use the selected computational logic to calculate a consistent shared key. The problem that a traditional bivariate polynomial secret sharing scheme cannot adapt to different security scenes due to fixed symmetry is solved, efficient cooperation in the same group and cross-group high-security flexible switching are achieved, and both high efficiency and high security are achieved.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of information security and cryptography, in particular to a secret sharing method and device based on conditional symmetric bivariate polynomial and medium. BACKGROUND

[0002] In the field of information security, secret sharing technology, as an important security mechanism, is widely used to protect sensitive data and keys. By dividing sensitive information into multiple shares and distributing them to different participants, the original secret can only be restored when the participants meet certain conditions. The core advantage of this technology is to reduce the risk of single node failure or leakage by decentralizing control points. Bivariate polynomials are widely used in secret sharing schemes due to their flexibility and scalability. Among them, symmetric bivariate polynomials can achieve equal key generation logic among participants, and perform well in internal collaboration scenarios, providing a guarantee for convenient communication between members.

[0003] However, this inherent symmetry shows obvious limitations in the face of complex and variable security scenarios. For example, within an organization, members need to quickly and conveniently establish shared keys, but when members of the organization communicate with external entities, this symmetry can become a security risk, because external entities may be able to derive the coefficients of the polynomial by obtaining multiple key values, thereby threatening the security of the entire system. To solve this problem, there are currently separate systems for internal and external communication, but this not only increases the complexity and cost of the system, but also brings management challenges. Therefore, there is an urgent need for a secret sharing scheme that can dynamically adapt to different security scenarios, both maintaining the convenience of internal collaboration and effectively preventing external security threats. SUMMARY

[0004] The purpose of the present application is to overcome the deficiencies of the prior art. To achieve the above purpose, a secret sharing method, device and medium based on conditional symmetric bivariate polynomial are used to solve the problems raised in the background technology.

[0005] A secret sharing method based on conditional symmetric bivariate polynomial, comprising the following steps: Step S1, construct a cryptographic algorithm conditional bivariate polynomial, the cryptographic algorithm conditional bivariate polynomial is determined by symmetric polynomial, asymmetric polynomial and condition function, wherein the condition function is configured to receive the feature information of the participants as input, and output a signal indicating to enable symmetric calculation logic or asymmetric calculation logic; Step S2, assign a unique identity to each participant, and calculate an identity feature value based on the identity; Step S3, generating and distributing secret shares for each participant based on the identity feature value; Step S4, when two participants need to generate a shared key, the two participants calculate the conditional function based on their respective identity feature values; Step S5, according to the output value of the conditional function, dynamically selecting the symmetric calculation logic or the asymmetric calculation logic, and using the selected calculation logic to calculate a consistent shared key by the two participants.

[0006] As a further scheme of the present application: the conditional symmetric bivariate polynomial in step S1 The construction formula is:

[0007] wherein, is a symmetric polynomial, is an asymmetric polynomial, is a conditional function, is a pre-selected large prime number.

[0008] As a further scheme of the present application: the output value of the conditional function is 0 or 1; When = 1, then , symmetric logic is enabled; When = 0, then , asymmetric logic is enabled.

[0009] As a further scheme of the present application: the conditional function The step implemented based on the identity information of the participants is: extracting a specific field or prefix in the identity identifier for consistency judgment.

[0010] As a further scheme of the present application: the conditional function The step implemented based on the biological feature information is: judging whether the biological feature information of the participants exists in a pre-defined trusted feature library.

[0011] As a further scheme of the present application: the conditional function The step implemented based on multi-layer judgment logic is: The multi-layer judgment logic includes identity identifier-based judgment and biological feature-based judgment.

[0012] As a further scheme of the present application: the symmetric polynomial is a symmetric bivariate polynomial, the asymmetric polynomial is an asymmetric bivariate polynomial, and the symmetric polynomial and the asymmetric polynomial have the same variable dimension; the symmetric polynomial ; comprises, ; the asymmetric polynomial satisfies .

