A privacy-preserving multi-party data statistics method
Through homomorphic encryption technology and key exchange mechanism, the problem of data privacy leakage in joint statistics of multiple parties is solved, and secure data statistics are achieved while protecting privacy.
Patent Information
- Application Number
- CN202410099978.1
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2024-01-24
- Publication Date
- 2025-04-29
- Estimated Expiration
- 2044-01-24
AI Technical Summary
In the joint statistical analysis of multi-party data, it is difficult for the existing technology to effectively protect the data privacy of all parties, resulting in some privacy data leakage.
Using homomorphic encryption technology, the first and second parties use keys k1 and k2 to encrypt the user identification and characteristic values, and homomorphic encryption is performed through the public key pk to form spliced ciphertext exchange. Through secondary encryption and scrambling sequence processing, we ensure that data privacy is not leaked during data statistics.
Data statistics are carried out on the premise of protecting the data privacy of all parties, effectively avoiding data leakage and ensuring the security of joint statistics of multiple parties.
Smart Images
Figure CN117614612B_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the field of encryption technology, and in particular to a multi-party data statistics method for protecting privacy. Background Art
[0002] With the development of computer technology and Internet technology, big data analysis has become an important technical means for business processing in related fields. Since different data parties often have different data, in order to fully tap the value of data, it is often necessary for multiple data parties to cooperate in joint statistical analysis of data in existing technologies. Especially in group companies or cross-institutions in the same industry, there is a general need for multiple parties to work together to do data statistics. Since the data of all parties are confidential, when doing joint statistics, each party needs to protect its own data and cannot disclose it to other parties, which brings great difficulties to the joint statistics of multiple parties.
[0003] At present, the method for the first party and the second party to perform joint data statistics is: first, the privacy set intersection of the user identifier held by the first party and the user identifier held by the second party is performed to obtain the intersection, the first party finds the feature value corresponding to the user identifier in the intersection and sums it to obtain the first statistical value, the second party finds the feature value corresponding to the user identifier in the intersection and sums it to obtain the second statistical value, and finally adds the first statistical value and the second statistical value to obtain the statistical result. This method does not expose the user information outside the intersection of the two parties and the feature value information held by both parties, which protects the user privacy to a certain extent, but exposes the intersection information and still leaks part of the privacy data of both parties. Summary of the invention
[0004] In order to solve the above technical problems, the present invention provides a privacy-protecting multi-party data statistics method, which can perform data statistics under the premise of protecting the data privacy of all parties and effectively avoid data leakage.
[0005] In order to solve the above problems, the present invention adopts the following technical solutions:
[0006] A privacy-protecting multi-party data statistics method of the present invention, wherein the multi-party includes a first party and a second party, the first party has a homomorphically encrypted public key pk and a private key sk, and the second party has a homomorphically encrypted public key pk, comprising the following steps:
[0007] S1: The first party uses key k1 and the second party uses key k2 to encrypt their respective user identifiers to obtain corresponding identifier ciphertexts. The first party and the second party use public key pk to homomorphically encrypt the feature values corresponding to their respective user identifiers to obtain corresponding feature ciphertexts. The identifier ciphertext and feature ciphertext corresponding to the same user identifier are concatenated to obtain the corresponding first concatenated ciphertext and sent to the other party.
[0008] S2: The first party uses the key k1 to re-encrypt the identification ciphertext in the first concatenated ciphertext sent by the second party to obtain a second concatenated ciphertext, and sends all the second concatenated ciphertexts to the second party after shuffling the order.
[0009] S3: The second party uses the key k2 to re-encrypt the identification ciphertext in the first concatenated ciphertext sent by the first party to obtain a third concatenated ciphertext, intersects all the second concatenated ciphertexts and the re-encrypted identification ciphertexts in the third concatenated ciphertexts to obtain an intersection, adds the characteristic ciphertexts in the second concatenated ciphertexts and the third concatenated ciphertexts having elements in the intersection by homomorphic addition to obtain a ciphertext statistical value and sends it to the first party;
[0010] S4: The first party uses the private key sk to decrypt the ciphertext statistical value to obtain the plaintext statistical value.
[0011] In this solution, the user ID held by the first party is first encrypted with key k1 and then encrypted twice with key k2. If a user ID held by the first party is consistent with a user ID held by the second party, the results of the two user IDs after double encryption are also consistent. Since the first party does not know key k2 and the second party does not know key k1, neither party will leak their data privacy.
