CN113518092B - Set intersection method for realizing multi-party privacy - Google Patents
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Abstract
The invention discloses a multi-party privacy set intersection method, which mainly solves the problem that the prior art only supports the hidden set size intersection under the environment of two parties, but the set intersection communication volume is large under the environment of a plurality of parties. The scheme is as follows: the parameter generating mechanism generates required parameters; other participants use the bloom filter to represent respective input sets and use the joint public key to encrypt the input sets and send the input sets to the appointed participants; the appointed party extracts the ciphertext by using the hash value of the set element, combines a plurality of ciphertexts into a polymerization ciphertext by using a radix number marking mode, and sends the polymerization ciphertext to other parties; and the appointed party and other parties jointly decrypt to obtain a joint plaintext, and a single plaintext is recovered from the joint plaintext to obtain an intersection. The method can support the privacy set intersection calculation of the hidden set size under the environment of a plurality of participants, reduces the communication traffic, and can be used for privacy protection of the input set elements and the hidden set sizes of the participants in the set intersection.
Description
Technical Field
The invention belongs to the technical field of security, and further relates to a multi-party privacy set intersection method which can be used for carrying out privacy protection on input set elements and sizes of participants in set intersection.
Background
The privacy preserving set intersection technology is a sub-problem with wide application scenarios in the field of multi-party security computing. Under the background of the era of big data and artificial intelligence, data is generated and utilized at all times in various application programs, and further more convenient service is brought to users. Meanwhile, a large amount of valuable private data is continuously mined, so that people continuously improve the awareness of protecting the data containing the sensitive information of the people, and further cause a trust gap, thereby causing a data island phenomenon and losing the value of the data. The problem of how to reasonably exert the data value on the premise of effectively protecting the data privacy of the user becomes the most important reason for the rise of the privacy protection set intersection technology.
At present, the privacy protection set intersection technology mainly performs set intersection in the environment of two parties, and in most cases, the sizes of input sets of the parties are public. When the size of the private input set implies sensitive information for the participant, the participant may require that it be kept secret. For example, when the homeland security agency DHS needs to know whether a flight passenger list of an airline intersects with the terrorist observation list TWL, the set size of the TWL is confidential information for the DHS and cannot be disclosed to any airline at all. If the supplementary 'dummy' mode is simply utilized, additional overhead problems are caused when data is processed. Meanwhile, in real life, the participants are not limited to two parties, sometimes a plurality of participants are involved, and if the privacy set intersection technology of the two parties is simply applied for multiple times, the problem of privacy data disclosure is brought.
Giuseppe Atenise et al, in its published paper (If) Size matrices, Size-mapping private set interaction, put forward the need for privacy protection set intersections to achieve stronger privacy attributes, hide the Size of the set owned by one of the two parties, i.e., the "client", and design a construction scheme that is secure under the RSA assumption of a random predictive model, using tools similar to RSA accumulators and unpredictable functions. However, the scheme uses an unpredictable function, the function is only limited to the representation of a single element in the set of the participants, and when the number of the participants is multiple, the function of simultaneous transaction is difficult to achieve, so that the feasibility of safely completing the transaction function if the function is expanded to the environment of multiple participants is not great; meanwhile, because the method uses a tool similar to an RSA accumulator, the calculation amount is too large in practical application, and the method is not suitable for practical application scenes.
Sumit Kumar denath et al proposed a bloom filter-based multiparty privacy set intersection negotiation protocol in its published paper Secure and effective privacy set intersection negotiation protocol, which mainly represents the input set elements of participants through a bloom filter structure, and compared with most privacy set negotiation protocols, it can save a lot of storage space, but after obtaining the intersection ciphertext, the specified participant needs to send the large and small number of ciphertexts of its set to all other participants for decryption, so after all other participants receive the ciphertexts, the set size of the specified participant can be inferred according to the number of ciphertexts, and the input set size of the participant cannot be hidden, and the communication traffic is relatively large.
