CN111552978B - Privacy protection set intersection solving method based on DH encryption and Hash table - Google Patents
Privacy protection set intersection solving method based on DH encryption and Hash table Download PDFInfo
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- CN111552978B CN111552978B CN202010316716.8A CN202010316716A CN111552978B CN 111552978 B CN111552978 B CN 111552978B CN 202010316716 A CN202010316716 A CN 202010316716A CN 111552978 B CN111552978 B CN 111552978B
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F21/00—Security arrangements for protecting computers, components thereof, programs or data against unauthorised activity
- G06F21/60—Protecting data
- G06F21/602—Providing cryptographic facilities or services
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F21/00—Security arrangements for protecting computers, components thereof, programs or data against unauthorised activity
- G06F21/60—Protecting data
- G06F21/62—Protecting access to data via a platform, e.g. using keys or access control rules
- G06F21/6218—Protecting access to data via a platform, e.g. using keys or access control rules to a system of files or objects, e.g. local or distributed file system or database
- G06F21/6245—Protecting personal data, e.g. for financial or medical purposes
Abstract
The invention discloses a privacy protection set intersection solving method based on DH encryption and a Hash table, wherein an initiating party initiates an intersection solving request to a participant, and the participant encrypts a data set of the participant by using the same module and different keys and sends the data set to the other participant; then the initiator and the participant encrypt the data sent by the other party by using own keys respectively, generate two hash tables for comparison, find the same elements therein, and finally obtain an intersection. The invention uses the idea of DH cipher key negotiation protocol to encrypt data to ensure the safety of both data, and uses Hash table to improve the intersection solving efficiency. The set elements of both sides are encrypted in one way and are difficult to crack, and because both sides are sequentially encrypted, the set security with a small definition domain can be ensured, and one side is prevented from carrying out comparison attack by acquiring a complete set; the invention does not need the SGX server for assistance, only needs the interaction of the two parties, and reduces the cost of the server.
Description
Technical Field
The invention belongs to the field of computer network communication data security and privacy protection, and particularly relates to a private protection set intersection solving method based on DH encryption and a Hash table.
Background
Protecting the privacy of a data set is a natural or even necessary requirement in many scenarios, for example, when the set is the address book of a user or the genome of a genetic diagnosis service user, such input must be protected by means of cryptography. Privacy Preserving Set Intersection (PSI) computation techniques allow two parties holding respective sets to jointly compute the Intersection operation of two sets. At the end of a protocol interaction, one or both parties should get the correct intersection and not get any information in the other party's set outside the intersection.
PSI has many practical application scenarios, such as finding contacts, and when a user registers to use a new service, such as WeChat, nailing, etc., it is a necessary operation in most cases to find out which services have been registered in the same class from the user's existing contacts. This can be done effectively by sending the user's contacts to the service provider, but at the same time the user's contact information, an information that is considered private in most cases, is also exposed to the service provider. Therefore, in this scenario, the PSI protocol is performed with the contact information of the user as the input of one party and all the user information of the service provider as the input of the other party, so as to complete the function of finding the contact, and prevent the information outside the intersection from being leaked to any party. Although the PSI protocol has been developed very rapidly and the demand for data privacy protection is becoming strong, in many current application scenarios, efficient and insecure protocols are the mainstream choice.
At present, a Baidu Mesatee platform realizes the intersection of privacy protection sets based on a Trusted Execution Environment (TEE) technology, the set intersection is calculated by an SGX (serving gateway) server of intel, and a multi-party set needs to encrypt own data and then sends the encrypted data to a server; but requires an additional SGX server as an intermediary to coordinate and compute the intersection.
Disclosure of Invention
The invention aims to provide a privacy protection set intersection solving method capable of resisting malicious attacks aiming at the defects of the prior art. The method and the device calculate the intersection of the two sets of data on the premise of protecting the security of the two sets of data, so that the data outside the intersection is not acquired by the other side.
