CN109525386A - A method of based on the privately owned intersection of Paillier homomorphic cryptography and - Google Patents
A method of based on the privately owned intersection of Paillier homomorphic cryptography and Download PDFInfo
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
- H04L9/008—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols involving homomorphic encryption
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Abstract
The present invention provides a kind of method based on the privately owned intersection sum of Paillier homomorphic cryptography, is related to cyberspace security and privacy protection technique field.The agreement of agreement and reversed privately owned intersection sum including the privately owned intersection sum based on Paillier homomorphic cryptography, in the agreement of privately owned intersection sum, both sides negotiate to encrypt about the basis instrument for encrypting privately owned intersection sum and by three-wheel, final 2 side using private key decryption acquire intersection and, in the agreement of reversed privately owned intersection sum, both sides negotiate about the basis instrument for encrypting reversed privately owned intersection sum and encrypt by two-wheeled, then 2 sides using private key decrypt intersection with disturbing factors and and judge whether intersection radix size is able to enter third round and decrypts, if meeting condition 1 side remove disturbing factors acquire intersection and.This method using modular arithmetic property propose ciphertext splitting scheme, efficiency with higher, and agreement both sides can accurately calculate intersection cardinal sum intersection and, avoid habit thinking calculate the information leakage that may cause two-by-two.
Description
Technical field
The present invention relates to cyberspace security and privacy protection technique fields, and in particular to one kind is based on Paillier homomorphism
The method for encrypting privately owned intersection sum.
Background technique
In recent years, data show the trend of explosive growth, and data volume and data class become to become increasingly complex, largely
Valuable customer information, personal privacy record, the operation data of enterprise is constantly mined.When this data is broken out
Generation, the Privacy Protection under big data are just particularly important.
Privacy set intersection (Private Set Intersection, PSI) is an important association of multi-party computations
View.Participate in calculating two sides or multi-party input data set, but can only obtain intersection as a result, cannot get any letter except intersection
Breath.Related protocol only allows whether the particular community of this several sides' understanding intersection, such as the radix of intersection or the size of intersection surpass
Cross certain threshold values.Various methods have been proposed in pervious work, including using semi-honesty model and malice model
Agreement.
Summary of the invention
In view of the problems of the existing technology, the present invention provides a kind of based on the privately owned intersection sum of Paillier homomorphic cryptography
Method, including based on the privately owned intersection sum of Paillier homomorphic cryptography agreement and based on Paillier homomorphic cryptography it is reversely privately owned
The agreement of intersection sum, there are two participants in above-mentioned two agreement --- 1 side and 2 sides, wherein " privately owned intersection and agreement "
Be hold the privately owned input data set containing user identifier in both sides, and wherein the data set of a side also additionally containing with it is every
The related integer value of a user identifier, both sides want the radix for understanding intersection and the basis with the sum of intersection relative integers value
On, do not allow both sides know intersection actual user's identifier or another party's data additional information it is (big in addition to intersection
It is small), i.e. the privacy information of user, by " privately owned intersection and agreement " obtain the result is that 1 side can only access the radix of intersection,
And 2 sides can only access intersection and；And " reversed privately owned intersection and agreement " if be then that intersection is too small is just being handed over by discovery
Collection and the mode for terminating communication before, it is ensured that the minimum value of intersection number of elements passes through to protect the privacy information of user
" reversed privately owned intersection and agreement " obtain the result is that both sides can access the radix of intersection, and only 1 can access friendship
Collection and.
