Privacy protection method for cloud ciphertext database association rule mining based on apriori

Abstract

This invention provides a privacy-preserving method for cloud-based encrypted database association rule mining based on Apriori. The method includes: the data owner DO running the TDE protocol to encrypt its private transaction database D, obtaining an encrypted database [D′]; and finding all 1-itemsets {x} in database D. 1 , ..., x m The ciphertext candidate 1-itemset C1 is obtained by encrypting the minimum support ms and the confidence threshold mc = α / β using the Paillier encryption algorithm. <α> and <β>; outsourcing all encrypted values to the cloud server CSP; both cloud servers CSP and Evaluator jointly find all the encrypted frequent itemsets on the encrypted database [D'] using the Apriori algorithm; computing all the strong association rules and adding them to the set SR; both cloud servers CSP and Evaluator and the data owner DO jointly decrypt all the encrypted frequent itemsets, compute all the plaintext tuples and add them to the set T p p and SR as the result of the association rules mining on the cloud encrypted database and return them to the data owner DO.​

Description

Technical Field

[0001] This invention relates to the field of data mining technology, and in particular to a privacy protection method for mining association rules in a cloud-based encrypted database based on Apriori. Background Technology

[0002] As the demand for cloud computing continues to expand, more and more customers are choosing to outsource their data mining tasks, experiencing the agility, resilience, and cost savings of this new paradigm. However, the raw data and mining results from outsourcing may contain privacy and confidentiality information, such as medical and financial information. To address privacy concerns and facilitate cloud-based data mining, many privacy-preserving solutions have been proposed. The scheme that efficiently performs privacy-preserving association rule mining on encrypted cloud databases, thereby achieving semantic security for offline users, is called the PPARM scheme. To clearly illustrate the purpose of PPARM, we provide the following example.

[0003] Suppose several hospitals want to share their medical databases in the cloud for better disease association analysis. However, they cannot disclose ordinary medical data containing patient privacy. Therefore, they encrypt the databases and outsource the database and related association rule mining tasks to a cloud service provider. After outsourcing, these hospitals can remain offline. The entire mining process is securely implemented by the cloud server, and the encrypted mining results are returned to each hospital. Finally, the corresponding doctors can decrypt the results and obtain valuable association rules from the aggregated cloud database.

[0004] To protect privacy, researchers initially used perturbation-based methods and substitution ciphers to transform plaintext. However, these solutions offered low security and were vulnerable to chosen-plaintext attacks. To achieve stronger security, later research utilized predicate encryption and homomorphic encryption to design the PPARM scheme. However, these schemes introduced significant computational overhead and could not fully support users' offline needs. To simultaneously achieve high security and efficiency, existing research has attempted to solve the privacy-preserving frequent itemset query problem. However, this scheme only allows single queries and does not support the complete process of association rule mining on ciphertext. Summary of the Invention

[0005] To support users' offline needs and improve the security and efficiency of association rule mining, this invention provides a privacy protection method for cloud-based encrypted database association rule mining based on Apriori.

[0006] The privacy protection method for cloud-based encrypted database association rule mining based on Apriori provided by this invention includes:

[0007] Step 1: The data owner DO runs the TDE protocol and uses the YASHE algorithm to encrypt its private transaction database D, obtaining the encrypted database [D′]; and outputs two encryption masks [S]. 1 ] and [S 0 ];

[0008] Step 2: Data owner DO finds all 1-itemsets {x} in database D. 1 , ..., x m}, and encrypt it to obtain the ciphertext candidate 1-itemset C1;

[0009] Step 3: The data owner (DO) uses the Paillier encryption algorithm to encrypt the minimum support (ms) and confidence threshold (mc) = α / β to obtain the ciphertext. ,<α> and<β>;

[0010] Step 4: Data owner DO encrypts all values ​​[D′], [S′], [D ... 1 ],[S 0 ],C1, <α> and <β> are outsourced to cloud server CSPs;

[0011] Step 5: The two cloud servers, CSP and Evaluator, work together to use the Apriori algorithm on the encrypted database [D′] to find the frequent itemsets of all ciphertexts;

[0012] Step 6: Based on the frequent itemsets of all ciphertexts, the two cloud servers CSP and Evaluator calculate all strong association rules and add them to the set SR;

[0013] Step 7: The two cloud servers CSP and Evaluator, together with the data owner DO, decrypt the frequent itemsets of all ciphertext and calculate all plaintext tuples. Add it to set T p In the middle; where x represents the plaintext itemset, I x S represents the index of x. x Let x represent the support, and k represent the itemset length;

[0014] Step 8: Place T p The SR is used as the result of association rule mining on the cloud-based encrypted database and returned to the data owner DO.

[0015] The beneficial effects of this invention are:

[0016] This invention introduces lower computational overhead for data owners (DOs) and effectively performs frequent itemset mining and association rule mining on encrypted databases. The computational overhead of a set of real and synthetic databases demonstrates that the proposed solution can be applied to databases of various sizes and attributes, showcasing its practicality in real-world scenarios. Furthermore, by dividing the encrypted database into several parts and executing the proposed protocol on multiple cloud servers, parallel operations can be easily achieved, further improving the efficiency of outsourced association rule mining. Simultaneously, after the data owner (DO) outsources the relevant encrypted values ​​to the cloud server (CSP), it can operate offline, meeting the user's offline requirements. Attached Figure Description

[0017] Figure 1 This is a schematic diagram of the architecture of the privacy protection method for cloud-based encrypted database association rule mining based on Apriori (hereinafter referred to as APARM scheme) provided in the embodiments of the present invention;

[0018] Figure 2 The computational overhead of the APARM scheme provided in this embodiment of the invention on the chess database;

