Privacy-preserving spectrum auction method

Abstract

The present invention relates to the technical field of communications. Disclosed is a privacy-preserving spectrum auction method. In the method, an auction party first divides an idle spectrum resource into a plurality of spectrum blocks of equal size; each bidder provides a bid for each spectrum block on the basis of a demand program, the bid being presented in the form of a bid vector; then, the bidder packages the bid vectors into an integer, encrypts the integer by means of a public key of a proxy party, and sends the encrypted bids to the auction party; the auction party first groups the bidders on the basis of geographical locations and interference radii of bidder base stations, places base stations that do not affect each other in a same group, and then converts, by using the homomorphic properties of homomorphic encryption, the encrypted bids of the bidders into a secret sharing form, which is simultaneously stored in the auction party and the proxy party; and the auction party and the proxy party use secure multi-party computation to complete spectrum allocation and spectrum pricing without obtaining bid information, and send an auction result to the bidders.

Description

A privacy-protected spectrum auction method TECHNICAL FIELD

[0001] The present application belongs to the technical field of wireless communication, and particularly relates to a privacy protection technique, and especially relates to a privacy-protected spectrum auction method. BACKGROUND

[0002] Dealing with the explosive mobile data traffic is one of the biggest challenges faced by the fifth generation (5G) network, and the problem of spectrum shortage is caused by limited spectrum resources, and on the other hand, the problem is aggravated by the partially static and strict spectrum allocation scheme. In order to optimize the use of 5G spectrum resources, in November 2011, the Radio Spectrum Policy Group (RSPG) proposed a new sharing concept, called Licensed Shared Access (LSA). It allows the user of the frequency band to temporarily share his own spectrum block with the mobile network operator (MNO) by issuing a license. Unlike the traditional spectrum sharing scheme without any guarantee of spectrum, in the LSA concept, the conditions for spectrum sharing are precisely defined in advance and written into the license issued to the second round of users.

[0003] For the problem of efficient allocation of licenses, a specific license allocation mechanism needs to be adopted. A common method is to design a spectrum auction scheme to allocate licenses by auction. The spectrum owner shares the spectrum with others by auction and gets benefits from it. The existing auction scheme generally takes the truthfulness (each bidder will give a true price under the interest-driven) as the basic requirement, and designs the scheme with fairness and efficiency as the target to maximize the global benefit (social welfare). Although the current scheme greatly improves the benefits, fairness and efficiency of the auction, from the practical application point of view, the basic feature of the scheme - truthfulness hinders its wide practical application. Due to the truthfulness feature, each bidder will provide his true valuation when bidding to maximize the benefit. The semi-honest bidder can infer the benefit of the spectrum to the bidder from the true valuation, and thus to a certain extent, the commercial privacy of the bidder. In addition, the malicious bidder can also launch an attack with the corrupt bidder to harm the interests of the honest bidder. The security problem greatly hinders the wide application of the spectrum auction mechanism.

[0004] SUMMARY

[0005] The present application aims at the problem that the existing auction algorithm under the LSA background cannot protect the privacy of the bidder, and proposes a privacy-protected spectrum auction method.

[0006] Technical scheme: A privacy-protected spectrum auction method, the auctioneer divides the idle spectrum resources into a plurality of spectrum blocks of equal size; the bidder bids for each spectrum block according to the demand program, and the bid is expressed in the form of a bid vector;

[0007] The bidder packs the bid vector into an integer, then encrypts the encrypted bid using the proxy's public key and sends it to the auctioneer;

[0008] The auctioneer first groups the bidders according to their geographical locations and interference radius, and puts the bidders that will not interfere with each other in the same group, and then uses the homomorphic property of homomorphic encryption to convert the encrypted bids of the bidders into a secret sharing form and store them in the auctioneer and the proxy at the same time;

[0009] The auctioneer and the proxy use secure multi-party computation to complete spectrum allocation and spectrum pricing without obtaining the bid information, and send the auction results to the bidders.