The purpose of the invention is realized by the following technical scheme: a privacy protection set intersection solving method based on DH encryption and Hash table is used for an initiator initiating an intersection solving request and a participant participating in the intersection solving request, and comprises the following steps:
(1) the initiator randomly generates a prime number n as an encrypted module and sends a privacy protection set intersection execution request containing the prime number n to the participants; simultaneously, randomly generating a prime number p as an encrypted key, and encrypting the initiator data set M in a one-way encryption mode 1 The elements in the system are sequentially encrypted to obtain data K after the first encryption of the initiator p ：
Wherein mod n represents the remainder of the division by n; after the encryption is completed, the data K is encrypted p Sending to the participant;
(2) randomly generating a prime number q as an encryption key by the participant, using the prime number n sent by the initiator in the step (1) as an encryption module, and using a one-way encryption mode to encrypt the participant data set M 2 The elements in the data K are sequentially encrypted to obtain the data K after the first encryption of the participator q ：
After the encryption is completed, the data K is encrypted q Sending to the initiator;
(3) the initiator receives the data K encrypted for the first time by the participant in the step (2) q Then, the prime p is used to pair the data K q The data K after the second encryption of the initiator is obtained by re-encryption qp ：
For data K qp Hash processing is carried out to calculate data K qp Hash table of 1 Size N of (d):
N＝max(N 1 /bucketSize，N 2 /bucketSize，1)
wherein N is 1 Is the size of the sender data set, N 2 Is the size of the participant data set, bucketSize is a hash table 1 A middle bucket size threshold; calculating key value key qp ：
key qp ＝K qp mod N
By key value key qp For bucket number, data K qp Element mapping to hash table 1 In (2), the generated hash table 1 Sending the data to a participant;
(4) the participator receives the data K encrypted for the first time by the initiator in the step (1) p Then, the prime number q is used to pair the data K p The data K after the second encryption of the participator is obtained by the re-encryption pq ：
For data K pq Hash processing is carried out according to the data K pq Hash table of 2 Size calculation key pq ：
key pq ＝K pq mod N
Wherein, the hash table 2 The size is also N; by key value key pq For bucket number, data K pq Element mapping to hash table 2 In (2), the generated hash table 2 Sending to the initiator;
(5) the initiator receives the hash table sent by the participant in the step (4) 2 Then, comparing the hash tables generated in the step (3) in sequence 1 And hash table 2 Whether the elements in the buckets with the same key value are equal or not; if the two data sets are equal, the elements of the initiator data set and the participant data set corresponding to the elements in the bucket are intersection elements; if not, then theElements in the bucket are not intersection elements; finally obtaining intersection elements; in the same way, the participator receives the hash table sent by the initiator in the step (3) 1 Then, the hash table generated in the step (4) is compared with the hash table 2 And comparing to obtain intersection elements.
Further, the prime number n, the prime number p and the prime number q are not less than 2048 bits.
Furthermore, the prime number n, the prime number p and the prime number q are all 2048 bits.
The invention has the beneficial effects that: the invention uses the idea of DH cipher key negotiation protocol to encrypt data to ensure the safety of both data, and uses Hash table to improve the intersection solving efficiency. The set elements of both sides are encrypted in one way and are difficult to crack, and because both sides are sequentially encrypted, the set security with a small definition domain can be ensured, and one side is prevented from carrying out comparison attack by acquiring a complete set; the invention does not need the SGX server for assistance, only needs the interaction of the two parties, and reduces the cost of the server.
Drawings
FIG. 1 is a flow chart of the implementation of the present invention;
FIG. 2 is a schematic diagram of a Hash table generation method;
FIG. 3 is a diagram illustrating a Hash table matching method.
