CN113821824A - Triple generation method and system based on careless linear evaluation (OLE) - Google Patents
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Abstract
The invention relates to a triplet generation method and a triplet generation system based on an inadvertent linear evaluation (OLE), wherein the triplet generation method comprises the following steps: step 1: generating a plurality of groups of mutually-associated random arrays based on the careless linear evaluation OLE, and constructing an OLE pool; step 2: and obtaining legal triplets MT by utilizing the random array in the OLE pool. The triple generating system includes: a storage module; the random array generating module is used for generating random arrays (u, v) and (x, w) based on the careless linear evaluation OLE, storing the random arrays on the storage module and constructing an OLE pool; and the triple MT generation module is used for calling the random array from the storage module to generate a triple MT. Compared with the prior art, the invention has the advantages of effectively reducing network communication traffic, improving service expandability and the like.
Description
Technical Field
The invention relates to the technical field of privacy computation, in particular to a triplet generation method and a triplet generation system based on an inadvertent linear evaluation (OLE).
Background
In the era of big data networking, the privacy protection problem of sensitive data becomes a prominent problem to be solved urgently, and in order to enable data to flow (available and invisible) without exposure, privacy computation plays an important role as a main tool and means in a series of environments requiring privacy protection, such as block chain, federal learning and the like.
In common privacy computation, operators of two-party privacy protection computation, such as two-party safe four-rule operation, comparison operation and the like, become the basis for constructing privacy computation. However, due to the calculation overhead and the network overhead of the existing implementation scheme, the calculation efficiency of the existing scheme cannot be well improved when the existing scheme is applied to large-scale data operation.
One of the schemes capable of realizing generation of multiplication pairs in the prior art is a generation method based on homomorphic encryption, and the bottleneck of the method is embodied in two aspects; first, due to the introduction of a homomorphic encryption algorithm, the computational performance for the generation of a large number of MTs is completely dependent on the speed of the underlying homomorphic encryption scheme. It is well known that the speed of homomorphic encryption is much slower than symmetric encryption operations, and therefore, this is a factor that limits the widespread use of this scheme; secondly, since the ciphertext of the homomorphic encryption algorithm is expanded by at least 32 times compared with the plaintext, the overhead of network communication is significantly increased in the transmission process. The second scheme capable of generating the multiplication pair in the prior art is to generate the MT by using Random-out (ROT), which requires the receiver to input a selection bit first, so that two values need to be determined first before the ROT is performed, which results in the operation of the ROT depending on the selection of the Random number, which is seriously disadvantageous to the early generation of the ROT (that is, the ROT must be coupled in the MT generation process); in addition, because the generation of the ROT needs to consume a large amount of bandwidth, the network communication overhead of the whole scheme is large. The two methods are not suitable for large-scale popularization, and the communication overhead of the network is also large.
Disclosure of Invention
The present invention aims to overcome the above-mentioned drawbacks of the prior art and provide a triplet generating method and system based on an inadvertent linear evaluation OLE, which effectively reduces the network traffic and improves the scalability of the service.
The purpose of the invention can be realized by the following technical scheme:
a triplet generating method for linear evaluation OLE based on carelessness, the triplet generating method comprising:
step 1: generating a plurality of groups of mutually-associated random arrays based on the careless linear evaluation OLE, and constructing an OLE pool;
step 2: and obtaining legal triplets MT by utilizing the random array in the OLE pool.
Preferably, the method for generating a group of correlated random numbers in step 1 includes:
P0reception finite field FnTwo random numbers (u, v), P1Reception finite field FnTwo random numbers (x, w) above, satisfying w ═ ux + v, where P0And P1Respectively, two parties participating in privacy computation.
Preferably, the construction method of the OLE pool is as follows:
P0storing each group of mutually associated random numbers (u, v) on corresponding storage devices to construct a first OLE pool;
P1and storing each group of the correlated random numbers (x, w) on the corresponding storage device to construct a second OLE pool.