[0010] Further, the method further comprises the following steps:

[0011] S1, bidder grouping: Two bidders that do not interfere with each other can use the same spectrum block resource at the same time, the auctioneer groups the bidders according to their address locations and interference ranges using a grouping algorithm, and the bidders in each group do not interfere with each other;

[0012] This step is used to convert the competition of the bidders for the spectrum block into the competition of the bidder groups for the spectrum block;

[0013] S2, spectrum allocation: the auctioneer uses the characteristics of the homomorphic encryption algorithm to convert the bid vector of each bidder encrypted using the public key of the proxy into an additive secret sharing form and store it in the auctioneer and the proxy respectively, so that the auctioneer and the proxy cannot restore the bid of the bidder; the auctioneer and the proxy locally calculate the group bid vector of each group, run a privacy-protected confusion algorithm on the group bid vector, and then use the secure multi-party computation method to complete spectrum allocation in groups;

[0014] S3, spectrum pricing: the auctioneer and the proxy use secure multi-party computation to respectively calculate the amount each bidder in the group should pay for each obtained spectrum block.

[0015] Based on the above scheme, the specific steps of the bidder submitting the bid and converting it into an additive secret sharing form and storing it in the auctioneer and the proxy in step S2 are as follows:

[0016] (2.1.1) The bid b of the bidder i is a vector with a length of K, K is the number of spectrum blocks, and each element represents the bid for a spectrum block, the bidder uses SIMD technology to pack it into an integer, and uses the public key pk B of the proxy to encrypt using the Paillier homomorphic encryption algorithm, and gets to the auctioneer;

[0017] (2.1.2) The auctioneer generates a random number vector r locally as a secret share of the bid for each bidder, packs the random number vector and encrypts it with the public key of the proxy, and calculates

[0018] to the proxy. This step is to get -r by negating each element of the random number vector, and then pack it into an integer, and then perform homomorphic addition on

[0019] (2.1.3) The proxy decrypts and unpacks the encrypted secret share of the bid vector using its own private key sk B i B i i A

[0020] In this method, the addition and subtraction operations on the vector are respectively the addition and subtraction of the corresponding elements in the two vectors.

[0021] Further, the specific steps of the auctioneer and the proxy calculating the group bid and running the privacy protection confusion algorithm in step S2 are as follows:

[0022] (2.2.1) The auctioneer and the proxy respectively calculate the secret share of the group bid of each group locally:

[0023] sum the secret shares of the bid vectors of the bidders in each group locally to obtain the secret share of the group bid of each group; where i A is the secret share value of the bid vector of the i-th bidder at the auctioneer, and i B is the secret share value of the bid vector of the i-th bidder at the proxy, and h A is the secret share value of the group bid vector of the h-th group at the auctioneer, and h B is the secret share value of the group bid vector of the h-th group at the proxy;

[0024] (2.2.2) The auctioneer packs the secret share of the group bid vector of each group and encrypts it using its own public key to obtain:

[0025] and sends it to the proxy; ​​​​​​​​​​​​

[0026] (2.2.3) The agent bids for each group and generates a secret sharing of the zero vector 0 = {0,0,0,…,0} ([0]). A [0] B ), for [0] A After packaging, it is encrypted using the auctioneer's public key and then obtained using a homomorphic addition operation. Calculate [B] h ] B +[0 h ] B Therefore, the secret sharing of each group's bid becomes: ([B h ]′ A ,[B h ]′ B )=([B h ] A +[0 h ] A ,[B h ] B +[0 h ] B )

[0027] (2.2.4) The agent uses the substitution function H to shuffle the order of group bids to obtain:

[0028] Will Send to the auctioneer;

[0029] (2.2.5) The auctioneer decrypts and unpacks the data. Then, the group bids after each group was replaced are obtained [H(B)]. h )]′ A .