To achieve the goals above, a method of and, including be based on based on the privately owned intersection of Paillier homomorphic cryptography
The agreement of the privately owned intersection sum of Paillier homomorphic cryptography and agreement based on the reversely privately owned intersection sum of Paillier homomorphic cryptography；
(1) agreement based on the privately owned intersection sum of Paillier homomorphic cryptography, comprising the following steps:
Step 1: both sides negotiate about the basis instrument for encrypting privately owned intersection sum, the specific steps are as follows:
Step 1.1: both sides negotiate setting security parameter λ, group G ∈ G (λ), user identifier space U=U (λ) and random
Prophesy machine RO:U → G, wherein user identifier is mapped in the random element of crowd G by random oracle RO；
Hold the input set U of m user identifier in the step side 1.2:11={ ui}i∈[m], wherein i-th of user of 1 side
ui∈U；
Hold n user identifier and therewith the set { (v of the relative integers value of expected pairing in the step side 1.3:2j,
tj)}j∈[n], wherein j-th of user v of 2 sidesj∈ U and therewith the relative integers value t of expected pairingi∈Z+, Z+For positive integer, make
Privately owned intersection and ∑ tjIt is suitble to the Paillier message space of security parameter λ, and defines U2={ vj}j∈[n]；
Step 1.4: each party a chooses a random secret exponent k in group Ga；
The step side 1.5:2 generates a new key pair using Pai.Gen (λ) function in Pailler encipherment scheme
(pk, sk), and public key pk is shared with 1 side；
The step side 2:1 encrypts the user identifier set U of oneself1And random ordering issues 2 sides, the specific steps are as follows:
The step side 2.1:1 is by each user u in oneself user identifier setiApplied to random oracle RO, then
Use key k1It encrypts, is obtained through the encrypted 1 side user ciphertext of 1 side for the first time
The step side 2.2:1 is by encrypted user's ciphertext cipheru1The set of compositionRandom ordering issues 2
Side；
The step side 3:2 encrypts the user data and the user identifier set U of oneself that 1 side sends2And random ordering issues 1
Side, the specific steps are as follows:
The step side 3.1:2 uses key k2To each of receiving through the encrypted 1 side user ciphertext of 1 sideElement carries out secondary encryption, obtains both sides jointly to the ciphertext after 1 side's user encryption
The step side 3.2:2 is by both sides jointly to the ciphertext cipher after 1 side's user encryptionu12The set of compositionRandom ordering issues 1 side；
The step side 3.3:2 uses key k2To set element (v will be inputtedj, tj) each user identifier v of centeringjIt is applied to
Element after random oracle RO mapping is encrypted, and reuses Paillier public key pk to input set element (vj, tj) centering
With each user identifier vjIt is expected that the relative integers value t of pairingjIt is encrypted, is obtained through the encrypted 2 side user ciphertext of 2 sidesWith the ciphertext cipher of the integer value through the encrypted 2 side user pairing of 2 sidest2=Pai (tj) right；
The step side 3.4:2 is by encrypted user's ciphertext cipherv2With paired integer value ciphertext ciphert2It is right
The set of compositionRandom ordering issues 1 side；
The step side 4:1 encrypts the data that 2 sides send and acquires cipherv12With cipheru12Intersection H, further according to set H
Obtain with intersection match integer value and ciphertext Pai (SH) and be sent to 2 sides, the specific steps are as follows:
The step side 4.1:1 uses key k1To receiving through the encrypted user's ciphertext cipher of 2 sidesv2With it is paired
Integer value ciphertext ciphert2To the set of compositionIn each elementIt carries out secondary
Encryption, obtains both sides jointly to the ciphertext cipher after 2 side's user encryptionsv12With paired integer value ciphertext ciphert2It is right
The step side 4.2:1 calculates cipherv12With cipheru12Intersection H:
Step 4.3: for each element h in set H, integer value ciphertext cipher that 1 side will match with ht2=Pai
(tj) be multiplied, obtain to homomorphism with the integer value of intersection pairing and SHCiphertext Pai (SH): Pai (SH)=Pai (∑j∈Htj)
=Pai.Sum ({ Pai (tj)}j∈H)；
The step side 4.4:1 by the integer value matched with intersection and SHCiphertext Pai (SH) it is sent to 2 sides；
The integer value with intersection pairing for the Paillier encryption that the step side 5:2 is received using Paillier private key sk decryption
And SHCiphertext Pai (SH), obtain with the integer value of intersection pairing and SH；
(2) agreement based on the reversely privately owned intersection sum of Paillier homomorphic cryptography, comprising the following steps:
S1: both sides negotiate about the basis instrument for encrypting privately owned intersection sum, the specific steps are as follows:
S1.1: both sides negotiate setting security parameter λ, group G ∈ G (λ), user identifier space U=U (λ) and random pre-
Speech machine RO:U → G, wherein user identifier is mapped in the random element of crowd G by random oracle RO；
Hold the input set U of m user identifier in the side S1.2:11={ ui}i∈[m], wherein i-th of user u of 1 sidei
∈U；
Hold n user identifier and therewith the set { (v of the relative integers value of expected pairing in the side S1.3:2j, tj)}j∈[n],
Wherein, j-th of user v of 2 sidesj∈ U and therewith the relative integers value t of expected pairingj∈Z+, Z+For positive integer, make privately owned intersection
