阅读说明：本技术 一种云计算环境下安全计算纳什均衡点的方法 (Method for safely calculating Nash equilibrium point in cloud computing environment ) 是由 张冬傲 郑培嘉 陈德霖 于 2020-11-16 设计创作，主要内容包括：本发明提出一种云计算环境下安全计算纳什均衡点的方法,涉及多媒体信息安全的技术领域,解决了如何更加安全地计算纳什均衡点,得到数据资源最优分配策略的问题,本发明从数据资源分配的问题出发,用户客户端与数据中心为得到最佳融合策略进行两方博弈决策时,双方需要利用收益矩阵来计算纳什均衡点以获得最优分配策略,将同态加密技术应用于数据资源分配,结合博弈论,在云端环境下,基于安全乘法协议和安全除法协议,计算过程中不需要向云服务器暴露过多隐私,直接对密文状态下的数据进行计算,在不泄露隐私数据的情况下完成多方计算并且得到纳什均衡点最优策略,而且基于同态加密技术也可以保证计算精度。(The invention provides a method for safely calculating Nash equilibrium points in a cloud computing environment, which relates to the technical field of multimedia information safety and solves the problem of how to calculate the Nash equilibrium points more safely to obtain an optimal distribution strategy of data resources, and starts from the problem of data resource distribution, when a user client and a data center carry out two-party game decision for obtaining an optimal fusion strategy, the two parties need to calculate the Nash equilibrium points by utilizing a gain matrix to obtain the optimal distribution strategy, a homomorphic encryption technology is applied to data resource distribution, and in combination with a game theory, under a cloud environment, based on a secure multiplication protocol and a secure division protocol, excessive privacy does not need to be exposed to a cloud server in the calculation process, data in a ciphertext state is directly calculated, multi-party calculation is completed under the condition that private data are not leaked, and the optimal strategy of the Nash equilibrium points is obtained, and the calculation accuracy can be ensured based on the homomorphic encryption technology.)

1. A method for securely computing Nash equilibrium points in a cloud computing environment, comprising:

s1, determining a user client and a data center which participate in game decision in a data resource allocation process;

s2, generating a public key pk and a private key sk locally, storing the private key sk locally, informing the cloud server of the public key pk, and informing the private server of the private key sk;

s3, determining an income matrix A of the user client and an income matrix B of the data center, carrying out homomorphic encryption on the income matrix A of the user client and the income matrix B of the data center respectively by using a public key pk, and uploading the encrypted income matrix A and the encrypted income matrix B to the cloud server;

s4, the cloud server calculates Nash equilibrium point encryption results of the user client and the data center through a secure multiplication protocol and a secure division protocol;

and S5, the cloud server returns the Nash equilibrium point encryption result to the local, and the local decrypts the Nash equilibrium point encryption result by using the private key.

2. The method for securely computing nash equilibrium point in cloud computing environment as claimed in claim 1, wherein the process of generating the public key pk and the private key sk in step 2 is:

s21, randomly taking a large prime number p and a large prime number q, and calculating intermediate parameters n and lambda to satisfy the following conditions:

n ═ pq, λ ═ lcm (p-1, q-1), where lcm denotes the least common multiple;

s22, defining a function L (u), wherein L (u) satisfies the following conditions:random accessSatisfy gcd (L (g)^λmodn²) N) is 1, wherein u represents an intermediate parameter, gcd represents the greatest common divisor,represents a positive integer;

s23, calculating an intermediate parameter u:

μ＝(L(g^λmodn²))^-1modn

the public key pk is (n, g) and the private key sk is (λ, μ).

3. The method for secure nash equilibrium point computation in cloud computing environment as claimed in claim 2, wherein let the revenue matrix a of the user client be PA and the revenue matrix B of the data center be P_BTo P_AAnd P_BEach element m in the set is encrypted, a positive integer r is randomly selected, r is less than n, and the encrypted ciphertext c of the element m satisfies the following conditions:

wherein the content of the first and second substances,representing the ciphertext under paillier homomorphic encryption.

4. The method for secure nash equilibrium point computation in cloud computing environment as claimed in claim 3, wherein the profit E of the user client is obtained based on the profit matrix A of the user client_ASatisfies the following conditions:

wherein S is_ARepresenting a user client decision matrix; p_AA revenue matrix A representing a user client; s^T _BRepresenting a transpose of a data center decision matrix;

nash equilibrium point of data center based on income E of user client_ADecision matrix S for user client_AEach element x in_iPartial derivatives ofCalculation whenThen we get the nash equilibrium point of the data center, i represents the element order.