[0013] As a further aspect of the present application: in the step S5, when the value of the condition function enables the asymmetric computation logic, the participants respectively locally compute and ; wherein the key agreement is achieved by exchanging and and the shared key is computed using a key derivation function.

[0014] The technical solution of the second aspect: a secret sharing device using the secret sharing method based on the conditional symmetric bivariate polynomial as described in any of the above, comprising: a polynomial construction module configured to construct a cryptographic algorithm conditional bivariate polynomial, the cryptographic algorithm conditional bivariate polynomial being determined by a symmetric polynomial, an asymmetric polynomial and a condition function, wherein the condition function is configured to receive the feature information of the participants as input and output a signal indicating to enable the symmetric computation logic or the asymmetric computation logic; an identity identifier generation module configured to assign a unique identity identifier to each participant and calculate an identity feature value based on the identity identifier; a share distribution module configured to generate a corresponding secret share for each participant based on the identity feature value and distribute the secret share; a key calculation module configured to, when two participants need to generate a shared key, the two participants calculate the condition function based on the respective identity feature values; and according to the output value of the condition function, dynamically select the symmetric computation logic or the asymmetric computation logic, and use the selected computation logic to calculate a consistent shared key by the two participants.

[0015] The technical solution of the third aspect: a storage medium having processor executable instructions stored therein, the processor executable instructions, when executed by a processor, are used to implement the secret sharing method based on the conditional symmetric bivariate polynomial as described in any of the above.

[0016] Compared with the prior art, the present application has the following technical effects: By introducing the conditional function as the symmetry switch, adaptive matching of different security scenes in the same system is realized, the convenience of internal communication is ensured, the security of external communication is enhanced, and the complexity of multi-system deployment is avoided. BRIEF DESCRIPTION OF DRAWINGS

[0017] The specific embodiments of the present application will be described in detail below with reference to the accompanying drawings: Figure 1 is a conditional symmetric double variable polynomial secret sharing method flowchart provided by the embodiment of the present application; Figure 2 is a judgment logic diagram based on double-layer verification provided by the embodiment of the present application; Figure 3 is a participant identity generation flowchart provided by the embodiment of the present application; Figure 4 is a share generation and distribution flowchart provided by the embodiment of the present application; Figure 5 is a biological feature information or unique hardware identifier collection flowchart provided by the embodiment of the present application; Figure 6 is a system internal unit block diagram provided by the embodiment of the present application. DETAILED DESCRIPTION

[0018] The technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the accompanying drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the scope of protection of the present application.

[0019] Please refer to Figure 1 In the embodiments of the present application, a conditional symmetric double variable polynomial secret sharing method includes the following steps: Step S1, a cryptographic algorithm conditional double variable polynomial is constructed, the cryptographic algorithm conditional double variable polynomial is determined by a symmetric polynomial, an asymmetric polynomial and a conditional function, wherein the conditional function is configured to receive feature information of a participant as input and output a signal indicating to enable symmetric calculation logic or asymmetric calculation logic; In the embodiment, the output value of the conditional function is 0 or 1; When =1, then , symmetric logic is enabled; When =0, then , asymmetric logic is enabled.

[0020] In this embodiment, the conditional function The steps implemented based on the identity information of the participant are: extracting a specific field or prefix in the identity identification for consistency judgment.

[0021] In this embodiment, the conditional function The steps implemented based on the biological feature information are: judging whether the biological feature information of the participant exists in a pre-defined trusted feature library.

[0022] In this embodiment, the conditional function The steps implemented based on multi-layer judgment logic are: The multi-layer judgment logic includes identity identification-based judgment and biological feature-based judgment.

[0023] Specifically, the symmetric polynomial is a symmetric bivariate polynomial, the asymmetric polynomial is an asymmetric bivariate polynomial, and the symmetric polynomial and the asymmetric polynomial have the same variable dimension; The symmetric polynomial ; It includes, ; The asymmetric polynomial satisfies .

[0024] In this embodiment, the conditional symmetric bivariate polynomial in step S1 is constructed according to the following formula:

[0025] Among them, is a symmetric polynomial, is an asymmetric polynomial, is a conditional function, is a pre-selected large prime number.