With ∑ tjIt is suitble to the Paillier message space of security parameter λ, and defines the input set U of 2 side's user identifiers2=
{vj}j∈[n]；
S1.4: each party a chooses a random secret exponent k in group Ga；
The side S1.5:2 using Pai.Gen (λ) function in Pailler encipherment scheme generate a new key pair (pk,
Sk), and by public key pk it is shared with 1 side；
The side S2:2 encrypts the user identifier set U of oneself2And 1 side is issued in order, the specific steps are as follows:
The side S2.1:2 uses key k2To set element (v will be inputtedj, tj) each user identifier v of centeringjApplied to
The element of machine prophesy machine RO is encrypted, and reuses Paillier public key pk to input set element (vj, tj) centering and each use
Family identifier vjIt is expected that the relative integers value t of pairingjIt is encrypted, is obtained through the encrypted 2 side user ciphertext of 2 sidesWith the ciphertext cipher of the integer value through the encrypted 2 side user pairing of 2 sidest2=Pai (tj) right；
The side S2.2:2 is by encrypted user's ciphertext cipherv2With paired integer value ciphertext ciphert2To composition
Set1 side is issued in order；
The side S3:1 encrypts the user data and the user identifier set U of oneself that 2 sides send1And 2 sides are issued in order,
Specific step is as follows:
The side S3.1:1 uses key k1To receiving through the encrypted user's ciphertext cipher of 2 sidesv2With it is paired
Integer value ciphertext ciphert2To the set of compositionEach ofElement carries out secondary add
It is close, both sides are obtained jointly to the ciphertext after 2 side's user encryptionsAnd under Paillier modulus N, with
Choose to machine mapping (j → rj), wherein rj∈Z+, pass through Pai (tj+rj)=Pai (tj)×Pai(rj) homomorphism to receiving
Each ofIn element with user identifier vjIt is expected that the relative integers value t of pairingjDisposably filled
Encryption, finally obtains both sides jointly to the ciphertext cipher after 2 side's user encryptionsv12With paired integer value ciphertext through filling out
The cipher filledtr2It is right
The side S3.2:1 saves mapping (j → rj) and by both sides jointly to the ciphertext cipher after 2 side's user encryptionsv12With with
Pairing the cipher that is filled through of integer value ciphertexttr2To the set of compositionIt sends out in order
To 2 sides；
The side S3.3:1 uses key k1To the user u that will be inputted in set 1iApplied to the member after random oracle RO mapping
Element is encrypted, and is obtained through the encrypted 1 side user ciphertext of 1 side
The side S3.4:1 is by encrypted user's ciphertext cipheru1The set of compositionRandom ordering issues 2 sides；
The side S4:2 encrypts the data that 1 side sends and acquires cipherv12With cipheru12Intersection indexed set J, then to subscript
Set J is filled encryption and obtains with the integer value of intersection pairing and SJrAnd it is sent to 1 side, the specific steps are as follows:
The side S4.1:2 uses key k2To each of receiving through the encrypted 1 side user ciphertext of 1 side
Secondary encryption is carried out, obtains both sides jointly to the ciphertext after 1 side's user encryption
The side S4.2:2 calculates cipherv12With cipheru12The indexed set J of intersection:
S4.3: judging whether intersection radix is less than given threshold, if so, 2 side's termination protocols, if it is not, then continuing S4.4；
The side S4.4:2 is by the corresponding all elements Pai (t of subscript in indexed set Jj+rj) be multiplied, reuse private key sk solution
It is close, obtain with the disposable integer value matched with intersection for filling encryption and SJr=∑j∈Jtj+rj；
The side S4.5:2 by encryption and the integer value of intersection pairing and SJrAnd indexed set J is sent to 1 side；
The side S5:1 calculate with intersection pairing integer value and
Beneficial effects of the present invention:
The present invention proposes a kind of method based on the privately owned intersection sum of Paillier homomorphic cryptography, studies and uses and is based on
The algorithm of Paillier homomorphic cryptography proposes ciphertext splitting scheme using the property of modular arithmetic, encrypts, have after plaintext is divided
Higher efficiency and encrypted result in plain text can be obtained without decryption.By this method offer based on Paillier homomorphism
The agreement of privately owned intersection sum and the agreement based on the reversely privately owned intersection sum of Paillier homomorphic cryptography are encrypted, agreement both sides can
Accurately calculate intersection cardinal sum intersection and, avoid habit thinking calculate the information leakage that may cause two-by-two, reversed
In privately owned intersection and agreement, if discovery cardinal of the set is too small, to prevent intersection and being got by one party, to be inferred to certain
The privacy information of user leads to the leakage of privacy of user, by the way of termination protocol, effectively prevent the leakage problem of privacy,
And during using based on Paillier homomorphic cryptography, wherein a side randomly selects mapping to encrypted user's id correlation
Integer value carries out blinding processing, acquires intersection with before, is removing the blind factor further according to mapping, substantially increase the safety of agreement
Property.