5. The method for secure Nash equilibrium point computation in cloud computing environment as claimed in claim 4, wherein the profit matrix P is based on data center_BIncome of data center E_BSatisfies the following conditions:

wherein S is_BRepresenting a data center decision matrix; p_BTo representA revenue matrix B of the data center;representing a transpose of a user client decision matrix;

nash equilibrium point of user client based on data center profit E_BDecision matrix S for data center_BEach element y in_iPartial derivatives ofCalculation whenThen get the Nash equilibrium point of the user client, i represents the element order.

6. The method for secure nash equilibrium point computation in cloud computing environment as claimed in claim 5, wherein the nash equilibrium point computation process of the user client and the nash equilibrium point computation process of the data center are performed in the encrypted domain.

7. The method for secure nash equilibrium point computation in cloud computing environment as claimed in claim 6, wherein the secure multiplication protocol of step S4 includes the process of:

s41, setting Nash equilibrium point of user client and parameter related to encryption domain in calculation process of Nash equilibrium point of data centerAndcalculating the product of (1);

s42, randomly generating an integer r by the cloud server₁And an integer r₂，r₁A, r2 > b, calculated by homomorphismAnd

s43, the cloud server willAndsending the data to the private server, and calculating c1 ═ a + r after decryption by the private server₁)(b+r₂) And encrypt the resultReturning to the cloud server;

s44, cloud server computing And obtaining the product result of the encryption domains of the plaintext a and the plaintext b.

8. The method for secure nash equilibrium point computation in cloud computing environment as claimed in claim 6, wherein the secure division protocol of step S4 includes the process of:

s401, setting Nash equilibrium point of user client and related to encrypted domain parameter in Nash equilibrium point calculation process of data centerAndcalculating the division of (1);

s402, the cloud server randomly generates an integer r and an integer Q, and calculates an intermediate ciphertext c2 by making S ═ r · Q:

s403, mixingS andsending to the private server, decrypting by the private serverObtain the plaintext m3Private server computingAnd returns it as an intermediate result to the cloud server;

and S404, the cloud server returns the intermediate result to the local in cooperation with the Q, and the encrypted domain division result is obtained after local decryption.

9. The method for secure computation of nash equilibrium point under cloud computing environment as claimed in claim 6, wherein the process of locally decrypting nash equilibrium point encryption result by using private key at step S5 satisfies the following steps:

let the nash equilibrium point encryption result be c3, and the formula for the nash equilibrium point encryption result to be decrypted as plaintext m5 is:

m₅＝L(c3^λmodn²)·μmod n

where μ represents a ciphertext parameter.

Technical Field

The invention relates to the technical field of multimedia information security, in particular to a method for safely calculating a Nash equilibrium point in a cloud computing environment.

Background

Under the traditional situation, when a computing center distributes data resources, the computing center collects information of each user under a user client, then the information of the users is integrated for analysis, Nash equilibrium points are obtained to serve as optimal results, then the data resources are distributed according to the optimal results, and the method is simple and clear, but the method is easy to expose privacy of the users and is not beneficial to guaranteeing safety privacy of the whole data interaction process.

In recent years, with the development and popularization of cloud computing, users tend to store data on the cloud more and more, and by utilizing rich computing and storage resources provided by a cloud server, more efficient and professional data services can be provided for the users, but the risk that private data is leaked to the cloud server also inevitably exists, in order to solve the problem that a cloud service provider is not trusted under a cloud environment, a privacy protection clustering data mining method is disclosed in a Chinese patent with publication number CN108881204A in 11/23/2018, the users encrypt the data and then distribute the data to the cloud service provider, the cloud service provider utilizes a homomorphic encryption algorithm to realize privacy protection, but the cloud service provider cannot directly access the user data to destroy the privacy of the users, the security in the data interaction computing process is improved, but the patent does not consider the distribution condition after data resource mining, if the data resource distribution is involved, when two sides of a user client and a data center perform game decision for obtaining an optimal fusion strategy, the two sides need to calculate the nash equilibrium points by using the income matrix to obtain an optimal distribution strategy, but the information of the income matrix in the game decision process is also sensitive, so that how to calculate the nash equilibrium points more safely under a cloud computing environment so as to obtain the optimal distribution strategy of data resources is a technical challenge faced by technical personnel in the field at present.

