METHOD FOR PRIVATE SET INTERSECTION IN SMART CITY SYSTEM, DEVICE, AND STORAGE MEDIUM

Abstract

The present invention discloses a method for private set intersection in a smart city system, a device, and a storage medium. According to the present invention, a threshold secret sharing technology is adopted to share a private set among three parties, so that an intersection cardinality is hidden and security of private set intersection is improved. Before two parties perform the private set intersection, a blockchain is used to verify identities of the two parties, which protects security of data of the two parties to a certain extent. In addition, according to the present invention, the private set is divided into a plurality of subsets with labels, which implements an interaction manner with finer granularity. Therefore, compared with a private set intersection solution in a previous smart city system, the present invention is greatly improved in practicability, security, and other aspects.

Description

CROSS-REFERENCE TO RELATED APPLICATIONS

The application claims priority to Chinese patent application No. 2023117022331, filed on Dec. 12, 2023, the entire contents of which are incorporated herein by reference.

TECHNICAL FIELD

The present invention belongs to the field of private set intersection, and specifically, relates to a method for private set intersection in a smart city system, a device, and a storage medium.

BACKGROUND

In a smart city management system, scenarios of performing intersection between two parties are becoming more and more common. A private set intersection solution in the smart city management system may ensure the privacy of set elements in addition to an intersection set of the two parties. However, in the private set intersection solution, sizes of two sets are required to be uniform, but in real life, the sizes of the sets are skewed. In addition, since a set in current private set intersection is only a single set, problems in storage, efficiency, and other aspects easily occur during set intersection.

SUMMARY

A purpose of the present invention is to provide a method for private set intersection in a smart city system, a device, and a storage medium.

The present invention adopts the following technical solutions:

A method for private set intersection in a smart city system, where the method includes the following steps:

• • (1) using, by all participants, a hash function generated by a third party Pc and respective public keys to perform encryption, to generate respective ciphertexts, and sending the respective ciphertexts to a blockchain, where all the participants include a participant Pa and a participant Pb;
  • (2) using the blockchain to verify identities of all the participants before private intersection is performed, to determine whether the private intersection can be performed;
  • (3) sharing, by the participant Pa and the participant Pb, subsets of respective private sets among three parties after it is determined that the private intersection can be performed;
  • (4) obtaining subvectors by the three parties after sharing, and then ranking subvectors of the participant P_a and the participant P_b;
  • (5) jointly calculating, by the three parties, a secret sharing vector of one token vector, and then performing secondary ranking on ranked subvectors of the participant P_a and the participant P_b according to the secret sharing vector, to obtain a ranked subsecret combination vector; and
  • (6) recovering, by the participant P_a and the participant P_b, respective subsecret combination vectors by invoking a Reveal algorithm, to obtain an intersection set R.

Further, the step (1) specifically is that:

• • the third party P_c uses a security parameter λ_{1, 2} to generate a hash function H₁ and a hash function H₂;
  • the participant P_a selects a random value a as a private key sk_a of the participant P_a, and uses the private key to calculate a public key pk_a; and similarly, the participant P_b selects a random value b as a private key sk_b of the participant P_b, and uses the private key to calculate a public key pk_b;
  • the participant P_a generates a ciphertext U₁ through the hash function H₁ and the public key pk_a, and the participant P_b generates a ciphertext U₂ through the hash function H₂ and the public key pk_b; and
  • then the ciphertext U₁ and the ciphertext U₂ are sent to the blockchain.

Further, the step (2) specifically is that:

• • first, the participant P_a exchanges an EOA address with the participant P_b; then, the participant P_b uses a public key of the participant P_a to encrypt a public key and a ciphertext of the participant P_b, and packs a ciphertext CI_b into a transaction to be sent to the blockchain; when private set intersection needs to be performed, the P_a inquires a recent transaction, extracts a ciphertext in the recent transaction, and then decrypts the ciphertext by using a private key of the P_a; a public key PK_b of the participant P_b is decrypted, a hash operation is performed on the public key, last 20 characters of an operation result are intercepted as R₁, the R₁ is matched with an address Addr that sends the transaction, and if the R₁ is the same as the address, it indicates that the participant P_b authorizes the other party and desires to perform a private set intersection operation; and the P_b inquires a recent transaction in the blockchain, and uses the EOA address to check whether the EOA address is an address of the P_a, and if the EOA address is the address of the P_a, it indicates that the P_a desires to perform a private set intersection operation.