[0012] Since the first party shuffles the order of the second concatenated ciphertext before sending it to the second party, the second party cannot infer the plaintext information corresponding to the intersection. The second party does not have the private key sk and cannot decrypt the characteristic ciphertext and ciphertext statistics. Although the first party holds the private key sk, the intersection operation is performed by the second party. Even if the first party decrypts the characteristic value, it cannot know which specific user the characteristic value belongs to. Finally, the first party uses the private key sk to decrypt the ciphertext statistics sent by the second party to obtain the plaintext statistics. During the entire data statistics process, neither party leaks any data privacy, effectively avoiding data leakage.
[0013] Preferably, the step S1 comprises the following steps:
[0014] The first party uses the key k1 to encrypt the user identification it holds to obtain the corresponding identification ciphertext, uses the public key pk to homomorphically encrypt the feature value corresponding to the user identification to obtain the corresponding feature ciphertext, and concatenates the identification ciphertext and feature ciphertext corresponding to the same user identification to obtain the corresponding first concatenated ciphertext and sends it to the second party;
[0015] The second party uses the key k2 to encrypt the user identifier it holds to obtain the corresponding identification ciphertext, uses the public key pk to homomorphically encrypt the characteristic value corresponding to the user identifier to obtain the corresponding characteristic ciphertext, and concatenates the identification ciphertext and characteristic ciphertext corresponding to the same user identifier to obtain the corresponding first concatenated ciphertext and sends it to the first party.
[0016] Preferably, the first party holds n user identifiers, which are sequentially denoted as X1, X2, ..., X n , 1≤i≤n,X i represents the i-th user ID held by the first party. The first party sets the user ID X i The corresponding identification ciphertext XC i 、Characteristic ciphertext XE i Concatenate to get the corresponding first concatenated ciphertext XF i The formula is as follows: ;
[0017] The second party holds m user identifiers, which are denoted as Y1, Y2, ..., Y m , 1≤j≤m,Y j represents the jth user ID held by the second party. The second party will use the user ID Y j The corresponding identification ciphertext YC j 、Feature ciphertext YE j Concatenate to get the corresponding first concatenated ciphertext YF j The formula is as follows: .
[0018] Preferably, the first party uses the key k1 to identify the user X i Encrypt to get the corresponding identification ciphertext XC i The formula is as follows: , N is a large prime number;
[0019] The second party uses the key k2 to identify the user Y j Encrypt to get the corresponding identification ciphertext YC j The formula is as follows: .
[0020] Preferably, the first party uses the key k1 to convert the first concatenated ciphertext YF sent by the second party into j The ciphertext YC in j The second encryption obtains the second concatenated ciphertext YG j The method is as follows:
[0021] The first party finds the identification ciphertext YC j In the first concatenated ciphertext YF j The position in the ciphertext YC is identified by key k1. jPerform secondary encryption to obtain the new identification ciphertext YD j , the formula is as follows:
[0022] ,
[0023] Identification ciphertext YD j With the characteristic ciphertext YE j Splice into the second splicing ciphertext YG j , .
[0024] Preferably, the second party uses the key k2 to convert the first concatenated ciphertext XF i The ciphertext XC in i The second encryption obtains the third concatenated ciphertext XG i The method is as follows:
[0025] The second party finds the identification ciphertext XC i In the first concatenation ciphertext XF i The position in the ciphertext XC is identified by key k2 i Perform secondary encryption to obtain a new identification ciphertext XD i , the formula is as follows:
[0026] ,
[0027] Identify the ciphertext XD i With the characteristic ciphertext XE i Splice into the third splicing ciphertext XG i , .
[0028] Preferably, in step S3, the second party intersects all the second concatenated ciphertexts and the second encrypted identification ciphertexts in the third concatenated ciphertexts to obtain the intersection as follows:
[0029] The second party takes out the twice-encrypted identification ciphertexts from all the second concatenated ciphertexts to form a second data set, takes out the twice-encrypted identification ciphertexts from all the third concatenated ciphertexts to form a third data set, and intersects the second data set and the third data set to obtain an intersection.