Disclosure of Invention
The present invention aims to provide a set intersection method for realizing multi-party privacy, so as to protect privacy attributes of multiple participants in original input data set elements and the sizes of the set elements, that is, any participant cannot exactly obtain the set data and the number of the elements in the private input sets of other participants, and reduce communication overhead.
In order to achieve the purpose, the technical scheme of the invention is as follows:
(1) a parameter generation means PG for generating parameters (G, q, G) of the encryption algorithm EL, wherein G represents a cyclic group, q represents an order of the cyclic group G, and G represents a generator of the cyclic group G, and sharing the parameters to all participants;
(2) all parties generate respective public and private key pairs (pk) according to the parameters i ,sk i ) And discloses a public key pk i Private key sk i Then, calculating a joint public key pk according to the public keys, wherein i is 1, …, n, n represents the number of participants;
(3) the parameter generation mechanism PG generates a public and private key pair (pk) according to the parameters (G, q, G) T ,sk T ) And using the public key required for encrypting the set size
Interacting with all participants to obtain the size m of the bloom filter, and finally generating k hash functions h of the bloom filter l And the parameter m and the hash function h are combined l Sending the hash function h to other participants l Is sent to a designated participant, wherein pk 1 Representing specified parametersThe public key of the party, l ═ 1, …, k, denotes the number of hash functions;
(4) specifying participants to generate t cardinalities w t Wherein t is 1, …, v 1 ，v 1 Represents the size of its input set;
(5) the other participants respectively represent the input sets by the bloom filter structure to obtain the respective bloom filters
Reuse joint public key pk to bloom filter structure
Encrypting to obtain respective encrypted bloom filters
And sends it to the designated party;
(6) hash function h of designated participants using bloom filters l Calculate the element x in its input set t From the received encrypted bloom filter
K (n-1) ciphertexts are extracted from the data
Obtaining an aggregation ciphertext by using homomorphism property of an encryption algorithm TEL for the ciphertexts, and sending the aggregation ciphertext to other participants;
(7) and the appointed party and other parties are combined for decryption to obtain a polymerization plaintext, and the polymerization plaintext is recovered to be a single plaintext to complete set intersection.
Compared with the prior art, the invention has the following advantages:
firstly, because a plurality of ciphertexts are combined into one aggregation cipher text by using a radix number marking mode, the data volume sent to other parties by a specified party is greatly reduced, and the aim of reducing communication traffic is fulfilled;
secondly, in the process of generating the size of the bloom filter, the input set sizes of other participants are encrypted by using a joint common key formed by the appointed participant and the parameter generating mechanism, and the input set sizes of other participants cannot be obtained by the appointed participant and the input set sizes corresponding to other participants cannot be definitely obtained by using the re-randomization mode, so that the problem that the input set sizes cannot be hidden in the prior art is solved, and the input set sizes of other participants are hidden;
thirdly, the invention has the advantages that the information sent by the appointed party to other parties only has one aggregation ciphertext, so that other parties can not obtain the input set size of the appointed party from the number of the aggregation ciphertexts, the effect of hiding the input set size of the appointed party is further improved, and the set intersection of multi-party privacy is realized.
Drawings
Fig. 1 is a general flow chart of an implementation of the present invention.
Fig. 2 is a sub-flow diagram of the present invention for a given participant to recover a single plaintext from an aggregated ciphertext.
Detailed Description
Embodiments of the present invention are described in further detail below with reference to the accompanying drawings.
This example includes three bodies, a parameter generation mechanism PG, a designated party and other parties, where:
a parameter generation mechanism PG, which is responsible for generating the parameters required for realizing intersection;
the method comprises the steps that a participant is appointed and used for inputting an original data set of the participant and obtaining a final intersection of all input sets;
other participants, which are used to input respective raw data sets.