Further, the three parties in the step (3) include the participant P_a, the participant P_b, and the third party P_c.

Further, the step (4) specifically is that:

• • the participant P_a obtains subvectors and the participant P_b obtains subvectors and and the P_c obtains subsecrets and then a set of subsecrets held by the participant P_a is combined and is represented as a vector and a set of subsecrets held by the participant P_b is combined and is represented as a vector and subsecret combination vectors and held by the participant P_a and the participant P_b are ranked according to element sizes, to generate vectors and

Further, the step (5) specifically is that:

• • three participants jointly calculate a secret sharing vector of one token vector and rank vectors and according to a value of [{right arrow over (f_k)}], to obtain a subsecret combination vector (a′₁, a′₂) ranked according to [{right arrow over (f_k)}].

Further, the step (6) specifically is that:

• • the participant P_a sends a subsecret vector (, a′₁) thereof to the participant P_b, and similarly, the participant P_b sends a subsecret combination vector (, a′₂) thereof to the P_a; the participant P_a and the participant P_b respectively invoke the Reveal algorithm according to held subsecret vectors and to recover a token vector [{right arrow over (f_k)}], and finally, a number of elements with [{right arrow over (f_k)}]=1 is a number N of intersection set elements; the participant P_a extracts last N elements in a′₁ and sends the elements to the participant P_b; similarly, the participant P_b extracts last N elements in a′₂ and sends the elements to the participant P_a; and the participant P_a and the participant P_b recover, according to the Reveal algorithm, last N subsecret vectors that are received, to obtain an intersection set R.

The present invention further provides an electronic device, including a memory and a processor, where the memory is configured to store a computer program, and the processor runs the computer program, to enable the electronic device to execute the above method for private set intersection in a smart city system.

The present invention further provides a computer-readable storage medium, having a computer program stored thereon, where the computer program, when executed by a processor, implements the above method for private set intersection in a smart city system.

Beneficial effects of the present invention are as follows:

The present invention has relatively high practicability and expandability. The present invention is suitable for a scenario in which private set intersection needs to be performed in a smart city system. According to the present invention, a secret sharing technology is used to reduce requirements on a size of a private set and protect an intersection cardinality of the private set; and intersection of fine granularity of the set is implemented through multi-subset division. According to the present invention, an identity verification technology is used to determine identities of two parties, which can ensure correctness of the identities of the two parties, improve a protection degree of the private set, and further reduce computational overheads of intersection greatly.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings show various embodiments by way of examples and not limitations, and are used in conjunction with the specification and the claims to describe the embodiments of the present invention. Appropriately, the same reference numerals used in all accompanying drawings denote the same or similar parts. Such embodiments are illustrative and are not intended as exhaustive or exclusive embodiments of the apparatus or method.

The FIGURE is a schematic flowchart of a method of the present invention.

DETAILED DESCRIPTION OF THE EMBODIMENTS

It should be noted that the embodiments and features in the embodiments of the present application may be combined with each other without conflict. The present application will be described in detail below with reference to the accompanying drawings and the embodiments.

• • 1) In an initialization phase, as a credible third party P_c, a blockchain uses a security parameter λ_{1, 2} to generate hash functions H₁ and H₂.
  • 2) In a key generation phase, there are two participants, which respectively are P_a and P_b. The participant P_a selects a random value a as a private key sk_a of the participant P_a, and uses the private key to calculate a public key pk_a. Similarly, the participant P_b selects a random value b as a private key sk_b of the participant P_b, and uses the private key to calculate a public key pk_b.
  • 3) During set encryption, it is assumed that the participant P_a has n subsets A=

{A₁, A₂, . . . , A_n}. As with the participant P_a, it is assumed that the participant P_b has m subsets B={B₁, B₂, . . . , B_m}.

