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CN110362537B - Full-parameter private information retrieval method based on sawtooth decoding - Google Patents

Full-parameter private information retrieval method based on sawtooth decoding Download PDF

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CN110362537B
CN110362537B CN201910615099.9A CN201910615099A CN110362537B CN 110362537 B CN110362537 B CN 110362537B CN 201910615099 A CN201910615099 A CN 201910615099A CN 110362537 B CN110362537 B CN 110362537B
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CN110362537A (en
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代明军
郑子英
邓海燕
林晓辉
苏恭超
陈彬
王晖
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Shenzhen University
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    • H04L1/004—Arrangements for detecting or preventing errors in the information received by using forward error control
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    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
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Abstract

The invention discloses a full-parameter private information retrieval method based on sawtooth decoding, which comprises the following steps: step S10, dividing m files into k alpha system packets, storing the k system packets in k system nodes of a distributed storage system, determining an encoding matrix, acquiring an encoding packet according to the encoding matrix, and storing the encoding packet in alpha parity check nodes; step S20, generating a query matrix, wherein the query matrix comprises a random matrix and a retrieval matrix, and querying the distributed storage system; and step S30, performing data decoding on the second data packet returned by the nodes, wherein the nodes comprise a system node and a parity check node. The invention can be suitable for all parameters, improves the application range, and has low calculation complexity and low communication cost.

Description

Full-parameter private information retrieval method based on sawtooth decoding
Technical Field
The invention belongs to the technical field of information retrieval, and particularly relates to a full-parameter private information retrieval method based on sawtooth decoding.
Background
At present, the technology of information retrieval is becoming more mature, for example, patent application No. CN107992582A, which is named as a private information retrieval method based on zigzag decoding, and only (2k, k) private information retrieval based on zigzag decoding is performed, that is, the method is only applicable to the case where n is 2k, but in practice, n and k are arbitrary, and have certain limitations in application, and thus, the problem of low practicability exists.
Therefore, the prior art is to be improved.
Disclosure of Invention
The invention mainly aims to provide a full-parameter private information retrieval method based on sawtooth decoding, aims to solve the technical problems mentioned in the background technology, and can be suitable for (n, k) of full parameters in the aspect of information retrieval, thereby improving the application range.
The invention discloses a full-parameter private information retrieval method based on sawtooth decoding, which comprises the following steps:
step S10, m files S1,s2,…smDividing the system into k alpha system packets, storing the system packets in k system nodes of a distributed storage system, determining a coding matrix, obtaining a coding packet according to the coding matrix, and storing the coding packet in alpha parity check nodes, wherein the distributed storage system has n nodes in total, alpha is n-k, and the coding matrix
Figure BDA0002123667100000011
Step S20, generating a query matrix, wherein the query matrix comprises a random matrix U and a retrieval matrix Ef,lQuerying the distributed storage system;
and step S30, performing data decoding on the second data packet returned by the nodes, wherein the nodes comprise a system node and a parity check node.
Preferably, in step S10, the obtaining the encoded packet according to the encoding matrix includes:
and S100, shifting the corresponding bit of the systematic packet of each line of the file to the right according to the line vector element of the coding matrix T, and adding in a binary field to obtain a coding packet.
Preferably, step S30 specifically includes:
step S31, after receiving the query matrix, the nodes of the distributed storage system shift the first data packet stored in the nodes to the right by corresponding bits according to the row vector elements of the query matrix, then add in the binary domain to obtain the second data packet, and the nodes return the obtained second data packet;
step S32, a first result packet returned by the system node and a second result packet returned by the parity check node are obtained, the first result packet is right-shifted by corresponding bits according to the row vector elements of the CP-BZD code coding matrix, then binary field addition is carried out to obtain a third data packet, and then the third data packet and the second result packet are subjected to zigzag decoding to obtain a fourth data packet, wherein the second data packet comprises the first result packet and the second result packet;
step S33, performing zigzag decoding on the fourth packet, and solving a total of α k systematic packets.