Preferably, the step 2 specifically comprises:
step 2-1: p0Randomly selecting a finite field FnFour random numbers a of0、b0R and S, and calculating a0b0;
Step 2-2: p1Randomly selecting a finite field FnTwo random numbers a of1And b1And calculate a1b1;
Step 2-3: p0And P1Selecting two OLE pairs (u) from the first OLE pool and the second OLE pool respectively0,v0) And (x, w)0) And (u)1,v1) And (x, w)1);
Step 2-4: p1Calculating and transmitting alpha0=b1-x and a1=a1-x for P0;
Step 2-5: p0Calculating and transmitting beta0=a0-u0、β1=b0-u1、γ0=a0u0+R-v0And gamma1=a1u1+S-v1To P1;
Step 2-6: p0Let c0=a0b0-R-S,P1Let c1=a1b1+β0b1+γ0+w0+β1a1+γ1+w1;
Step 2-7: completing a triplet (a)0,b0,c0) And (a)1,b1,c1) And (4) generating.
More preferably, two OLE pairs in the step 2-3 satisfy:
more preferably, said triad (a)0,b0,c0) And (a)1,b1,c1) Satisfies the following conditions:
(a0+a1)(b0+b1)=c0+c1。
a triplet generating system for use in the above triplet generating method, the triplet generating system comprising:
a storage module;
the random array generating module is used for generating random arrays (u, v) and (x, w) based on the careless linear evaluation OLE, storing the random arrays on the storage module and constructing an OLE pool;
and the triple MT generation module is used for calling the random array from the storage module to generate a triple MT.
Preferably, the random array generating module is specifically:
P0reception finite field FnTwo random numbers (u, v), P1Reception finite field FnTwo random numbers (x, w) above, satisfying w ═ ux + v, where P0And P1Respectively two parties participating in privacy calculation;
the construction method of the OLE pool comprises the following steps:
P0storing each group of mutually associated random numbers (u, v) on corresponding storage devices to construct a first OLE pool;
P1and storing each group of the correlated random numbers (x, w) on the corresponding storage device to construct a second OLE pool.
Preferably, the triplet MT generating module is specifically:
P0randomly selecting a finite field FnFour random numbers a of0、b0R and S, and calculating a0b0;
P1Randomly selecting a finite field FnTwo random numbers a of1And b1And calculate a1b1;
P0And P1Selecting two OLE pairs (u) from the first OLE pool and the second OLE pool respectively0,v0) And (x, w)0) And (u)1,v1) And (x, w)1);
P1Calculating and transmitting alpha0=b1-x and a1=a1-x for P0;
P0Calculating and transmitting beta0=a0-u0、β1=b0-u1、γ0=a0u0+R-v0And gamma1=a1u1+S-v1To P1;
P0Let c0=a0b0-R-S,P1Let c1=a1b1+β0b1+γ0+w0+β1a1+γ1+w1;
Completing a triplet (a)0,b0,c0) And (a)1,b1,c1) And (4) generating.
More preferably, the two OLE pairs satisfy:
triplet (a)0,b0,c0) And (a)1,b1,c1) Satisfies the following conditions:
(a0+a1)(b0+b1)=c0+c1。
compared with the prior art, the invention has the following beneficial effects:
one, effectively reduce network traffic: in addition, compared with the ROT-based method, the ROT method completes the generation of an MT pair through 128 ROTs and 128 integer communication, but the method in the invention can be completed only by 6 integers, thereby greatly reducing the time required by the generation of the MT pair and the network communication overhead.
Secondly, improving the expandability of the service: the triplet generation method and the system based on the careless linear evaluation OLE decouple the ROT in the generation process of the MT, change the architecture of the system again, and can increase the corresponding service calculation/storage performance according to the corresponding requirements when the requirements of the OLE service or the MT service performance are increased, thereby effectively improving the expandability of the online calculation service.
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FIG. 1 is a schematic flow chart of a triple generation method according to the present invention;
fig. 2 is a schematic diagram of an implementation manner of online computing in the embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, not all, embodiments of the present invention. All other embodiments, which can be obtained by a person skilled in the art without any inventive step based on the embodiments of the present invention, shall fall within the scope of the present invention.
