CN109818729B - Privacy protection average distance query method based on Paillier homomorphic encryption - Google Patents
Privacy protection average distance query method based on Paillier homomorphic encryption Download PDFInfo
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Abstract
The invention provides a privacy protection average distance query method based on Paillier homomorphic encryption, and relates to the technical field of information security. The method comprises an average distance query processing protocol based on a server side and an average distance query processing protocol based on a client side, position selection is optimized according to average distance query, two types of privacy protection query processing protocols are adopted, partial homomorphic encryption is used as a building block, sensitive data of the server and the client side are encrypted, and further disguise operation is carried out on the encrypted data to protect the privacy of the two sides, so that the client side can answer the query based on the position without sharing data with other enterprises or accessing sensitive information. The method is beneficial to effectively sharing the sensitive data between the entities of various application programs and the joint analysis under the condition of not invading the privacy of the client, greatly improves the quality of service, and can also reduce the logistics cost of enterprises.
Description
Technical Field
The invention relates to the technical field of information security, in particular to a privacy protection average distance query method based on Paillier homomorphic encryption.
Background
With the rapid development of network technology, databases around the world collect and analyze a large amount of location information. More and more location data from mobile services, applications and network operators, etc. provides convenience and new opportunities for the development of some enterprises. These location data owners are able to keep track of the user's location information explicitly, and businesses also want to be able to apply the location information owned by the location data owners to their own developments, such as finding the best location for a new branch office of the business. However, the location information of the client is a very important personal privacy data, and the personal identity can be leaked by a little carelessness, for example, the relevant information of the family or the work can be deduced through the location information of the client. Location data owners are therefore unable to share this type of specific information with other businesses due to legal requirements and privacy concerns. Businesses have begun seeking a way to run location-based analytical queries without violating customer privacy. In addition to this, we need to prevent service providers who own customer location information from tracking users individually, who may possibly collaborate with the enterprise, being compensated for by obtaining useful information for them. Similarly, enterprises do not wish to share their own customer lists with location-based service providers in order to maximize their own growth advantages. Based on the above situation, it is necessary to develop an efficient privacy-preserving location information query processing protocol, which is helpful to find the optimal location of a new branch according to the location distribution condition on the premise of considering the security of the client location data.
Optimal location selection is a common location-based analysis that seeks to find the best location for a new facility, optimizing an objective function given a set of existing facilities and a set of customers. One common approach is to use a corresponding geometric computation method at the customer location, assuming the location is known. However, third party enterprises and analysts cannot use these geometric computation methods in real life because the enterprises cannot know the location of their customers in real time. In order to successfully perform location-based queries, businesses need the latest locations that can be collected from location data owners (such as mobile operators and location-based service providers). For example, while a retail store or bank may know their customer's address, they may also wish to know their location at certain times of the day. However, the customer's work address may be lost, changed or outdated in its database, and data that is not updated in real time greatly affects the selection of the optimal location. There is therefore a need to collect the user's location information from the data owner while retaining some sensitive information of the data owner, as well as the relevant privacy of the customer, including their identity and address, etc.
For privacy preserving solutions, it is necessary to hide the user list of the client and the user list of the server from each other, and also to hide the answer to the query from the server. Otherwise, the server will master the best candidate for the new facility and possibly share this information with competitors. Privacy protection solutions that aggregate queries that allow analysis of location data in the server and selection of the best facility location are therefore important. With the proposed solution, a client can obtain aggregated information about the user's location without sharing the user list with the server. Given a set of existing facilities and a set of users, the optimal location query is to find a location for the most influential new facility, one of the methods is to minimize the average distance between each user and its nearest device using the privacy protection of Paillier homomorphic encryption. The average distance is a valuable information for the customer and can be minimized to maximize the user's interest. There are many practical applications of this technology, which aim to improve the quality of service or to reduce the logistics cost of an enterprise.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides a privacy protection average distance query method based on Paillier homomorphic encryption, which optimizes position selection according to average distance query, adopts two types of privacy protection query processing protocols, uses partial homomorphic encryption as a building block, encrypts sensitive data of a server and a client, and performs further disguise operation on the encrypted data to protect the privacy of both sides.
