A key reconstruction method based on blockchain and rational secret sharing

Abstract

The present invention discloses a key reconstruction method based on blockchain and rational secret sharing, which mainly includes three stages: key distribution stage, evolutionary game model construction and solution stage and key reconstruction stage. The secret distribution stage is that the key owner splits the secret into n sub-secrets, and then distributes the sub-secrets to n blockchain sub-nodes for storage; the game model construction and solution stage refers to constructing an evolutionary game model of the secret reconstruction process according to the attributes of the nodes, and solving the dynamic evolution equilibrium point, so that the nodes can maximize their benefits on the basis of participating in secret reconstruction; the key reconstruction stage refers to the node responding to the key reconstruction request after the key owner issues a key reconstruction request. In this process, a smart contract is designed to dynamically adjust the incentive value of the evolutionary game, so that the node dynamically adjusts its own behavior to participate in the key reconstruction process. When the number of participants is greater than t, the key can be reconstructed.

Description

Technical Field

[0001] The present invention belongs to the fields of cryptography, information security, privacy protection, etc., and specifically relates to a key reconstruction method based on blockchain and rational secret sharing. Background Art

[0002] In the field of cryptography and information security, key management is crucial. Keys are used to encrypt and decrypt data, verify identities, and ensure the confidentiality and integrity of communications. Effective key management can prevent unauthorized access and data leakage, ensuring the security and reliability of the system.

[0003] Key management also involves key generation, storage, distribution, rotation, and destruction, which are essential to ensure information security. Secure storage of keys can prevent unauthorized access to keys and malicious operations on the system. If the key is leaked, it may lead to data leakage, information security risks, and system attacks. Therefore, key storage is a very important part of key management. It is necessary to ensure that only authorized entities can access and use keys to maintain the security and reliability of the system.

[0004] Compared with other key storage methods, distributed storage of keys can improve the security and reliability of the system. By distributing the keys in multiple locations or entities, the system can continue to operate even if a storage node is attacked or fails. This approach can reduce the risk of single point failure and increase the system's ability to resist attacks. In addition, distributed storage can also improve the availability of keys, allowing the system to better respond to needs in various situations.

[0005] In recent years, various methods for distributed key storage have been proposed.

[0006] For example, the invention patent with Chinese patent publication number CN114866230A discloses a method and system for distributed key storage for big data platforms. In the process of storing keys in a distributed key storage module and restoring the original key, all key fragments are cached in the key management module. After the key call is completed, the complete key is directly deleted from the cache without the need for storage, thereby ensuring that the complete key is not leaked. At the same time, the keys are distributedly stored in multiple physical machines or virtual machines, and no leakage will occur if any storage node is compromised, thereby ensuring key security.

[0007] In addition, the invention patent with publication number CN108197484A adopts an all-or-nothing transformation algorithm to transform the stored data to achieve the confidentiality of the distributed storage node data. It also adopts erasure coding technology to encode the all-or-nothing transformation package for distributed storage and use it to restore the correct data to achieve data recoverability.

[0008] However, most of these schemes have various limitations. First, providing a distributed key storage scheme that combines passwords or biometrics with secret sharing will lead to new security issues, such as how to ensure the security and immutability of passwords and biometrics. Second, most schemes still cannot avoid the problem of response delay, which will cause the key owner to be unable to reconstruct the key on schedule. In addition, the existing schemes cannot dynamically adjust the incentive strategy of participants, which will still lead to the problem of node silence.

[0009] Therefore, as a way to solve the problems of immutability and limited storage resources, blockchain has wide applications in distributed scenarios. However, due to the recoverability, customizability and limited rationality of rational secret sharing, combining blockchain with rational secret sharing remains a challenge to be solved. Summary of the invention

[0010] In order to solve the problems existing in the prior art mentioned in the background technology, the purpose of the present invention is to propose a key reconstruction method based on blockchain and rational secret sharing, construct an incentive-compatible evolutionary game model, and then design a smart contract to dynamically adjust the incentive strategy, so as to encourage all nodes to honestly share sub-secrets to reconstruct the user's private key.

[0011] Furthermore, the sub-secret owners are divided into two parties, those who participate in and those who do not participate in secret reconstruction, to construct a dynamic game model of secret reconstruction. The dynamic game model is constructed according to factors such as the credibility, responsiveness, and cooperation coefficient of the sub-secret owners, and the replication dynamics equation of the model is derived. The evolutionary stability strategy of the model is obtained through differential equations, and then smart contracts are designed to dynamically adjust the strategies of the participants, so that the dynamic evolutionary game model achieves incentive compatibility.