One of the schemes for generating multiplication pairs in the prior art is a generation method based on homomorphic encryption, which includes:
A.P0generating a pair of public and private keys (sk, pk) of PHE (semi-homomorphic encryption), and then sending the public key pk to P1;
B.P0Random selection of FnAn integer of (a)0And b0Encrypting to obtain E (a)0) And E (b)0) And sent to P1;
C.P1Random selection of FnAn integer of (a)1、b1And r, order c1=a1b1-r;
E.P0Calculating a0b0Decryption of a0b1+a1b0+ r, and c0=a0b0+a0b1+a1b0+r。
Thus, P0And P1An MT is calculated by homomorphic encryption.
The bottleneck of this scheme is represented in two aspects. Firstly, due to the introduction of a homomorphic encryption algorithm, for the generation of a large number of MTs, the calculation performance completely depends on the speed of an underlying homomorphic encryption scheme, and as is well known, the speed of homomorphic encryption is far slower than that of symmetric encryption operation, so that the scheme is a factor for limiting the wide use; secondly, since the ciphertext of the homomorphic encryption algorithm is expanded by at least 32 times compared with the plaintext, the overhead of network communication is significantly increased in the transmission process.
The second prior art scheme is to use ROT to generate MT, and before introducing the second prior art scheme, the function of ROT is introduced:
first, ROT requires that both computing parties have two roles, i.e., sender and receiver. For the sender, through the ROT, the sender receives two random bit strings(s) with length λ0,s1) (ii) a For the receiver, the receiver needs to take a selection bit b as input, and through the ROT, the receiver will receive sb。
How to generate MT using ROT is described below, assuming that a hash function h (—) can map a bit string of length λ to FnThe method comprises the following steps:
A.P0random selection of FnAn integer of (a)0And b0,P1Random selection of FnAn integer of (a)1And b1;
B.P0As a sender, P1As the receiving party with b1Each bit b of1[i]Make 64 ROTs for the input, thus P0To obtainP1To obtainP0ComputingAnd sent to P1;
D.P1As a sender, P0As the receiving party with b0Each bit b of0[i]Make 64 ROTs for the input, thus P1To obtainP0To obtainP1ComputingAnd sent to P0;
The above procedure achieves the final result by 128 ROT.
For ROT, the receiver is required to input a selection bit first, therefore, b0And b1Is first determined before the ROT is performed. This results in the running of the ROT depending on the choice of random number, which is seriously disadvantageous for the early generation of the ROT (i.e. the ROT must be coupled in the MT generation process). In addition, because the generation of the ROT consumes a large amount of bandwidth, the network communication overhead of the whole scheme is large.
The invention improves the existing MT generation scheme and improves the MT generation efficiency. Meanwhile, the generation process of random number correlation and the generation process of MT are completely decoupled, so that the online calculation and the network traffic are reduced.
The embodiment relates to a triplet generation method based on an inadvertent linear evaluation OLE, and the flow of the method is shown in fig. 1, and includes:
step 1: generating a plurality of groups of mutually-associated random arrays based on the careless linear evaluation OLE, and constructing an OLE pool;
P0reception finite field FnTwo random numbers (u, v), P1Reception finite field FnTwo random numbers (x, w) above, satisfying w ═ ux + v, where P0And P1Respectively two parties participating in privacy calculation;
the construction method of the OLE pool comprises the following steps:
P0storing each group of mutually associated random numbers (u, v) on corresponding storage devices to construct a first OLE pool;
P1storing each group of the correlated random numbers (x, w) on the corresponding storage device to construct a second OLE pool;
step 2: and obtaining legal triplets MT by utilizing the random array in the OLE pool.