Disclosure of Invention

In order to solve the problem of how to more safely calculate the Nash equilibrium points and obtain the optimal distribution strategy of data resources in a cloud computing environment, the invention provides a method for safely calculating the Nash equilibrium points in the cloud computing environment, which can complete multi-party calculation and obtain the optimal strategy of the Nash equilibrium points without revealing privacy data and ensure the calculation precision.

In order to achieve the technical effects, the technical scheme of the invention is as follows:

a method for secure computation of nash equilibrium points in a cloud computing environment, comprising:

s1, determining a user client and a data center which participate in game decision in a data resource allocation process;

s2, generating a public key pk and a private key sk locally, storing the private key sk locally, informing the cloud server of the public key pk, and informing the private server of the private key sk;

s3, determining an income matrix A of the user client and an income matrix B of the data center, carrying out homomorphic encryption on the income matrix A of the user client and the income matrix B of the data center respectively by using a public key pk, and uploading the encrypted income matrix A and the encrypted income matrix B to the cloud server;

s4, the cloud server calculates Nash equilibrium point encryption results of the user client and the data center through a secure multiplication protocol and a secure division protocol;

and S5, the cloud server returns the Nash equilibrium point encryption result to the local, and the local decrypts the Nash equilibrium point encryption result by using the private key.

Preferably, the process of generating the public key pk and the private key sk in step 2 is as follows:

s21, randomly taking a large prime number p and a large prime number q, and calculating intermediate parameters n and lambda to satisfy the following conditions:

n ═ pq, λ ═ lcm (p-1, q-1), where lcm denotes the least common multiple;

s22, defining a function L (u), wherein L (u) satisfies the following conditions:random accessSatisfy gcd (L (g)^λmodn²) N) is 1, wherein u represents an intermediate parameter, gcd represents the greatest common divisor,represents a positive integer;

s23, calculating an intermediate parameter u:

μ＝(L(g^λmodn²))^-1modn

the public key pk is (n, g) and the private key sk is (λ, μ).

Preferably, let the revenue matrix A of the user client be denoted as PA and the revenue matrix B of the data center be denoted as P_BTo P_AAnd P_BEach element m in the set is encrypted, a positive integer r is randomly selected, r is less than n, and the encrypted ciphertext c of the element m satisfies the following conditions:

wherein the content of the first and second substances,representing the ciphertext under paillier homomorphic encryption.

Preferably, the user client revenue E_ASatisfies the following conditions:

wherein S is_ARepresenting a user client decision matrix; p_AA revenue matrix A representing a user client; s^T _BRepresenting a transpose of a data center decision matrix;

nash equilibrium point of data center based on income E of user client_ADecision matrix S for user client_AEach element x in_iPartial derivatives ofCalculation whenThen we get the nash equilibrium point of the data center, i represents the element order.

Preferably, the profit E of the user client is obtained based on the profit matrix A of the user client_ASatisfies the following conditions:

wherein S is_BRepresenting a data center decision matrix; p_BA revenue matrix B representing the data center;representing a transpose of a user client decision matrix;

nash equilibrium point of user client based on data center profit E_BDecision matrix S for data center_BEach element y in_iPartial derivatives ofCalculation whenThen get the Nash equilibrium point of the user client, i represents the element order.

Preferably, the process of nash balance point calculation of the user client and nash balance point calculation of the data center are both completed in the encrypted domain.

Preferably, the secure multiplication protocol of step S4 includes the following procedures:

s41, setting Nash equilibrium point of user client and parameter related to encryption domain in calculation process of Nash equilibrium point of data centerAndcalculating the product of (1);

s42, randomly generating an integer r by the cloud server₁And an integer r₂，r₁A, r2 > b, calculated by homomorphismAnd

s43, the cloud server willAndsending the data to the private server, and calculating c1 ═ a + r after decryption by the private server₁)(b+r₂) And encrypt the resultReturning to the cloud server;

s44, cloud server computing And obtaining the product result of the encryption domains of the plaintext a and the plaintext b.

Preferably, the secure division protocol of step S4 includes the following procedures:

s401, setting Nash equilibrium point of user client and related to encrypted domain parameter in Nash equilibrium point calculation process of data centerAndcalculating the division of (1);

s402, the cloud server randomly generates an integer r and an integer Q, and calculates an intermediate ciphertext c2 by making S ═ r · Q:

s403, mixingS andsending to the private server, decrypting by the private serverObtain the plaintext m3Private server computingAnd returns it as an intermediate result to the cloud server;

and S404, the cloud server returns the intermediate result to the local in cooperation with the Q, and the encrypted domain division result is obtained after local decryption.