[0030] Furthermore, the specific steps for the auctioneer and the agent to allocate spectrum in groups using secure multi-party computation in step S2 are as follows:

[0031] (2.3.1) The auctioneer and the agent use the secure comparison protocol SecCmp under the additive secret sharing to compare the group bid vector of each group and obtain the secret sharing of the largest 2K group bid elements;

[0032] (2.3.2) The auctioneer and the agent exchange bid vectors for each group after grouping permutation ([H(B h )]′ A ,[H(B h )]′ B From the top 2K group bids in the previous step, find the top K elements from the other groups, sort them in ascending order, and use them as the competition vector for that group ([H(C h )]′A ,[H(C h )]′ B );

[0033] (2.3.4) The auctioneer and the agent use a privacy-preserving obfuscation algorithm to repeatedly manipulate the group bid vector and the competition vector, restoring the positions of the group bid vector and the competition vector to obtain ([B h ] A ,[B h ] B ) and ([C h ] A ,[C h ] B );

[0034] (2.3.5) The auctioneer and the agent use the secure comparison protocol SecCmp to compare the elements of the bid vector and the competition vector of each group in turn. The number of spectrum blocks obtained by the group is the number of elements in the bid vector that are greater than the corresponding competition vector.

[0035] Based on the above scheme, the specific steps for the auctioneer and the agent to calculate the amount payable by each bidder in step S3 are as follows:

[0036] (3.1) The auctioneer and the agent jointly invoke the secure division protocol SecDiv to secretly share the weight vector of each bidder's bid as a percentage of the group's bid ([w i ] A ,[w i ] B );

[0037] For one element of the weight vector

[0038] (3.2) The auctioneer and the agent jointly invoke the secure multiplication protocol SecMul to multiply each element in the bidding vector with the competition vector corresponding to its group, calculating the secret sharing of the vector of the amount each bidder should pay ([p i ] A ,[p i ] B ):

[0039] For one element p in the amount vector i,n =w i,n *C h,n

[0040] The auctioneer and the agent each use two multipliers to secretly share the result, thus each obtaining a secret share value of the multiplication result.

[0041] (3.3) The agent will secretly share the vector of each bidder's payment amount [pi ] B Send to the auctioneer, the auctioneer restores the payment amount vector locally: p i = [p i ] A + [p i ] B

[0042] Where [p i ] A Indicates the secret sharing value of the auctioneer;

[0043] Complete the spectrum auction.

[0044] Further, in the method, in the secure division protocol, the auctioneer and the agent use the secret sharing of the divisor and the dividend respectively, and the auctioneer and the agent obtain the secret sharing value of the division result respectively, and their inputs will not be leaked to the other party;

[0045] In the secure multiplication protocol, the auctioneer and the agent use the secret sharing of two multipliers respectively, and the auctioneer and the agent obtain the secret sharing value of the multiplication result respectively, and their inputs will not be leaked to the other party.

[0046] Further, in the method, the bidder bids for each spectrum block according to the demand program, and the element in the bid vector corresponds to the bid of each spectrum block, and the value shows a decrease one by one.

[0047] Beneficial effects: the spectrum auction method provided by the present application divides the spectrum resource of the spectrum provider into multiple spectrum blocks according to the demand and auctions; the bidder respectively bids for each spectrum block according to the demand and sends the encrypted bid value to the auctioneer; the auctioneer and the agent use the secure multi-party technology to complete the spectrum auction while protecting the bid privacy of the bidder. The method can improve the performance of the spectrum auction while protecting the bid privacy of the user, and the performance includes efficiency, income and fairness. BRIEF DESCRIPTION OF DRAWINGS

[0048] Fig. 1 is a schematic diagram of the overall model of the multi-block spectrum auction method with privacy protection in the present application;

[0049] Fig. 2 is a schematic diagram of the spectrum allocation process in the present application;

