CN106788980A - Safe encryption method in a kind of matrix multiplication sub-contract management towards cloud computing - Google Patents

Safe encryption method in a kind of matrix multiplication sub-contract management towards cloud computing Download PDF

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CN106788980A
CN106788980A CN201710032412.7A CN201710032412A CN106788980A CN 106788980 A CN106788980 A CN 106788980A CN 201710032412 A CN201710032412 A CN 201710032412A CN 106788980 A CN106788980 A CN 106788980A
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matrix
module
matrix multiplication
calculation
encrypting
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CN106788980B (en
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于运鹏
徐�明
付绍静
王冬升
罗玉川
黄凯
贾楠
黄宇锋
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National University of Defense Technology
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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
    • H04L9/08—Key distribution or management, e.g. generation, sharing or updating, of cryptographic keys or passwords
    • H04L9/0861—Generation of secret information including derivation or calculation of cryptographic keys or passwords
    • H04L9/0869—Generation of secret information including derivation or calculation of cryptographic keys or passwords involving random numbers or seeds
    • 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
    • H04L9/06—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols the encryption apparatus using shift registers or memories for block-wise or stream coding, e.g. DES systems or RC4; Hash functions; Pseudorandom sequence generators
    • H04L9/0618—Block ciphers, i.e. encrypting groups of characters of a plain text message using fixed encryption transformation

Abstract

The invention discloses safe encryption method in a kind of matrix multiplication sub-contract management towards cloud computing, the technical problem to be solved is to overcome the shortcomings of prior art leak data privacy, preferably protects matrix multiplication input data privacy.The present invention by improving after matrix multiplication outsourcing software complete, mainly improve cipher key module, encrypting module, deciphering module；Cipher key module generates key according to matrix size, and key is made up of 4k random vector；Then encrypting module adds the matrix Z using key generation to input matrix X, Y respectively1And Z2, each element method in scrambled matrix X, Y；Computing module calculates the matrix multiplication problem of encryption；Authentication module verifies result of calculation；Deciphering module is according to the final result of calculation of secret key decryption.Can encrypt each element in input matrix X, Y during present invention encryption, protect the privacy of each element, including neutral element number, preferably protect the privacy of input data.