Referring to fig. 1, the implementation steps of this example are as follows:
1.1) the parameter generation means PG generates and discloses parameters (G, q, G) by using an ElGamal encryption algorithm EL, wherein G represents a cyclic group, q represents the order of the cyclic group G, and G represents a generator of the cyclic group G;
1.2) all parties generate respective public and private key pairs (pk) according to the parameters i ，sk i ) And discloses a public key pk i Private key sk i Then, the joint public key is calculated according to the public respective public keys
Wherein, i is 1, …, n, n represents the number of participants;
1.3) the parameter generation mechanism PG generates a public and private key pair (pk) thereof according to the parameters (G, q, G) T ，sk T ) Public key pk T Private secret key sk T And sends its public key pk T With the public key pk of the designated party 1 Multiplying to obtain the public key needed by the size of the encrypted set
1.4) other parties all utilize the public key
For respective input set size v i Encrypting to obtain ciphertext
And sending it to the designated participant, where i ═ 2, …, n, denotes the number of participants;
1.5) specifying that the participant received the ciphertext
Then, the cipher text is encrypted by using the private key of the user
Partially decrypted into
Then from group Z q In which a random number is selected
Using the random number
The ciphertext is encrypted
Re-randomizing to obtain re-randomized cipher text
And encrypt the ciphertext
Disorder, and sending to a parameter generation mechanism PG, wherein the group Z q Is a group of integers of order q;
1.6) the parameter generation mechanism PG obtains the scrambled ciphertext
Then, the clear text v is obtained by utilizing the private key of the user to decrypt i By comparison of v i To obtain a maximum value v max And then calculating the size m of the bloom filter:
v max ＝max(v i )，
where i ═ 2, …, n, n denotes the number of participants, k denotes the number of hash functions, and the notation
Means to round up the values inside the symbol;
1.7) parameter Generation mechanism PG chooses k Hash functions h of bloom Filter l And the size m of the bloom filter and the hash function h l Sending the hash function h to other participants l Sending to the designated participant, l ═ 1, …, k, k denotes the number of hash functions;
1.8) specifying the participants to generate t cardinalities w t :
w t ＝(k(n-1)+1) t-1 ,
Wherein t is 1, …, v 1 ，v 1 Representing the size of the input set of the specified participant, k representing the number of bloom filter hash functions, and n representing the number of participants.
Step 2, other participants all represent their respective input sets by adopting the bloom filter structure to obtain their respective bloom filters
And encrypting the data to obtain respective encrypted bloom filters
2.1) other participants all use k hash functions of the bloom filter to pair the elements x in their respective input sets ζ And calculating the index value:
h 1 (x ζ ),...,h l (x ζ ),...,h k (x ζ )，
wherein h is l (x ζ ) Representing element x ζ By a hash function h l Calculated index value ζ 1, …, v i ，v i A set of representations X i L 1, …, k, k denotes the number of hash functions, i 2, …, n, n denotes the number of participants;
2.2) all other participants generate an empty bloom Filter BF i BF of bloom filter i The value of each position in (a) is initialized to 1;
2.3) other participators are in BF of the empty bloom filter according to the index values obtained in the step 2.1) i Finding the corresponding position and changing the value to 0, thereby obtaining the respective bloom filters of other participants
Wherein the bloom filter
The value of the jth position is expressed as:
m represents the size of the bloom filter.
2.4) other participants use TEL encryption algorithm to filter bloom
Encrypting to obtain respective encrypted bloom filters
Wherein,
bloom filter representing encryption
The jth location of (1).
Step 3, appointing the hash function h of the participant by utilizing the bloom filter l Calculating the element x in its input set t From the received encrypted bloom filter
K (n-1) ciphertexts are extracted from the data
3.1) Ha of a designated participant Using bloom FilterH function of Hig l Calculating the element x in its input set t Index value of (d):
h 1 (x t ),...,h l (x t ),...,h k (x t )，
wherein h is l (x t ) Represents the element x t By a hash function h l The calculated index value t 1, …, v 1 ，v 1 A set of representations X 1 1, …, k, k representing the number of hash functions;
3.2) specifying the Party to use the encrypted bloom Filter
Extracting index value h l (x t ) The corresponding ciphertext, is represented as follows:
wherein,
represent
The middle index value is h l (x t ) I 2, …, n, n indicates the number of participants.