Preferably, the process of locally decrypting the nash equilibrium point encryption result by using the private key at step S5 satisfies the following conditions:

let the nash equilibrium point encryption result be c3, and the formula for the nash equilibrium point encryption result to be decrypted as plaintext m5 is:

m₅＝L(c3^λmodn²)·μmod n

where μ represents a ciphertext parameter.

Compared with the prior art, the technical scheme of the invention has the beneficial effects that:

the invention provides a method for safely calculating Nash equilibrium points in a cloud computing environment, which is based on the problem of data resource allocation, and aims to solve the problem that when a user client and a data center carry out two-party game decision for obtaining an optimal fusion strategy, the two parties need to calculate the Nash equilibrium points by utilizing a revenue matrix so as to obtain the optimal allocation strategy.

Drawings

FIG. 1 is a schematic block diagram illustrating a data center distributing data resources in a conventional case;

FIG. 2 is a flow chart illustrating a method for securely computing a Nash equilibrium point in a cloud computing environment according to an embodiment of the present invention;

fig. 3 is a graph showing a calculation error curve of the method for securely calculating the nash equilibrium point in the cloud computing environment according to the present invention.

Detailed Description

The drawings are for illustrative purposes only and are not to be construed as limiting the patent;

for better illustration of the present embodiment, certain parts of the drawings may be omitted, enlarged or reduced, and do not represent actual dimensions;

it will be understood by those skilled in the art that certain well-known descriptions of the figures may be omitted.

The technical solution of the present invention is further described below with reference to the accompanying drawings and examples.

Example 1

As shown in fig. 1, conventionally, after private information of users User1, … and User in a User client is collected by a computing center, the computing center integrates the information of the users to analyze, and obtains nash equilibrium points as optimal results, and then data resources are allocated to the users according to the optimal results, as can be seen from fig. 1, in this way, the privacy of each User is exposed to the computing center, which is not beneficial to ensuring the security and privacy of the whole data interaction process.

Referring to fig. 2, the method for securely computing a nash equilibrium point in a cloud computing environment provided in the embodiment of the present invention includes:

s1, determining a user client and a data center which participate in game decision in a data resource allocation process, setting the user client as Alice, the data center as Bob, and each party has different decisions, and safely calculating a Nash equilibrium point in a cloud computing environment through a cloud server so as to obtain an optimal fusion strategy of each party;

s2, generating a public key pk and a private key sk locally, storing the private key sk locally, informing the cloud server of the public key pk, and informing the private server of the private key sk;

the process of generating the public key pk and the private key sk is as follows:

s21, randomly taking a large prime number p and a large prime number q, and calculating intermediate parameters n and lambda to satisfy the following conditions:

n ═ pq, λ ═ lcm (p-1, q-1), where lcm denotes the least common multiple;

s22, defining a function L (u), wherein L (u) satisfies the following conditions:random accessSatisfy gcd (L (g)^λmodn²) N) is 1, wherein u represents an intermediate parameter, gcd represents the greatest common divisor,represents a positive integer;

s23, calculating an intermediate parameter u:

μ＝(L(g^λmodn²))^-1modn

obtaining the public key pk ═ (n, g), and the private key sk ═ λ, μ;

s3, determining an income matrix A of the user client and an income matrix B of the data center, carrying out homomorphic encryption on the income matrix A of the user client and the income matrix B of the data center respectively by using a public key pk, and uploading the encrypted income matrix A and the encrypted income matrix B to the cloud server; specifically, the method comprises the following steps:

let the revenue matrix A of the user client be represented as PA, and the revenue matrix B of the data center be represented as P_BTo P_AAnd P_BEach element m in the network is encrypted, and a revenue matrix P of the user client Alice is taken as an example and is set_AExpressed as:

and (3) assuming that each element in the matrix is uniformly expressed as m, randomly selecting a positive integer r, and if r is less than n, the ciphertext c after the element m is encrypted meets the following conditions:

wherein the content of the first and second substances,representing a ciphertext under the paillier homomorphic encryption, and uploading to a cloud server after encrypting each element; in addition, based on the revenue matrix A of the user client, E of the user client revenue_ASatisfies the following conditions:

wherein S is_ARepresents the user client decision matrix, in this embodiment, set S_AIs [ x ]₁x₂x₃]；P_AA revenue matrix A representing a user client; s^T _BTranspose representing decision matrix of data center, expressed as