Detailed Description
A private protection set intersection solving method flow based on DH encryption and Hash table, the execution flow is as shown in figure 1, used for initiating the initiator of the intersection solving request this time and participating in the participant of the intersection solving request this time, including the following steps:
(1) the initiator randomly generates a 2048-bit (decimal) prime number n as an encryption module and sends a privacy protection set intersection PSI execution request containing the prime number n to the participants; simultaneously randomly generating a 2048-bit prime number p as an encryption key, and encrypting the initiator data set M in a one-way encryption mode 1 The elements in the sequence are encrypted to obtain data K after the first encryption of the initiator p The method specifically comprises the following steps:
where mod n represents the remainder of the division by n, i.e., K p Is composed of
The remainder of the division by n; after the encryption is finished, the encrypted data K is sent to the host computer p And sending the data to the participants.
(2) The participant randomly generates a 2048-bit prime number q as an encryption key, and uses the prime number n sent by the initiator in the step (1) as an encryption module to encrypt the participant data set M in a one-way encryption mode 2 The elements in the data K are sequentially encrypted to obtain data K after the first encryption of the participants q The method specifically comprises the following steps:
after the encryption is finished, the encrypted data K is sent to the host computer q And sending the data to the initiator.
Because p, n and q are large enough prime numbers generated randomly, the original data cannot be reversely deduced according to the encrypted data on the basis of the discrete logarithm difficulty, and the result of the data encrypted for many times is independent of the encryption sequence due to the particularity of the encryption algorithm. When the prime number is generated randomly, an odd number with a given digit is randomly selected, and then whether the odd number is the prime number is judged by a prime number judgment method. If not, reselect. However, given a number x, the number of prime numbers less than x is approximately x/lnx, according to the prime theorem, that is, given a number, the probability of being a prime number is approximately 1/lnx. Even if the given number is an odd number, the probability can only rise to 2/lnx. If the prime requirement is 2048 bits, then an odd number is randomly chosen with a probability of passing the prime test of about 2/2048 × log (e) ═ 0.22%. That is, about 500 times of selection is required to pass the prime number judgment once, and if the number of bits is large, the number of selection is increased, and the efficiency is low. In the invention, the randomly generated prime numbers are preferably 2048 bits which exceed 2048 bits, the calculation efficiency is reduced and are less than 2048 bits, the safety cannot be met, the prime numbers are 1024 bits which are used in the cryptography before, but the prime numbers are attacked by means of calculation power exhaustion, the calculation power required by the long bit length is large, and the 2048 bits are generally used in important occasions at present.
(3) The initiator receives the data K encrypted for the first time by the participant in the step (2) q Then, the prime p is used to pair the data K q The data K after the second encryption of the initiator is obtained by re-encryption qp The method specifically comprises the following steps:
adopting the mode of FIG. 2 to encrypt the data K of the initiating party for the second time qp Generating a hash table 1 The method specifically comprises the following steps: firstly, for data K qp Hash processing is carried out, and data K is calculated qp Hash table of 1 Size N of (d):
N＝max(N 1 /bucketSize，N 2 /bucketSize，1)
wherein N is 1 Is the size of the sender data set, N 2 Is the size of the participant data set, bucketSize is a hash table 1 One bucket size threshold (e.g., take 20); then obtaining the key value key by the following formula calculation qp ：
key qp ＝K qp mod N
Finally, key value key is used qp For bucket number, data K qp Element mapping to hash table 1 In (2), the generated hash table 1 And sending the data to the participants.
(4) The participator receives the data K which is encrypted for the first time by the initiator in the step (1) p Then, the prime number q is used to pair the data K p The data K after the second encryption of the participator is obtained by the re-encryption pq The method specifically comprises the following steps:
adopting the mode of FIG. 2 to encrypt the data K of the participant for the second time pq Generating a hash table 2 The method specifically comprises the following steps: logarithm at firstAccording to K pq Performing hash processing according to the data K pq Hash table of 2 Size calculation key pq ：
key pq ＝K pq mod N
Wherein, the hash table 2 The size is also N; finally, key value key is used pq For bucket number, data K pq Element mapping to hash table 2 In (2), the generated hash table 2 And sending the data to the initiator.