Step 4, appointing the participant pair k (n-1) ciphertexts
And obtaining an aggregation ciphertext by using the homomorphism property of the encryption algorithm TEL, and sending the aggregation ciphertext to other participants.
4.1) appointing the participator to utilize the addition homomorphism of the encryption algorithm TEL to encrypt k (n-1) ciphertexts
Multiplying to obtain the element x t Corresponding ciphertext C t Expressed as follows:
C t ＝(α t ,β t )，
wherein alpha is t Is C t The first portion of ciphertext, represented as:
β t is C t The second portion of the ciphertext, represented as:
r ij is group Z q Wherein, i is 2, …, n represents the number of participants, j is 1, …, m, m represents the size of the bloom filter;
4.2) specifying participant utilization floor w t And number-by-number homomorphism of the encryption algorithm TEL, for element x t Corresponding ciphertext C t Exponentiation is performed to obtain a marked ciphertext
Is represented as follows:
wherein,
for marking ciphertext
The first portion of ciphertext, represented as:
n represents the number of participants;
4.3) assigning participants the addition homomorphism of v using the encryption algorithm TEL 1 Individual mark cipher text
Multiplying to obtain an aggregate ciphertext C, represented as follows:
C＝(α，β)，
where α is the first partial ciphertext of the aggregate ciphertext C, expressed as:
β is the second partial ciphertext of the aggregate ciphertext C, represented as:
and 5, the appointed party and other parties are combined for decryption to obtain a polymerization plaintext, and the polymerization plaintext is recovered to be a single plaintext to complete set intersection.
5.1) other parties all utilize their own private keys sk i And exponentiating the first part of ciphertext alpha of the aggregation ciphertext C to obtain a part of value required for decryption:
and sends it to the designated participant, where i ═ 2, …, n, n denotes the number of participants;
5.2) appointing the participant to get T i Then, use its private key sk 1 Exponentiating a first part of ciphertext alpha of the aggregated ciphertext C to obtain another part of value required for decryption:
then will T 1 And T i Multiplying to obtain all values rho required for decryption:
5.3) the appointed party decrypts the aggregation ciphertext C by using all the values rho required by decryption to obtain an aggregation plaintext mu:
wherein, w t Representing the cardinality, b t Representing a single plaintext, b t ∈[0,…,k(n-1)]；
5.4) appointing the participant to obtain the plaintext b by using a plaintext recovery algorithm t Wherein t is 1, …, v 1 ，v 1 A set of representations X 1 The size of (2):
referring to fig. 2, the specific implementation of this step is as follows:
5.4.1) let variable t ═ v 1 ；
5.4.2) calculating the plaintext corresponding to the variable t: b t ＝(μ-μmodw t )/w t ；
5.4.3) calculating the polymerization plaintext corresponding to the residual variable t: mu ═ mu- (w) t ·b t )；
5.4.2) determine whether the variable t ═ 1 holds:
if yes, ending the process and outputting b t ；
Otherwise, let t equal t-1, return 5.4.2).
5.5) appointing the participant to reinitialize an empty set W 0 And judging a single plaintext b t Whether or not it is 0:
if so, the element x is added t Put into the set W 0 And (5) outputting a final set W, namely the intersection of the input sets of all the participants.
Otherwise, for the set W 0 No operation is performed.
The foregoing description is only an example of the present invention and is not intended to limit the invention, so that it will be apparent to those skilled in the art that various changes and modifications in form and detail may be made therein without departing from the spirit and scope of the invention.
Claims (10)
1. A set intersection method for realizing multi-party privacy is characterized by comprising the following steps:
(1) the parameter generating mechanism PG generates parameters (G, q, G) of an encryption algorithm ElGamal, and shares the parameters to all participants, wherein G represents a cyclic group, q represents the order of the cyclic group G, and G represents a generator of the cyclic group G;
(2) all parties generate respective public and private key pairs (pk) according to the parameters i ，sk i ) And discloses a public key pk i Private secret key sk i Then, a joint public key pk is calculated according to the public keys, wherein i is 1.