Detailed description of the invention
Fig. 1 is privately owned intersection and diagram of protocol architecture in the embodiment of the present invention；
Fig. 2 is privately owned intersection and agreement timing diagram in the embodiment of the present invention；
Fig. 3 is privately owned intersection and agreement flow chart in the embodiment of the present invention；
Fig. 4 is reversed privately owned intersection and diagram of protocol architecture in the embodiment of the present invention；
Fig. 5 is reversed privately owned intersection and agreement timing diagram in the embodiment of the present invention；
Fig. 6 is reversed privately owned intersection and agreement flow chart in the embodiment of the present invention.
Specific embodiment
It is right in the following with reference to the drawings and specific embodiments in order to be more clear the purpose of the present invention, technical solution and advantage
The present invention is described in further details.Described herein specific examples are only used to explain the present invention, is not used to limit this
Invention.
A method of based on the privately owned intersection of Paillier homomorphic cryptography and, including it is privately owned based on Paillier homomorphic cryptography
The agreement of intersection sum and agreement based on the reversely privately owned intersection sum of Paillier homomorphic cryptography；
(1) agreement based on the privately owned intersection sum of Paillier homomorphic cryptography
In the present embodiment, the framework based on the privately owned intersection of Paillier homomorphic cryptography and agreement is as shown in Figure 1, in privately owned friendship
In collection and agreement, two sides input oneself all user resource identifier set, and 1 side obtains the radix of intersection when output, and 2 sides obtain
To intersection and.Two sides of privately owned intersection and agreement realize the process for the sum that seeks common ground by setting and three-wheel interaction, such as Fig. 2 institute
Show.
Figure it is seen that link is being arranged in both sides, with regard to a security parameter λ and a group G ∈ G (λ) and a use
Reach an agreement at family identifier space U=U (λ).Both sides can use a random oracle RO:U → G.The first round, 1 side use k1
The user identifier set for encrypting oneself, sends it to 2 sides.Second wheel, 2 sides use k2Encrypt the set and use k that 1 side sends2
The user identifier set of oneself is encrypted with pk, and sends it to 1 side.Cipher is calculated in 1 sidev12With cipheru12's
Intersection H.Encrypted set H is sent to 2 sides by third round, 1 side, and 2 sides acquire the integer value matched with intersection using sk decryption
Sum, i.e. intersection and SH。
In the present embodiment, for convenience of subsequent descriptions, expression as shown in Table 1 and explanation are provided.
The denotational description communicated between each entity of table 1
Detailed process is as shown in Figure 3, comprising the following steps:
Step 1: both sides negotiate about the basis instrument for encrypting privately owned intersection sum, the specific steps are as follows:
Step 1.1: both sides negotiate setting security parameter λ, group G ∈ G (λ), user identifier space U=U (λ) and random
Prophesy machine RO:U → G, wherein user identifier is mapped in the random element of crowd G by random oracle RO；
Hold the input set U of m user identifier in the step side 1.2:11={ ui}i∈[m], wherein i-th of user of 1 side
ui∈U；
Hold n user identifier and therewith the set { (v of the relative integers value of expected pairing in the step side 1.3:2j,
tj)}j∈[n], wherein j-th of user v of 2 sidesj∈ U and therewith the relative integers value t of expected pairingj∈Z+, Z+For positive integer, make
Privately owned intersection and ∑ tjIt is suitble to the Paillier message space of security parameter λ, and defines U2={ vj}j∈[n]；
Step 1.4: each party a chooses a random secret exponent k in group Ga；
The step side 1.5:2 generates a new key pair using Pai.Gen (λ) function in Pailler encipherment scheme
(pk, sk), and public key pk is shared with 1 side；
The step side 2:1 encrypts the user identifier set U of oneself1And random ordering issues 2 sides, the specific steps are as follows:
The step side 2.1:1 is by each user u in oneself user identifier setiApplied to random oracle RO, then
Use key k1It encrypts, is obtained through the encrypted 1 side user ciphertext of 1 side for the first time
The step side 2.2:1 is by encrypted user's ciphertext cipheru1The set of compositionRandom ordering issues 2
Side；
The step side 3:2 encrypts the user data and the user identifier set U of oneself that 1 side sends2And random ordering issues 1