In order to achieve the purpose, a privacy protection average distance query method based on Paillier homomorphic encryption comprises an average distance query processing protocol based on a server side and an average distance query processing protocol based on a client side;
(1) the server-side-based average distance query processing protocol comprises the following steps:
s1: setting the location data owner as a server S and the service requesting inquiry as a clientC, wherein the server S has nSIndividual user
Client C has nCIndividual user
Set U ═ US∪UC＝{U1，U2，...，Un}, set UI＝US∩UC＝{U1，...，Ui，...，UmThe server S for each user at different time periodsjProviding location information;
s2: setting basic information of an average distance query processing protocol based on a server side;
s2.1: the server side selects the set U and sends the set U to the client side, and therefore the server user U is hidden in the client sideS；
S2.2: public key PK generated by Paillier homomorphic encryption system for serverSAnd a private key SKS；
S2.3: will aggregate U and public key PKSSending the data to a client;
s3: the client sends the facility position F and the query request to the server;
s4: server computing F facility and user USThe distance between them, determine each user Ui∈USDistance d to nearest facilityiBuilding a set D ═ D1，d2，...，dn}；
S5: the server calculates the encryption value of each element in the set D to obtain an encryption result T]SAnd sent to the client, thereby hiding the server user U in the clientSAnd server user USThe position of (a);
s6: the client calculates each facility position F by utilizing the multiplication homomorphism property of the Paillier cryptosystemjE.g. F, to obtain ciphertext X]S；
S7: the client selects two random values v1And v2For ciphertext[X]SCamouflage is carried out to obtain ciphertext [ X']SAnd sent to the server, thereby hiding the U on the serverCAnd UCThe query result of (2);
s8: the server decrypts the encrypted disguised result to obtain a decrypted result X 'and sends the decrypted result X' to the client;
s9: the client carries out disguise calculation on the ciphertext X' to obtain a required query result z;
(2) the average distance query processing protocol based on the client comprises the following steps:
c1: setting a position data owner as a server S and a service requesting inquiry as a client C, wherein the server S has nSIndividual user
Client C has nCIndividual user
Set U ═ US∪UC＝{U1，U2，...，Un}, set UI＝US∩UC＝{U1，...，Ui，...，UmThe server S for each user at different time periodsjProviding location information;
c2: setting basic information of a client-based average distance query processing protocol;
c2.1: the server selects the set U and sends the set U to the client, so that the server user U is hidden in the clientS；
C2.2: client generates public key PK by using property of Paillier homomorphic encryption systemCAnd a private key SKCClient sharing PK with serverC；
C2.3: selecting a random non-zero integer riModulo m with the group generated by client CCAll the other properties of the Chinese herbs
C2.4: customerAccording to user list UCComputing an encryption result [ T ]]C；
C2.5: client side will [ T]CPublic key PKCR and the number of client users ncSending the data to a server;
c3: the server verifies the encrypted result, thereby hiding the user U at the clientCThe query result of (2);
c4: the client sends the facility position F and the query request to the server;
c5: server computing F facility and user USThe distance between them, determine each user Ui∈USDistance d to nearest facilityiBuilding a set D ═ D1，d2，...，dn}；
C6: the client uses the multiplication homomorphism property of the Paillier cryptosystem and uses T]CTo calculate the ciphertext [ X ] of the query result]C；
C7: server sends cipher text [ X]CMultiplying the query result by zero encryption to obtain an anonymized and encrypted query result [ X']CAnd sending the data to the client to prevent the server from tracking the position of the user through the client;
c8: and the client decrypts the anonymized and encrypted query result to obtain the query result.
Further, the server in the step C3 verifies the encryption result by determining
Whether or not equal to EC(nC) If so, continuing the protocol, if not, terminating the protocol, wherein,
number n of users for clientCEncryption of mCModulus, g, for the group generated by client CCR is a random number, which is a generator of the group generated by the client C.
The invention has the beneficial effects that:
the invention provides a privacy protection average distance query method based on Paillier homomorphic encryption, which comprises an average distance query processing protocol based on a server side and an average distance query processing protocol based on a client side, wherein in the protocol execution process, a user list and a query result of the client side are hidden on the server by using homomorphic encryption, and the user list and position data of the server are hidden on the client side, and then a client (such as an enterprise) is introduced to query the optimal facility position on a database (such as a position-based service provider) of the server, so that the safety and reliability of data can be greatly ensured on the premise of realizing basic requirements, and the method has high practical value and expansion space. In the protocol based on the server, the server executes most of calculations, so that the workload of the client is very low, and when the computing capability of the client is limited, the calculation can be conveniently and quickly performed; in a client-based protocol, most of the calculations performed by the client occur only once, reducing communication overhead to some extent. In the query method provided by the invention, enterprises do not need to know the positions of users, but analyze the position data through requests, hide user lists of the two parties by utilizing a potential user space union and a method of returning aggregate information, and help the enterprises to find the optimal position of a new facility among several candidates, thereby improving the safety.