Preferably, when n <2k, step S20 specifically includes:
in the step of S21,
generating a retrieval matrix and a random matrix in the query matrix, the random matrix being
Figure BDA0002123667100000021
The search matrix is Ef,l，
Figure BDA0002123667100000022
Ef,1Is the search matrix sent by the user to the first node, where r is n-k, and when l is 2, …, k, Ef,lIs composed of Ef,l-1The row vector is obtained by cyclic shift once;
in step S22, the user sends the query matrix to the corresponding node.
Preferably, when n ≧ 2k, step S20 specifically includes:
step S25, generating a retrieval matrix and a random matrix in the query matrix, wherein the random matrix is a random matrix
Figure BDA0002123667100000023
Retrieval matrix Ef,l＝[E1,…,Ef,…,Em],l∈{k+1,k+2,…,n}；
Step S26, sending the random matrix to the system node
Figure BDA0002123667100000031
The random matrix and the search matrix are sent to the parity check nodes.
The full-parameter private information retrieval method based on the sawtooth decoding has the following beneficial effects:
the invention is a private information retrieval scheme based on sawtooth decoding in a distributed storage system, which adopts a binary shift addition technology and can meet the requirements: the user downloads the file and does not display which file is being downloaded. Because binary shift-add and zigzag decoding are used, the computational complexity is relatively low. The communication cost is also low. The present invention can be applied to any (n, k) system, and is not limited to n ═ 2 k.
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FIG. 1 is a schematic flowchart of a full parameter private information retrieval method based on sawtooth decoding according to a first embodiment of the present invention;
fig. 2 is a schematic diagram illustrating a refinement process of obtaining a coded packet according to a coding matrix in a first embodiment;
fig. 3 is a detailed flowchart of step S30 in the first embodiment;
FIG. 4 is a detailed flowchart of step S20 if n is less than 2k in the first embodiment;
FIG. 5 is a schematic diagram illustrating a detailed flow of step S20 if n is greater than or equal to 2k in the first embodiment;
FIG. 6 is a diagram illustrating a full parameter private information retrieval method based on sawtooth decoding according to the present invention
Figure BDA0002123667100000032
A coded packet decoding process;
FIG. 7 is a diagram illustrating a full parameter private information retrieval method based on sawtooth decoding according to the present invention
Figure BDA0002123667100000033
A sawtooth decoding process.
The implementation, functional features and advantages of the objects of the present invention will be further explained with reference to the accompanying drawings.
Detailed Description
It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. It is noted that relative terms such as "first," "second," and the like may be used to describe various components, but these terms are not intended to limit the components. These terms are only used to distinguish one component from another component. For example, a first element could be termed a second element, and, similarly, a second element could be termed a first element, without departing from the scope of the present invention. The term "and/or" refers to a combination of any one or more of the associated items and the descriptive items.
As shown in fig. 1, fig. 1 is a schematic flowchart of a full-parameter private information retrieval method based on zigzag decoding according to a first embodiment of the present invention;
the invention discloses a full-parameter private information retrieval method based on sawtooth decoding, which comprises the following steps:
step S10, m files S1,s2,…smDividing into k alpha system packets, storing in k system nodes of distributed storage system, and using CP-BZD code to make m files s1,s2,…smEncoding is carried out, and an encoding matrix is determined according to k and alpha
Figure BDA0002123667100000041
Obtaining coded packets from a coding matrix
Figure BDA0002123667100000042
Storing the encoded packets in alpha parity check nodes, wherein n nodes are shared in the distributed storage system, and alpha is n-k, and the encoding matrix
Figure BDA0002123667100000043
In step S10, for example, such as
Figure BDA0002123667100000044
siRepresents the ith file, i ∈ {1,2, …, m },
Figure BDA0002123667100000045
to represent
Figure BDA0002123667100000046
The w-th bit of (a) e {1,2, …, α }, b e {1,2, …, k }; for coded packet
Figure BDA0002123667100000047
Wherein i represents the same as siThe files are related, x is obtained by encoding the x-th row of encoding vectors of the encoding matrix T, x belongs to {1,2, …, alpha }, y is the y-th encoding packet formed by encoding the same encoding vector of the same file, and y belongs to {1,2, …, alpha }. In particular, the document siThe system package in the jth column of (1) is stored in the jth node, j belongs to {1,2, …, k }, and the k nodes are called system nodes because the system package is stored; the coded packet obtained from the x-th row of coded vectors is stored in the k + x-th node, and since the coded packet is stored, the α -n-k nodes are called parity nodes.