[0050] Fig. 3 is a schematic diagram of the performance of the auction method in the present application, wherein Fig. 3(a) is the verification result of the method in the present application in the auction fairness, Fig. 3(b) is the test result of the present application in the auction income, and Fig. 3(c) is the performance diagram of the present application in the efficiency;

[0051] Fig. 4 is a time and space overhead diagram of the privacy-protected spectrum auction method in the present application, wherein Fig. 4(a) is the influence of the number of spectrum blocks on the communication overhead, and Fig. 4(b) is the influence of the number of spectrum blocks on the calculation overhead. DETAILED DESCRIPTION

[0052] The above scheme is further described below in combination with specific embodiments. It should be understood that these embodiments are used to illustrate the present application and do not limit the scope of the present application. Based on the embodiments of the present application, all other embodiments obtained by those of ordinary skill in the art without creative efforts are within the protection scope of the present application.

[0053] The present application provides a privacy-protected spectrum auction method. The specific setting environment of the problem to be solved can be that a bidder sends his bid after encryption, and requires that his bid is not obtained by a second participant except himself during the bidding process. Each of the auctioneer and the proxy has a secret share value of the bid, and completes the auction without obtaining the bid, and sends the result to the bidder.

[0054] Referring to Fig. 1, the privacy-protected spectrum auction method in the present embodiment is as follows: the auctioneer divides the idle spectrum resource into a plurality of spectrum blocks of equal size, a base station requiring additional spectrum resource is a bidder, bids for each spectrum block, integrates into a bid vector, the first element in the bid vector represents the bid value for a spectrum block if the spectrum block is not obtained, and the second element in the bid vector represents the bid value for a second spectrum block if a spectrum block is obtained. The bidder packs the bid vector into an integer, then encrypts using the public key of the proxy, and sends the encrypted bid to the auctioneer. The auctioneer first groups the bidders according to the geographical position and interference radius of the base station of the bidder, and places the base stations that will not affect each other in the same group. Then, the auctioneer uses the homomorphism property of homomorphic encryption to convert it into a secret share form and store it in the auctioneer and the proxy at the same time. Finally, the auctioneer and the proxy use secure multi-party computation to complete the spectrum allocation and spectrum pricing without obtaining the bid information, and send the auction result to the bidder.

[0055] The specific implementation steps are as follows:

[0056] The present application performs two groups of experiments, respectively discusses the influence of the number of spectrum block divisions of a spectrum resource on the performance of the auction algorithm (fairness, effectiveness, and revenue), and the influence of the number of bidders and the number of spectrum blocks on the calculation overhead and the communication overhead of the auction algorithm.

[0057] In the first set of experiments, assume that there are 100 bidders, randomly distributed in a 3000m X 3000m area, and the interference range is 600m. The LSA spectrum can be divided into 10 blocks, 5 blocks, 2 blocks, or can be auctioned as an independent spectrum block. The bids of the bidders are selected from a uniform distribution of (0, 100). Each bidder generates 10 bids, and then sorts them in non-decreasing order. The first bid represents the bidder's bid for the spectrum block if the bidder does not get the spectrum block, and the second bid represents the bidder's bid for the second spectrum block if the bidder gets a spectrum block. The bidder generates a bid vector from the 10 bids according to the number of spectrum blocks, for example, if the number of spectrum blocks is one, the bid is the sum of the ten bids. This embodiment performs experiments with the number of spectrum blocks being [1, 2, 5, 10] respectively, and calculates the auction performance. For each performance indicator (fairness, efficiency and auction revenue), this embodiment repeats the experiment 1000 times to take the average value.

[0058] In the second set of experiments, the number of bidders varies in the range of [1000, 2000, 3000, 4000, 5000, 6000], and is randomly distributed in a 3000m X 3000m area. The bid of each bidder is selected from a uniform distribution of (0, 100), and the bid vector is generated. The number of spectrum blocks is [1, 2, 5, 10]. This embodiment repeats the experiment 1000 times for each number of bidders and number of spectrum blocks, and calculates the computational overhead and communication overhead.

