CN115333726A - Fixed point number secure multiplication method based on vector space secret sharing - Google Patents
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Abstract
The invention belongs to the technical field of data security, and particularly relates to a fixed point number secure multiplication method based on vector space secret sharing. The method comprises the following basic steps: the participant precomputes the vector triple required by the secure multiplication in the off-line stage; in the online stage, data in a vector space secret sharing form is used as input, and safe multiplication is interactively carried out; and performing truncation processing on a result obtained by the secure multiplication. The invention has the advantages that: the vector space secret sharing technology supports secure multiplication operation, so that the vector space secret sharing technology is better applied to the field of privacy protection machine learning to deal with more complex practical application scenes.
Description
Technical Field
The invention belongs to the technical field of data security, and particularly relates to a fixed point number secure multiplication method based on vector space secret sharing.
Background
In the big data era, almost all activities are data driven. These data are typically distributed among a plurality of data controllers and contain a lot of sensitive or private information that is protected by legal regulations, such as the european union's regulations on general data protection, the chinese ' network security laws ', ' data security laws ', ' personal information protection laws ', etc. Therefore, the direct collection, combination and sharing of the data containing the user information are severely punished by law, and the phenomenon of data islanding is aggravated. Mr. Yao in 1982 proposed a safe multiparty computing technology [1] to solve the problem of the millionaire, namely, two millionaire want to compare with each other and get rich, but do not want to let the other know how much wealth the millionaire is, so let them know who is rich without the help of a third party. The secure multiparty computation technique then extends to the secure computation of a general definition of any polynomial computable function. The secure multi-party computing technique enables a group of mutually untrusted participants to securely compute an agreed function without relying on a trusted third party and without revealing original sensitive information other than the result. Therefore, the technology can make the data invisible, and better utilize the value of the data on the premise of meeting the compliance. Secure multi-party computing has a variety of underlying technologies, such as secret sharing, garbled circuits, and ubiquitous transmission.
Space vector secret sharing [2]Is a common secret sharing technique in secure multi-party computing. Order to
In order to be a group of participants,
for the group of participants
An access structure of (1), wherein B j Is the authorized subset. Only the participants in the authorization set cooperate to recover the secret value. p is a large prime number, the positive integer d is more than or equal to 2,
is composed of
The vector space above. Assume that there is a function Φ:
the following properties are satisfied:
(1, 0) can be represented by the set { Φ (P) } i )|P i ∈B j Linear representation of the element in
Then there is a set of constants c 0 ,c 1 ,…,c m-1 M is B j The number of middle participants such that:
secret distribution stage: the participant with secret value x first generates d-1 random numbers and constructs a vector
Then calculate
Sent to the corresponding participant P i 。
Secret recovery phase: when a grant subset B j When it is desired to recover the secret value x. Known from the secret distribution phase described above
Then
Disclosure of Invention
The invention aims to provide a general safe multiplication method based on vector space secret sharing for fixed point number, which can be used for training of privacy protection machine learning.
The vector space secret sharing-based fixed point number secure multiplication calculation method provided by the invention can give the values < x > and < y > after vector space secret sharing to the fixed point numbers x and y under the premise that data is available and invisible, and obtain the result of secure multiplication < z > = < x y >. In order to keep the fixed-point number expression consistent, the result after the secure multiplication needs to be truncated. Since the following equation holds true:
x*y＝x*(y+v)-x*v＝x*(y+v)-v*(x+u-u)
＝x*(y+v)-v*(x+u)+u*v
then:
<z>＝<x>*(y+v)-<v>*(x+u)+<u*v>
by taking the idea of multiplication triples in additive secret sharing into account, it is assumed that participants have generated vector triples (< u >, < v >, < h >) in the form of vector space secret sharing during the offline phase, and then each participant masks < x >, < y > with < u >, < v > for secure multiplication, respectively. The number of bits of a fixed-point number is represented by k, wherein the number of decimal places is f. The decimal place number will become 2f after the multiplication of two fixed-point numbers is completed, and in order to ensure that the representation mode of the result of the secure multiplication is consistent with the input of the result, the result < z > obtained by the secure multiplication needs to be cut off to obtain < z' >.
The method comprises the following specific steps:
firstly, a participant pre-generates a vector triple required by the secure multiplication in an off-line stage;
in the online stage, data in a vector space secret sharing mode is used as input, and safe multiplication calculation is carried out interactively;
and (III) carrying out truncation processing on the result obtained by the safe multiplication calculation.