For example, suppose that the distributed storage system has n-5 nodes, where k-3 nodes are used for storing system packets and are called system nodes, n-k-2 nodes are used for storing coding packets and are called parity check nodes, and the system stores m-3 files, each of which is s1,s2,s3. The user wants to retrieve a document sfI.e. f is 1 and α is n-k is 2, then the document siIs divided into 6 systematic packets, the bit length of each data packet is set as L10,
Figure BDA0002123667100000051
node 1 stores siFirst column of (2), node 2 stores siSecond column of (3), node 3 stores siThe third column of (c), since the system stores 3 files, each node stores 6 packets. Coding matrix
Figure BDA0002123667100000052
siAccording to the vector [0,1,2 ] in the matrix T]Bit shifting is carried out, and then the bit shifting and the binary field addition are carried out to obtain a coded packet which comprises
Figure BDA0002123667100000053
Figure BDA0002123667100000054
And stored in node 4. siAccording to the vector 0,2,4 in the matrix T]Bit shifting to obtain coded packet, the coded packet comprises
Figure BDA0002123667100000055
Figure BDA0002123667100000056
And stored in the node 5. I.e., nodes 4 and 5 are parity nodes. This example is used to explain a simple application of the present application, and the following examples are related to this example. Wherein a bit represents a bit value comprising the values of the row vector elements in the coding matrix.
Step S20, generating a query matrix, wherein the query matrix comprises a random matrix U and a retrieval matrix Ef,lQuerying the distributed storage system;
in step S20, when the user searches for a document, a query matrix is generated, where the query matrix includes a random matrix U and a search matrix Ef,lQuerying the distributed storage system; specific examples of step S20 of the present embodiment are described together with step S30, which will be described in the following embodiments.
And step S30, performing data decoding on the second data packet returned by the nodes, wherein the nodes comprise a system node and a parity check node.
The full-parameter private information retrieval method based on the sawtooth decoding has the following beneficial effects:
the invention is a private information retrieval scheme based on sawtooth decoding in a distributed storage system, which adopts a binary shift addition technology and can meet the requirements: the user downloads the file and does not display which file is being downloaded. Because binary shift-add and zigzag decoding are used, the computational complexity is relatively low. The communication cost is also low. The present invention can be applied to any (n, k) system, and is not limited to n ═ 2 k. The difference between the present invention and the comparison document mentioned in the background art lies in the difference of the coding matrix T constructed in step S10 and the document being divided into k α parts to adapt to the full parameters (n, k); n represents the total number of nodes in the distributed storage system, and k represents the number of system nodes; the nodes include system nodes and parity nodes.
As shown in fig. 2, preferably, in step S10, the obtaining of the encoded packet according to the encoding matrix includes:
step S100, using CP-BZD code to m files S1,s2,…smCoding is carried out, and the systematic packets in each row of the file are right-shifted by corresponding bits according to row vector elements of the coding matrix T;
step S101, adding in binary field to obtain coding packet.
For step S100 and step S101, for example, the coding matrix
Figure BDA0002123667100000061
siAccording to the vector [0,1,2 ] in the matrix T]Bit shifting and adding in binary domain to obtain coded packet
Figure BDA0002123667100000062
Figure BDA0002123667100000063
The encoded packets are stored in parity check nodes.