• • 4) The participant P_a performs hash on element subsets, to generate a ciphertext U₁, and sends the ciphertext U₁ to the blockchain; and the participant P_b uses the public key of the participant P_b to execute a same operation, to generate a ciphertext U₂, and sends the ciphertext U₂ to the blockchain.
  • 5) Two parties of the participants exchange an EOA address before private intersection is performed.
  • 6) Then, the participant P_b uses the public key of the participant P_a to encrypt the public key and the ciphertext of the participant P_b, to generate CI_b=PK_a (PK_b∥U₂), and packs the ciphertext CI_b into a transaction to be sent to the blockchain.
  • 7) When private set intersection needs to be performed, the P_a inquires a recent transaction, extracts a ciphertext in the recent transaction, and then decrypts the ciphertext by using the private key of the P_a. The public key PK_b of the participant P_b is decrypted, a hash operation is performed on the public key, and last 20 characters of an operation result is intercepted as R₁. The R₁ is matched with an address Addr that sends the transaction, and if the R₁ is the same as the address, it indicates that the participant P_b authorizes the other party and desires to perform a private set intersection operation.
  • 8) The P_b inquires a recent transaction in the blockchain, and uses the EOA address to check whether the EOA address is an address of the P_a, and if the EOA address is the address of the P_a, it indicates that the P_a desires to perform a set intersection operation.
  • 9) The participant P_a and the participant P_b share subsets of respective private

sets among three parties after it is determined that the intersection operation may be performed.

• • 10) The participant P_a obtains subvectors and ; and similarly, the participant P_b obtains subvectors and , and the P_c obtains subsecrets and .
  • 11) A set of subsecrets held by the participant P_a is combined and is represented as a vector and a set of subsecrets held by the participant P_b is represented as a vector .
  • 12) The participant P_a and the participant P_b rank held subsecret combination vectors and according to element sizes, to generate vectors and
  • 13) Three participants jointly calculate a secret sharing vector =(, . . . , ) of one token vector where a generation manner of a subvector of each token vector is as follows:
  • (1) initializing =[0]; and
  • (2) for 2≤k≤n, if a value of a latter term is the same as that of a previous term, =1; and if a value of a latter term is different from that of a previous term, =0.
  • 14) The participants rank a₁ and a₂ according to a value of , to obtain subsecret combination vectors a′₁ and a′₂ ranked according to .
  • 15) The participant P_a sends a subsecret vector (, a′₁) thereof to the participant P_b, and similarly, the P_b sends a subsecret combination vector (, a′₂) thereof to the P_a.
  • 16) The participant P_a and the participant P_b respectively invoke a Reveal algorithm according to held subsecret vectors and , to recover a token vector , and finally, a number of elements with =1 is a number N of intersection set elements.
  • 17) The participant P_a extracts last N elements in a′₁ and sends the elements to the P_b. Similarly, the participant P_b extracts last N elements in a′₂ and sends the elements to the P_a.
  • 18) The participant P_a and the participant P_b recover, by invoking the Reveal algorithm, last N subsecret vectors that are received, to obtain an intersection set R.

In step 1): the security parameter needs to be used to generate two hash functions, and the two hash functions respectively are used to encrypt a set A and a set B.

In step 12): the elements are ranked according to the element sizes. Since same elements may not appear in each set, after elements of two sets are combined, the elements are ranked according to the element sizes, so that same elements in the two sets may be at adjacent positions.

In step 14): after the elements are ranked again according to a size of a token vector, elements with a token vector being 1 may be ranked at the rear of the set, and these elements are intersection set elements. A reason is that when the token vector is generated, a latter element needs to be compared with a previous element, and the latter element is the same as the previous element, the token vector is labeled as 1, which indicates that this element is an intersection set element of two sets. After ranking is performed again by using the token vector, this intersection set element is ranked backward with the size of the token vector, which means that elements with the token vector being 1 may be extracted, to obtain the intersection set elements.

In step 16): the token vector is recovered through the Reveal algorithm, and a

Reveal recovery algorithm is an algorithm in a secret sharing technology, which means that a secret message is recovered and revealed, and when any two sub-token vectors are known, a linear secret sharing solution may recover and reveal this token vector.

In step 18): the intersection element is recovered through the Reveal algorithm, and as with the above, a Reveal recovery algorithm is an algorithm in a secret sharing technology, which means that a secret message is recovered and revealed. After two participants find an intersection set subelement in respective subsecrets through the token vector, the two participants send the intersection set subelements to each other, and the Reveal recovery algorithm in the linear secret sharing solution may recover and reveal this intersection set element.