Side, the specific steps are as follows:
The step side 3.1:2 uses key k2To each of receiving through the encrypted 1 side user ciphertext of 1 sideElement carries out secondary encryption, obtains both sides jointly to the ciphertext after 1 side's user encryption
The step side 3.2:2 is by both sides jointly to the ciphertext cipher after 1 side's user encryptionu12The set of compositionRandom ordering issues 1 side；
The step side 3.3:2 uses key k2To set element (v will be inputtedj, tj) each user identifier v of centeringjIt is applied to
Element after random oracle RO mapping is encrypted, and reuses Paillier public key pk to input set element (vj, tj) centering
With each user identifier vjIt is expected that the relative integers value t of pairingjIt is encrypted, is obtained through the encrypted 2 side user ciphertext of 2 sidesWith the ciphertext cipher of the integer value through the encrypted 2 side user pairing of 2 sidest2=Pai (tj) right；
The step side 3.4:2 is by encrypted user's ciphertext cipherv2With paired integer value ciphertext ciphert2It is right
The set of compositionRandom ordering issues 1 side；
The step side 4:1 encrypts the data that 2 sides send and acquires cipherv12With cipheru12Intersection H, further according to set H
Obtain with intersection match integer value and ciphertext Pai (SH) and be sent to 2 sides, the specific steps are as follows:
The step side 4.1:1 uses key k1To receiving through the encrypted user's ciphertext cipher of 2 sidesv2With it is paired
Integer value ciphertext ciphert2To the set of compositionIn each elementIt carries out secondary
Encryption, obtains both sides jointly to the ciphertext cipher after 2 side's user encryptionsvl2With paired integer value ciphertext ciphert2It is right
The step side 4.2:1 calculates cipherv12With cipheru12Intersection H:
Step 4.3: for each element h in set H, integer value ciphertext cipher that 1 side will match with ht2=Pai
(tj) be multiplied, obtain to homomorphism with the integer value of intersection pairing and SHCiphertext Pai (SH): Pai (SH)=Pai (∑j∈Htj)
=Pai.Sum ({ Pai (tj)}j∈H)；
The step side 4.4:1 by the integer value matched with intersection and SHCiphertext Pai (SH) it is sent to 2 sides；
The integer value with intersection pairing for the Paillier encryption that the step side 5:2 is received using Paillier private key sk decryption
And SHCiphertext Pai (SH), obtain intersection and SH；
(2) agreement based on the reversely privately owned intersection sum of Paillier homomorphic cryptography
In the present embodiment, based on Paillier homomorphic cryptography reversely the framework of privately owned intersection and agreement as shown in figure 4, anti-
Into privately owned intersection and agreement, two sides equally input oneself all user resource identifier set, if intersection radix when output
It is too small with regard to termination protocol.Otherwise, 1 side obtain intersection radix and intersection and, 2 sides obtain the radix of intersection.Reversed privately owned friendship
Two sides of collection and agreement realize the process for the sum that seeks common ground by setting and three-wheel interaction, as shown in Figure 5.
From fig. 5, it can be seen that link is being arranged in both sides, with regard to a security parameter λ and a group G ∈ G (λ) and a use
Reach an agreement at family identifier space U=U (λ).Both sides can use a random oracle RO:U → G.The first round, 2 sides use k2
The user identifier set that oneself is encrypted with pk, sends it to 1 side.Second wheel, 1 side use k1Encrypt the user identifier of oneself
Gather, each element in the set sent for 2 sides uses k1After encrypting user identifier, be added a disturbing factors, and by its
It is sent to 2 sides.Cipher is calculated in 2 sidesv12With cipheru12The indexed set J of intersection, and decrypt band using sk and thanks for your hospitality
The random factor with intersection pairing integer value and SJr, the termination protocol if intersection radix is too small.Third round, 2 sides thanks for your hospitality band
The random factor with intersection pairing integer value and SJrAnd indexed set J is sent to 1 side, 1 side remove disturbing factors acquire with
The sum of the integer value of intersection pairing, i.e. intersection and SJ。
Detailed process is as shown in Figure 6, comprising the following steps:
S1: both sides negotiate about the basis instrument for encrypting privately owned intersection sum, the specific steps are as follows:
S1.1: both sides negotiate setting security parameter λ, group G ∈ G (λ), user identifier space U=U (λ) and random pre-
Speech machine RO:U → G, wherein user identifier is mapped in the random element of crowd G by random oracle RO；
Hold the input set U of m user identifier in the side S1.2:11={ ui}i∈[m], wherein i-th of user u of 1 sidei