Step 2-1: p0Randomly selecting a finite field FnFour random numbers a of0、b0R and S, and calculating a0b0;
Step 2-2: p1Randomly selecting a finite field FnTwo random numbers a of1And b1And calculate a1b1;
Step 2-3: p0And P1Selecting two OLE pairs (u) from the first OLE pool and the second OLE pool respectively0,v0) And (x, w)0) And (u)1,v1) And (x, w)1) Two OLE pairs satisfy:
w0=u0x+v0
w1=u1x+v1
step 2-4: p1Calculating and transmitting alpha0=b1-x and a1=a1-x for P0;
Step 2-5: p0Calculating and transmitting beta0=a0-u0、β1=b0-u1、γ0=a0u0+R-v0And gamma1=a1u1+S-v1To P1;
Step 2-6: p0Let c0=a0b0-R-S,P1Let c1=a1b1+β0b1+γ0+w0+β1a1+γ1+w1;
Step 2-7: completing a triplet (a)0,b0,c0) And (a)1,b1,c1) Generating;
triplet (a)0,b0,c0) And (a)1,b1,c1) Satisfies the following conditions: (a)0+a1)(b0+b1)=c0+c1。
The embodiment also relates to a triplet generation system for the triplet generation method, which includes:
a storage module;
the random array generating module is used for generating random arrays (u, v) and (x, w) based on the careless linear evaluation OLE, storing the random arrays on the storage module and constructing an OLE pool;
and the triple MT generation module is used for calling the random array from the storage module to generate a triple MT.
The random array generation module is specifically as follows:
P0reception finite field FnTwo random numbers (u, v), P1Reception finite field FnTwo random numbers (x, w) above, satisfying w ═ ux + v, where P0And P1Respectively two parties participating in privacy calculation;
the construction method of the OLE pool comprises the following steps:
P0storing each group of mutually associated random numbers (u, v) on corresponding storage devices to construct a first OLE pool;
P1and storing each group of the correlated random numbers (x, w) on the corresponding storage device to construct a second OLE pool.
The triple MT generation module specifically comprises:
P0randomly selecting a finite field FnFour random numbers a of0、b0R and S, and calculating a0b0;
P1Randomly selecting a finite field FnTwo random numbers a of1And b1And calculate a1b1;
P0And P1Selecting two OLE pairs (u) from the first OLE pool and the second OLE pool respectively0,v0) And (x, w)0) And (u)1,v1) And (x, w)1);
P1Calculating and transmitting alpha0=b1-x and a1=a1-x for P0;
P0Calculating and transmitting beta0=a0-u0、β1=b0-u1、γ0=a0u0+R-v0And gamma1=a1u1+S-v1To P1;
P0Let c0=a0b0-R-S,P1Let c1=a1b1+β0b1+γ0+w0+β1a1+γ1+w1;
Completing a triplet (a)0,b0,c0) And (a)1,b1,c1) And (4) generating.
Two OLE pairs satisfy:
triplet (a)0,b0,c0) And (a)1,b1,c1) Satisfies the following conditions:
(a0+a1)(b0+b1)=c0+c1。
the present embodiment provides an online computing service system using the triplet generating method, and the structure of the online computing service system is shown in fig. 2, and includes:
and (3) a service layer: composed of an OLE service and an MT service in an offline phase, in which the OLE service is used
The online calculation method comprises an OLE service, an MT service and an online calculation service, wherein the OLE service is used for generating mutually-correlated random arrays based on careless linear evaluation of the OLE, the MT service is used for generating triples MT, the OLE service and the MT service are offline services, the OLE service provides offline services for the MT service, and the MT service provides offline services for the online calculation service.
A storage layer: all service level storage is stored in a Redis cluster form. The MT may also be calculated directly from the MTs stored within the Redis cluster when it needs to be called by an online service. In addition, if too much random number information is generated by the offline service, then it needs to be further considered to export this information from Redis to a file or database.
While the invention has been described with reference to specific embodiments, the invention is not limited thereto, and various equivalent modifications and substitutions can be easily made by those skilled in the art within the technical scope of the invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.