Drawings
Fig. 1 is a schematic overall architecture diagram of a privacy-preserving average distance query method based on Paillier homomorphic encryption in the embodiment of the present invention;
FIG. 2 is a timing diagram of a server-based query processing protocol in an embodiment of the present invention;
FIG. 3 is a flow diagram of a server-based query processing protocol in an embodiment of the present invention;
FIG. 4 is a timing diagram of a client-based query processing protocol in an embodiment of the present invention;
FIG. 5 is a flow chart of a client-based query processing protocol in an embodiment of the invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more clear, the present invention will be further described in detail with reference to the accompanying drawings and specific embodiments. The specific embodiments described herein are merely illustrative of the invention and are not intended to be limiting.
A privacy protection average distance query method based on Paillier homomorphic encryption is disclosed, the architecture of which is shown in figure 1, and the method comprises an average distance query processing protocol based on a server side and an average distance query processing protocol based on a client side;
(1) based on the average distance query processing protocol of the server, the server S and the client C implement the process of average distance query through five rounds of interaction, as shown in fig. 2, and the specific flow is shown in fig. 3, and the process includes the following steps:
s1: setting a position data owner as a server S and a service requesting inquiry as a client C, wherein the server S has nSIndividual user
Client C has nCIndividual user
Set U ═ US∪UC＝{U1，U2，...，Un}, set UI＝US∩UC＝{U1，...，Ui，...，UmThe server S for each user at different time periodsjLocation information is provided.
S2: and setting basic information of the average distance query processing protocol based on the server side.
S2.1: the server side selects the set U and sends the set U to the client side, and therefore the server user U is hidden in the client sideS。
S2.2: public key PK generated by Paillier homomorphic encryption system for serverSAnd a private key SKS。
In this embodiment, the public key PK generated for the message xS＝(gS，mS) And a private key SKS＝(λS，μS) Two large prime numbers p and q are randomly selected to satisfy gcd (pq, (p-1) (q-1)) 1, i.e. to ensure that the two prime numbers are of equal length, the modulus m of the cluster generated by the server S is calculatedS＝p·q，λSOne integer is randomly selected as a generator of the group generated by the server S (p-1) (q-1)
μS＝(L(gS λ mod mS 2))-1 mod mS，
Thereby generating a public key PKSAnd a private key SKS。
S2.3: will aggregate U and public key PKSAnd sending the data to the client.
S3: the client sends the facility location F and the query request to the server.
S4: server computing F facility and user USThe distance between them, determine each user Ui∈USDistance d to nearest facilityiBuilding a set D ═ D1，d2，...，dn}。
S5: the server calculates the encryption value of each element in the set D to obtain a 2 xn matrix T]SAnd sent to the client, thereby hiding the server user U in the clientSAnd server user USThe position of (a).
The 2 xn matrix [ T]SThe formula of (1) is as follows:
wherein [ T1i]SIs formed by a public key PKSEncryption matrix [ T ] obtained by encryption]SRow 1, column i element, [ T ]2i]SIs formed by a public key PKSEncryption matrix [ T ] obtained by encryption]SElement of row 2, column i, diThe distance of user i to the nearest facility.
S6: client side multiplication using Paillier cryptosystemState property, calculating each facility location FjE.g. F, to obtain ciphertext X]S。
Said obtaining a ciphertext [ X ]]SThe method of (1) is as follows:
[X]S＝{[x1]S，[x2]S}；
wherein the content of the first and second substances,
and
by public keys PK on the server S for line 1 messages and line 2, respectivelySEncrypted to obtain a ciphertext, nIIs a set UIThe total number of users.
S7: the client selects two random values v1And v2For ciphertext [ X]SCamouflage is carried out to obtain ciphertext [ X']SAnd sent to the server, thereby hiding the U on the serverCAnd UCThe query result of (2).
Obtaining ciphertext [ X']SThe method of (1) is as follows:
[X′]S＝{[x1′]S，[x2′]S}；
wherein, [ x ]1′]S＝[x1]S·ES(v1) And [ x ]2′]S＝[x2]S·ES(v2) Respectively, for line 1 message ciphertext [ x1]SAnd line 2 message ciphertext [ x2]SAnd carrying out disguise to obtain a ciphertext.
S8: the server decrypts the encrypted disguised result to obtain a decrypted result X 'and sends the decrypted result X' to the client.
The way to obtain the decryption result X "is as follows:
X″＝{x1″，x2″}；
wherein x is1″＝DS([x1′]S) And x2″＝DS([x2′]S) Respectively, for line 1 message ciphertext [ x1′]SAnd line 2 message ciphertext [ x2′]SAnd decrypting the obtained message.
S9: and the client performs disguise calculation on the ciphertext X' to obtain a required query result z.