[0019] Figure 3 The computational overhead of the APARM solution provided in this embodiment of the invention on the mushroom database;

[0020] Figure 4 The computational overhead of the APARM solution provided in this embodiment of the invention on the connect database;

[0021] Figure 5 The computational overhead of the APARM scheme provided in this embodiment of the invention on the synthetic database (m = 100, ms = 0.93);

[0022] Figure 6 The computational overhead of the APARM scheme provided in this embodiment of the invention on the synthetic database (n = 5000, ms = 0.95);

[0023] Figure 7 The computational overhead of the APARM scheme provided in this embodiment of the invention on the synthetic database (n = 10000, m = 100). Detailed Implementation

[0024] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of the embodiments of this invention will be clearly described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0025] Example 1

[0026] The privacy protection method for cloud-based encrypted database association rule mining based on Apriori (hereinafter referred to as APARM scheme) provided in this embodiment of the invention has the following system architecture: Figure 1 As shown. There are multiple data owners (DOs). l And two cloud servers, CSP and Evaluator. Evaluator generates a public and private key pair, and then uses the public key with the CSP and DO... l Shared, but the private key is owned by the Evaluator. Data owner DO l There are some private transaction databases D l They are encrypted as [D] l The association mining is then outsourced to a CSP. Specifically, the CSP and Evaluator collaborate to perform Apriori association rule mining on the aggregated encrypted database [D]. Finally, the cloud server returns the encrypted frequent itemsets and strong association rules to the data owner, DO. l By data owner DO l Perform decryption and obtain the corresponding plaintext result. Specifically, this includes the following steps:

[0027] S101: Data owner DO runs the TDE protocol, uses the YASHE algorithm to encrypt its private transaction database D, obtaining the encrypted database [D′]; and outputs two encryption masks [S 1 ] and [S 0 ];

[0028] Specifically, the Transaction Database Encryption Protocol (TDE) takes a plaintext transaction database D as input, calculates and outputs an encrypted database [D′], and outsources this database to a cloud server for encrypted data mining. The protocol also generates two encryption vectors [S]. 1 ] and [S 0 The support level is used for inserting and deleting forged data. It should be noted that this invention supports situations where the data owner has multiple databases that are horizontally or vertically partitioned.

[0029] S102: Data owner DO finds all 1-itemsets {x} in database D. 1 , ..., x m }, and encrypt it to obtain the ciphertext candidate 1-itemset C1;

[0030] S103: The data owner DO uses the Paillier encryption algorithm to encrypt the minimum support ms and the confidence threshold mc = α / β to obtain the ciphertext. , <α> and <β>;

[0031] S104: The data owner DO encrypts all encrypted values [D′], [S 1 , [S 0 , C1, , <α> and <β> to the cloud server CSP; at this point, the data owner DO can enter an offline state.

[0032] S105: Two cloud servers CSP and Evaluator jointly use the Apriori algorithm on the encrypted database [D′] to find all frequent itemsets of ciphertext;

[0033] Specifically, this step includes the following sub-steps:

[0034] S1051: Obtain the set F1 containing all ciphertext frequent 1-itemsets from the ciphertext candidate 1-itemset C1 by using the SFIM protocol; the SFIM protocol refers to the secure frequent itemset mining protocol;

[0035] S1052: For each ciphertext itemset pair ([x j , [x j ), CSP calculates its ciphertext join itemset and adds [z] = {[z1], ..., [z m} to the ciphertext candidate 2-itemset C2;

[0036] S1053: CSP obtains the set F2 containing all ciphertext frequent 2-itemsets from the ciphertext candidate 2-itemset C2 by using the SFIM protocol;

[0037] S1054: Set the itemset length k = 3;

[0038] S1055: Initialize two sets C k and F k ;

[0039] S1056: For each ciphertext itemset pair ([x], [y]) in set F k-1 , calculate its ciphertext join itemset, and add it to the ciphertext candidate k-itemset C k ;

[0040] S1057: For each ciphertext itemset [x] in the ciphertext candidate k-itemset C k , determine whether to delete this ciphertext itemset [x] from C k ;

[0041] S1058: Obtain the set F containing all ciphertext frequent k-itemsets from the ciphertext candidate k-itemset C k by using the SFIM protocol k ;

[0042] S1059: Increment the itemset length k by 1, and iterate through steps 5.6 to 5.8 until no new ciphertext frequent itemset is found, then terminate the iteration;

[0043] S1060: Set F = {F1, ..., F...} k-2 }, where each F s It contains all the frequent s-itemsets of the ciphertext, s = 1, 2, ..., k-2.

[0044] S106: Based on the frequent itemset T of all ciphertexts x =([x],I x , x >, k), the two cloud servers CSP and Evaluator calculate all strong association rules and add them to the set SR;

[0045] S107: Two cloud servers, CSP and Evaluator, together with the data owner DO, decrypt the frequent itemsets of all ciphertexts and compute all plaintext tuples. Add it to set T p In the middle; where x represents the plaintext itemset, I x S represents the index of x. x Let x represent the support, and k represent the itemset length;

[0046] S108: T p The SR is used as the result of association rule mining on the cloud-based encrypted database and returned to the data owner DO.

[0047] To more clearly illustrate the solution of this invention, the algorithm code of the solution is shown in Table 1.

[0048] Table 1

[0049]

[0050]

[0051] This embodiment also includes the following security analysis. We assume that the data owner does not fully trust the CSP and Evaluator; that is, both cloud servers are semi-honest and will strictly follow the steps of the scheme, but will attempt to obtain private information during execution. Furthermore, we assume that the two cloud servers cannot collude. The security of this scheme can be demonstrated using the following simulated protocol execution image method.