[0030] Preferably, in step S3, the second party uses homomorphic addition to add the characteristic ciphertexts in the second concatenated ciphertext and the third concatenated ciphertext having the elements in the intersection to obtain the ciphertext statistics as follows:
[0031] The second party finds all the second concatenated ciphertexts corresponding to the elements in the intersection, takes out the characteristic ciphertexts in the found second concatenated ciphertexts and puts them into the set to be counted, finds all the third concatenated ciphertexts corresponding to the elements in the intersection, takes out the characteristic ciphertexts in the found third concatenated ciphertexts and puts them into the set to be counted, and adds all the characteristic ciphertexts in the set to be counted using homomorphic addition to obtain the ciphertext statistical value.
[0032] Preferably, in step S2, the first party uses a shuffle algorithm to shuffle the order of all the second concatenated ciphertexts.
[0033] Preferably, the first party uses a key generator to randomly generate a key k1, and the second party uses a key generator to randomly generate a key k2.
[0034] The beneficial effect of the present invention is that data statistics can be performed under the premise of protecting the data privacy of all parties, thereby effectively avoiding data leakage. BRIEF DESCRIPTION OF THE DRAWINGS
[0035] Figure 1 is a flow chart of an embodiment. DETAILED DESCRIPTION
[0036] The technical solution of the present invention is further specifically described below through embodiments and in conjunction with the accompanying drawings.
[0037] Embodiment: In this embodiment, a privacy-preserving multi-party data statistics method is provided. The multi-party includes a first party and a second party. The first party has a homomorphically encrypted public key pk and a private key sk. The second party has a homomorphically encrypted public key pk. The first party holds n user identifiers, which are sequentially recorded as X1, X2, ...X n , 1≤i≤n,X i The first party holds the i-th user ID, and the second party holds m user IDs, which are denoted as Y1, Y2, ..., Y m , 1≤j≤m,Y j represents the jth user ID held by the second party, such as Figure 1 As shown, the following steps are included:
[0038] S1: The first party uses a key generator to randomly generate a key k1, and the second party uses a key generator to randomly generate a key k2;
[0039] The first party uses the key k1 to encrypt each user identifier it holds to obtain the corresponding identifier ciphertext, uses the public key pk to homomorphically encrypt the feature value corresponding to each user identifier to obtain the corresponding feature ciphertext, concatenates the identifier ciphertext and feature ciphertext corresponding to the same user identifier to obtain the corresponding first concatenated ciphertext and sends it to the second party;
[0040] The first party uses the key k1 to identify the user X iEncrypt to get the corresponding identification ciphertext XC i The formula is as follows: , N is a large prime number;
[0041] The first party will use the user ID X i The corresponding identification ciphertext XC i 、Characteristic ciphertext XE i Concatenate to get the corresponding first concatenated ciphertext XF i The formula is as follows: ;
[0042] The second party uses the key k2 to encrypt each user identifier it holds to obtain the corresponding identifier ciphertext, uses the public key pk to homomorphically encrypt the feature value corresponding to each user identifier to obtain the corresponding feature ciphertext, concatenates the identifier ciphertext and feature ciphertext corresponding to the same user identifier to obtain the corresponding first concatenated ciphertext and sends it to the first party;
[0043] The second party uses the key k2 to identify the user Y j Encrypt to get the corresponding identification ciphertext YC j The formula is as follows: ;
[0044] The second party will use the user ID Y j The corresponding identification ciphertext YC j 、Feature ciphertext YE j Concatenate to get the corresponding first concatenated ciphertext YF j The formula is as follows: ;
[0045] S2: The first party uses the key k1 to re-encrypt the identification ciphertext in the first concatenated ciphertext sent by the second party to obtain the corresponding second concatenated ciphertext, uses the shuffle algorithm to shuffle the order of all the second concatenated ciphertexts and sends them to the second party;
[0046] The first party uses the key k1 to convert the first concatenated ciphertext YF sent by the second party j The ciphertext YC in j The second encryption obtains the corresponding second concatenated ciphertext YG j The method is as follows:
[0047] The first party finds the identification ciphertext YC j In the first concatenated ciphertext YF j The position in the ciphertext YC is identified by key k1. j Perform secondary encryption to obtain the new identification ciphertext YD j , the formula is as follows:
[0048] ,
[0049] Identification ciphertext YD j With the characteristic ciphertext YE j Splice into the second splicing ciphertext YG j , ;
[0050] S3: The second party uses the key k2 to re-encrypt the identification ciphertext in the first concatenated ciphertext sent by the first party to obtain the corresponding third concatenated ciphertext, intersects all the re-encrypted identification ciphertexts in the second concatenated ciphertexts and the third concatenated ciphertexts to obtain an intersection, adds the characteristic ciphertexts in the second concatenated ciphertexts and the third concatenated ciphertexts having elements in the intersection by homomorphic addition to obtain a ciphertext statistical value and sends it to the first party;
[0051] The second party uses the key k2 to convert the first concatenated ciphertext XF sent by the first party i The ciphertext XC in i The second encryption obtains the corresponding third concatenated ciphertext XG i The method is as follows:
[0052] The second party finds the identification ciphertext XC i In the first concatenation ciphertext XF i The position in the ciphertext XC is identified by key k2 i Perform secondary encryption to obtain a new identification ciphertext XD i , the formula is as follows:
[0053] ,
[0054] Identify the ciphertext XD i With the characteristic ciphertext XE i Splice into the third splicing ciphertext XG i , ;
[0055] S4: The first party uses the private key sk to decrypt the ciphertext statistical value to obtain the plaintext statistical value.