In step (one), a participant pre-generates vector triples (< u >, < v >, < h >) required by the secure multiplication in an off-line stage, wherein u and v are random numbers, and h = u × v, and the specific process is as follows:
(1) Generating<u>And<v>: first of all each participant P i (i =1,2, \8230;, n) generates a random number u i And v i And respectively using vector space secret sharing technique to divide u i And v i Sharing to other participants; participants P after sharing i Respectively hold n share values<u 1 > i ,<u 2 > i ,…,<u n > i And n shares of common value<v 1 > i ,<v 2 > i ,…,<v n > i (ii) a Finally each participant P i Locally adding the shared values respectively<u> i ＝<u 1 > i +<u 2 > i +…+<u n > i ,<v> i ＝<v 1 > i +<v 2 > i +…+<v n > i I.e. required in vector triplets<u>And<v>；
(2) Generating<h>: from the above<u>And<v>the process of (1) can know that u = u 1 +u 2 +…+u n ,v＝v 1 +v 2 +…+v n And then:
h＝u*v＝(u 1 +u 2 +…+u n )*(v 1 +v 2 +…+v n )
＝u 1 *v 1 +u 1 *v 2 +…+u 1 *v n +…+u n *v 1 +u n *v 2 +…+u n *v n
each participant P i (i =1, 2.... N), h is first calculated i ＝u i *v i +[u i *v j +u j *v i ](j＝1，2,....，n；j≠i)，
Wherein u is i *v i Can be provided by each participant P i (i =1,2...., n) is calculated locally, and u & i *v j +u j *v i Is added to the secret shared value u i *v j +u j *v i ]Needs to be made by the participant P i And P j (i, j =1, 2.. Gtn.; i ≠ j) interactive security is computed, with the common techniques of transmission being at a loss. Thereafter each participant P i (i =1,2.... N.) h is shared using a vector space secret sharing technique i Sharing to other participants; after sharing is completed, all the participators respectively hold n sharing values<h 1 > i ，<h 2 > i ，...，<h n 〉 i (ii) a Finally each participant P i Locally adding the n shared values to obtain<h> i ＝<h 1 > i +<h 2 > i +…+<h n > i I.e. required in vector triplets<h>。
In the step (II), each participant takes the data in the secret sharing form as input in the online stage, and carries out safe multiplication calculation by utilizing the vector triples (< u >, < v >, < h >) pre-generated in the offline stage in an interactive way; the specific process is as follows:
first, each participant P i (i =1, 2.. N.) local computation<x> i +<u> i And<y> i +<v> i i.e. in three groups of vectors respectively<u> i ，<v> i To hide<x> i ，<y> i ；
Then, each participant P i Transmit each other own<x> i +<u> i ，<y> i +<v> i Giving other participants to recover the plaintext x + u and y + v; since x and y are already masked by the random numbers u and v, no private information about the plaintext x and y is revealed;
finally, each participant P i Local computing<z> i ＝<x> i *(y+v)-<v> i *(x+u)+<h> i I.e. the shared value of the secure multiplication result of x and y. In the process of the safe multiplication calculation, no private information is leaked, and each participant only needs 1 round of communication at the present stage, namely, only needs to communicate when the plaintext x + u and y + v are recovered, and x + u and y + v are recoveredy + v may be processed in parallel.
In the third step, the result obtained by the safe multiplication is cut off; the concrete description is as follows:
in the present invention, k represents the number of fixed-point bits, and the decimal place occupies f bits. Because the decimal place number can become 2f place after the multiplication of two fixed-point numbers is finished once, f place is required to be cut off for the result < z > obtained by the safe multiplication in order to ensure the consistency of the representation modes of the fixed-point numbers. According to the principle of vector space secret sharing technology, the following steps are carried out:
z＝c 1 *<z> 1 +c 2 *<z> 2 +…+c n *<z> n ，
wherein, c 1 ，c 2 ，...，c n Is a constant, then:
then, the safe truncation is performed on < z >, and the specific process is as follows:
first, each participant needs to pre-generate<r>And<r′>wherein r is a random number and r' = r/2 f ；
Then, each participant P i (i =1,2, \8230;, n) local computation<z> i -<r> i And send each other to the other participants to recover the plaintext z-r. Since r is a random number, z-r in the plaintext does not reveal privacy information about z;
finally, by one of the participants P i (i epsilon {1,2, \8230;, n }) is obtained by local calculation
And the other party P j (j =1,2, \ 8230;, n; j ≠ i) only needs to be set<z′> j ＝<r′> j 。<z′>Namely, is a pair<z>And performing safety truncation on the result of the f bit. No private information is leaked in the whole process of safe truncation; and at the present stage, each participant only needs 1 round of communication, namely only needs to communicate when the plaintext z-r is restored.