(3) The parameter generation mechanism PG generates a public and private key pair (pk) thereof according to the parameters (G, q, G) T ，sk T ) And using the public key required for encrypting the set size
Interacting with all participants to obtain the size m of the bloom filter, and finally generating k hash functions h of the bloom filter l And the parameter m and the hash function h are combined l To all the participantsAnd then the hash function h is used l Is sent to a designated participant, wherein pk 1 A public key representing a given participant, l 1.., k, k representing the number of hash functions;
(4) specifying participants to generate t cardinalities w t Wherein t is 1 1 ，v 1 Represents the size of its input set;
(5) the other participants respectively represent the input sets by the bloom filter structure to obtain the respective bloom filters
Reuse joint public key pk to bloom filter structure
Encrypting to obtain respective encrypted bloom filters
And sends it to the designated party;
(6) hash function h of designated participants using bloom filters l Calculating the element x in its input set t From the received encrypted bloom filter
K (n-1) ciphertexts are extracted from the data
Obtaining a polymerization ciphertext by using homomorphism property of an encryption algorithm TEL for the ciphertexts, and sending the polymerization ciphertext to other participants;
(7) and the appointed party and other parties are combined for decryption to obtain a polymerization plaintext, and the polymerization plaintext is recovered to be a single plaintext to complete set intersection.
2. The method of claim 1, wherein all participants in (2) calculate a joint public key pk from the public individual public keys, as follows:
wherein, pk i A public key representing the ith participant, i 1, 2.
3. The method of claim 1, wherein (3) the parameter generation mechanism PG interacts with all participants to obtain the bloom filter size m as follows:
(3a) the other parties all using the public key
For respective input set size v i Encrypting to obtain ciphertext
And send it to the designated participants, where i ═ 2.., n, n represents the number of participants;
(3b) the designated party receives the ciphertext
Then, the cipher text is encrypted by using the private key of the user
Partially decrypted into
Then from group Z q In which a random number is selected
Using the random number
Cipher text
Re-randomizing to obtain re-randomized cipher text
And encrypt the ciphertext
Disorder, and sending to a parameter generation mechanism PG, wherein the group Z q Is a group of integers of order q;
(3c) the parameter generation mechanism PG obtains the scrambled ciphertext
Then, the clear text v is obtained by utilizing the private key of the user to decrypt i By comparison of v i To obtain a maximum value v max And then calculating the size m of the bloom filter:
v max ＝max(v i )，
where k represents the number of hash functions, the symbol
Meaning rounding up the values inside the symbol.
4. The method of claim 1, wherein t cardinalities w generated by a given participant in (4) t Expressed as follows:
w t ＝(k(n-1)+1) t-1 ，
wherein, t is 1 1 ，v 1 Representing the size of the input set of the specified participant, k representing the number of bloom filter hash functions, and n representing the number of participants.
5. The method of claim 1, wherein the other participants in (5) represent respective sets of inputs by a bloom filter structure, resulting in respective bloom filters
The method is realized as follows:
(5a) the other participants all have to the element x in their respective input sets ζ And calculating by using k hash functions of the bloom filter to obtain an index value:
h 1 (x ζ )，…，h l (x ζ )，…，h k (x ζ )，
wherein h is l (x ζ ) Representing element x ζ By a hash function h l The calculated index value, ζ ═ 1 i ，v i A set of representations X i K, k denotes the number of hash functions, i 2, n, n denotes the number of participants;
(5b) bloom Filter BF with other participants all generating null i BF of bloom filter i The value of each position in (a) is initialized to 1;
(5c) other participants are in the empty bloom filter BF according to the index value obtained in the step (5a) i Finding the corresponding position and changing the value to 0, thereby obtaining the respective bloom filters of other participants
Wherein the bloom filter
The value of the jth position is expressed as:
j ═ 1., m, m denote the size of the bloom filter.