[0052] Definition 1: Assume ∏ P (π) is the actual execution mirror of participant P when executing protocol π, with protocol inputs and outputs a and b, respectively. Then, if the simulated execution mirror...​ Mirror image of the actual execution ∏ P If (π) is computationally indistinguishable, then protocol π is secure.

[0053] Because our APARM scheme uses semantically safe YASHE and Paillier encryption algorithms, neither the CSP nor the Evaluator can obtain any private information during protocol execution. Therefore, under the semi-honest model, the APARM scheme is secure for both the CSP and the Evaluator.

[0054] The proposed SPCI protocol is secure for semi-honest CSPs, provided that YASHE and Paillier encryption are semantically secure, and is also secure for semi-honest Evaluators that leak privacy from intermediate computation results, provided that the non-collusion assumption is satisfied.

[0055] Example 2

[0056] Based on the above embodiment 1, in step S101, the encryption process using the TDE protocol in this embodiment of the invention is illustrated by the algorithm code shown in Table 2.

[0057] Table 2

[0058]

[0059]

[0060] The purpose of all-zero transaction data is to insert forged transactions during subsequent mining processes, thereby protecting the privacy of the mining results from leakage. The data owner, DO, calculates two binary vectors S of length n+f. 1 and S 0 In vector S 1 In the middle, the element value corresponding to the position of the inserted all-zero transaction. All elements are set to 1, and all other elements are set to 0 (1≤i≤n+f). (This is related to S.) 1 Conversely, in vector S 0 In the middle, the element value corresponding to the position where the all-zero transaction was inserted. All values ​​are set to 0, and all other elements are set to 1 (1≤i≤n+f). z represents the number of encrypted transaction data blocks after packaging, z←(n+f) / M, where M represents the order of the polynomial modulus of the YASHE encryption algorithm (e.g., M=4096). To ensure correct packaging of all plaintext data, we require that the number of transactions in database D′ (i.e., n+f) is divisible by M. Then, for each encrypted transaction data block (1≤a≤z) and each element in the transaction vector (1≤j≤m), the data owner DO packages the identical vector elements of M transactions into {t}. ij , t i+1，j , ..., t i+M-1，j } M Then encrypt it as [D] aj Ultimately, the encrypted transaction database [D′] contains z×m ciphertexts. Similarly, DO will store vector S 1 and S 0 The package is encrypted as [S] 1 ] and [S 0 Both contain z ciphertexts. After encryption, the data owner DO will transfer the ciphertext transaction database [D′] and the two ciphertext vectors [S] to the ciphertext transaction database [D′]. 1 ] and [S 0 Upload to the cloud server CSP for frequent itemset mining.

[0061] In step S102 above, this embodiment of the invention provides a method for processing 1-itemsets {x} 1 , ..., x m The encryption protocol used is called the EOI protocol, which stands for 1-itemset encryption protocol; it specifically includes the following steps: for each 1-itemset The data owner, DO, packages and encrypts it to obtain ciphertext. Then the ciphertext [x] i Add the ciphertext candidate 1-itemset C1; randomly arrange the ciphertext candidate 1-itemset C1. The algorithm code for the EOI protocol is shown in Table 3.

[0062] Table 3

[0063]

[0064] Specifically, in the 1-itemset encryption protocol EOI, the data owner (DO) uses the YASHE algorithm to encapsulate and encrypt all plaintext 1-itemsets using ciphertext encapsulation technology. Here, 1-itemsets... In the case where j = i, All other elements are 0. The output of the EOI protocol is the candidate set C1 = {[x 1 ],...,[x m ]}, which contains all 1-itemsets [x i (1≤i≤m). After the data owner DO completes the EOI protocol, he will outsource the candidate itemset C1 to the cloud server CSP for encrypted frequent itemset mining.

[0065] Example 3

[0066] Based on the above embodiments, this embodiment of the invention uses the SFIM protocol to mine frequent ciphertext itemsets. SFIM stands for Secure Frequent Itemset Mining Protocol. The Secure Frequent Itemset Mining Protocol (SFIM) performs frequent itemset mining on a given ciphertext itemset [x] on an outsourced ciphertext database [D′]. This protocol can securely determine whether a ciphertext itemset [x] is frequent without leaking any sensitive information and outputs a tuple T. x =([x],I x , x >, k). Here, I x It is the unique index value of the ciphertext itemset [x]. x > represents the ciphertext support of the ciphertext itemset [x]. The algorithm code for this protocol is shown in Table 4.

[0067] Table 4

[0068]

[0069]

[0070] As shown in Algorithm 3, the Secure Frequent Itemset Mining Protocol (SFIM) requires complex interactive computation between the cloud server CSP and the Evaluator. Its execution process can be divided into four parts. In the first part (steps 1-11), the corresponding plaintext is either 0 or a random number. Here, the number of plaintext 0s represents the support of the scrambled ciphertext query itemset [x]. In the second part (steps 12-17), the Evaluator decrypts the ciphertext [w] and then checks the corresponding plaintext w. ab The value of , and set u according to it. ab The value of is then calculated. Next, the Evaluator computes the ciphertext [u] and sends it to the CSP. In the third part (steps 18-25), the CSP removes the influence of the inserted forged transactions on the support and then computes the ciphertext [β], which contains the scrambled partial support of the ciphertext query item set [x]. In the final part (steps 26-33), the CSP and the Evaluator first compute the Paillier ciphertext support of the ciphertext query item set [x]. x Then compare it with the Paillier ciphertext minimum support threshold. The itemset [x] is compared to determine whether it is frequent. If it is frequent, the encrypted itemset [x] is added to the set F. k .