As shown in fig. 3, preferably, step S30 specifically includes:
step S31, after receiving the query matrix, the nodes of the distributed storage system shift the first data packet stored in the nodes to the right by corresponding bits according to the row vector elements of the query matrix, then add in the binary domain to obtain the second data packet, and the nodes return the obtained second data packet;
in step S31, together with step S20, for example, the user needs to send k ═ 3 times of queries to each node, and the three queries can unify the query contents sent by the user to each node into a 3 × 6 random matrix and a 3 × 6 searchAnd (4) matrix. Setting random matrix
Figure BDA0002123667100000071
Since r-n-k-2, the search matrix sent to node 1 is
Figure BDA0002123667100000072
The search matrix sent to node 2 passes through E1,1Is shifted to obtain
Figure BDA0002123667100000073
The search matrix sent to node 3 passes through E1,2Is shifted to obtain
Figure BDA0002123667100000074
E1,4＝E1,5＝[0]. So that the query matrix sent by the user to the node is Q1＝U+E1,1，Q2＝U+E1,2，Q3＝U+E1,3，Q4＝U，Q5The subscript of Q denotes a query matrix sent to the corresponding node, e.g. Q1Is the query matrix sent to node 1. The ith row of the query matrix is the ith query of the user for the node, i ∈ {1,2,3 }. Data stored by node 1 is according to Q1The row vector elements are subjected to bit shift and then correspondingly added in a binary domain to obtain
Figure BDA0002123667100000075
Three packets and then node 1 returns the three packets to the user. The nodes 2 will
Figure BDA0002123667100000076
Returning to the user, node 3 will
Figure BDA0002123667100000077
Returning to the user, node 4 will
Figure BDA0002123667100000078
Returning to the user, node 5 will
Figure BDA0002123667100000079
Returning to the user; i.e. the second packet comprises the return of node 1
Figure BDA00021236671000000710
Three data packets, node 2 returning
Figure BDA00021236671000000711
Three data packets, node 3 returns
Figure BDA00021236671000000712
Three data packets, node 4 returning
Figure BDA00021236671000000713
Three data packets and returned by node 5
Figure BDA00021236671000000714
Three data packets.
Step S32, obtaining a first result packet returned by the system node and a second result packet returned by the parity node, right-shifting the first result packet by corresponding bits according to the row vector element of the CP-BZD code encoding matrix, then performing binary field addition to obtain a third data packet, and performing zigzag decoding on the third data packet and the second result packet to obtain a fourth data packet, where the second data packet includes the first result packet and the second result packet.
Step S33, performing zigzag decoding on the fourth packet, and decoding α k systematic packets.
In the above steps S32 and S33, step S31, step S32 and step S33 are applied to both cases where n <2k and n ≧ 2 k.
For step S32 and step S33, for example, for
Figure BDA00021236671000000715
Right-shifting the corresponding bit with respect to (0,1,2) in the coding matrix T is performed and then binary field addition is performed to obtain a third packet, which is
Figure BDA0002123667100000081
Then to
Figure BDA0002123667100000082
Performing sawtooth decoding
Figure BDA0002123667100000083
As shown in fig. 6. To pair
Figure BDA0002123667100000084
Bit shifting with respect to the coding matrix T (0,2,4) is performed, and the third packet is binary field added to
Figure BDA0002123667100000085
Then to
Figure BDA0002123667100000086
Performing sawtooth decoding
Figure BDA0002123667100000087
Then to
Figure BDA0002123667100000088
Can be decoded by performing sawtooth decoding
Figure BDA0002123667100000089
As shown in fig. 1-2. In the same way, by
Figure BDA00021236671000000810
And
Figure BDA00021236671000000811
can be decoded respectively
Figure BDA00021236671000000812
And
Figure BDA00021236671000000813
thus document s1All of the 6 packets of (1) are obtained. Privacy communication cost for whole document retrieval
Figure BDA00021236671000000814
As shown in fig. 4, preferably, when n <2k, step S20 specifically includes:
step S21, generating a retrieval matrix and a random matrix in the query matrix, wherein the random matrix is
Figure BDA00021236671000000815
The random matrix is a matrix with the size of k multiplied by m alpha and is independent of the storage file, the ith row represents the ith query random vector, and the retrieval matrix is Ef,l， l＝1,2,...,k,
Figure BDA00021236671000000816
Ef,1Is the search matrix sent by the user to the first node, Ef,lAccording to Ef,l-1The row vector is obtained by cyclic shift once; when l is 2f,lIs composed of Ef,l-1The row vector of (a) is obtained by cyclic shifting once. When k is more than l and less than or equal to n, Ef,l＝[0]That is, the search matrix sent to the parity check node is a zero matrix. And when k is more than l and less than or equal to n, the retrieval matrix is a zero matrix.