[0059] This embodiment is performed on a 64-bit macOS Venture operating system, with an Apple M1 chip and 16G of memory.

[0060] Referring to FIG. 2, the implementation steps of the spectrum auction process in this embodiment are as follows:

[0061] S1: Bidder grouping: Two bidders who do not interfere with each other can use the same spectrum block resource at the same time. The auctioneer groups the bidders according to their address locations and interference ranges using a grouping algorithm, ensuring that the bidders in each group will not interfere with each other. This converts the competition for spectrum blocks by bidders into competition for spectrum blocks by groups of bidders, greatly improving the utilization of spectrum resources and the fairness of the auction.

[0062] S2: Spectrum allocation: The auctioneer uses the characteristics of the homomorphic encryption algorithm to convert the bid vector of each bidder encrypted using the proxy public key into the form of additive secret sharing and store it in the auctioneer and the proxy. This makes it impossible for the auctioneer and the proxy to restore the bid of the bidder. The auctioneer and the proxy locally calculate the group bid vector of each group, run a privacy-protected confusion algorithm on the group bid vector, and then use secure multi-party computation technology to complete the spectrum allocation in groups.

[0063] Step S2, where bidders submit their bids and the information is converted into an additive secret shared between the auctioneer and the agent, involves the following specific steps:

[0064] S21: Bidder's bid b i It is a vector of length K, where K is the number of spectrum blocks. Each element represents a bid for a spectrum block. Bidders use SIMD technology to package these bids into an integer and then use the Paillier homomorphic encryption algorithm with the proxy's public key to pk. B Encrypt, obtain Send it to the auctioneer.

[0065] S22: The auctioneer locally generates a random number vector r for each bidder's bid as a secret sharing of the bid. [b] i ] A =r, the random number vector is packaged and encrypted using the proxy's public key, and then calculated using homomorphic encryption properties:

[0066] Will Send to the agent. This step involves inverting each element of the random number vector to obtain -r, then packaging it into an integer, and then... It is obtained by performing homomorphic addition.

[0067] S23: The agent uses its own private key sk B A secret sharing of the bid vector obtained by decrypting and unpacking [b] i ] B =b i -[b i ] A .

[0068] In this method, the addition and subtraction operations on vectors are performed by adding or subtracting the corresponding elements in the two vectors respectively.

[0069] The specific steps of step S2, where the auctioneer and the agent calculate the group bids and run the privacy-preserving obfuscation algorithm, are as follows:

[0070] S24: The secret sharing of how the auctioneer and the agent calculate the bids for each group locally:

[0071] The secret share of bids for each group is obtained by summing the secret share of bids within each group locally. [b] i ] A It is the secret share of the bid vector of the i-th bidder at the auctioneer, [b i ] BIt is the secret shared value of the bid vector of the i-th bidder at the agent. [B] h ] A It is the secret share value of the group bid vector of the h-th group at the auctioneer, [B h ] B It is the secret share value of the group bid vector of the h-th group at the agent.

[0072] S25: The auctioneer packages the secret share of each group's group bid vector and encrypts it using their own public key, resulting in:

[0073] And send it to the agent.

[0074] S26: The agent bids for each group, generating the secret sharing of the zero vector 0 = {0,0,0,…,0} ([0]). A [0] B ), for [0] A After packaging, it is encrypted using the auctioneer's public key and then obtained using a homomorphic addition operation. Calculate [B] h ] B +[0 h ] B Therefore, the secret sharing of each group's bid becomes: ([B h ]′ A ,[B h ]′ B )=([B h ] A +[0 h ] A ,[B h ] B +[0 h ] B )

[0075] S27: The agent uses a substitution function to shuffle the order of group bids to obtain:

[0076] Will Send it to the auctioneer.