[0071] Specifically, in the first part (steps 1-11), CSP first randomly generates vector elements for forged transactions (step 4), and then uses the ciphertext vector... The positions of actual transactions are filtered out, while the positions of all-zero transactions inserted in the TDE protocol are retained. Next, CSP calculation These forged transactions are then inserted into the ciphertext database [D′]. Since the values ​​at the positions corresponding to the real transactions in vector S1 are all 0, adding forged transactions does not affect the values ​​of the real transactions. At this point, the new ciphertext database [D″] = {[D 11 "],...,[D 1m "],...,[D z1 "],...,[D zm f randomly generated forged transactions were added to the query item set x to perturb the true support of the query item set x, thereby protecting the privacy of the mining results. Next, CSP will encrypt the [D]... aj "] and the encrypted query vector element [x j Multiplying them yields the ciphertext product. j (1≤j≤m), then add these ciphertext products together to get the ciphertext inner product [IP] a (1≤a≤z). Next, CSP extracts data from the plaintext space of the YASHE cryptosystem. A random set of M positive integers r is generated. a ←{r a1 ,...,r aM } M As a random perturbation, the ciphertext [w] is then calculated. a ]←([IP a ]-{k} M )×r a (1≤a≤z, [k] is the length of the ciphertext lookup itemset). Here, each ciphertext [w a The plaintext values ​​contained in the ciphertext are either 0 or random numbers, where a position of 0 indicates that the corresponding transaction contains the query itemset x. This is because if a transaction contains x, the vector dot product of the two is k, which is the length of the query itemset x. Since we package M plaintexts into one ciphertext, the above operations achieve efficient parallel computation without incurring additional overhead. Finally, CSP generates a random permutation function π, which is used to permutate the ciphertext [w] = {[w1], ..., [w...]}. z The data is sorted and then the randomly sorted results are sent to the cloud server Evaluator.

[0072] In the second part (steps 12-17), the Evaluator first decrypts each ciphertext [w a ]Get the packaged plaintext w ab (1≤a≤z, 1≤b≤M). Next, if w ab =0, then set u ab =1, otherwise set u ab =0. Here, The value is the support of the scrambled query itemset x. To calculate the true support while protecting privacy, the Evaluator will use u... ab (1≤b≤M) is packaged and encrypted as [u a ], and set the ciphertext [u] = {[u1], ..., [u] = {u1 ... z Send to CSP.

[0073] In the third part (steps 18-25), CSP first calculates the inverse permutation function inv(π) of π and uses it to permutate the ciphertext [u]. Then, CSP uses the ciphertext vector... Remove perturbations from the query itemset support. At this point, the ciphertext [u a The number of plaintext values ​​of 1 contained in the [] is the true support of the query item set x. To protect privacy, CSP randomly generates noise r. ab Add it to the ciphertext [u a The scrambled ciphertext [u] is obtained from ′] a Next, CSP calculates the ciphertext. It includes partial support for M scrambled query item sets x. Furthermore, CSP calculates the overall perturbation value. (P is the plaintext modulus of the YASHE cryptosystem), and it is encrypted into <δ> using the Paillier encryption algorithm. Finally, the CSP sends the ciphertext [β] to the Evaluator.

[0074] In the final part (steps 26-33), the Evaluator first decrypts [β] to obtain {β1, ..., β}. M } M Then calculate (η represents the true support of the scrambled query itemset x). Then, the Evaluator uses the Paillier algorithm to encrypt η to obtain the ciphertext <η>, and sends it to the CSP. Next, the CSP and the Evaluator perform the Secure Compare (SC) protocol. [1] To determine the relative sizes of the ciphertexts <η> and <δ>, output the comparison result θ. If θ = 0, it indicates that η < δ. In this case, CSP calculates <η>←<η>·mod N. 2 Then, CSP calculates the true support for Paillier encryption. x >=<η>·<δ> -1 mod N 2 Finally, the CSP and Evaluator execute the Secure Compare (SC) protocol. [1] Support for ciphertext x >and minimum support threshold for ciphertext The comparison is performed; if θ = 1 (indicating that the query itemset x is frequent), then T is set. x =([x],I x , x >,k), and T x Add [x] to set T, and add [x] to set F. k .

[0075] In this embodiment of the invention, the SJFI protocol is used to compute the encrypted join itemset. SJFI stands for Secure Frequent Itemset Join Protocol; specifically, it includes:

[0076] Step A1: CSP and Evaluator cooperate to check whether there are k-2 identical encryption properties between ciphertext itemset [x] and ciphertext itemset [y]. If so, it indicates that the two ciphertext itemsets [x] and [y] can be merged. Evaluator calculates the ciphertext concatenation itemset [z3] and sends it to CSP.

[0077] Specifically, for a ciphertext item set [x] = {[x1], ..., [x2] containing m encrypted attributes... m ]} and a ciphertext item set [y] = {[y1], ..., [y2]} containing m encrypted attributes. m CSP computes encrypted join itemsets Where z 1j ∈{0, 1, 2}. Here, z 1j =2 indicates that both x and y contain the j-th attribute; CSP generates a positive random number r j According to [z 1j ] and r j Calculation yields [z] 2j ]=([z 1j ]-{2} M )×{r j } M ;{r j } M Represents a set of M numerical values ​​r j , where if z 1j =2 then z 2j =0, otherwise z 2j For random values; to protect privacy, CSP generates random permutation functions π pairs [z2] = {[z... 21 ],...,[z 2m The ciphertext concatenation itemset [z2] is randomly arranged and sent to the Evaluator; the Evaluator evaluates each [z2] item. 2j Decrypt and examine the plaintext z. 2j The value of z is calculated using counter CT1, and the value of z is 0. 2j ​, if CT1<k-2, which means the number of identical attributes of x and y is less than k-2, the protocol is terminated; if CT1=k-2, according to z 2j calculate z 3j , encrypt the calculated z, and send the ciphertext connection item set [z3] = {[z 31 , ..., [z 3m} to the CSP; wherein, if z 2j = 0, then z 3j = 1; otherwise, z 3j = 0.