Drawings
Fig. 1 is a schematic flow chart of a fixed-point number secure multiplication method based on vector space secret sharing.
Detailed Description
The present invention is described in detail below with reference to the attached drawings.
In the left half of fig. 1 n participants P 1 ,P 2 ,…,P n The fixed point number in the form of secret sharing of vector space in the hands of the user<x>And<y>as input, the multiplication computation is performed safely. Wherein the fixed-point number is represented by k bits, and f represents the number of decimal places. In the whole operation process, except for the final result, no privacy information is leaked.
(1) The method comprises the following steps that a participant pre-generates vector triples (< u >, < v >, < h >) required by the safety multiplication in an off-line stage, wherein u and v are random numbers, and h = u × v;
(2) Each participant points fixed point in the form of vector space secret sharing<x>And<y>as input, pre-generated vector triplets are utilized (<u>,<v>,<h>) By using<u>,<v>Separately covering up<x>And<y>then, each participant interacts with a recovery plaintext x + u and y + v, and finally, local calculation is carried out to obtain<z> i ＝<x> i *(y+v)-<v> i *(x+u)+<h> i ；
(3) Since after one multiplication is finished<z>The decimal place of (2 f) is changed, and in order to make the representation form of the safe multiplication result identical with the input form, the safe multiplication result needs to be processed<z>Truncating the f-bit to obtain<z′>. Any one participant P i (i ∈ {0,1, \8230;, n }) local computation
The remaining participants P j (j＝0,1,…,n；jNot ≠ i) hold<z′> j ＝<r′> j 。
Example (b): here, taking a three-way multiplication as an example, assuming x =2.01 and y =3.02, a matrix is disclosed
c 1 ＝-1/2,c 2 ＝1/2,c 3 The 1/2 decimal part is two bits. (decimal is taken as an example here for ease of understanding, the same reason applies to binary.)
Inputting: three participants P 1 、P 2 、P 3 The shared values of x and y (shown in the following table) are used as input
And (3) outputting: the share value < x y >
(1) The three participants pre-generate the vector triples (< u >, < v >, < h >) required for the secure multiplication in the off-line phase, where u, v are random numbers and h = u v.
(1.1) production<u>，<v>: participant P i Respectively generate random numbers u i ，v i And respectively use vector space secret sharing technique to divide u i And v i Sharing to other participants; each participant P i Will hold 3 shares respectively<u 1 > i ，<u 2 > i ，<u 3 > i And 3 shares of value<v 1 > i ，<v 2 > i ，<v 3 > i Add to obtain<u> i ＝<u 1 > i +<u 2 > i +<u 3 > i ，<v> i ＝<v 1 > i +<v 2 > i +<v 3 > i I.e. required in vector triplets<u>And<v>specific values are shown in the following table:
(1.2) production<h>：P 1 And P 2 Collaborative security generation u 1 *v 2 +u 2 *v 1 ]，P 1 And P 3 Collaborative generation of [ u ] 1 *v 3 +u 3 *v 1 ]，P 2 And P 3 Collaborative generation of [ u ] 2 *v 3 +u 3 *v 2 ]，P 1 Local computation h 1 ＝u 1 *v 1 +[u 1 *v 2 +u 2 *v 1 ] 1 +[u 1 *v 3 +u 3 *v 1 ] 1 ，P 2 Local computation h 2 ＝u 2 *v 2 +[u 1 *v 2 +u 2 *v 1 ] 2 +[u 2 *v 3 +u 3 *v 2 ] 2 ，P 3 Local computation h 3 ＝u 3 *v 3 +[u 1 *v 3 +u 3 *v 1 ] 3 +[u 2 *v 3 +u 3 *v 2 ] 3 . Thereafter each participant P i (i =1,2, 3) using vector space secret sharing technique to divide h i Sharing to other participants; finally each participant P i Locally adding the held 3 shares to obtain<h> i ＝<h 1 > i +<h 2 > i +<h 3 > i I.e. required in vector triplets<h>. Specific values are shown in the following table:
(2) Each participant P i With the compounds produced in (1)<u>，<v>Separately covering<x>And<y>then, plaintext x + u and y + v are recovered, and finally, calculation is carried out locally to obtain<z> i ＝<x> i *(y+v)-<v> i *(x+u)+<h> i Specific values are shown in the following table:
(3) Obtained<z> i The decimal place becomes 4 bits, so two bits after the decimal point need to be cut off. First, each participant needs to pre-generate<r>And<r′>where r is a random number and r 'is the value of two digits after r truncation, where decimal point remains (equivalent to r' = r/2 in binary system) f ) (ii) a Then, each participant P i (i =1,2,3) local calculation<z> i -<r> i And recovering z-r of the plaintext. Finally, by one of the participants P i (i ∈ {1,2,3 }) (denoted here as P) 1 For example) locally calculating (z-r)/c 1 And truncating the result, reserving the last two digits of the decimal point to obtain (z-r)', and then calculating<z′> 1 ＝(z-r)′+<r′> 1 And the other party P j (j =2,3, j ≠ i) only needs to be set up<z′> j ＝<r′> j And (4) finishing. Specific values are shown in the following table:
reference documents
[1]A.C.Yao，″Protocols for secure computations，″23rd Annual Symposium on Foundations of Computer Science(sfcs 1982)，1982，pp.160-164.
[2]Brickell E F.Some ideal secret sharing schemes[C]//Workshop onthe Theory and Application of of Cryptographic Techniques.Springer，Berlin，Heidelberg，1989：468-475。
Claims (5)
1. A vector space secret sharing-based fixed point number secure multiplication calculation method is characterized in that on the premise that data can be used and cannot be seen, for fixed point numbers x and y, values < x > and < y > after vector space secret sharing are given, and a secure multiplication < z > = < x y > result is obtained; in order to keep the expression modes of the fixed point numbers consistent, the result after the safe multiplication is cut off; since the following equation holds:
x*y＝x*(y+v)-x*v＝x*(y+v)-v*(x+u-u)
＝x*(y+v)-v*(x+u)+u*v
then:
<z>＝<x>*(y+v)-<v>*(x+u)+<u*v>
suppose that a participant has generated a vector triplet (< u >, < v >, < h >) in the form of a secret share of vector space during the offline phase, after which each participant masks < x >, < y > with < u >, < v > for secure multiplications, respectively; expressing the number of bits of a fixed point number by k, wherein the number of decimal places is f; the decimal place number becomes 2f after the multiplication of the two fixed-point numbers is finished for one time; in order to ensure that the expression mode of the result of the secure multiplication is consistent with the input of the result, the result < z > obtained by the secure multiplication is subjected to truncation processing to obtain < z' >.
2. The fixed-point number secure multiplication method according to claim 1, comprising the steps of:
firstly, a participant pre-generates a vector triple required by the secure multiplication in an off-line stage;
in the online stage, data in a vector space secret sharing mode is used as input, and safe multiplication calculation is carried out interactively;
and (III) performing truncation processing on the result obtained by the secure multiplication calculation.