(5) The initiator receives the hash table sent by the participant in the step (4) 2 Then, the method of fig. 3 and the hash table generated by the initiator in step (3) are adopted 1 Comparing and obtaining intersection elements, wherein the intersection elements are as follows: comparing the hash table in sequence 1 And hash table 2 Whether the elements in the buckets with the same key value are equal or not; if the two elements are equal, the elements of the initiator data set and the participant data set corresponding to the elements in the bucket are intersection elements; if not, then the elements within the bucket are not intersection elements. In the same way, the participator receives the hash table sent by the initiator in the step (3) 1 Then, the hash table generated by the participator in the step (4) is compared with the hash table generated by the participator in the step (4) 2 And comparing to obtain intersection elements.
The invention utilizes the hash table to accelerate the comparison efficiency, and the simplest method for finding out the intersection of the two sets is to use all numbers in the A array to match the numbers in the B array. Assuming that the size of both arrays is n, the temporal complexity of this traversal is O (n ^ 2). This is also the most complex case, with hash tables to solve the problem. That is, hash array a into the hash table, then continue to hash array B into the hash table, the same elements will be mapped into the same bucket, and finally the intersection can be obtained. The temporal complexity is the complexity of hashing all elements, o (n).
The method can be applied in many practical scenarios, and an example is given below (only simple numbers of the same nature are given as examples since the data after specific encryption is tens of bits long):
many mobile phone social APP require to access the mobile phone address book of the new registered user, and through comparing the address book with the registered user of the APP server, the new user is recommended friends who use the APP together. However, the fact that the APP is allowed to access the mobile phone address book of the user exposes all contact information of the user to the APP service provider, and a great privacy disclosure problem exists. By operating PSI protocols at the APP mobile phone end and the APP server end, intersection between the mobile phone address book and the server registered user set is calculated, and contact person and friend recommendation can be carried out under the condition that user privacy information is not revealed.
The initiator is an APP server a, and holds a registered user set a {18700000001, 18700000002, 18700000003, 18700000004, 18700000005}, the participant is a new registered user B, and holds an address book data set B {18700000011, 18700000002, 18700000003, 18700000014, 18700000015}, a wants to obtain a mobile phone address book of a new user B to recommend a friend who uses the APP together for the new user B, and the mobile phone terminals of the servers a and B can execute the following steps to obtain a friend set which uses the APP together with B.
The initiator randomly generates a 2048-bit prime number N as a modulus of encryption, randomly generates a 2048-bit prime number P as an encryption key, sends a PSI request (with N sent to the participant, the initiator encrypts with P and N, the encryption result is Ap (10, 11, 13, 21, 19), and sends Ap to the participant
After receiving PSI request, the participator randomly generates 2048-bit prime number Q as encryption key, encrypts Q and N with the encryption result Bq (32, 34, 35, 39, 36), and sends Bq to the initiator
After receiving Bq, the initiator performs encryption again using P and N to obtain twice-encrypted data set Bqp (41, 43, 44, 45, 46), and generates hash table 1 using N-3
| Barrel element | 41 | 43 | 44 | 45 | 46 |
| 0 | √ | ||||
| 1 | √ | √ | |||
| 2 | √ | √ |
After receiving Ap, the participant encrypts again with Q and N to obtain twice encrypted data sets Apq (51, 43, 44, 55, 56), and generates hash table 2 using N-3
Then the participator sends a hash table 2 to the initiator, the initiator sends a hash table 1 to the participator, and the participator and the initiator respectively use the following method to compare and calculate the intersection
Comparing elements in the same barrel sequence number
In bucket 0: 45-51 have no equivalent elements
In the barrel 1: 43, 46-43, 5543 is equal to 43, i.e. 43 corresponds to the intersection of the data 3 before encryption
In the barrel 2: 41, 44-44, 5644 is equal to 44, i.e. 44 corresponds to the intersection of the data 4 before encryption
And (4) finding the intersection of the encrypted data (43, 44), and then obtaining the corresponding data set (18700000002, 18700000003) before encryption as the friend set which uses the APP together by the b.