[0026] Based on step S1, the step is implemented, specifically: The distributor first defines three core components, and then fuses and constructs the conditional symmetric polynomial: Component 1: Symmetric polynomial . Used in the scene where the participant meets the associated conditions (such as the same group, trusted group), needs to meet . For example, select , or design other symmetric forms according to security needs (such as ), the core is to protect the equal cooperation of participants under the same conditions.

[0027] Component 2: Asymmetric polynomial . For the scenario where the participants do not meet the associated conditions (such as cross-group, untrusted group), it is necessary to meet . For example, design , exchange , and the result is , which is different from the original result, avoiding external personnel from reversing the internal logic through the key.

[0028] Component 3: Condition function . Used to judge whether the participants and meet the associated conditions, the essence is the mathematical implementation of "feature extraction + logical judgment", and the output result is only 0 or 1: output 1 indicates that the participants meet the associated conditions (such as the same group, biological feature matching); output 0 indicates that the participants do not meet the associated conditions (such as cross-group, biological feature mismatch). The design logic of the condition function: the first layer of judgment is based on the judgment of the identity prefix. Extract the numerical prefix of and and compare (such as employee prefix is "10", external partner prefix is "20"), if the prefix is consistent, it passes the first layer of judgment; otherwise, it does not pass; the second layer of judgment is based on the judgment of biological feature matching. Get the "biological feature information" or "unique hardware identifier" of the participant, and get the hash value by hashing algorithm (SHA-256) operation, and check whether it exists in the trusted feature library, if it exists, it passes the second layer of judgment; otherwise, it does not pass. Based on the results of the two layers of judgment, calculate the condition function , if both pass, then ; otherwise, .

[0029] After defining the above three components, the distributor constructs the conditionally symmetric polynomial: . Where is a preset large prime number (such as 1000003, 1000007), and the modulus operation further strengthens the security of the polynomial, preventing malicious attackers from cracking the polynomial structure through mathematical analysis.

[0030] Step S2, assign a unique identity to each participant, and calculate the identity feature value based on the identity; Specifically: The distributor generates a unique identity for each participant The rules can adopt a hierarchical fixed-length coding structure, including a subject type identifier segment, an organization affiliation code segment, a unique identity serial number segment, and a check bit. The subject type identifier segment is 2 bits, distinguishing the subject type of the participant; the organization affiliation code segment is 8 bits, identifying the organization / department to which the participant belongs; and the unique identity serial number segment is 18 bits, ensuring... Global uniqueness; 4-bit check bit used to verify the integrity of the code.

[0031] right Perform hash operations (using secure hash algorithms such as SHA-256), and convert the hash output into a finite field. An element on it, as its identity feature Hash operations can prevent To prevent tampering or forgery, and to ensure the security of identity information, It is a public index key.

[0032] Step S3: Based on the identity feature value, generate a corresponding secret share for each participant and distribute the secret share; Identity-based shares have been distributed to participants, specifically as follows: Combining participant identity characteristics The distributor will construct the conditional polynomial in step 1. As "identity-based shares," they are distributed to the corresponding participants. Each participant holds only their own corresponding share (i.e. (This means that) information on the share of other participants cannot be obtained.

[0033] Step S4: When two participants need to generate a shared key, the two participants calculate the condition function based on their respective identity feature values; The specific steps for calculating the conditional function based on identity features are as follows: When participants and When confidential information needs to be shared, both parties shall follow the procedure below: S401, Participants and Exchange of publicly available identity tokens and .

[0034] S402. Both parties use the same cryptographic hash function (such as SHA-256) locally to calculate their identity characteristics. calculate ; calculate This converts variable-length identity identifiers into fixed-length identifiers that are evenly distributed within a finite field.

[0035] S403, both parties independently calculate the condition function locally based on the same predefined rule . The double-layer judgment logic includes a first layer judgment based on an identity prefix and a second layer judgment based on a trusted feature library. If both layers pass the judgment, , if any judgment fails, .