∈U；
Hold n user identifier and therewith the set { (v of the relative integers value of expected pairing in the side S1.3:2j, tj)}j∈[n],
Wherein, j-th of user v of 2 sidesj∈ U and therewith the relative integers value t of expected pairingj∈Z+, Z+For positive integer, make privately owned intersection
With ∑ tjIt is suitble to the Paillier message space of security parameter λ, and defines the input set U of 2 side's user identifiers2=
{vj}j∈[n]；
S1.4: each party a chooses a random secret exponent k in group Ga；
The side S1.5:2 using Pai.Gen (λ) function in Pailler encipherment scheme generate a new key pair (pk,
Sk), and by public key pk it is shared with 1 side；
The side S2:2 encrypts the user identifier set U of oneself2And 1 side is issued in order, the specific steps are as follows:
The side S2.1:2 uses key k2To set element (v will be inputtedj, tj) each user identifier v of centeringjApplied to
The element of machine prophesy machine RO is encrypted, and reuses Paillier public key pk to input set element (vj, tj) centering and each use
Family identifier vjIt is expected that the relative integers value t of pairingjIt is encrypted, is obtained through the encrypted 2 side user ciphertext of 2 sidesWith the ciphertext cipher of the integer value through the encrypted 2 side user pairing of 2 sidest2=Pai (tj) right；
The side S2.2:2 is by encrypted user's ciphertext cipherv2With paired integer value ciphertext ciphert2To composition
Set1 side is issued in order；
The side S3:1 encrypts the user data and the user identifier set U of oneself that 2 sides send1And 2 sides are issued in order,
Specific step is as follows:
The side S3.1:1 uses key k1To receiving through the encrypted user's ciphertext cipher of 2 sidesv2With it is paired
Integer value ciphertext ciphert2To the set of compositionEach ofElement carries out secondary add
It is close, both sides are obtained jointly to the ciphertext after 2 side's user encryptionsAnd under Paillier modulus N, with
Choose to machine mapping (j → rj), wherein rj∈Z+, pass through Pai (tj+rj)=Pai (tj)×Pai(rj) homomorphism to receiving
Each ofIn element with user identifier vjIt is expected that the relative integers value t of pairingjDisposably filled
Encryption, finally obtains both sides jointly to the ciphertext cipher after 2 side's user encryptionsv12With paired integer value ciphertext through filling out
The cipher filledtr2It is right
The side S3.2:1 saves mapping (j → ri) and by both sides jointly to the ciphertext cipher after 2 side's user encryptionsv12With with
Pairing the cipher that is filled through of integer value ciphertexttr2To the set of compositionIt sends out in order
To 2 sides；
The side S3.3:1 uses key k1To the user u that will be inputted in set 1iApplied to the member after random oracle RO mapping
Element is encrypted, and is obtained through the encrypted 1 side user ciphertext of 1 side
The side S3.4:1 is by encrypted user's ciphertext cipheru1The set of compositionRandom ordering issues 2 sides；
The side S4:2 encrypt the data sent of 1 side and acquire with the integer value of intersection pairing and indexed set J, then to subscript
Set J is filled encryption and obtains with the integer value of intersection pairing and SJrAnd it is sent to 1 side, the specific steps are as follows:
The side S4.1:2 uses key k2To each of receiving through the encrypted 1 side user ciphertext of 1 sideSecondary encryption is carried out, obtains both sides jointly to the ciphertext after 1 side's user encryption
The side S4.2:2 calculates cipherv12With cipheru12The indexed set J of intersection:
S4.3: judging whether intersection radix is less than given threshold, if so, 2 side's termination protocols, if it is not, then continuing S4.4；
The side S4.4:2 is by the corresponding all elements Pai (t of subscript in indexed set Jj+rj) be multiplied, reuse private key sk solution
It is close, obtain with the disposable integer value matched with intersection for filling encryption and SJr=∑j∈Jtj+rj；
The side S4.5:2 by encryption and the integer value of intersection pairing and SJrAnd indexed set J is sent to 1 side；
The side S5:1 calculate with intersection pairing integer value and
Finally, it should be noted that the above embodiments are merely illustrative of the technical solutions of the present invention, rather than its limitations；Although
Present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that；It still may be used
To modify to technical solution documented by previous embodiment, or some or all of the technical features are equal
Replacement；Thus these are modified or replaceed, defined by the claims in the present invention that it does not separate the essence of the corresponding technical solution
Range.