[0077] S28: The auctioneer decrypts and unpacks the data. Then, the group bids after each group was replaced are obtained [H(B)]. h )]′ A Step S2, where the auctioneer and the agent use secure multi-party computation to allocate spectrum in groups, follows these steps:

[0078] S29: The auctioneer and the proxy compare each group's group bid vector using the secure comparison protocol SecCmp under additive secret sharing, and obtain the secret sharing of the largest 2K group bid elements.

[0079] S210: The auctioneer and the proxy permute the group bid vector ([H(B h )]' of each group. A ,[H(B h )]' of each group. B ) from the largest 2K group bid elements in the previous step, find the largest K elements in the group bid elements of other groups in ascending order as the competition vector ([H(C h )]' of the group. A ,[H(C h )]' of the group. B ).

[0080] S211: The auctioneer and the proxy repeat the privacy protection confusion algorithm on the group bid vector and the competition vector, restore the positions of the group bid vector and the competition vector to obtain ([B h ] A ,[B h ] B ) and ([C h ] A ,[C h ] B ).

[0081] S212: The auctioneer and the proxy use the secure comparison protocol SecCmp to compare the elements of the group bid vector and the competition vector of each group in turn, and the number of spectrum blocks obtained by the group is the number of elements in the group bid vector that are greater than the corresponding elements in the competition vector.

[0082] S3: Spectrum pricing: The auctioneer and the proxy use secure multi-party computation technology to calculate the amount each bidder in the group should pay for each obtained spectrum block.

[0083] The specific steps of the auctioneer and the proxy calculating the amount each bidder should pay in step S3 are as follows:

[0084] S31: The auctioneer and the proxy jointly call the secure division protocol to calculate the weight vector of the proportion of each bidder's bid in the group bid, that is, the secret sharing ([w i ] A ,[w i ] B ) of each bidder. For one element of the weight vector

[0085] S32: The auctioneer and the agent jointly invoke the secure multiplication protocol SecMul to calculate the secret share of the amount each bidder should pay. Assuming group h receives 3 spectrum blocks, the secret share of the bidder's payment for each spectrum block needs to be calculated separately. For the i-th bidder in the group, its payment for the second spectrum block is: p i,2 =C h,2 *w i,2

[0086] Through a secure multiplication protocol, the auctioneer and the agent obtain a secret sharing of the payment amount, with the auctioneer receiving [p] i,2 ] A The agent received [p] i,2 ] B .

[0087] S33: The agent will secretly share the vector of each bidder's payment amount. The payment amount vector is sent to the auctioneer, who then reconstructs it locally: p i =[p i ] A +[p i ] B

[0088] The spectrum auction was completed.

[0089] For the first group of experiments:

[0090] Fairness is represented using the Jain index, calculated as follows:

[0091] Where α i This represents the number of spectrum blocks obtained by the i-th bidder, where N is the total number of bidders, and α = (α1, ..., α2). N )

[0092] The efficiency calculation formula is:

[0093] This represents the sum of the values ​​offered by bidders for the spectrum they own.

[0094] The income calculation formula is as follows:

[0095] This represents the sum of payments made by all bidders.

[0096] The experimental results are shown in Figure 3. It can be seen that dividing the spectrum resources into multiple spectrum blocks can significantly improve auction performance (fairness, efficiency, and revenue) compared to auctioning the spectrum resources as a whole.

[0097] The experimental results of the second set of experiments are shown in Figure 4: it can be seen that, since the SIMD mechanism is used to pack the vector into an integer for encryption and decryption before encryption and decryption, the change in the number of spectral blocks has little effect on the computing overhead and the communication overhead. As the number of bidders increases, the computing overhead and the communication overhead increase linearly. The overhead is mainly used for encryption and decryption operations, which can be completed by multi-threading. Since the experimental environment of the present embodiment uses 8 threads, in actual applications, an environment with more than 32 threads is generally used. Therefore, in a real scenario, the computing overhead of the present application can be at least one quarter of the experimental results.