[0078] Step A2: The CSP calculates and obtains the ciphertext connection item set [z6] by using [x], [y] and [z3];

[0079] Specifically, the CSP permutes [z3] by using the inverse function inv(π) of the function π; the CSP calculates 1 ≤ j ≤ m; finally obtains the ciphertext connection item set [z6] = {[z 61 , ..., [z 6m}.

[0080] Step A3: The CSP and the Evaluator jointly check whether the ciphertext connection item set [z6] belongs to C k , if [z6]∈C k , the protocol is terminated; if [z6] does not belong to C k , the CSP sets [x&y] = [z6] and adds [x&y] to C k .

[0081] Specifically, the CSP uses each ciphertext item set [v] in C k and the ciphertext connection item set [z6] to calculate and obtain In order to enable counting while protecting privacy, the CSP generates a positive random number r j , and according to [z 7j and r j calculates to obtain [z 8j = ([z 7j - {2} M ) × {r j} M ; the CSP randomly permutes the ciphertext connection item set [z8] = {[z 81 , ..., [z 8m}, and sends the randomly permuted ciphertext connection item set [z8] to the Evaluator; the Evaluator decrypts each [z 8j , checks the value of the plaintext z 8j , and uses the counter CT2 to count the number of z with a value of 0 8j The quantity, if CT2 = k, C k If [v] = [z6], then the protocol terminates, because [z6] is already included in C. k In the middle; otherwise, CSP[x&y] = [z6] is set and [x&y] is added to C. k middle.

[0082] The algorithm code for the SJFI protocol is shown in Table 5.

[0083] Table 5

[0084]

[0085]

[0086] Specifically, in the Secure Frequent Itemset Join Protocol (SJFI), the CSP and Evaluator jointly and securely perform the join operations in the Apriori algorithm. Specifically, for set F... k-1 Given two ciphertext frequent (k-1)-itemsets [x] and [y], two cloud servers first check if [x] and [y] have k-2 identical ciphertext elements. If this condition is met, CSP and Evaluator securely connect [x] and [y] to obtain the ciphertext k-itemset [x&y]. If the k-itemset [x&y] is not a candidate itemset C... k Then add it to the candidate set C. k .

[0087] Pruning can be easily performed on plaintext by computing all (k-1)-subsets and checking if they are frequent. However, it is difficult to directly compute encrypted subsets of the encrypted itemset [x] because we cannot distinguish between 1s and 0s in ciphertext while maintaining semantic security. Nevertheless, we have found another method to perform secure pruning on ciphertext. It is important to note that for a regular k-itemset x, according to the combinatorial formula... Its (k-1)-subsets number k. Therefore, if an encrypted k-itemset [x] is a "good" candidate (not to be removed), it should be selected from F. k-1 Find k frequently encrypted itemsets that are exactly all (k-1)-subsets of encrypted [x]. In this embodiment of the invention, the SPCI protocol is used to determine whether to extract from C. k Delete the ciphertext itemset [x]. The SPCI protocol represents the Security Candidate Items Pruning Protocol; specifically, it includes:

[0088] Initialize counter CT1 = 0;

[0089] For F k-1 ciphertext frequent (k-1)-itemset [y] containing m encryption attributes=[y1], ..., [y m}, the CSP calculates where 1≤j≤m;

[0090] the CSP generates a positive random number r j and calculates [z 2j =([z 1j -{2} M )×{r j} M ;

[0091] the CSP randomly permutes [z2] and sends the randomly permuted [z2] to the Evaluator;

[0092] the Evaluator decrypts each [z 2j and checks the value of the plaintext z 2j and uses a counter CT2 to calculate the number of z 2j with a value of 0;

[0093] if CT2=k-1, it indicates that the Evaluator increments the counter CT1 by 1; if CT1=k, [x] is retained in C k and the SPCI protocol is terminated; if after checking all ciphertext frequent (k-1)-itemsets [y] in F k-1 , CT1<k, [x] is deleted from C k .

[0094] The algorithm code of the SPCI protocol is shown in Table 6.

[0095] Table 6

[0096]

[0097] Specifically, in the secure candidate itemset pruning protocol SPCI, the CSP and the Evaluator jointly and securely perform the pruning operation in the Apriori algorithm. For the ciphertext k-itemset [x] in the candidate itemset C k , the two cloud servers securely determine whether all (k-1)-sub-itemsets are frequent. If all sub-itemsets of the k-itemset [x] are frequent, it is retained; otherwise, it is deleted from the candidate itemset C k .

[0098] Example 4

[0099] Based on the foregoing examples, in the embodiment of the present invention, two cloud servers, CSP and Evaluator, use the SARM protocol to calculate all strong association rules, which specifically includes:

[0100] For each frequent itemset of the ciphertext ([x], [y]), determine whether the following four conditions are met:

[0101] Condition 1:

[0102] Condition 2: x∪y is frequent;

[0103] Condition 3: S x∪y / S x ≥mc

[0104] Condition 4: S x∪y / S y ≥mc;

[0105] If the ciphertext frequent itemset ([x], [y]) satisfies conditions 1, 2, and 3 simultaneously, then a strong association rule is set.

[0106] If the ciphertext frequent itemset ([x], [y]) satisfies conditions 1, 2, and 4 simultaneously, then a strong association rule is set.

[0107] Among them, I x I y I x∪y These represent the index values ​​of [x], [y], and [x∪y], respectively.