In step S21, it is assumed that the user is to retrieve the document SfAnd f is equal to {1,2, …, m }, a user needs to inquire each node for k times, and returns one data packet from each node in each inquiry, so that a total of nk data packets are returned, and alpha k system packets need to be solved. Random matrix
Figure BDA00021236671000000817
Where row i represents the query random vector for the ith time. The size of the retrieval matrix is kXm alpha, wherein the ith row represents the retrieval vector of the ith query, i is more than or equal to 1 and less than or equal to k, and at most one 1 is arranged in each row and column;
step S22, the user sends the query matrix to the corresponding node; it can also be understood that: sending the retrieval matrix and the random matrix to corresponding nodes; in practice, the query matrix is composed of a search matrix and a random matrix, and sending the query matrix to the corresponding node is equivalent to sending the search matrix and the random matrix to the corresponding node.
As shown in FIG. 5, preferably, when n ≧ 2k, step S20 specifically includes:
step S25, generating a retrieval matrix and a random matrix in the query matrix, wherein the random matrix is a random matrix
Figure BDA0002123667100000091
Retrieval matrix Ef,l＝[E1,…,Ef,…,Em]L ∈ { k +1, k +2, …, n }; wherein E isqIs a k x α matrix, q ∈ {1,2, …, m }, f is the f-th file to be retrieved, EqOnly E in the sub-matrixfInstead of a zero matrix, the remaining m-1 sub-matrices are all zero matrices. Ef,k+1Submatrix E inf＝[Ik×k,0k×(α-k)]，Ef,k+2Submatrix E infIs Ef,k+1E in (A)f＝[Ik×k,0k×(α-k)]The column vector in (A) is circularly shifted to the right by one bit, and the like, Ef,lSubmatrix E infIs Ef,l-1E in (A)fThe column vector in (1) is obtained by circularly shifting right by one bit. Query matrix Q to be generated by a userxAnd sending the data to the corresponding node, wherein x represents sending to the x-th node.
Step S26, sending the random matrix to the system node
Figure BDA0002123667100000092
The random matrix and the search matrix are sent to the parity check nodes.
For n ≧ 2k, the privacy communication cost is the same as for the case of n <2 k.
For n ≧ 2k, for example, it is assumed that there are n ═ 5 nodes in the distributed storage system, where k ═ 2 nodes are used for storing system packets and are called system nodes, and the remaining n-k ═ 3 nodes are used for storing coded packets and are called parity nodes. Let the system store m equal to 3 files, s respectively1、s2、s3. Each file si(i e {1,2,3}) is divided into 2 equal-length data packets, and then each data packet is divided into a equal-length data packets, wherein α -n-k-3, namely
Figure BDA0002123667100000101
Each file is divided into 6 packets. siIs stored in the first column of nodes 1, siThe second column of (2) is stored in the node, and the storage system has 3 files coexisting, so each system node needs to store m α ═ 9 original packets, and each parity check node also needs to store m α ═ 9 coded packets. Coding matrix of CP-ZD adopted by (5,2) code
Figure BDA0002123667100000102
siIs right-shifted by the corresponding bit according to the first row element of the matrix T, and then added in binary field to obtain the second data packet
Figure BDA0002123667100000103
And is stored in the node 3. siRight-shifted by corresponding bits according to the second row element of the matrix T, and then added in binary domain to obtain a second data packet
Figure BDA0002123667100000104
And is stored in the node 4. siIs right-shifted by the corresponding bit according to the third row element of the matrix T, and then binary field addition is performed to obtain the second data packet
Figure BDA0002123667100000105
And is stored in the node 5. And i represents a data packet corresponding to the ith file.
Suppose that a user wants to retrieve a document s1If f is 1, the user needs to query the node for k 2 times to decode the file s1. Firstly, a user generates a random matrix with k × m α being 2 × 9
Figure BDA0002123667100000106
Query matrix Q to system nodes 1,21＝U,Q2A query matrix Q sent to the parity check nodes3＝U+E1,3，Q4＝U+E1,4，Q5＝U+E1,5Wherein
Figure BDA0002123667100000107
The ith row of the query matrix is the query vector for the ith query from the user to the node, i ∈ {1,2, …, k }.