(2) Based on the average distance query processing protocol of the client, the server S and the client C implement the process of average distance query through four rounds of interactions, as shown in fig. 4, and the flow is shown in fig. 5, and includes the following steps:
c1: setting a position data owner as a server S and a service requesting inquiry as a client C, wherein the server S has nSIndividual user
Client C has nCIndividual user
Set U ═ US∪UC＝{U1，U2，...，Un}, set UI＝US∩UC＝{U1，...，Ui，...，UmThe server S for each user at different time periodsjLocation information is provided.
C2: basic information of the average distance query processing protocol based on the client is set.
C2.1: the server selects the set U and sends the set U to the client, so that the server user U is hidden in the clientS。
C2.2: client generates public key PK by using property of Paillier homomorphic encryption systemCAnd a private key SKCClient sharing PK with serverC。
In this embodiment, the public key PK generated for the message xC＝(gC，mC) And a private key SKC＝(λC，μC) Randomly selecting two large prime numbers p and q to satisfy gcd (pq, (p-1) (q-1)) ═ 1, namely ensuring that the two prime numbers are equal in length, and calculating the modulus m of the group generated by the client CC＝p·q，λCLcm (p-1) (q-1), an integer is randomly selected as the generator of the group generated by client C
μC＝(L(gC λ mod mC 2))-1 mod mC，
Thereby generating a public key PKCAnd a private key SKC。
C2.3: selecting a random non-zero integer riModulo m with the group generated by client CCAll the other properties of the Chinese herbs
In this embodiment, the use of the random value r in the encryption ensures that two identical messages are encrypted to the same value, but with negligible probability.
C2.4: the client end is according to the user list UCComputing an encryption result [ T ]]C；
Wherein [ T]CIs formed by a public key PKCAnd encrypting the ith element in the obtained message ciphertext set.
C2.5: client side will [ T]CPublic key PKCR and the number of client users ncSending the data to a server;
c3: the server verifies the encrypted result, thereby hiding the user U at the clientCThe query result of (2);
in this embodiment, to ensure that a malicious client cannot obtain a query of a specific userThe result inquiry server verifies the obtained encryption result in a way of judging
Whether or not equal to EC(nC) If so, continuing the protocol, if not, terminating the protocol, wherein,
number n of users for clientCEncryption of mCModulus, g, for the group generated by client CCIs the generator of the cluster generated by client C, r is a random number,
wherein the number of 1 is Ui∈UCShould be equal to the total number n of users at the client endcIf they are not equal, the number n of users is describedcAnd an encryption list [ T]CNot corresponding, indicating an error.
C4: the client sends the facility location F and the query request to the server.
C5: server computing F facility and user USThe distance between them, determine each user Ui∈USDistance d to nearest facilityiBuilding a set D ═ D1，d2，...，dn}。
C6: the client uses the multiplication homomorphism property of the Paillier cryptosystem and uses T]CTo calculate the ciphertext [ X ] of the query result]C。
Said obtaining a ciphertext [ X ]]CThe method of (1) is as follows:
[X]C＝{[x1]C，[x2]C}；
wherein the content of the first and second substances,
and
by public keys PK on client C for line 1 messages and line 2, respectivelyCAnd encrypting to obtain a ciphertext.
C7: server sends cipher text [ X]CMultiplying the query result by zero encryption to obtain an anonymized and encrypted query result [ X']CAnd sending the data to the client to prevent the server from tracking the position of the user through the client. The obtained anonymized and encrypted query result [ X']CThe method of (1) is as follows:
[X′]C＝{[x1′]C，[x2′]C}；
wherein, [ x ]1′]C＝[x1]C·EC(0) And [ x ]2′]C＝[x2]C·EC(0) Respectively, ciphertext [ x ] on client C for line 1 messages1]CAnd ciphertext [ x ] of line 2 message on client C2]CAnd carrying out anonymization and encryption on the query result.
In this embodiment, since the result of the encryption multiplication with zero does not change, in order to prevent the server from tracking the location of the user through the client, the server anonymizes the encryption result by multiplying the result with the encryption of zero.
C8: and the client decrypts the anonymized and encrypted query result to obtain the query result.
The decryption operation mode of the query result after anonymization and encryption is as follows:
[X″]C＝{[x1″]C，[x2″]C}；
wherein x is1″＝DC([x1′]C)＝q·nIAnd x2″＝DC([x2′]C)＝nIRespectively, for line 1 message ciphertext [ x1′]SAnd line 2 message ciphertext [ x2′]SAnd decrypting the obtained message.