Claims (10)
1. A triplet generation method based on an inadvertent linear evaluation (OLE), the triplet generation method comprising:
step 1: generating a plurality of groups of mutually-associated random arrays based on the careless linear evaluation OLE, and constructing an OLE pool;
step 2: and obtaining legal triplets MT by utilizing the random array in the OLE pool.
2. The method as claimed in claim 1, wherein the generating method of the correlated random array in step 1 is as follows:
P0reception finite field FnTwo random numbers (u, v), P1Reception finite field FnTwo random numbers (x, w) above, satisfying w ═ ux + v, where P0And P1Respectively, two parties participating in privacy computation.
3. The method of claim 1, wherein the method for constructing the OLE pool comprises:
P0storing each group of mutually associated random numbers (u, v) on corresponding storage devices to construct a first OLE pool;
P1and storing each group of the correlated random numbers (x, w) on the corresponding storage device to construct a second OLE pool.
4. The method for generating triples based on an inadvertent linear evaluation OLE according to claim 1, wherein the step 2 specifically comprises:
step 2-1: p0Randomly selecting a finite field FnFour random numbers a of0、b0R and S, and calculating a0b0;
Step 2-2: p1Randomly selecting a finite field FnTwo random numbers a of1And b1And calculate a1b1;
Step 2-3: p0And P1Selecting two OLE pairs (u) from the first OLE pool and the second OLE pool respectively0,v0) And (x, w)0) And (u)1,v1) And (x, w)1);
Step 2-4: p1Calculating and transmitting alpha0=b1-x and a1=a1-x for P0;
Step 2-5: p0Calculating and transmitting beta0=a0-u0、β1=b0-u1、γ0=a0u0+R-v0And gamma1=a1u1+S-v1To P1;
Step 2-6: p0Let c0=a0b0-R-S,P1Let c1=a1b1+β0b1+γ0+w0+β1a1+γ1+w1;
Step 2-7: completing a triplet (a)0,b0,c0) And (a)1,b1,c1) And (4) generating.
6. the method of claim 4, wherein the triplet (a) is generated based on the OLE0,b0,c0) And (a)1,b1,c1) Satisfies the following conditions:
(a0+a1)(b0+b1)=c0+c1。
7. a triplet generation system for use in the triplet generation method of claim 1 wherein the triplet generation system comprises:
a storage module;
the random array generating module is used for generating random arrays (u, v) and (x, w) based on the careless linear evaluation OLE, storing the random arrays on the storage module and constructing an OLE pool;
and the triple MT generation module is used for calling the random array from the storage module to generate a triple MT.
8. The triplet generating system according to claim 7, wherein the random array generating module specifically comprises:
P0reception finite field FnTwo random numbers (u, v), P1Reception finite field FnTwo random numbers (x, w) above, satisfying w ═ ux + v, where P0And P1Respectively two parties participating in privacy calculation;
the construction method of the OLE pool comprises the following steps:
P0storing each group of mutually associated random numbers (u, v) on corresponding storage devices to construct a first OLE pool;
P1and storing each group of the correlated random numbers (x, w) on the corresponding storage device to construct a second OLE pool.
9. The triplet generation system according to claim 7, wherein the triplet MT generation module specifically comprises:
P0randomly selecting a finite field FnFour random numbers a of0、b0R and S, and calculating a0b0;
P1Randomly selecting a finite field FnTwo random numbers a of1And b1And calculate a1b1;
P0And P1Selecting two OLE pairs (u) from the first OLE pool and the second OLE pool respectively0,v0) And (x, w)0) And (u)1,v1) And (x, w)1);
P1Calculating and transmitting alpha0=b1-x and a1=a1-x for P0;
P0Calculating and transmitting beta0=a0-u0、β1=b0-u1、γ0=a0u0+R-v0And gamma1=a1u1+S-v1To P1;
P0Let c0=a0b0-R-S,P1Let c1=a1b1+β0b1+γ0+w0+β1a1+γ1+w1;
Completing a triplet (a)0,b0,c0) And (a)1,b1,c1) And (4) generating.
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