Nash equilibrium point of data center based on income E of user client_ADecision matrix S for user client_AEach element x in_iPartial derivatives ofAnd (3) calculating, specifically:

when in useThen, we get the nash equilibrium point of the data center, i represents the element order, in this embodiment, 1,2 are taken:

y₃＝1-y₁-y₂

in the same way, the data center gains E_BSatisfies the following conditions:

wherein S is_BRepresenting a data center decision matrix; p_BA revenue matrix B representing the data center;representing a transpose of a user client decision matrix;

nash equilibrium point of user client based on data center profit E_BDecision matrix S for data center_BEach element y in_iPartial derivatives ofCalculation whenObtaining the nash equilibrium point of the user client, i represents the element order, and the calculation processes of the nash equilibrium point of the user client and the nash equilibrium point of the data center are all completed in the encryption domain, and the specific execution step S4;

s4, the cloud server calculates Nash equilibrium point encryption results of the user client and the data center through a secure multiplication protocol and a secure division protocol;

the secure multiplication protocol includes the processes of:

s41, setting Nash equilibrium point of user client and parameter related to encryption domain in calculation process of Nash equilibrium point of data centerAndthe product of (c), here encrypted domain parameters for ease of illustrationAndrefers to a general finger of the safe multiplication calculation parameters (not related to division calculation) involved in the calculation of the Nash equilibrium point;

s42, randomly generating an integer r by the cloud server₁And an integer r₂，r₁A, r2 > b, calculated by homomorphismAndat this time, the integer r₁And an integer r₂Are integers much larger than a and much larger than b, respectively;

s43, the cloud server willAndsending the data to the private server, and calculating c1 ═ a + r after decryption by the private server₁)(b+r₂) And encrypt the resultReturning to the cloud server;

s44, cloud server computing And obtaining the product result of the encryption domains of the plaintext a and the plaintext b.

The secure division protocol includes the processes of:

s401, setting Nash equilibrium point of user client and related to encrypted domain parameter in Nash equilibrium point calculation process of data centerAndthe division calculation of (2), for ease of explanation, the encrypted domain parameter at this timeAndrefers to a general finger of division calculation parameters (not related to division calculation) involved in the calculation of the Nash equilibrium point;

s402, the cloud server randomly generates an integer r and an integer Q, and calculates an intermediate ciphertext c2 by making S ═ r · Q:

s403, mixingS andsending to the private server, decrypting by the private serverObtain the plaintext m3Private server computingAnd returns it as an intermediate result to the cloud server;

and S404, the cloud server returns the intermediate result to the local in cooperation with the Q, and the encrypted domain division result is obtained after local decryption.

And S5, the cloud server returns the Nash equilibrium point encryption result to the local, and the local decrypts the Nash equilibrium point encryption result by using the private key.

The process of locally utilizing the private key to decrypt the Nash equilibrium point encryption result meets the following requirements:

let the nash equilibrium point encryption result be c3, and the formula for the nash equilibrium point encryption result to be decrypted as plaintext m5 is:

m₅＝L(c3^λmodn²)·μmod n

where μ represents a ciphertext parameter.

To further verify the accuracy of the method for securely calculating nash equilibrium points in a cloud computing environment, in this embodiment, the calculation error of the method provided by the present invention is counted, taking the user client as an example, and based on a homomorphic encryption technique, the nash equilibrium points of the user client are calculated in an encryption domain, see fig. 3, in fig. 3, the abscissa represents the magnification factor of each numerical element in the revenue matrix a of the user client, and herein, considering that the decimal place will be truncated in the calculation process, the influence on the calculation result of the nash equilibrium points will be smaller as the truncated decimal place is smaller as the magnification factor is increased, and the ordinate represents the logarithm value of the nash equilibrium point error obtained in 1000 nash equilibrium point calculations by applying the method provided by the present invention, in this embodiment, when the amplification factor of the income matrix A is small, the truncated decimal place is more, the value of the error of the calculation result of the Nash equilibrium point after logarithm is taken is positive, the calculation result is greatly influenced by the amplification factor, the truncated decimal place is less along with the increase of the amplification factor, the influence on the calculation result of the Nash equilibrium point is smaller, the error is negative after logarithm is taken, the calculation error is infinitely close to 0, and the calculation precision of the method is high.

The positional relationships depicted in the drawings are for illustrative purposes only and are not to be construed as limiting the present patent;

it should be understood that the above-described embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the embodiments of the present invention. Other variations and modifications will be apparent to persons skilled in the art in light of the above description. And are neither required nor exhaustive of all embodiments. Any modification, equivalent replacement, and improvement made within the spirit and principle of the present invention should be included in the protection scope of the claims of the present invention.