After receiving the query matrix, the system nodes shift the stored data packets according to the query matrix, add the data packets in the binary domain, and each node can obtain two new data packets and return the data packets to the user. Downloaded from node 1 to
Figure BDA0002123667100000108
From node 2 to
Figure BDA0002123667100000109
Is downloaded from node 3 to
Figure BDA00021236671000001010
Downloaded from node 4 to
Figure BDA00021236671000001011
From node 5 to
Figure BDA00021236671000001012
When n ≧ 2k, data decoding is the same as when n <2k, and therefore, no description is given here.
According to the invention, when n is larger than or equal to 2k and n is smaller than 2k, the transmitted random matrix and the transmitted retrieval matrix are different, and the transmitted node objects are different, so that the full parameter (n, k) can be adapted.
The above description is only a preferred embodiment of the present invention, and not intended to limit the scope of the present invention, and all modifications of equivalent structures and equivalent processes, which are made by using the contents of the present specification and the accompanying drawings, or directly or indirectly applied to other related technical fields, are included in the scope of the present invention.

Claims (3)

1. A full parameter private information retrieval method based on sawtooth decoding is characterized by comprising the following steps:
step S10, m files S1,s2,...smDividing the system into k alpha system packets, storing the system packets in k system nodes of a distributed storage system, determining a coding matrix, obtaining a coding packet according to the coding matrix, and storing the coding packet in alpha parity check nodes, wherein the distributed storage system has n nodes in total, alpha is n-k, and the coding matrix
Figure FDA0003314285050000011
Step S20, generating a query matrix, wherein the query matrix comprises a random matrix U and a retrieval matrix Ef,lQuerying the distributed storage system;
step S30, decoding the second data packet returned from the nodes of the distributed storage system, wherein the nodes comprise system nodes and parity check nodes;
wherein, when n is less than 2k, the step S20 specifically includes:
step S21, generating a retrieval matrix and a random matrix in the query matrix, wherein the random matrix is
Figure FDA0003314285050000012
Search matrix of
Figure FDA0003314285050000013
Ef,1Is the search matrix sent by the user to the first node, where r is n-k, and when l is 2f,lIs composed of Ef,l-1The row vector of (a) is obtained by cyclic shift once, f belongs to {1,2, …, m }, and f represents the sequence number of the file to be retrieved;
step S22, the user sends the query matrix to the corresponding node;
wherein, when n is greater than or equal to 2k, the step S20 specifically includes:
step S25, generating a retrieval matrix and a random matrix in the query matrix, wherein the random matrix is a random matrix
Figure FDA0003314285050000014
Retrieval matrix Ef,l＝[E1,…,Ef,…,Em],l∈{k+1,k+2,…,n}；
Step S26, sending the random matrix to the system node
Figure FDA0003314285050000015
The random matrix and the search matrix are sent to the parity check nodes.
2. The full-parameter private information retrieval method based on zigzag decoding as claimed in claim 1, wherein in step S10, obtaining the encoded packet according to the encoding matrix comprises:
s100, shifting the system package of each line of the file to the right by corresponding bits according to the line vector elements of the coding matrix T;
step S101, adding in binary field to obtain coding packet.
3. The full-parameter private information retrieval method based on the zigzag decoding as claimed in claim 1, wherein said step S30 specifically includes:
step S31, after receiving the query matrix, the nodes of the distributed storage system shift the first data packet stored in the nodes to the right by corresponding bits according to the row vector elements of the query matrix, then add in the binary domain to obtain the second data packet, and the nodes return the obtained second data packet;
step S32, a first result packet returned by the system node and a second result packet returned by the parity check node are obtained, the first result packet is right-shifted by corresponding bits according to the row vector elements of the CP-BZD code coding matrix, then binary field addition is carried out to obtain a third data packet, and then the third data packet and the second result packet are subjected to zigzag decoding to obtain a fourth data packet, wherein the second data packet comprises the first result packet and the second result packet;
step S33, performing zigzag decoding on the fourth packet, and solving a total of α k systematic packets.
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