[0012] Since the participants' interests can be maximized only when they choose to share sub-secrets honestly in the designed dynamic evolutionary game model, the risk of silence or delayed response of the participants is solved. The key reconstruction method based on blockchain and rational secret sharing is helpful in solving the problem of distributed key storage.

[0013] The complete technical solution of the present invention includes constructing a key reconstruction scheme based on blockchain and rational secret sharing, which is divided into three stages: key distribution stage, evolutionary game model construction and solution stage and key reconstruction stage; wherein the key distribution stage includes the following steps:

[0014] Step 1 Initialization: First define a large prime number p, and there is a large prime factor q of p-1. And it is a q-order element. Where t is the threshold value, n is the number of participants, and S is shared as the initial secret.

[0015] Step 2: Secret distribution: The secret distributor can select random elements a1, a2, ..., a from the finite field GF(p) t-1 , construct a t-1 dimensional polynomial f(x)=a0+a1x+…+a t-1 x t-1 modp, the constant term S = a0 is the initial secret, and the secret fragment y is calculated at this time i = f(i), transmit the secret fragment to participant P via a secure channel i , i = 1, ..., n, and broadcast the corresponding verification information at the same time

[0016] Step 3 Sub-secret verification: When the node receives the verification information α j Afterwards, the equation can be calculated If the equation holds true, it means that the secret fragment received by the node is correct, otherwise it means that it has received a forged secret fragment.

[0017] As a further preferred solution, the specific implementation of the evolutionary game model construction and solution stage includes the following steps:

[0018] Step 1 Initialization: The evolutionary game model consists of a quaternion, G = (P, N, S, U), where P is all nodes that have sub-secrets, N is the set of nodes that participate in sub-secret sharing, S is the strategy space, and U is the payoff matrix of both parties. In the secret sharing game model, sub-nodes decide whether to participate in sharing by calculating sharing benefits and sharing costs. The benefits of sub-nodes can be divided into two types: direct benefits and cooperative benefits.

[0019] Step 2: Calculate direct benefits: Direct benefits refer to the benefits that a node can obtain by participating in secret sharing. For the i-th node, the direct benefit is mainly related to the participation degree ρ of the secret sharing request. i and node reputation c i Participation refers to the degree of response of the child node after the user issues a secret reconstruction request. When other nodes fail to respond in time and this node responds in time, the participation is higher than other nodes, and vice versa. The direct benefit is recorded as (k1ρ i +k2c i )+I i -S i (k1>0, k2>0), S i is the cost of nodes participating in secret sharing, I i Dynamic benefits for nodes participating in secret reconstruction.

[0020] Step 3: Calculate indirect benefits: When nodes i and j both choose to participate in secret sharing, the process of secret reconstruction is promoted, and the nodes participating in secret sharing can gain cooperation benefits in the process of secret reconstruction. Based on the above analysis, the cooperation benefits between nodes can be recorded as λ(k1ρ i +k2c i )+I i -S i (λ>1). According to the rationality analysis in the real environment, the benefits of collaboration need to satisfy 1+1>2 to promote the sub-secret sharing of participating nodes.

[0021] Step 4: Establish and solve the replication dynamics equation: According to the Malthusian equation, the user replication dynamics equation can be expressed by the growth rate of the sharing strategy:

[0022] F(x)=x(1-x)((x[λ(k1ρ i +k2c i )+I i -S i ]+(1-x)[(k1ρ i +k2c i )+I i -S i ])

[0023] +c′ i )

[0024] Where x is the probability of a node participating in key reconstruction. If F(x) = 0, we can get three stable states of the node replication dynamic equation F(x).

[0025]

[0026] Step 5 analyzes the evolution of node strategies under different concepts.

[0027] As a further preferred solution, according to the characteristics of the strategy changes of nodes in different states, a smart contract is designed to dynamically adjust the incentive mechanism. The smart contract design is as follows:

[0028] Step 1: Design the function SetTotal(). SetTotal() is based on the node set P = {P1, P2, ..., P N} to set the total number of nodes participating in the evolutionary game model, defined as total.

[0029] Step 2: Calculate the probability of a node participating in key reconstruction under the existing incentive mechanism.

[0030] Step 3: Calculate the proportion of nodes participating in key reconstruction in the current state

[0031] Step 4 If Then adjust the incentive strategy i = S ic′ i -[(λ-1)x+1](k1ρ i +k2c i )+1; otherwise go to step 5.

[0032] Step 5 returns the expected return value.