Embodiment 1

First, in an initialization phase, as a credible third party P_c, a blockchain uses a security parameter 21, 2 to generate hash functions H₁ and H₂; and in a key generation phase, there are two participants, which respectively are P_a and P_b. The participant P_a selects a random value a as a private key sk_a of the participant P_a, and uses the private key to calculate a public key pk_a. Similarly, the participant P_b selects a random value b as a private key sk_b of the participant P_b, and uses the private key to calculate a public key pk_b. Then, a set is encrypted, and during set encryption, it is assumed that the participant P_a has n subsets A={A₁, A₂, . . . , A_n}. As with the participant P_a, it is assumed that the participant P_b has m subsets B={B₁, B₂, . . . , B_m}. During encryption, the participant P_a performs hash on element subsets, to generate a ciphertext U₁, and sends the ciphertext U₁ to the blockchain; and the participant P_b uses the public key of the participant P_b to execute a same operation, to generate a ciphertext U₂, and sends the ciphertext U₂ to the blockchain.

Then, the blockchain is used to verify identities of two parties before private intersection is performed. First, the two parties of the participants exchange an EOA address; and then, the participant P_b uses the public key of the participant P_a to encrypt the public key and the ciphertext of the participant P_b, to generate CI_b=PK_a (PK_b∥U₂), and packs the ciphertext CI_b into a transaction to be sent to the blockchain. When private set intersection needs to be performed, the P_a inquires a recent transaction, extracts a ciphertext in the recent transaction, and then decrypts the ciphertext by using the private key of the P_a. The public key PK_b of the participant P_b is decrypted, a hash operation is performed on the public key, and last 20 characters of an operation result is intercepted as R₁. The R₁ is matched with an address Addr that sends the transaction, and if the R₁ is the same as the address, it indicates that the participant P_b authorizes the other party and desires to perform a private set intersection operation. As with an operation of the P_a, the P_b inquires a recent transaction in the blockchain, and uses the EOA address to check whether the EOA address is an address of the P_a, and if the EOA address is the address of the P_a, it indicates that the P_a desires to perform a set intersection operation.

The participant P_a and the participant P_b share subsets of respective private sets among three parties after it is determined that the intersection operation may be performed. The participant P_a obtains subvectors and ; and similarly, the participant P_b obtains subvectors and and the P_c obtains subsecrets and . Then, a set of subsecrets held by the participant P_a is combined and is represented as a vector and a set of subsecrets held by the participant P_b is represented as a vector . The participant P_a and the participant P_b rank held subsecret combination vectors and according to element sizes, to generate vectors and .

Then, three participants jointly calculate a secret sharing vector =(, , . . . , ) of one token vector , and the participants rank (a₁, a₂) according to a value of to obtain a subsecret combination vector (a′₁, a′₂) ranked according to .

The participant P_a sends a subsecret vector (, a′₁) thereof to the participant P_b, and similarly, the participant P_b sends a subsecret combination vector (, a′₂) thereof to the P_a; and the participant P_a and the participant P_b respectively invoke a Reveal algorithm according to held subsecret vectors and to recover a token vector and finally, a number of elements with =1 is a number N of intersection set elements. The participant P_a extracts last N elements in a′₁ and sends the elements to the P_b. Similarly, the participant P_b extracts last N elements in a′₂ and sends the elements to the P_a; and the participant P_a and the participant P_b recover, by invoking the Reveal algorithm, last N subsecret vectors that are received, to obtain an intersection set R.

Therefore, the secret sharing technology used in the present invention is that two participants may obtain an intersection set of sets on condition that sizes of private sets are different, and during execution, a size of an intersection set cardinality is not revealed. In addition, the set is divided into multiple subsets, which not only can implement a fine granularity operation, but also is helpful for extensive application in real life. In conclusion, the private set intersection solution may be applied to the smart city system more widely and securely through technologies such as blockchain verification, multi-subset division, secret sharing, and the like.

The foregoing descriptions are merely preferred specific implementations of the present invention, but are not intended to limit the protection scope of the present invention. Any equivalent replacement or variation made by a person skilled in the art according to the technical solutions of the present invention and the inventive concept thereof within the technical scope disclosed in the present invention shall fall within the protection scope of the present invention.