3. The fixed-point number secure multiplication method according to claim 2, wherein in step (one), the participant pre-generates vector triples (< u >, < v >, < h >) required for secure multiplication in an off-line phase, where u and v are random numbers and h = u × v, and the specific flow is as follows:
(1) Generating<u>And<v>: first of all each participant P i (i =1,2, \8230;, n) generating a random number u i And v i And respectively use vector space secret sharing technique to divide u i And v i Sharing to other participants; after sharing each participant P i Respectively hold n share values<u 1 > i ,<u 2 > i ,…,<u n > i And n shares of common value<v 1 > i ,<v 2 > i ,…,<v n > i (ii) a Finally each participant P i Locally adding the shared values respectively to obtain<u> i ＝<u 1 > i +<u 2 > i +…+<u n > i ,<v> i ＝<v 1 > i +<v 2 > i +…+<v n > i I.e. required in vector triplets<u>And<v>；
(2) Generating<h>: generated by the above<u>And<v>known as u = u 1 +u 2 +…+u n ,v＝v 1 +v 2 +…+v n And then:
h＝u*v＝(u 1 +u 2 +…+u n )*(v 1 +v 2 +…+v n )
＝u 1 *v 1 +u 1 *v 2 +…+u 1 *v n +…+u n *v 1 +u n *v 2 +…+u n *v n
each participant P i (i =1,2, \8230;, n), h is first calculated i ＝u i *v i +[u i *v j +u j *v i ]J =1,2, \ 8230;, n; j is not equal to i, wherein u i *v i By each participant P i (i =1,2, \8230;, n) is calculated locally, and u i *v j +u j *v i Added secret shared value of [ u ] i *v j +u j *v i ]By a participant P i And P j (i, j =1,2, \ 8230;, n; i ≠ j) interactionsObtaining through safety calculation; then each participant P i (i =1,2, \8230;, n) secret sharing technique using vector space i Sharing to other participants; after sharing is completed, all the participators respectively hold n shares of shared values<h 1 > i ,<h 2 > i ,…,<h n > i (ii) a Finally each participant P i Locally adding the n shared values to obtain<h> i ＝<h 1 > i +<h 2 > i +…+<h n > i I.e. required in vector triplets<h>。
4. The fixed-point secure multiplication method according to claim 3, wherein in step (two), the participating parties perform secure multiplication using vector triples (< u >, < v >, < h >) pre-generated in an offline stage with data in a secret sharing form as input in the online stage; the specific process comprises the following steps:
first, each participant P i (i =1,2, \8230;, n) local computation<x> i +<u> i And<y> i +<v> i i.e. in three groups of vectors respectively<u> i ,<v> i To cover up<x> i ,<y> i ；
Then, each participant P i Mutually transmit the information held by themselves<x> i +<u> i ,<y> i +<v> i Giving other participants to recover the plaintext x + u and y + v;
finally, each participant P i Local computing<z> i ＝<x> i *(y+v)-<v> i *(x+u)+<h> i I.e. the shared value of the secure multiplication results of x and y.
5. The fixed-point-number secure multiplication method according to claim 4, wherein in step (three), the result obtained by the secure multiplication is truncated; the principle of the vector space secret sharing technology is as follows:
z＝c 1 *<z> 1 +c 2 *<z> 2 +…+c n *<z> n ，
wherein, c 1 ,c 2 ,…,c n Is a constant, then:
then, the process of safely truncating < z > includes:
first, each participant needs to pre-generate<r>And<r′>wherein r is a random number and r' = r/2 f ；
Then, each participant P i (i =1,2, \8230;, n) local computation<z> i -<r> i And mutually send to other participants to recover the z-r of the plaintext;
finally, by one of the participants P i (i epsilon {1,2, \8230;, n }) is obtained by local calculation
And the other party P j (j =1,2, \ 8230;, n; j ≠ i) only needs to be set<z′> j ＝<r′> j ；<z′>Namely, is a pair<z>And performing safety truncation on the result of the f bit.
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Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN115982747A (en) * | 2023-03-20 | 2023-04-18 | 建信金融科技有限责任公司 | Secure multiparty multiplication method, device, equipment, medium and product thereof |
| CN116108473A (en) * | 2023-04-10 | 2023-05-12 | 极术(杭州)科技有限公司 | Data processing method and device in multiparty security calculation |
| CN117009723A (en) * | 2023-09-27 | 2023-11-07 | 长春吉大正元信息技术股份有限公司 | Multiparty computing method, device, equipment and storage medium |
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN115982747A (en) * | 2023-03-20 | 2023-04-18 | 建信金融科技有限责任公司 | Secure multiparty multiplication method, device, equipment, medium and product thereof |
| CN116108473A (en) * | 2023-04-10 | 2023-05-12 | 极术(杭州)科技有限公司 | Data processing method and device in multiparty security calculation |
| CN116108473B (en) * | 2023-04-10 | 2023-06-27 | 极术(杭州)科技有限公司 | Data processing method and device in multiparty security calculation |
| CN117009723A (en) * | 2023-09-27 | 2023-11-07 | 长春吉大正元信息技术股份有限公司 | Multiparty computing method, device, equipment and storage medium |
| CN117009723B (en) * | 2023-09-27 | 2024-01-30 | 长春吉大正元信息技术股份有限公司 | Multiparty computing method, device, equipment and storage medium |
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