[0056] In step S3, the second party intersects all the second concatenated ciphertexts and the second encrypted identification ciphertexts in the third concatenated ciphertexts to obtain the intersection as follows:
[0057] The second party takes out the twice-encrypted identification ciphertexts from all the second concatenated ciphertexts to form a second data set, takes out the twice-encrypted identification ciphertexts from all the third concatenated ciphertexts to form a third data set, and intersects the second data set and the third data set to obtain an intersection.
[0058] In step S3, the second party uses homomorphic addition to add the characteristic ciphertexts in the second concatenated ciphertext and the third concatenated ciphertext with elements in the intersection to obtain the ciphertext statistics value as follows:
[0059] The second party finds all the second concatenated ciphertexts corresponding to the elements in the intersection, takes out the characteristic ciphertexts in the found second concatenated ciphertexts and puts them into the set to be counted, finds all the third concatenated ciphertexts corresponding to the elements in the intersection, takes out the characteristic ciphertexts in the found third concatenated ciphertexts and puts them into the set to be counted, and adds all the characteristic ciphertexts in the set to be counted using homomorphic addition to obtain the ciphertext statistical value.
[0060] In this solution, the user ID can be an ID number, a mobile phone number, etc. N is a large prime number of 2048 bits.
[0061] The user ID held by the first party is first encrypted once with key k1, and then encrypted twice with key k2. The user ID held by the first party is first encrypted once with key k2, and then encrypted twice with key k1. If the user ID held by the first party is X i The user ID Y held by the second party j Consistent, that is, X i =Y j , then according to the encryption formula:
[0062] ,
[0063] ,
[0064] It can be seen XD i =YD j .
[0065] Therefore, the second party intersects all the second concatenated ciphertexts and the second concatenated ciphertexts with the twice-encrypted identification ciphertexts. The plaintext corresponding to the obtained intersection is the intersection of the user identification held by the first party and the user identification held by the second party. Since the first party does not know the key k2 and the second party does not know the key k1, neither party will leak their respective data privacy.
[0066] Since the first party shuffles the second concatenated ciphertext and sends it to the second party, the second party cannot infer the plaintext information corresponding to the intersection. The second party does not have the private key sk and cannot decrypt the characteristic ciphertext and ciphertext statistics. Although the first party holds the private key sk, the intersection operation is performed by the second party. Even if the first party decrypts the characteristic value, it cannot know which specific user the characteristic value belongs to.
[0067] Finally, the second party uses homomorphic addition to add the characteristic ciphertexts in the second concatenated ciphertext and the third concatenated ciphertext with elements in the intersection to obtain the ciphertext statistical value. Due to the lack of the private key sk, the plaintext of the ciphertext statistical value cannot be obtained. The first party uses the private key sk to decrypt the ciphertext statistical value sent by the second party to obtain the plaintext statistical value. During the entire data statistical process, both parties did not disclose any data privacy, effectively avoiding data leakage.
[0068] For example:
[0069] Company A and Company B need to calculate the total consumption amount of common users. Company A is the first party and Company B is the second party. The first party has the homomorphically encrypted public key pk and private key sk, and the second party has the homomorphically encrypted public key pk.