[0033] In some embodiments, a smart contract based on the evolutionary game reconstruction model can also be designed to encourage nodes to participate in secret reconstruction and minimize the incentive cost. When the key owner issues a secret reconstruction request, at least t nodes need to participate in secret sharing to reconstruct the key. The proportion of nodes participating in secret sharing is at least Smart contracts are used to record the participation ratio of nodes in the current state. If the current participation ratio x meets the condition in It is necessary to dynamically adjust the benefits and evolve the node's decision into a participation strategy.

[0034] When the key owner sends a key reconstruction request to the blockchain node, the node is motivated by the evolutionary game model to participate in the key reconstruction. When recovering the key, due to the trend of the incentive mechanism, the number of participants P who meet the threshold requirement is i , i=1,…,n all send their secret fragment y i , and by the equation To verify the correctness of the secret fragment, if the secret fragment y i If the result is correct after verification, the participant can restore the initial secret S through the Lagrange difference formula.

[0035] Beneficial effects of the present invention: The present invention proposes a key reconstruction method based on blockchain and rational secret sharing, which is used for secret reconstruction in the case of distributed key storage; the present invention uses blockchain to store sub-secrets split from keys, realizes automatic management and control of sub-secrets, and improves the flexibility and customizability of key management; in addition, the present invention introduces evolutionary game theory, which can consider the dynamic behavior and strategy changes of participating nodes, so that the secret reconstruction scheme can adapt to changes in different environments and participants, and can analyze the strategy selection and evolution process between different participants, so as to design a more robust and stable secret reconstruction scheme. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1A diagram of a key distribution and reconstruction model in one embodiment of the present invention is shown. DETAILED DESCRIPTION

[0037] The preferred embodiments of the present invention will be described in detail below in conjunction with the accompanying drawings so that the purpose, features and advantages of the present invention can be more clearly understood. It should be understood that the embodiments shown in the accompanying drawings are not intended to limit the scope of the present invention, but are only intended to illustrate the essential spirit of the technical solution of the present invention.

[0038] In the following description, certain specific details are set forth for the purpose of illustrating the various disclosed embodiments to provide a thorough understanding of the various disclosed embodiments. However, those skilled in the relevant art will recognize that the embodiments may be practiced without one or more of these specific details. In other cases, well-known devices, structures, and techniques associated with the present application may not be shown or described in detail to avoid unnecessarily obscuring the description of the embodiments.

[0039] References throughout the specification to "one embodiment" or "an embodiment" indicate that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment. Thus, the appearances of "in one embodiment" or "in an embodiment" in various places throughout the specification are not necessarily all referring to the same embodiment. Furthermore, the particular features, structures, or characteristics may be combined in any manner in one or more embodiments.

[0040] Embodiment 1:

[0041] The three main stages involved in this embodiment are: key distribution stage, evolutionary game model construction and solution stage, and key reconstruction stage. The secret distribution stage is that the key owner splits the secret into n sub-secrets, and then distributes the sub-secrets to n blockchain sub-nodes for storage; the game model construction and solution stage refers to building an evolutionary game model of the secret reconstruction process based on the attributes of the node (such as reputation value, response degree, cooperation coefficient, storage cost, etc.), and solving the dynamic evolution equilibrium point, so that the node can maximize its benefits on the basis of participating in secret reconstruction; the key reconstruction stage refers to the node responding to the key reconstruction request after the key owner issues a key reconstruction request. This process designs a smart contract to dynamically adjust the incentive value of the evolutionary game, so that the node dynamically adjusts its own behavior to participate in the key reconstruction process. When the number of participants is greater than t, the key can be reconstructed.

[0042] The specific process is as follows:

[0043] (1) Key distribution phase

[0044] Step 1 Initialization: First define a large prime number p, and there is a large prime factor q of p-1. And it is a q-order element. Where t is the threshold value, n is the number of participants, and S is shared as the initial secret.

[0045] Step 2: Secret distribution: The secret distributor can select random elements a1, a2, ..., a from the finite field GF(p) t-1 , construct a t-1 dimensional polynomial f(x)=a0+a1x+…+a t-1 x t-1 mod p, the constant term S = a0 is the initial secret, and the secret fragment y is calculated at this time i = f(i), transmit the secret fragment to participant P via a secure channel i , i = 1, ..., n, and broadcast the corresponding verification information at the same time

[0046] Step 3 Sub-secret verification: When the node receives the verification information α j Afterwards, the equation can be calculated If the equation holds true, it means that the secret fragment received by the node is correct, otherwise it means that it has received a forged secret fragment.