As can be seen from the above formula, the calculation formula of the query result is as follows:
finally, it should be noted that: the above examples are only intended to illustrate the technical solution of the present invention, but not to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those skilled in the art; the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; such modifications and substitutions do not depart from the spirit and scope of the corresponding technical solutions as defined in the appended claims.
Claims (2)
1. A privacy protection average distance query method based on Paillier homomorphic encryption is characterized by comprising an average distance query processing protocol based on a server side and an average distance query processing protocol based on a client side;
(1) the server-side-based average distance query processing protocol comprises the following steps:
s1: setting a position data owner as a server S and a service requesting inquiry as a client C, wherein the server S has nSIndividual user
Client C has nCIndividual user
Set U ═ US∪UC＝{U1，U2，...，Un}, set UI＝US∩UC＝{U1，...，Ui，...，UmA server provides position information for each user Sj in different time periods;
s2: setting basic information of an average distance query processing protocol based on a server side;
s2.1: the server side selects the set U and sends the set U to the client side, so that the server is hidden in the client sideHousehold US；
S2.2: public key PK generated by Paillier homomorphic encryption system for serverSAnd a private key SKS；
S2.3: will aggregate U and public key PKSSending the data to a client;
s3: the client sends the facility position F and the query request to the server;
s4: server computing F facility and user USThe distance between them, determine each user Ui∈USDistance d to nearest facilityiBuilding a set D ═ D1，d2，...，dn}；
S5: the server calculates the encryption value of each element in the set D to obtain an encryption result T]SAnd sent to the client, thereby hiding the server user U in the clientSAnd server user USThe position of (a);
s6: the client calculates each facility position F by utilizing the multiplication homomorphism property of the Paillier cryptosystemjE.g. F, to obtain ciphertext X]S；
S7: the client selects two random values v1And v2For ciphertext [ X]SCamouflage is carried out to obtain ciphertext [ X']SAnd sent to the server, thereby hiding the U on the serverCAnd UCThe query result of (2);
s8: the server decrypts the encrypted disguised result to obtain a decrypted result X 'and sends the decrypted result X' to the client;
s9: the client carries out disguise calculation on the ciphertext X' to obtain a required query result z;
(2) the average distance query processing protocol based on the client comprises the following steps:
c1: setting a position data owner as a server S and a service requesting inquiry as a client C, wherein the server S has nSIndividual user
Client C has nCIndividual user
Set U ═ US∪UC＝{U1，U2，...，Un}, set UI＝US∩UC＝{U1，...，Ui，...，UmThe server S for each user at different time periodsjProviding location information;
c2: setting basic information of a client-based average distance query processing protocol;
c2.1: the server selects the set U and sends the set U to the client, so that the server user U is hidden in the clientS；
C2.2: client generates public key PK by using property of Paillier homomorphic encryption systemCAnd a private key SKCClient sharing PK with serverC；
C2.3: selecting a random non-zero integer riModulo m with the group generated by client CCAll the other properties of the Chinese herbs
C2.4: the client end is according to the user list UCComputing an encryption result [ T ]]C；
C2.5: client side will [ T]CPublic key PKCR and the number of client users ncSending the data to a server;
c3: the server verifies the encrypted result, thereby hiding the user U at the clientCThe query result of (2);
c4: the client sends the facility position F and the query request to the server;
c5: server computing F facility and user USThe distance between them, determine each user Ui∈USDistance d to nearest facilityiBuilding a set D ═ D1，d2，...，dn}；
C6: the client uses the multiplication homomorphism property of the Paillier cryptosystem and uses T]CTo calculate the ciphertext [ X ] of the query result]C；
C7: server sends cipher text [ X]CMultiplying the query result by zero encryption to obtain an anonymized and encrypted query result [ X']CAnd sending the data to the client to prevent the server from tracking the position of the user through the client;
c8: and the client decrypts the anonymized and encrypted query result to obtain the query result.
2. The privacy-preserving average distance query method based on Paillier homomorphic encryption according to claim 1, wherein the way for the server to verify the encryption result in the step C3 is to judge
Whether or not equal to EC(nC) If so, continuing the protocol, if not, terminating the protocol, wherein,
number n of users for clientCEncryption of mCModulus, g, for the group generated by client CCR is a random number, a generator of a group generated by the client C;
[Ti]Cis formed by a public key PKCAnd encrypting the ith element in the obtained message ciphertext set.
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| CN114662147B (en) * | 2022-03-24 | 2023-04-07 | 云南电网有限责任公司信息中心 | Private information retrieval method and system suitable for large-scale database |
| CN117349898B (en) * | 2023-12-05 | 2024-03-08 | 中国电子科技集团公司第十研究所 | Ciphertext K neighbor query method and system with hidden access mode |
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