Claims

1. A privacy-preserving spectrum auction method, characterized in that, The auctioneer divides the idle spectrum resources into several spectrum blocks of equal size; bidders bid for each spectrum block according to the demand program, and the bids are expressed in the form of a bid vector. Bidders package their bid vectors into an integer, encrypt it using the agent's public key, and send the encrypted bid to the auctioneer. The auctioneer first groups the bidders based on the geographical location and interference radius of their base stations, placing base stations that will not affect each other in the same group. Then, using the homomorphic property of homomorphic encryption, the bidders' encrypted bids are converted into a secret sharing form and stored simultaneously by the auctioneer and the agent. The auctioneer and its agents use secure multi-party computation to complete spectrum allocation and pricing without obtaining bidding information, and then send the auction results to the bidders.

2. The privacy-preserving spectrum auction method according to claim 1, characterized in that, The method further includes the following steps: S1. Bidder Grouping: Two non-interfering bidders can use the same spectrum block resource at the same time. The auctioneer uses a grouping algorithm to group the bidders according to their address location and interference range. Bidders in each group do not interfere with each other. This step is used to transform the competition among bidders for a spectrum block into a competition among groups of bidders for a spectrum block. S2. Spectrum Allocation: The auctioneer utilizes the characteristics of homomorphic encryption to convert the bid vector of each bidder, encrypted with the agent's public key, into an additive secret-sharing form and store it separately with the auctioneer and the agent, making it impossible for either the auctioneer or the agent to decipher the bidder's bid. The auctioneer and the agent locally calculate the group bid vector for each group, run a privacy-preserving obfuscation algorithm on the group bid vector, and then use a secure multi-party computation method to complete the spectrum allocation on a group basis. S3. Spectrum Pricing: The auctioneer and the agent use a secure multi-party computation method to calculate the amount each bidder in the spectrum group should pay for each obtained spectrum block.

3. The privacy-preserving spectrum auction method according to claim 1 or 2, characterized in that, The specific steps in step S2 where bidders submit their bids and the information is converted into an additive secret sharing format and stored between the auctioneer and the agent are as follows: (2.1.1) Bidder's offer b i It is a vector of length K, where K is the number of spectrum blocks. Each element in the vector represents a bid for a spectrum block. Bidders use SIMD technology to package these bids into an integer and then use the Paillier homomorphic encryption algorithm with the proxy's public key to PK. B Encrypt, obtain Send it to the auctioneer; (2.1.2) The auctioneer locally generates a random number vector r for each bidder's bid as a secret share of the bid. The random number vector is packaged, encrypted with the agent's public key, and calculated using homomorphic encryption. The expression is: Will Sending it to the agent involves inverting each element of the random number vector to obtain -r, then packaging it into an integer, and then... We obtain it by performing homomorphic addition; (2.1.3) The agent uses its own private key sk B A secret sharing of the bid vector obtained by decrypting and unpacking [b] i ] B =b i -[b i ] A ; In this method, the addition and subtraction operations on vectors are performed by adding or subtracting the corresponding elements in the two vectors respectively.

4. The privacy-preserving spectrum auction method according to claim 1 or 2, characterized in that, The specific steps in step S2, where the auctioneer and the agent calculate the group bids and run the privacy-preserving obfuscation algorithm, are as follows: (2.2.1) The auctioneer and the agent separately share the secrets of calculating the bids for each group locally: The secret share of bids within each group is summed locally to obtain the secret share of bids for each group; where [b i ] A It is the secret share of the bid vector of the i-th bidder at the auctioneer, [b i ] B It is the secret shared value of the bid vector of the i-th bidder at the agent, [B h ] A It is the secret share value of the group bid vector of the h-th group at the auctioneer, [B h ] B It is the secret share value of the group bid vector of the h-th group at the agent; (2.2.2) The auctioneer packages the secret share of each group's group bid vector and encrypts it using their own public key, resulting in: And send it to the agent; (2.2.3) The agent bids for each group and generates a secret sharing of the zero vector 0 = {0,0,0,…,0} ([0]). A [0] B ), for [0] A After packaging, it is encrypted using the auctioneer's public key and then obtained using a homomorphic addition operation. Calculate [B] h ] B +[0 h ] B Therefore, the secret sharing of each group's bid becomes: ([B h ]′ A ,[B h ]′ B )=([B h ] A +[0 h ] A ,[B h ] B +[0 h ] B ) (2.2.4) The agent uses the substitution function H to shuffle the order of group bids to obtain: Will Send to the auctioneer; (2.2.5) The auctioneer decrypts and unpacks the data. Then, the group bids after each group was replaced are obtained [H(B)]. h )]′ A .