[0047] (2) Evolutionary game model construction and solution stage

[0048] Step 1 Initialization: The evolutionary game model consists of a quaternion, G = (P, N, S, U), where P is all nodes that have sub-secrets, N is the set of nodes that participate in sub-secret sharing, S is the strategy space, and U is the payoff matrix of both parties. In the secret sharing game model, sub-nodes decide whether to participate in sharing by calculating sharing benefits and sharing costs. The benefits of sub-nodes can be divided into two types: direct benefits and cooperative benefits.

[0049] Step 2: Calculate direct benefits: Direct benefits refer to the benefits that a node can obtain by participating in secret sharing. For the i-th node, the direct benefit is mainly related to the participation degree ρ of the secret sharing request. i and node reputation c i Participation refers to the degree of response of the child node after the user issues a secret reconstruction request. When other nodes fail to respond in time and this node responds in time, the participation is higher than other nodes, and vice versa. The direct benefit is recorded as (k1ρ i +k2c i )+I i -S i (k1>0, k2>0), S i is the cost of nodes participating in secret sharing, I i Dynamic benefits for nodes participating in secret reconstruction.

[0050] Step 3: Calculate indirect benefits: When nodes i and j both choose to participate in secret sharing, the process of secret reconstruction is promoted, and the nodes participating in secret sharing can gain cooperation benefits in the process of secret reconstruction. Based on the above analysis, the cooperation benefits between nodes can be recorded as λ(k1ρ i +k2c i )+I i -S i (λ>1). According to the rationality analysis in the real environment, the benefits of collaboration need to satisfy 1+1>2 to promote the sub-secret sharing of participating nodes.

[0051] Step 4: Establish and solve the replication dynamics equation: According to the Malthusian equation, the user replication dynamics equation can be expressed by the growth rate of the sharing strategy:

[0052] F(x)=x(1-x)((x[λ(k1ρ i +k2c i )+I i -S i ]+(1-x)[(k1ρ i +k2c i )+I i -S i ])

[0053] +c′ i )

[0054] Where x is the probability of a node participating in key reconstruction. If F(x) = 0, we can get three stable states of the node replication dynamic equation F(x):

[0055]

[0056] Step 5 analyzes the evolution of node strategies under different concepts.

[0057] (3) Secret reconstruction stage

[0058] Step 1: Design the function SetTotal(). SetTotal() is based on the node set P = {P1, P2, ..., P N} to set the total number of nodes participating in the evolutionary game model, defined as total.

[0059] Step 2: Calculate the probability of a node participating in key reconstruction under the existing incentive mechanism.

[0060] Step 3: Calculate the proportion of nodes participating in key reconstruction in the current state

[0061] Step 4 If Then adjust the incentive strategy i =S i -c′ i -[(λ-1)x+1](k1ρ i +k2c i )+1; otherwise go to step 5.

[0062] Step 5 returns the expected return value and proceeds to step 6.

[0063] Step 6: There are more than or equal to t participants P i , i=1,…,n all send their secret fragment y i , through the equation To verify the correctness of the secret fragment, if the secret fragment y i If the verification result is correct, the secret owner can restore the initial secret S through the Lagrange difference formula.

[0064] In summary, the core of the rational secret sharing scheme designed using the evolutionary game model is to introduce evolutionary games on the basis of the existing secret sharing scheme. The sub-secret owners are divided into two parties, those who participate in secret reconstruction and those who do not, to construct a dynamic game model for secret reconstruction. The dynamic game model is constructed based on the reputation value, response degree, cooperation coefficient and other factors of the sub-secret owners, and the replication dynamics equation of the model is derived. The evolutionary stability strategy of the model is obtained through differential equations, and then the smart contract is designed to dynamically adjust the participant strategy, so that the dynamic evolutionary game model achieves incentive compatibility. In the designed dynamic evolutionary game model, the interests of the participants can only be maximized when the participants choose to share the sub-secrets honestly, which solves the risk of silence or delayed response of the participants.

[0065] The above shows and describes the basic principles and main features of the present invention and the advantages of the present invention. It should be understood by those skilled in the art that the present invention is not limited to the above embodiments. The above embodiments and descriptions are only for explaining the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, which fall within the scope of the present invention to be protected. The scope of protection of the present invention is defined by the attached claims and their equivalents.