6. The method of claim 1, wherein (5) the other participants obtain respective encrypted bloom filters
Is represented as follows:
wherein,
bloom filters represented as ciphers
J-th position ciphertext of (1), m, m represents the size of the bloom filter, and i-2.
7. The method of claim 1, wherein the hash function h of (6) specifying that the participant utilizes a bloom filter l Calculating the element x in its input set t Index value of (d):
h 1 (x t )，…，h l (x t )，…，h k (x t )，
wherein h is l (x t ) Represents the element x t At the hash function h l Index value of 1, t 1 ，v 1 Set of representations X 1 Is 1, …, k, k denotes the number of hash functions.
8. The method of claim 1, wherein the method is performed in a batch processThe bloom Filter specifying Party to encrypt from
Extracting index value h l (x t ) The corresponding ciphertext, expressed as follows:
wherein,
to represent
The middle index value is h l (x t ) K, k denotes the number of hash functions, t 1 1 ，v 1 A set of representations X 1 N, n represents the number of participants.
9. The method of claim 1, wherein k (n-1) ciphertext pairs are specified in the (6)
Obtaining a polymerization ciphertext by using the homomorphism property of an encryption algorithm TEL, and realizing the following steps:
(6a) appointing the participants to use the addition homomorphism of the encryption algorithm TEL to encrypt k (n-1) ciphertexts
Multiplying to obtain the element x t Corresponding ciphertext C t Expressed as follows:
C t ＝(α t ，β t )，
wherein alpha is t Is C t The first portion of ciphertext, represented as:
β t is C t The second portion of ciphertext, expressed as:
r ij is a group Z q N, n represents the number of participants, j represents 1, the.
t＝1，...，v 1 ，v 1 a set of representations X 1 The size of (d);
(6b) specifying participant utilization cardinality w t And number multiplication homomorphism of encryption algorithm TEL for element x t Corresponding ciphertext C t Exponentiation is performed to obtain a marked ciphertext
Is represented as follows:
wherein,
for marking cryptograph
The first portion of ciphertext, represented as:
k represents the number of bloom filter hash functions;
n represents the number of participants;
(6c) specifying participants to use the addition homomorphism of the encryption algorithm TEL to convert v 1 Individual mark cipher text
Multiplying to obtain a combined ciphertext C, as follows:
C＝(α，β)，
where α is the first partial ciphertext of the aggregate ciphertext C, expressed as:
β is the second partial ciphertext of the aggregate ciphertext C, represented as:
10. the method according to claim 1, characterized in that the implementation of (7) is as follows:
(7a) other parties all utilize their own private keys sk i Exponentiation is performed on the first part of ciphertext alpha of the aggregate ciphertext C to obtain a solutionPartial values required for encryption:
and send it to the designated participants, where i ═ 2.., n, n represents the number of participants;
(7b) designating a participant to get T i Then, use its private key sk 1 Exponentiating a first part of ciphertext alpha of the aggregated ciphertext C to obtain another part of value required for decryption:
then will T 1 And T i Multiplying to obtain all values rho required for decryption:
(7c) and the appointed party decrypts the aggregation ciphertext C by using all the values rho required by decryption to obtain an aggregation plaintext mu:
wherein, w t Representing the cardinality, b t Representing a single plaintext, b t ∈[0，...，k(n-1)]；
(7d) The appointed participator obtains a single plaintext b by using a plaintext recovery algorithm t Reinitializing an empty set W 0 And judging a single plaintext b t Whether or not it is 0:
if so, the element x is added t Put into the set W 0 In the method, a final set W is output, namely the intersection of input sets of all the participants;
otherwise, for the set W 0 No operation is performed.
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| CN113901501B (en) * | 2021-10-20 | 2022-11-08 | 苏州斐波那契信息技术有限公司 | Private domain user image expansion method based on federal learning |
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