5. The privacy-preserving spectrum auction method according to claim 1 or 2, characterized in that, The specific steps for the auctioneer and the agent to allocate spectrum in groups using secure multi-party computation in step S2 are as follows: (2.3.1) The auctioneer and the agent use the secure comparison protocol SecCmp under the additive secret sharing to compare the group bid vector of each group and obtain the secret sharing of the largest 2K group bid elements; (2.3.2) The auctioneer and the agent exchange bid vectors for each group after grouping permutation ([H(B h )]′ A ,[H(B h )]′ B From the largest 2K group bids in the previous step, find the K largest group bids from the other groups and sort them in ascending order. The column serves as the competition vector for the elements in this group ([H(C)). h )]′ A ,[H(C h )]′ B ); (2.3.4) The auctioneer and the agent use a privacy-preserving obfuscation algorithm to repeatedly manipulate the group bid vector and the competition vector, restoring the positions of the group bid vector and the competition vector to obtain ([B h ] A ,[B h ] B ) and ([C h ] A ,[C h ] B ); (2.3.5) The auctioneer and the agent use the secure comparison protocol SecCmp to compare the elements of the bid vector and the competition vector of each group in turn. The number of spectrum blocks obtained by the group is the number of elements in the bid vector that are greater than the corresponding competition vector.

6. The privacy-preserving spectrum auction method according to claim 1 or 2, characterized in that, The specific steps in step S3 for the auctioneer and the agent to calculate the amount payable by each bidder are as follows: (3.1) The auctioneer and the agent jointly invoke the secure division protocol SecDiv to secretly share the weight vector of each bidder's bid as a percentage of the group's bid ([w i ] A ,[w i ] B ); For one element of the weight vector (3.2) The auctioneer and the agent jointly invoke the secure multiplication protocol SecMul to multiply each element in the bidding vector with the competition vector corresponding to its group, calculating the secret sharing of the vector of the amount each bidder should pay ([p i ] A ,[p i ] B ): For one element p in the amount vector i,n =w i,n *C h,n The auctioneer and the agent each use two multipliers to secretly share the result, thus each obtaining a secret share value of the multiplication result. (3.3) The agent will secretly share the vector of each bidder's payment amount [p i ] B The payment amount vector is sent to the auctioneer, who then reconstructs it locally. p i =[p i ] A +[p i ] B Among them, [p i ] A This represents the secret share value of the auctioneer; The spectrum auction was completed.

7. The privacy-preserving spectrum auction method according to claim 6, characterized in that, In the aforementioned secure division protocol, the auctioneer and the agent use secret sharing of the divisor and dividend respectively. The auctioneer and the agent each obtain a secret shared value of the division result, and their inputs will not be leaked to the other party. In the secure multiplication protocol, the auctioneer and the agent each use a secret share of the two multipliers. The auctioneer and the agent each obtain a secret share of the multiplication result, and their inputs are not leaked to the other party.

8. The privacy-preserving spectrum auction method according to claim 1 or 2, characterized in that, In this method, bidders bid for each spectrum block according to the demand procedure. The elements in the bid vector correspond to the bid for each spectrum block, and their value decreases sequentially.

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