[0108] Specifically, follow these steps to determine whether each condition is true:

[0109] Step B1: For the itemset pairs (T) in set T x T y CSP calculates k = k x +k y ;k x k y T represents respectively x T y Item set length; if k>k max If so, then check the next itemset pair in set T;

[0110] Step B2: If k≤k max Then check whether condition 1 is true, specifically including:

[0111] For 1≤j≤m, CSP calculation CSP generates positive random numbers r i And calculate [z] 2j ]=([z 1j ]-{2} M )×{r j } M ;CSP random permutation[z2]={[z 21 ],...,[z 2m ]} and send the randomly arranged [z2] to the Evaluator; the Evaluator evaluates each [z 2j Decrypt and examine the plaintext z. 2j The value of z; if all plaintext values ​​z 2i If ≠0, it means that condition 1 is true, and the subsequent steps are executed; otherwise, it means that condition 1 is false, and the process returns to the previous step to continue checking the next item set pair in T.

[0112] Step B3: Check if condition 2 is true, specifically including:

[0113] For F k For each ciphertext frequent itemset [v] in the CSP, the CSP is computed. CSP generates positive random numbers r j And calculate [z] 4j ]=([z 3j ]-{2} M )×{r j } M ;CSP random permutation[z4]={[z 41 ],...,[z 4m ]} and send the randomly arranged [z4] to the Evaluator; the Evaluator evaluates each [z 4j Decrypt and examine the plaintext z. 4j The value of z is calculated using the counter CT to count values ​​of 0. 4j The quantity, if CT = k, indicates that [v] = [x∪y], set T x∪y =T v If the condition is not met, proceed with the next step; otherwise, return to check F. k The next ciphertext frequent itemset [v] in the F, if the check is complete k If all frequent ciphertext itemsets [v] are not equal to [z1], then x∪y is not frequent, i.e., condition 2 is not true. At this time, return to step B1.

[0114] Step B4: Check if condition 3 is true, specifically including:

[0115] CSP and Evaluator use a secure multiplication protocol to compute the multiplication of two Paillier ciphertexts and obtain <αS x >,<αS y > and <βS x∪y >;

[0116] CSP and Evaluator perform a secure comparison protocol to determine βS. x∪y ≥αS x If the condition is met, then set a strong association rule.

[0117] CSP and Evaluator perform a secure comparison protocol to determine βS. x∪y ≥αS y If the condition is met, then set a strong association rule.

[0118] Add strong association rules to the strong association rule set SR.

[0119] The algorithm code for the SARM protocol is shown in Table 7.

[0120] Table 7

[0121]

[0122]

[0123] Specifically, in the Secure Association Rule Mining Protocol (SARM), for frequent ciphertext itemsets, the Cloud Server (CSP) and the Evaluator jointly and securely perform ciphertext association rule mining tasks. The input to this protocol is a set T (containing all tuples T). x ), set F (containing all sets F) k To obtain all strong association rules, for each set of frequent ciphertext itemsets ([x], [y]), the protocol needs to determine whether the following three conditions are met: (1) (2) x∪y is frequent; (3) or Here, mc = α / β (where α and β are integers) represents the lowest confidence level during association rule mining. In this protocol, we use the index values ​​of [x], [y], and [x∪y] to represent strong association rules. In this protocol, DO only needs to perform noise removal, which requires minimal computation. In cases with multiple data owners, only one data owner needs to execute the SFID protocol and share the calculated plaintext mining results with the other data owners.

[0124] Example 5

[0125] Based on the above embodiments, in this embodiment of the invention, two cloud servers (CSP and Evaluator) and the data owner (DO) jointly execute the SFID protocol to decrypt all ciphertext frequent itemsets. The SFID protocol stands for Secure Frequent Itemset Decryption Protocol; specifically, it includes:

[0126] For 1≤j≤m, CSP generates noise r j and the noise r j Add to ciphertext [x j In the end, the perturbed ciphertext [x′] = {[x1′], ..., [x...} is obtained. m CSP generates noise ε and adds the noise ε to the support. x >In the process, the perturbation ciphertext (S) is obtained. x CSP will combine [x'] and (S') x Send the data to the Evaluator, where r = (r1, ..., r...). m ), noise ε, index I x The itemset length k is sent to the data owner DO;

[0127] The Evaluator performs the decryption operation and perturbs the plaintext mining results x′ and S. x Send to data owner DO;

[0128] Data owner DO removes noise to obtain the frequent plaintext itemset x and its support S. x Combine it with index I x Put it into a tuple along with the itemset length k. middle.

[0129] The algorithm code for the SFID protocol is shown in Table 8.

[0130] Table 8

[0131]

[0132] Specifically, because the private keys for YASHE and Paillier are stored on the cloud server Evaluator to reduce the risk of key leakage, the data owner (DO) cannot directly decrypt the ciphertext mining results. In this protocol, the two cloud servers and the data owner (DO) jointly and securely decrypt the ciphertext frequent itemsets and their support. All decrypted plaintext mining results are known only to the data owner (DO) and will not be disclosed to any third party.

[0133] Table 9 shows the meanings of the parameters represented by some of the symbols used in the embodiments of the present invention.

[0134] Table 9. Parameter meanings of symbols used in this invention

[0135]

[0136]

[0137] Example 6

[0138] ​To demonstrate the performance of the APARM scheme proposed in this invention, the following experiments were conducted. Experimental results show that our scheme requires relatively low computational costs and is suitable for use on large databases.

[0139] (I) Experimental Platform and Related Parameter Settings

[0140] All experiments were conducted on Windows 10, with an Intel Core i7-7700HQ 2.80GHz CPU and 16GB of RAM.

[0141] The SEAL library is used to perform 128-bit secure YASHE encryption. In the YASHE algorithm, the degree of the polynomial modulus M is set to 4096, and the plaintext modulus P is set to 114689 to ensure efficiency and correctness; another YASHE parameter, decomposition bit count (dbc), is set to 16 to reduce noise budget consumption.