Claims

1. A method for private set intersection in a smart city system, wherein the method comprises the following steps: (1) using, by all participants, a hash function generated by a third party Pc and respective public keys to perform encryption, to generate respective ciphertexts, and sending the respective ciphertexts to a blockchain, wherein all the participants comprise a participant Pa and a participant Pb;(2) using the blockchain to verify identities of all the participants before private intersection is performed, to determine whether the private intersection can be performed;(3) sharing, by the participant Pa and the participant Pb, subsets of respective private sets among three parties after it is determined that the private intersection can be performed;(4) obtaining subvectors by the three parties after sharing, and then ranking subvectors of the participant Pa and the participant Pb;(5) jointly calculating, by the three parties, a secret sharing vector of one token vector, and then performing secondary ranking on ranked subvectors of the participant Pa and the participant Pb according to the secret sharing vector, to obtain a ranked subsecret combination vector; and(6) recovering, by the participant Pa and the participant Pb, respective subsecret combination vectors by invoking a Reveal algorithm, to obtain an intersection set R.

2. The method for private set intersection in a smart city system according to claim 1, wherein the step (1) specifically is that: the third party Pc uses a security parameter 21, 2 to generate a hash function H1 and a hash function H2;the participant Pa selects a random value a as a private key ska of the participant Pa, and uses the private key to calculate a public key pka; and similarly, the participant Pb selects a random value b as a private key skb of the participant Pb, and uses the private key to calculate a public key pkb;the participant Pa generates a ciphertext U1 through the hash function H1 and the public key pka, and the participant Pb generates a ciphertext U2 through the hash function H2 and the public key pkb; andthen the ciphertext U1 and the ciphertext U2 are sent to the blockchain.

3. The method for private set intersection in a smart city system according to claim 1, wherein the step (2) specifically is that: first, the participant Pa exchanges an EOA address with the participant Pb; then, the participant Pb uses a public key of the participant Pa to encrypt a public key and a ciphertext of the participant Pb, and packs a ciphertext CI into a transaction to be sent to the blockchain; when private set intersection needs to be performed, the Pa inquires a recent transaction, extracts a ciphertext in the recent transaction, and then decrypts the ciphertext by using a private key of the Pa; a public key PKb of the participant Pb is decrypted, a hash operation is performed on the public key, last 20 characters of an operation result are intercepted as R1, the R1 is matched with an address Addr that sends the transaction, and if the R1 is the same as the address, it indicates that the participant Pb authorizes the other party and desires to perform a private set intersection operation; and the Pb inquires a recent transaction in the blockchain, and uses the EOA address to check whether the EOA address is an address of the Pa, and if the EOA address is the address of the Pa, it indicates that the Pa desires to perform a private set intersection operation.

4. The method for private set intersection in a smart city system according to claim 1, wherein the three parties in the step (3) comprise the participant Pa, the participant Pb, and the third party Pc.

5. The method for private set intersection in a smart city system according to claim 1, wherein the step (4) specifically is that: the participant Pa obtains subvectors and the participant Pb obtains subvectors and and the Pc obtains subsecrets and then a set of subsecrets held by the participant Pa is combined and is represented as a vector and a set of subsecrets held by the participant Pb is combined and is represented as a vector and subsecret combination vectors and held by the participant Pa and the participant Pb are ranked according to element sizes, to generate vectors and .

6. The method for private set intersection in a smart city system according to claim 1, wherein the step (5) specifically is that: three participants jointly calculate a secret sharing vector of one token vector and rank vectors and according to a value of ], to obtain a subsecret combination vector (a′1, a′2) ranked according to ].

7. The method for private set intersection in a smart city system according to claim 1, wherein the step (6) specifically is that: the participant Pa sends a subsecret vector (, a′1) there thereof to the participant Pb, and similarly, the participant Pb sends a subsecret combination vector (, a′2) thereof to the Pa; the participant Pa and the participant Pb respectively invoke the Reveal algorithm according to held subsecret vectors and to recover a token vector ], and finally, a number of elements with =1 is a number N of intersection set elements; the participant Pa extracts last N elements in a′1 and sends the elements to the participant Pb; similarly, the participant Pb extracts/last N elements in a′2 and sends the elements to the participant Pa; and the participant Pa and the participant Pb recover, according to the Reveal algorithm, last N subsecret vectors that are received, to obtain an intersection set R.

8. An electronic device, comprising a memory and a processor, wherein the memory is configured to store a computer program, and the processor runs the computer program, to enable the electronic device to execute the method for private set intersection in a smart city system according to claim 1.

9. A computer-readable storage medium, having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the method for private set intersection in a smart city system according to claim 1.