[0070] The four user data held by the first party are: (user ID 2, consumption amount 12), (user ID 3, consumption amount 13), (user ID 4, consumption amount 14), (user ID 5, consumption amount 15);
[0071] The four user data held by the second party are: (user ID 2, consumption amount 22), (user ID 3, consumption amount 23), (user ID 6, consumption amount 26), and (user ID 7, consumption amount 27).
[0072] The first party uses the key k1 to encrypt the user identity it holds to obtain the corresponding identity ciphertext, uses the public key pk to homomorphically encrypt the feature value corresponding to the user identity to obtain the corresponding feature ciphertext, and concatenates the identity ciphertext and feature ciphertext corresponding to the same user identity to obtain the corresponding first concatenated ciphertext and sends it to the second party. The four first concatenated ciphertexts are: , , , , Enc(x) represents the ciphertext obtained by homomorphically encrypting data x using the public key pk;
[0073] The second party uses the key k2 to encrypt the user identity it holds to obtain the corresponding identity ciphertext, and uses the public key pk to homomorphically encrypt the feature value corresponding to the user identity to obtain the corresponding feature ciphertext. The identity ciphertext and feature ciphertext corresponding to the same user identity are concatenated to obtain the corresponding first concatenated ciphertext and sent to the first party. The four first concatenated ciphertexts are: , , , .
[0074] The first party uses the key k1 to re-encrypt the identification ciphertext in the four first concatenated ciphertexts sent by the second party to obtain the second concatenated ciphertext, and shuffles the order of the four second concatenated ciphertexts to obtain the following: , , , , and send the 4 second concatenated ciphertexts in shuffled order to the second party.
[0075] The second party uses the key k2 to re-encrypt the identification ciphertext in the first concatenated ciphertext sent by the first party to obtain the third concatenated ciphertext. The four third concatenated ciphertexts are: , , , ;
[0076] The intersection of the 4 second concatenated ciphertexts and the 4 third concatenated ciphertexts after double encryption is obtained, and the intersection is , Enc(22), Enc(23), Enc(12), and Enc(13) are added together using homomorphic addition to obtain the ciphertext statistical value Enc(70) and sent to the first party.
[0077] The first party uses the private key sk to decrypt the ciphertext statistical value Enc(70) and obtains the plaintext statistical value 70, which is consistent with the plaintext calculation result.
[0078] During the entire data statistics process mentioned above, neither the first party nor the second party disclosed any data privacy, effectively avoiding data leakage.
Claims
1. A privacy-preserving multi-party data statistics method, wherein the multi-party includes a first party and a second party, the first party has a homomorphically encrypted public key pk and a private key sk, and the second party has a homomorphically encrypted public key pk, characterized in that: The following steps are involved: S1: The first party uses key k1 and the second party uses key k2 to encrypt their respective user identifiers to obtain corresponding identifier ciphertexts. The first party and the second party use public key pk to homomorphically encrypt the feature values corresponding to their respective user identifiers to obtain corresponding feature ciphertexts. The identifier ciphertext and feature ciphertext corresponding to the same user identifier are concatenated to obtain the corresponding first concatenated ciphertext and sent to the other party. S2: The first party uses the key k1 to re-encrypt the identification ciphertext in the first concatenated ciphertext sent by the second party to obtain a second concatenated ciphertext, and sends all the second concatenated ciphertexts to the second party after shuffling the order. S3: The second party uses the key k2 to re-encrypt the identification ciphertext in the first concatenated ciphertext sent by the first party to obtain a third concatenated ciphertext, intersects all the second concatenated ciphertexts and the re-encrypted identification ciphertexts in the third concatenated ciphertexts to obtain an intersection, adds the characteristic ciphertexts in the second concatenated ciphertexts and the third concatenated ciphertexts having elements in the intersection by homomorphic addition to obtain a ciphertext statistical value and sends it to the first party; S4: The first party uses the private key sk to decrypt the ciphertext statistical value to obtain the plaintext statistical value; In step S3, the second party intersects all the second concatenated ciphertexts and the second encrypted identification ciphertexts in the third concatenated ciphertexts to obtain the intersection as follows: The second party extracts the twice-encrypted identification ciphertexts from all the second concatenated ciphertexts to form a second data set, extracts the twice-encrypted identification ciphertexts from all the third concatenated ciphertexts to form a third data set, and intersects the second data set and the third data set to obtain an intersection set; In step S3, the second party uses homomorphic addition to add the characteristic ciphertexts in the second concatenated ciphertext and the third concatenated ciphertext with elements in the intersection to obtain the ciphertext statistics as follows: The second party finds all the second concatenated ciphertexts corresponding to the elements in the intersection, takes out the characteristic ciphertexts in the found second concatenated ciphertexts and puts them into the set to be counted, finds all the third concatenated ciphertexts corresponding to the elements in the intersection, takes out the characteristic ciphertexts in the found third concatenated ciphertexts and puts them into the set to be counted, and adds all the characteristic ciphertexts in the set to be counted using homomorphic addition to obtain the ciphertext statistical value.