[0142] For Paillier encryption, 1024-bit security is implemented using the Crypto++ 5.6.3 library.

[0143] In addition, the number of all-zero data items was set to f = n / 2, and some extra data was added to ensure M|(n+f).

[0144] (II) Experimental Results

[0145] To better demonstrate the performance, we conducted experiments on real and synthetic databases, and the results are shown below.

[0146] (1) Experiments on real databases

[0147] We used three real-world databases: chess, mushroom, and connect, to conduct our experiments. We first presented the computational cost of the proposed protocol with the minimum support value in Table 10. Then, we varied the minimum support thresholds for the three databases and... Figures 2-4 The table shows the runtime of FIM (Phase 1 of APARM) and ARM (Phase 2 of APARM), as well as the total computational cost of APARM.

[0148] Here, all computational costs are averaged over 1000 iterations. In the table, n and m represent the database size and the number of data attributes for each transaction, respectively, ms represents the minimum support threshold, and N... f This indicates the number of frequent itemsets obtained from running the scheme.

[0149] Table 10. Computational overhead of each protocol on a real database (unit: seconds)

[0150]

[0151] (2) Conduct experiments on a synthetic database.

[0152] To better demonstrate the performance of our APARM scheme, we randomly generate multiple synthetic databases by varying the database size n and attribute m. Here, the average number of items in a transaction is m / 2. We then run the experiment by changing one parameter and fixing the other two parameters for different n, m, and ms, calculating the cost as follows. Figures 5-7 As shown, this is the average of 1000 times.

[0153] Analysis of the experimental results reveals that our proposed APARM scheme introduces lower computational overhead for data owners (DOs) and effectively performs frequent itemset mining and association rule mining on encrypted databases. Computational overhead from a set of real and synthetic databases demonstrates that the APARM scheme can be applied to databases of various sizes and attributes, showcasing its practicality in real-world scenarios. Furthermore, by dividing the encrypted database into several parts and executing the proposed protocol across multiple cloud servers, parallel operations can be easily achieved, further improving the efficiency of outsourced association rule mining.

[0154] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention. ​​ ​​​

Claims

1. A privacy-preserving method for cloud-based encrypted database association rule mining based on Apriori, characterized in that, include: Step 1: The data owner (DO) runs the TDE protocol and uses the YASHE algorithm on its private transaction database. Encryption is performed to obtain an encrypted database. It outputs two encryption masks. and ; Step 2: The data owner (DO) identifies all databases. 1-itemsets in Then encrypt it to obtain the ciphertext candidate 1-itemset. ; Step 3: The data owner (DO) uses the Paillier encryption algorithm to apply minimum support. and confidence threshold Encryption, obtaining ciphertext , and ; Step 4: The data owner, DO, encrypts all values. , , , , , and Outsource to cloud server CSP; Step 5: The two cloud servers, CSP and Evaluator, work together in the encrypted database. The Apriori algorithm is used to find all frequent itemsets of the ciphertext; specifically including: Step 5.1: Use the SFIM protocol to ciphertext candidate 1-itemsets Get the set containing all frequent 1-itemsets of ciphertext. SFIM protocol stands for Secure Frequent Itemset Mining Protocol. Step 5.2: For the set Each ciphertext itemset in CSP calculates its ciphertext concatenation itemset. , and will Add to ciphertext candidate 2-itemset ; Step 5.3: CSP uses the SFIM protocol in the ciphertext candidate 2-itemset Get the set containing all frequent 2-itemsets of ciphertext. ; Step 5.4: Set the itemset length ; Step 5.5: Initialize two collections and ; Step 5.6: For the set Each ciphertext itemset in Calculate its ciphertext concatenation itemset and add it to the ciphertext candidate k-itemset. ; Step 5.7: For candidate k-itemsets of ciphertext Each ciphertext item set Determine whether to start from Delete the ciphertext itemset Among them, the SPCI protocol is used to determine whether to use from Delete the ciphertext itemset SPCI protocol stands for Security Candidate Pruning Protocol; specifically, it includes: Initialize the counter ; against Ciphertext containing m encryption attributes is frequently - Itemset CSP calculation ,in ; CSP generates positive random numbers ,calculate ; Represents a group Number of values ; CSP random arrangement And the randomly arranged Send to Evaluator; Evaluator for each Decrypt and examine the plaintext. The value is determined using a counter. The calculated value is 0 Quantity; if , then it means The Evaluator will use a counter. Add 1; if Then Retained in In the process, terminate the SPCI protocol; if the check is complete All ciphertext frequently - Itemset after, Then from Delete; Step 5.8: Use the SFIM protocol in the ciphertext candidate k-itemset Get the set containing all frequent k-itemsets of ciphertext. ; Step 5.9: Set the itemset length Increment by 1, iterate through steps 5.6 to 5.8 until no new frequent ciphertext itemsets are found, then terminate the iteration; Step 5.10: Settings , of which each Contains all ciphertext frequent s-itemsets, ; Step 6: Based on the frequent itemsets of all ciphertexts, the two cloud servers, CSP and Evaluator, calculate all strong association rules and add them to the set. middle; Step 7: The two cloud servers CSP and Evaluator, together with the data owner DO, decrypt the frequent itemsets of all ciphertext and calculate all plaintext tuples. and add it to the collection In; among them, Indicates plain text itemsets, express index, express Support Indicates the length of the itemset; Step 8: [The text appears to be incomplete and contains several grammatical errors. A more accurate translation would require the full context.] and The results of association rule mining on the cloud-based encrypted database are returned to the data owner, DO.