Claims (7)
1. a kind of method based on the privately owned intersection sum of Paillier homomorphic cryptography, which is characterized in that including same based on Paillier
The privately owned intersection of state encryption and agreement and reversed privately owned intersection and agreement based on Paillier homomorphic cryptography；
(1) privately owned intersection and agreement based on Paillier homomorphic cryptography, comprising the following steps:
Step 1: both sides negotiate about the basis instrument for encrypting privately owned intersection sum, the specific steps are as follows:
Step 1.1: both sides negotiate setting security parameter λ, group G ∈ G (λ), user identifier space U=U (λ) and random oracle
Machine RO:U → G, wherein user identifier is mapped in the random element of crowd G by random oracle RO；
Hold the input set U of m user identifier in the step side 1.2:11={ ui}i∈[m], wherein i-th of user u of 1 sidei∈
U；
Hold n user identifier and therewith the set { (v of the relative integers value of expected pairing in the step side 1.3:2j, tj)}j∈[n],
Wherein, j-th of user v of 2 sidesj∈ U and therewith the relative integers value t of expected pairingj∈Z+, Z+For positive integer, make privately owned intersection
With ∑ tjIt is suitble to the Paillier message space of security parameter λ, and defines U2={ vj}j∈[n]；
Step 1.4: each party a chooses a random secret exponent k in group Ga；
The step side 1.5:2 using Pai.Gen (λ) function in Pailler encipherment scheme generate a new key pair (pk,
Sk), and by public key pk it is shared with 1 side；
The step side 2:1 encrypts the user identifier set U of oneself1And random ordering issues 2 sides；
The step side 3:2 encrypts the user data and the user identifier set U of oneself that 1 side sends2And random ordering issues 1 side；
The step side 4:1 encrypts the data that 2 sides send and acquires cipherv12With cipheru12Intersection H, obtained further according to set H
With intersection pairing integer value and ciphertext Pai (SH) and be sent to 2 sides；
The step side 5:2 using Paillier private key sk decryption receive Paillier encryption with intersection pairing integer value and
SHCiphertext Pai (SH), obtain with the integer value of intersection pairing and SH；
(2) reversed privately owned intersection and agreement based on Paillier homomorphic cryptography, comprising the following steps:
S1: both sides negotiate about the basis instrument for encrypting privately owned intersection sum, the specific steps are as follows:
S1.1: both sides negotiate setting security parameter λ, group G ∈ G (λ), user identifier space U=U (λ) and random oracle
RO:U → G, wherein user identifier is mapped in the random element of crowd G by random oracle RO；
Hold the input set U of m user identifier in the side S1.2:11={ ui}i∈[m], wherein i-th of user u of 1 sidei∈U；
Hold n user identifier and therewith the set { (v of the relative integers value of expected pairing in the side S1.3:2j, tj)}j∈[n],
In, j-th of user v of 2 sidesj∈ U and therewith the relative integers value t of expected pairingj∈Z+, Z+For positive integer, make privately owned intersection and
∑tjIt is suitble to the Paillier message space of security parameter λ, and defines the input set U of 2 side's user identifiers2={ vj}j∈[n]；
S1.4: each party a chooses a random secret exponent k in group Ga；
The side S1.5:2 generates a new key pair (pk, sk) using Pai.Gen (λ) function in Pailler encipherment scheme, and
Public key pk is shared with 1 side；
The side S2:2 encrypts the user identifier set U of oneself2And 1 side is issued in order；
The side S3:1 encrypts the user data and the user identifier set U of oneself that 2 sides send1And 2 sides are issued in order；
The side S4:2 encrypts the data that 1 side sends and acquires cipherv12With cipheru12The indexed set J of intersection, then to subscript collection
Conjunction J is filled encryption and obtains with the integer value of intersection pairing and SJrAnd it is sent to 1 side；
The side S5:1 calculate with intersection pairing integer value and
2. the method according to claim 1 based on the privately owned intersection sum of Paillier homomorphic cryptography, which is characterized in that described
Step 2 the following steps are included:
The step side 2.1:1 is by each user u in oneself user identifier setiApplied to random oracle RO, then using close
Key k1It encrypts, is obtained through the encrypted 1 side user ciphertext of 1 side for the first time
The step side 2.2:1 is by encrypted user's ciphertext cipheru1The set of compositionRandom ordering issues 2 sides.
3. the method according to claim 1 based on the privately owned intersection sum of Paillier homomorphic cryptography, which is characterized in that described
Step 3 the following steps are included:
The step side 3.1:2 uses key k2To each of receiving through the encrypted 1 side user ciphertext of 1 sideElement carries out secondary encryption, obtains both sides jointly to the ciphertext after 1 side's user encryption
The step side 3.2:2 is by both sides jointly to the ciphertext cipher after 1 side's user encryptionu12The set of composition
Random ordering issues 1 side；
The step side 3.3:2 uses key k2To set element (v will be inputtedj, tj) each user identifier v of centeringjApplied to random
Element after prophesy machine RO mapping is encrypted, and reuses Paillier public key pk to input set element (vj, tj) centering and every
A user identifier vjIt is expected that the relative integers value t of pairingjIt is encrypted, is obtained through the encrypted 2 side user ciphertext of 2 sidesWith the ciphertext cipher of the integer value through the encrypted 2 side user pairing of 2 sidest2=Pai (tj) right；
The step side 3.4:2 is by encrypted user's ciphertext cipherv2With paired integer value ciphertext ciphert2To composition
SetRandom ordering issues 1 side.