2. The privacy-preserving multi-party data statistics method according to claim 1, characterized in that: The step S1 comprises the following steps: The first party uses the key k1 to encrypt the user identification it holds to obtain the corresponding identification ciphertext, uses the public key pk to homomorphically encrypt the feature value corresponding to the user identification to obtain the corresponding feature ciphertext, and concatenates the identification ciphertext and feature ciphertext corresponding to the same user identification to obtain the corresponding first concatenated ciphertext and sends it to the second party; The second party uses the key k2 to encrypt the user identifier it holds to obtain the corresponding identification ciphertext, uses the public key pk to homomorphically encrypt the characteristic value corresponding to the user identifier to obtain the corresponding characteristic ciphertext, and concatenates the identification ciphertext and characteristic ciphertext corresponding to the same user identifier to obtain the corresponding first concatenated ciphertext and sends it to the first party.
3. The privacy-preserving multi-party data statistics method according to claim 1, characterized in that: The first party holds n user identities, which are denoted as X1, X2, ...X n , 1≤i≤n,X i represents the i-th user ID held by the first party. The first party sets the user ID X i The corresponding identification ciphertext XC i 、Characteristic ciphertext XE i Concatenate to get the corresponding first concatenated ciphertext XF i The formula is as follows: ; The second party holds m user identifiers, which are denoted as Y1, Y2, ..., Y m , 1≤j≤m,Y j represents the jth user ID held by the second party. The second party will use the user ID Y j The corresponding identification ciphertext YC j 、Feature ciphertext YE j Concatenate to get the corresponding first concatenated ciphertext YF j The formula is as follows: .
4. The privacy-preserving multi-party data statistics method according to claim 3, characterized in that: The first party uses the key k1 to identify the user X i Encrypt to get the corresponding identification ciphertext XC i The formula is as follows: , N is a large prime number; The second party uses the key k2 to identify the user Y j Encrypt to get the corresponding identification ciphertext YC j The formula is as follows: .
5. The privacy-preserving multi-party data statistics method according to claim 4, characterized in that: The first party uses the key k1 to convert the first concatenated ciphertext YF sent by the second party j The ciphertext YC in j The second encryption obtains the second concatenated ciphertext YG j The method is as follows: The first party finds the identification ciphertext YC j In the first concatenated ciphertext YF j The position in the ciphertext YC is identified by key k1. j Perform secondary encryption to obtain the new identification ciphertext YD j , the formula is as follows: ， Identification ciphertext YD j With the characteristic ciphertext YE j Splice into the second splicing ciphertext YG j , .
6. The privacy-preserving multi-party data statistics method according to claim 4, characterized in that: The second party uses the key k2 to convert the first concatenated ciphertext XF sent by the first party i The ciphertext XC in i The second encryption obtains the third concatenated ciphertext XG i The method is as follows: The second party finds the identification ciphertext XC i In the first concatenation ciphertext XF i The position in the ciphertext XC is identified by key k2 i Perform secondary encryption to obtain a new identification ciphertext XD i , the formula is as follows: ， Identify the ciphertext XD i With the characteristic ciphertext XE i Splice into the third splicing ciphertext XG i , .
7. The privacy-preserving multi-party data statistics method according to claim 1, characterized in that: In step S2, the first party uses a shuffle algorithm to shuffle the order of all the second concatenated ciphertexts.
8. The privacy-preserving multi-party data statistics method according to claim 1, characterized in that: The first party uses a key generator to randomly generate a key k1, and the second party uses a key generator to randomly generate a key k2.
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