Claims (3)
1. A privacy protection set intersection solving method based on DH encryption and Hash table is used for an initiator initiating an intersection solving request and a participant participating in the intersection solving request, and is characterized by comprising the following steps:
(1) the initiator randomly generates a prime number n as an encrypted module and sends a privacy protection set intersection execution request containing the prime number n to the participants; simultaneously, randomly generating a prime number p as an encrypted key, and encrypting the initiator data set M in a one-way encryption mode 1 The elements in the system are sequentially encrypted to obtain data K after the first encryption of the initiator p ：
Wherein m isod n represents the remainder of the division by n; after the encryption is completed, the data K is encrypted p Sending the data to a participant;
(2) the participant randomly generates a prime number q as an encryption key, and uses the prime number n sent by the initiator in the step (1) as an encryption module to encrypt the participant data set M in a one-way encryption mode 2 The elements in the data K are sequentially encrypted to obtain data K after the first encryption of the participants q ：
After the encryption is completed, the data K is encrypted q Sending to the initiator;
(3) the initiator receives the data K encrypted for the first time by the participant in the step (2) q Then, the prime p is used to pair the data K q The data K after the second encryption of the initiator is obtained by re-encryption qp ：
For data K qp Hash processing is carried out to calculate data K qp Hash table of 1 Size N of (d):
N＝max(N 1 /bucketSize，N 2 /bucketSize，1)
wherein N is 1 Is the size of the sender data set, N 2 Is the size of the participant data set, bucketSize is a hash table 1 A middle bucket size threshold; calculating key value key qp ：
key qp ＝K qp mod N
By key value key qp For bucket number, data K qp Element mapping to hash table 1 In (2), the generated hash table 1 Sending the data to a participant;
(4) the participator receives the data K encrypted for the first time by the initiator in the step (1) p Then, the prime number q is used to pair the data K p The second encryption is obtained by the second encryption of the participatorThe latter data K pq ：
For data K pq Hash processing is carried out according to the data K pq Hash table of 2 Size calculation key value key pq ：
key pq ＝K pq mod N
Wherein, the hash table 2 The size is also N; by key value key pq For bucket number, data K pq Element mapping to hash table 2 In (2), the generated hash table 2 Sending to the initiator;
(5) the initiator receives the hash table sent by the participant in the step (4) 2 Then, comparing the hash tables generated in the step (3) in sequence 1 And hash table 2 Whether elements in the buckets with the same key value are equal or not; if the two elements are equal, the elements of the initiator data set and the participant data set corresponding to the elements in the bucket are intersection elements; if not, the elements in the bucket are not intersection elements; finally obtaining intersection elements; in the same way, the participator receives the hash table sent by the initiator in the step (3) 1 Then, the hash table generated in the step (4) is compared with the hash table 2 And comparing to obtain intersection elements.
2. The method of claim 1, wherein the prime n, the prime p, and the prime q are no less than 2048 bits.
3. The method of claim 1, wherein the prime n, the prime p, and the prime q are all 2048 bits.
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| CN112312313B (en) * | 2020-09-10 | 2023-07-04 | 神州融安数字科技(北京)有限公司 | PSI-based geographical area entry judging method, device and system |
| CN112073196B (en) * | 2020-11-10 | 2021-02-23 | 腾讯科技（深圳）有限公司 | Service data processing method and device, electronic equipment and storage medium |
| CN112632608A (en) * | 2020-12-23 | 2021-04-09 | 上海同态信息科技有限责任公司 | Cooperative processing method for private data based on numerical calculation |
| CN112671789B (en) * | 2020-12-29 | 2022-09-27 | 杭州趣链科技有限公司 | Data transmission optimization method, device and system based on Chinese remainder theorem |
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