[0036] Step S5, according to the output value of the condition function, dynamically select the symmetric calculation logic or the asymmetric calculation logic, and use the selected calculation logic to calculate a consistent shared key by the two participants.

[0037] In this embodiment, in step S5, when the value of the condition function enables the asymmetric calculation logic, the participants locally calculate and respectively; wherein the key agreement is achieved by exchanging and , and the shared key is calculated using a key derivation function.

[0038] The shared key is generated, and the specific steps are as follows: When the participants and need to generate a shared key, according to the value of , the two parties generate a shared key according to one of the following two cases: Case one: when , the symmetric logic is enabled uses its held secret share to calculate ; uses its held secret share to calculate . Since the symmetric polynomial is enabled at this time, and , it is natural that . This value is the shared key of the two parties.

[0039] Case two: when , the asymmetric logic When the asymmetric logic is enabled, in order to ensure that the two parties can calculate the same shared key, first, the participant uses its held secret share to calculate ; the participant uses its held secret share to calculate ; then, the two parties exchange and The authentication channel needs to ensure the authenticity and integrity of the exchanged data, which can be achieved by digital signature or message authentication code (MAC) technology, while exchanging a session random number Finally, both sides calculate the final shared key Wherein is a key derivation function (such as ), is a random number for this session, which can be generated by one party and sent to the other party.

[0040] As shown in Figure 2 , based on the judgment logic of double-layer verification, the following steps are taken: First layer judgment: Step 1, participants and exchange public identity through communication channel and ; Step 2, participants and extract the prefix of the pre-agreed length from the received and respectively; Step 3, consistency judgment is made on the two extracted prefixes. If the two prefixes are consistent, the corresponding participants of and belong to the same sub-group, and the first layer judgment is passed at this time; otherwise and corresponding participants belong to cross-subgroup, and do not pass.

[0041] Second layer judgment: The trusted feature library is a security database of all participants maintained by the system, which stores the mapping relationship between the identity of all registered participants and its corresponding biological feature hash value . The database provides a secure query interface to the outside.

[0042] Step 1, participants access the trusted feature library query interface provided by the distribution end through a secure query request (for example: based on TLS protocol), check whether the "biological feature information" or "unique hardware identifier" hash value corresponding to exists in the library; Step 2, similarly, participant queries the trusted feature library to check whether the "biological feature information" or "unique hardware identifier" hash value corresponding to exists in the library; Step 3, if and If all features are found to exist in the trusted feature library, the second-level judgment result is "pass"; otherwise, it is "fail".

[0043] Calculate the condition function by combining the results of the two-level judgment. If both judgments pass... ,otherwise .

[0044] like Figure 3 As shown, assign identity tokens to participants. Follow these steps: Step 1: Participants submit their entity name and organization name to the system; Step 2: The system assigns each participant according to the rules. Generate a unique identifier The rule adopts a hierarchical fixed-length coding structure, including a subject type identifier segment, an organization affiliation coding segment, a unique identity serial number segment, and a check bit. The subject type identifier segment is 2 bits, the organization affiliation coding segment is 8 bits, the unique identity serial number segment is 18 bits, and the check bit is 4 bits. Step 3: Generate the identity identifier Passed to participants and used as a public index key.

[0045] like Figure 4 As shown, the participant distribution share is calculated and distributed according to the following steps: Step 1: Enter the participant's identity information ; Step 2, for Perform hash operations (using secure hash algorithms such as SHA-256) to obtain identity characteristics. And encoded as decimal numbers; Step 3: Substitute the decimal number into the conditional polynomial to generate the participant's secret share. It is then sent to the participants via a secure channel, which can be established using industry-standard protocols such as TLS / SSL.

[0046] like Figure 5 As shown, collect the participant's "biometric information" or "unique hardware identifier" by following these steps: Step 1: During registration, collect the participant's (person's) biometric information (such as fingerprints, face) or the participant's (device's) unique hardware identifier (such as MAC address); Step 2: Perform a hash operation (using a secure hash algorithm such as SHA-256) on the collected "biometric information" or "unique hardware identifier" to obtain... ; Step 3, identify the identity of the participant bind with the and store into the trusted feature library.