2. The privacy protection method for cloud-based encrypted database association rule mining based on Apriori according to claim 1, characterized in that, In step 5.6, the ciphertext linked itemset is computed using the SJFI protocol, which stands for Secure Frequent Itemset Linking Protocol; specifically, it includes: Step A1: CSP and Evaluator collaborate to check if there are k-2 identical cryptographic properties between ciphertext itemset [x] and ciphertext itemset [y]. If so, it indicates that the two ciphertext itemsets [x] and [y] can be merged, and Evaluator calculates the ciphertext concatenation set. And send it to the CSP; Step A2: CSP uses [x], [y] and The ciphertext join itemset is calculated. ; Step A3: CSP and Evaluator examine the encrypted linked itemset together. Does it belong to ,if If, then the agreement is terminated; if Not belonging to Then CSP sets [x&y] = [z6] and adds [x&y] to middle.

3. The privacy protection method for cloud-based encrypted database association rule mining based on Apriori according to claim 2, characterized in that, Step A1 specifically includes: For a ciphertext itemset containing m encryption attributes and a ciphertext item set containing m encryption attributes CSP computes ciphertext join itemsets = , ; CSP generates positive random numbers ,according to and Calculated ; Represents a group Number of values ; CSP generates random permutation function right Randomly arrange the ciphertext and concatenate the itemsets. Send to Evaluator; Evaluator for each Decrypt and examine the plaintext. The value, and use a counter Statistical value of 0 The quantity, if If, then the agreement is terminated; if According to calculate And encrypt it, then concatenate the ciphertext itemset. Send to CSP; where, if ,but ;on the contrary, .

4. The privacy protection method for cloud-based encrypted database association rule mining based on Apriori according to claim 3, characterized in that, Step A2 specifically includes: CSP uses functions inverse function right Arrange; CSP Calculation ; ; Finally, the encrypted join itemset is obtained. .

5. The privacy protection method for cloud-based encrypted database association rule mining based on Apriori according to claim 4, characterized in that, Step A3 specifically includes: CSP utilization Each ciphertext item set in ciphertext link itemset Calculated ; ; CSP generates positive random numbers ,according to and Calculated ; CSP randomly arranges the ciphertext concatenation itemset Connect the randomly arranged ciphertext itemsets Send to Evaluator; Evaluator for each Decrypt and examine the plaintext. The value is determined using a counter. The calculated value is 0 The quantity, if If it does not, the agreement is terminated; otherwise, it is set by the CSP. Add [x&y] to middle.

6. The privacy protection method for cloud-based encrypted database association rule mining based on Apriori according to claim 1, characterized in that, In step 6, the two cloud servers, CSP and Evaluator, execute the SARM protocol to calculate all strong association rules and add them to the set. In this context, the SARM protocol represents a security association rule mining protocol; specifically, it includes: For each set of ciphertext frequent itemsets Determine whether the following four conditions are met: Condition 1: ; Condition 2: frequently; Condition 3: Condition 4: ; If ciphertext frequent itemsets If conditions 1, 2, and 3 are all met, then a strong association rule is set. ; If ciphertext frequent itemsets If conditions 1, 2, and 4 are all met, then a strong association rule is set. ; in, They represent , and The index value.

7. The privacy protection method for cloud-based encrypted database association rule mining based on Apriori according to claim 6, characterized in that, Step 6, the SARM protocol specifically includes: Step B1: For the set The project set in CSP calculation ; , They represent Project set length; if Then check the set The next itemset pair in; Step B2: If Then check whether condition 1 is true, specifically including: for CSP calculation CSP generates positive random numbers. and calculate CSP random arrangement and the random arrangement Send to the Evaluator; the Evaluator evaluates each Decrypt and examine the plaintext. The value; if all plaintext values If the condition is true, then condition 1 is met, and the next step is executed; otherwise, if the condition is false, then the process returns to the previous step to continue checking. The next itemset pair in; Step B3: Check if condition 2 is true, specifically including: for Each ciphertext frequent itemset CSP calculation CSP generates positive random numbers. and calculate CSP random arrangement and the random arrangement Send to the Evaluator; the Evaluator evaluates each Decrypt and examine the plaintext. The value is determined using a counter. Statistical value of 0 The quantity, if This indicates ,set up If the condition is met, proceed with the next steps; otherwise, return to the previous step for further inspection. The next ciphertext frequent itemset If the inspection is completed All ciphertext frequent itemsets All ciphertext frequent itemsets None of them are equal to , then it means If it is infrequent, meaning condition 2 is not met, then return to step B1. Step B4: Check if condition 3 is true, specifically including: CSP and Evaluator use a secure multiplication protocol to compute the multiplication of two Paillier ciphertexts and obtain... , and ; CSP and Evaluator perform a security comparison protocol to determine... If the condition is met, then set a strong association rule. ; CSP and Evaluator perform a security comparison protocol to determine... If the condition is met, then set a strong association rule. ; Add strong association rules to the strong association rule set SR.

8. The privacy protection method for cloud-based encrypted database association rule mining based on Apriori according to claim 1, characterized in that, In step 7, the two cloud servers CSP and Evaluator, together with the data owner DO, execute the SFID protocol to decrypt all ciphertext frequent itemsets. SFID stands for Secure Frequent Itemset Decryption Protocol; specifically, it includes: for CSP generates noise and noise Add to encrypted Finally, the perturbed ciphertext is obtained. CSP generates noise and noise Add to support In the middle, the perturbed ciphertext is obtained. CSP will and Send to Evaluator, Noise ,index and itemset length Send to the data owner, DO; The Evaluator performs the decryption operation and perturbs the mining results in plaintext. and Send to the data owner, DO; The data owner (DO) removes noise to obtain frequent plaintext itemsets. and its support Combine it with the index and itemset length Put them together into a tuple middle.

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