4. the method according to claim 1 based on the privately owned intersection sum of Paillier homomorphic cryptography, which is characterized in that described
Step 4 the following steps are included:
The step side 4.1:1 uses key k1To receiving through the encrypted user's ciphertext cipher of 2 sidesv2With it is paired whole
Numerical value ciphertext ciphert2To the set of compositionIn each elementCarry out secondary add
It is close, both sides are obtained jointly to the ciphertext cipher after 2 side's user encryptionsv12With paired integer value ciphertext ciphert2It is right
The step side 4.2:1 calculates cipherv12With cipheru12Intersection H:
Step 4.3: for each element h in set H, integer value ciphertext cipher that 1 side will match with ht2=Pai (tj) phase
Multiply, obtains to homomorphism with the integer value of intersection pairing and SHCiphertext Pai (SH): Pai (SH)=Pai (∑j∈Htj)=
Pai.Sum({Pai(tj)}j∈H)；
The step side 4.4:1 by the integer value matched with intersection and SHCiphertext Pai (SH) it is sent to 2 sides.
5. the method according to claim 1 based on the privately owned intersection sum of Paillier homomorphic cryptography, which is characterized in that described
S2 the following steps are included:
The side S2.1:2 uses key k2To set element (v will be inputtedj, tj) each user identifier v of centeringjApplied to random oracle
The element of machine RO is encrypted, and reuses Paillier public key pk to input set element (vj, tj) centering and each user identifier
Accord with vjIt is expected that the relative integers value t of pairingjIt is encrypted, is obtained through the encrypted 2 side user ciphertext of 2 sidesWith the ciphertext cipher of the integer value through the encrypted 2 side user pairing of 2 sidest2=Pai (tj) right；
The side S2.2:2 is by encrypted user's ciphertext cipherv2With paired integer value ciphertext ciphert2To the collection of composition
It closes1 side is issued in order.
6. the method according to claim 1 based on the privately owned intersection sum of Paillier homomorphic cryptography, which is characterized in that described
S3 the following steps are included:
The side S3.1:1 uses key k1To receiving through the encrypted user's ciphertext cipher of 2 sidesv2With paired integer
It is worth ciphertext ciphert2To the set of compositionEach ofElement carries out secondary encryption,
Both sides are obtained jointly to the ciphertext after 2 side's user encryptionsAnd under Paillier modulus N, at random
Choose mapping (j → r in groundj), wherein rj∈Z+, pass through Pai (tj+rj)=Pai (tj)×Pai(rj) homomorphism to receiving
EachIn element with user identifier vjIt is expected that the relative integers value t of pairingjDisposable filling is carried out to add
It is close, both sides are finally obtained jointly to the ciphertext cipher after 2 side's user encryptionsv12It is filled through with paired integer value ciphertext
Ciphertr2It is right
The side S3.2:1 saves mapping (j → rj) and by both sides jointly to the ciphertext cipher after 2 side's user encryptionsv12With it is paired
The cipher that is filled through of integer value ciphertexttr2To the set of composition2 sides are issued in order；
The side S3.3:1 uses key k1To the user u that will be inputted in set 1iApplied to random oracle RO mapping after element into
Row encryption, obtains through the encrypted 1 side user ciphertext of 1 side
The side S3.4:1 is by encrypted user's ciphertext cipheru1The set of compositionRandom ordering issues 2 sides.
7. the method according to claim 1 based on the privately owned intersection sum of Paillier homomorphic cryptography, which is characterized in that described
S4 the following steps are included:
The side S4.1:2 uses key k2To each of receiving through the encrypted 1 side user ciphertext of 1 sideInto
The secondary encryption of row, obtains both sides jointly to the ciphertext after 1 side's user encryption
The side S4.2:2 calculates cipherv12With cipheru12The indexed set J of intersection:
S4.3: judging whether intersection radix is less than given threshold, if so, 2 side's termination protocols, if it is not, then continuing S4.4；
The side S4.4:2 is by the corresponding all elements Pai (t of subscript in indexed set Jj+rj) be multiplied, private key sk decryption is reused, is obtained
To band disposable filling encryption and the integer value of intersection pairing and
The side S4.5:2 by encryption and the integer value of intersection pairing and SJrAnd indexed set J is sent to 1 side.
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