[0047] The technical solution of the second aspect: a secret sharing device using the secret sharing method based on the conditional symmetric bivariate polynomial of any one of the above, comprising: A polynomial construction module is configured to construct a conditional bivariate polynomial of a cryptographic algorithm, wherein the conditional bivariate polynomial of the cryptographic algorithm is determined by a symmetric polynomial, an asymmetric polynomial and a conditional function, wherein the conditional function is configured to receive the feature information of the participant as the input and output a signal indicating the symmetric calculation logic or the asymmetric calculation logic; An identity identifier generation module is configured to assign a unique identity to each participant and calculate an identity feature value based on the identity; A share distribution module is configured to generate a corresponding secret share for each participant based on the identity feature value and distribute the secret share; A key calculation module is configured to calculate the conditional function based on the identity feature value of each participant when two participants need to generate a shared key; and configured to dynamically select the symmetric calculation logic or the asymmetric calculation logic according to the output value of the conditional function, and calculate a consistent shared key by the two participants using the selected calculation logic.

[0048] As Figure 6 shown, the system device internal unit block diagram, the device is used for executing the above method, adopts the modular design, including four core modules: 1) Conditional polynomial construction module The core function is to define the symmetric polynomial , the asymmetric polynomial and the conditional function , and construct the conditional polynomial according to the formula Support dynamic configuration of polynomial parameters (such as the coefficients of , and conditional function judgment logic (such as identity prefix rule and trusted feature library), adapt to different application scenarios.

[0049] 2) Identity identification generation module The core function is to generate a unique identity for each participant , perform hash operation (using SHA-256 and other secure hash algorithms) on , get identity feature , and encode it into decimal number , which is a public index key.

[0050] 3) Share Distribution Module Based on the participants' identity characteristics Calculate the conditional polynomial The share was calculated. The shares are distributed to the corresponding participants via a secure channel. The share at this point... It has an identity verification function to ensure that the shares are distributed only to legitimate participants and to prevent the shares from being illegally obtained.

[0051] 4) Key Calculation Module This module resides locally on the participant's device, and its core function is to... and When communicating, Use your own secret share ,calculate The identity feature value, and substitute it into Make a judgment and select based on the judgment result. or Participants calculate locally That's fine. At the same time, Also use their own share ,calculate The participant calculates the identity feature value locally. Due to polynomials The symmetry construction, when When the final calculation result satisfies This value is the key shared by both parties; when At that time, due to the choice of an asymmetric polynomial To ensure that both communicating parties can calculate the same shared key, they need to perform a key negotiation protocol. Specifically, this involves the communication participants... and Exchange their publicly disclosed identity tokens and Calculate identity feature values and Subsequently, both parties performed local calculations. and Combined, the two sides exchanged and Finally, both parties use key derivation functions to compute the final shared key. ,in For hash operations (using secure hash algorithms such as SHA-256). This is a random number for this session. Through this mechanism, even... Both sides can also obtain the same results through derivation. .

[0052] The content in the method embodiments is applicable to the device embodiments, the device embodiments specifically implement the functions of the method embodiments, and achieve the same beneficial effects as the method embodiments.

[0053] The third aspect of the technical solution is a storage medium, which stores processor-executable instructions. When the processor-executable instructions are executed by a processor, the processor-executable instructions are used to implement a secret sharing method based on a conditional symmetric bivariate polynomial.

[0054] When these stored instructions are read and executed by a processor (such as the processor in the device described above), they precisely guide the processor to complete a series of operations, and the ultimate purpose and effect is to implement the complete process and functions of the photoacoustic image segmentation method according to any one of the preceding claims. That is, the storage medium is a carrier for storing the code of the segmentation method, and when the code is executed by the processor, the functions of the method are embodied on the hardware.