Claims

1. A key reconstruction method based on blockchain and rational secret sharing, characterized in that: Construct an incentive-compatible evolutionary game model, and then design smart contracts to dynamically adjust the incentive strategy, so that all nodes share sub-secrets honestly to reconstruct the user's private key; divide the sub-secret owners into two parties who participate in secret reconstruction and those who do not participate in secret reconstruction, and construct a dynamic game model for secret reconstruction. According to the reputation value, response degree, and cooperation coefficient of the sub-secret owner, a dynamic game model is constructed and the replication dynamics equation of the model is derived. The evolutionary stability strategy of the model is obtained through differential equations, and then the smart contract is designed to dynamically adjust the participant strategy, so that the dynamic evolutionary game model achieves incentive compatibility; Specifically, the key reconstruction method includes at least the following three stages: key distribution stage, evolutionary game model construction and solution stage and key reconstruction stage; The key distribution phase includes the following steps: Step 11 Initialization: First define a large prime number p, and there is a large prime factor q of p-1; Step 12: Secret distribution: The secret distributor selects random elements a1, a2, …, a from the finite field GF(p) t-1 , construct a t-1 dimensional polynomial f(x)=a0+a1x+…+a t-1 x t-1 modp, constant term S = a0, where a0 is the initial secret, and the secret fragment y is calculated at this time i = f(i), transmit the secret fragment to participant P via a secure channel i ,i=1,…,n, and broadcast the corresponding verification information at the same time And it is a q-order element; where t is the threshold value, n is the number of participants, and S is shared as the initial secret; Step 13 Sub-secret verification: When the node receives the verification information α j After that, calculate the equation If the equation holds true, it means that the secret fragment received by the node is correct, otherwise it means that it has received a forged secret fragment; The evolutionary game model construction and solution stage includes the following steps: Step 21 Initialization: The evolutionary game model consists of a four-tuple, G = (P, N, S, U), where P is all nodes that have sub-secrets, N is the set of nodes that participate in sub-secret sharing, S is the strategy space, and U is the payment matrix of both parties in the game; in the secret sharing game model, the sub-node decides whether to participate in sharing by calculating the sharing benefits and sharing costs; Step 22: Calculate direct benefits: Direct benefits refer to the benefits that a node can obtain by participating in secret sharing; direct benefits are recorded as (k1ρ i +k2c i )+I i -S i , where k1>0, k2>0, S i is the cost of nodes participating in secret sharing, I i is the dynamic benefit of the node participating in secret reconstruction; for the i-th node, the direct benefit and the participation degree of the secret sharing request ρ i and node reputation c i related; Step 23: Calculate the indirect benefits: The cooperation benefits between nodes are recorded as λ(k1ρ i +k2c i )+I i -S i ,λ>1; the benefit of collaboration satisfies 1+1>2 to promote the sub-secret sharing of participating nodes; Step 24: Establish and solve the replication dynamics equation: According to the Malthusian equation, the user replication dynamics equation is expressed by the growth rate of the sharing strategy: F(x)=x(1-x)((x[λ(k1ρ i +k2c i )+I i -S i ]+(1-x)[(k1ρ i +k2c i )+I i -S i ])+c′ i ) Where x is the probability of a node participating in key reconstruction; assuming F(x) = 0, we get three stable states of the node replication dynamic equation F(x): Step 25 analyzes the evolution of node strategies under different states; The key reconstruction phase includes the following steps: Step 31 designs the function SetTotal(), which is based on the node set P = {P1, P2, ..., P N } to set the total number of nodes participating in the evolutionary game model, defined as total; Step 32 calculates the probability of a node participating in key reconstruction under the existing incentive mechanism Step 33 calculates the proportion of nodes participating in key reconstruction in the current state Step 34 If Then adjust the incentive strategy i =S i -c′ i -[(λ-1)x+1](k1ρ i +k2c i )+1; otherwise go to step 5; Step 35 returns the expected return value and proceeds to step 36; Step 36: greater than or equal to t participants P i , i=1,…,n all send their secret fragments y i , through the equation To verify the correctness of the secret fragment, if the secret fragment y i If the verification result is correct, the secret owner can restore the initial secret S through the Lagrange difference formula.

2. The key reconstruction method based on blockchain and rational secret sharing according to claim 1 is characterized in that: Design a smart contract based on the evolutionary game reconstruction model to encourage nodes to participate in secret reconstruction and minimize the incentive cost; when the key owner issues a secret reconstruction request, at least t nodes need to participate in secret sharing to reconstruct the key, and the proportion of nodes participating in secret sharing is at least Smart contracts are used to record the participation ratio of nodes in the current state. If the current participation ratio x meets the condition in It is necessary to dynamically adjust the benefits and evolve the node's decision into a participation strategy.

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