[0055] Although the embodiments of the present application have been shown and described, it can be understood by those skilled in the art that various changes, modifications, replacements and variations can be made to the embodiments without departing from the principles and spirits of the present application, the scope of the present application is defined by the appended claims and their equivalents, and all should be included in the protection scope of the present application.

Claims

1. A method of secret sharing based on a conditionally symmetric bivariate polynomial, characterized by, The method comprises the following steps: Step S1, constructing a conditional bivariate polynomial of a cryptographic algorithm, wherein the conditional bivariate polynomial of the cryptographic algorithm is determined by a symmetric polynomial, an asymmetric polynomial and a conditional function, wherein the conditional function is configured to receive feature information of a participant as input and output a signal indicating to enable symmetric computation logic or asymmetric computation logic; Step S2, assigning a unique identity to each participant and calculating an identity feature value based on the identity; Step S3, generating a corresponding secret share for each participant based on the identity feature value and distributing the secret share; Step S4, when two participants need to generate a shared key, the two participants calculate the conditional function based on their respective identity feature values; Step S5, dynamically selecting the symmetric computation logic or the asymmetric computation logic according to the output value of the conditional function, and calculating a consistent shared key by the two participants using the selected computation logic.

2. The method of claim 1, wherein the conditionally symmetric bivariate polynomial is defined as The conditional symmetric bivariate polynomial in step S1 The construction formula is: wherein is a symmetric polynomial, is an asymmetric polynomial, is a conditional function, is a preselected large prime number.

3. The method of claim 2, wherein the condition is a function of the two variables. The condition function has an output value of 0 or 1; When =1, then , enable symmetric logic; When = 0, then , enabling asymmetric logic.

4. The method of claim 3, wherein the condition is a condition of a symmetric bivariate polynomial. The condition function The step implemented based on the identity information of the participant is to extract a specific field or prefix in the identity identification for consistency judgment.

5. The method of claim 3, wherein the condition is a function of the two variables. The condition function The step of implementing based on the biometric information is: judging whether the biometric information of the participant exists in a predefined trusted feature library.

6. The method of claim 3, wherein the conditionally symmetric bivariate polynomial is defined as The condition function The step implemented based on the multi-layer judgment logic is: The multi-layer judgment logic comprises identity-based judgment and biometric feature-based judgment.

7. The method of claim 1, wherein the conditionally symmetric bivariate polynomial is defined as The symmetric polynomial is a symmetric bivariate polynomial, the asymmetric polynomial is an asymmetric bivariate polynomial, and the symmetric polynomial and the asymmetric polynomial have the same variable dimension; the symmetric polynomial ; It comprising, ; the asymmetric polynomial satisfies .

8. The method of claim 1, wherein, S5, when the value of the condition function enables the asymmetric computation logic, the parties locally compute and respectively; whereby the exchange and Key agreement is achieved and a shared key is computed using a key derivation function.

9. A secret sharing apparatus using a secret sharing method based on a conditionally symmetric bivariate polynomial according to any one of claims 1 to 8, characterized by Comprises: A polynomial construction module for constructing a conditional bivariate polynomial of a cryptographic algorithm, wherein the conditional bivariate polynomial of the cryptographic algorithm is determined by a symmetric polynomial, an asymmetric polynomial and a conditional function, wherein the conditional function is configured to receive feature information of a participant as input and output a signal indicating to enable symmetric computation logic or asymmetric computation logic; An identity identifier generation module for assigning a unique identity to each participant and calculating an identity feature value based on the identity; A share distribution module for generating a corresponding secret share for each participant based on the identity feature value and distributing the secret share; A key calculation module for calculating the conditional function based on the respective identity feature values when two participants need to generate a shared key; And for dynamically selecting the symmetric computation logic or the asymmetric computation logic according to the output value of the conditional function, and calculating a consistent shared key by the two participants using the selected computation logic.

10. A storage medium having stored therein instructions executable by a processor, the instructions causing the processor to: The instructions executable by the processor when executed by the processor are used to implement the secret sharing method based on the conditional symmetric bivariate polynomial according to any one of claims 1-8. ​

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