Description

Safe encryption method in a kind of matrix multiplication sub-contract management towards cloud computing
Technical field
The invention belongs to cloud computing security fields, more specifically, it is related to outside a kind of matrix multiplication towards cloud computing Safe encryption method in packet procedures.
Background technology
Cloud computing provides the user the numerical procedure of economical and efficient, and user can share the computing resource of Cloud Server and deposit Storage resource, the equipment for making the computing capability of user be no longer limited by them.Therefore, the not enough user of some computing resources can be by Large-scale calculating is sent to the powerful Cloud Server treatment of computing capability to the mode that usage amount is paid and then saving is calculated as This.User calculates the mode call outsourcing that the calculating task of oneself is sent to third party's calculating.
Although outsourcing is calculated has many benefits, directly Cloud Server treatment is given calculating new in the presence of some Safety problem and challenge.Often comprising some sensitive informations such as financial transaction record, Customer Information, individual in the task that outsourcing is calculated Person health data etc., but Cloud Server is always incredible.Therefore, the topmost problem that outsourcing is calculated is that safety is asked How topic, i.e., protect the privacy of the inputoutput data of outsourcing calculating task.User terminal will be to input data before outsourcing calculating Encryption, is decrypted to the result that cloud server end is returned.Secondly, the details of operation of cloud server end is opaque to user terminal 's.Cloud server terminal is perhaps to the economic interests of oneself, reduce calculation times；Meanwhile, hacker can be by various attack patterns Control Cloud Server, so that altered data, does not perform according to agreement, does not perform even, returns to the result of mistake.Therefore, check The correctness of cloud server end returning result is that outsourcing calculates Second Problem.
Safely outsourced calculation stress pays close attention to the scientific algorithm that computation complexity is high and data volume is big at this stage.For example it is extensive Matrix multiplication, matrix inversion, system of linear equations and linear programming, sequence compare.
The form of calculation of matrix multiplication computational problem is Z=XY, and wherein X is dimension m * n matrix, and Y is dimension n × s squares Battle array, Z is dimension m × s matrixes, and m, n, s are the dimension sizes of matrix.Matrix X, Y are input data, and matrix Z is output data (meter Calculate result).For the safely outsourced computational algorithm of matrix multiplication, 2014, Lei et al. was in periodical Information Sciences Roll up and deliver " Achieving security, robust cheating resistance, and high- on page 280 205-217 efficiency for outsourcing large matrix multiplication computation to a Malicious cloud " (the extensive matrix multiplication of safety, anti-fraud, efficient outsourcing towards malice cloud is calculated).Matrix multiplication Outsourcing software is completed, and matrix multiplication outsourcing software five modules as shown in figure 1, be made up of, five modules are cipher key module, encryption Module, computing module, authentication module, deciphering module.Wherein cipher key module, encrypting module, authentication module, deciphering module are arranged on User terminal.Computing module is arranged on cloud server end.Cipher key module generates key according to matrix size, and key is sent to encryption Module and deciphering module.The matrix multiplication problem that encrypting module is encrypted using key to the encryption generation of matrix multiplication problem, and The matrix multiplication problem of encryption is sent to computing module.Computing module receives the matrix multiplication problem of encryption, calculates encryption Matrix multiplication problem, authentication module is sent to by result of calculation.Authentication module is tested the result of calculation that computing module is returned Card, if result of calculation is sent to deciphering module by result of calculation by checking, otherwise, returns to computing module and recalculates.Solution Close module is decrypted to the result of calculation by verifying using key and obtains final result of calculation.The program is comprised the following steps：
The first step, structural matrix multiplication outsourcing software, from input file read in carry out matrix multiplication calculating matrix X and Matrix Y, X are dimension m * n matrixes, and Y is dimension n × s matrixes, and m, n, s are positive integers.
Second step, cipher key module generates key according to matrix size.
According to m, the value of n, s, wherein m, n, s are the dimension size of matrix, generation 1,2 ..., the displacement of m to 2.1 cipher key modules Function π1, the permutation function π of 1,2 ..., n2, the permutation function π of 1,2 ..., s3。
2.2 cipher key modules are according to permutation function π1, π2, π3Randomly select m+n+s random value r1,...,rm,rm+1,..., rm+n,rm+n+1,...,rm+n+s.Generate the elementary transition matrix that m dimension is m × m respectively according to formula (1), (2), (3) A1,…,Ae,…,Am(1≤e≤m), n dimension is the elementary transition matrix B of n × n1,…,Bf,…,Bn(1≤f≤n), s dimension Number is the elementary transition matrix C of s × s1,…,Cg,…,Cs(1≤g≤s)。
Wherein Ae(i1,j1) it is matrix AeI-th1Row jth1Column element, Bf(i2,j2) it is matrix BfI-th2Row jth2Column element, Cg(i3,j3) it is Matrix CgI-th3Row jth3Column element.
2.3 cipher key modules calculate P1=A1×A2×…×Am, P1-1=A1 -1×A2 -1×…×Am -1, P2=B1×B2×… ×Bn, P2 -1=B1 -1×B2 -1×…×Bn -1, P3=C1×C2×…×Cs, P3 -1=C1 -1×C2 -1×…×Cs -1。
The parameter of more than 2.4 generations constitutes key SK={ P1, P2, P3, π1, π2, π3, r1,...,rm+n+s}。
3rd step, encrypting module utilizes key scrambled matrix multiplication problem.
3.1 encrypting modules calculate X '=P1×X×P2 -1, wherein matrix X ' i-th4Row jth4Column element isThat is, matrix X ' i-th4Row jth4Row unit Element is matrix X π1(i4) row π2(j4) column element is multiplied byObtain.
3.2 encrypting modules calculate Y '=P2×Y×P3-1, wherein matrix Y ' i-th5Row jth5Column element isThat is, matrix Y ' i-th5Row jth5Row Element is matrix Y π2(i5) row π3(j5) column element is multiplied byObtain.
3.3 encrypting modules are sent to the matrix X ' and Y ' of encryption the computing module of cloud server end.
4th step, computing module calculates the matrix multiplication problem of encryption.
After matrix X ' and Y ' that 4.1 computing modules receive encryption from the encrypting module of user terminal, Z '=X ' × Y ' is calculated.
4.2 authentication modules that result of calculation Z ' is sent to user terminal.
5th step, authentication module checking result of calculation.
5.1 authentication modules generate l random vector ri(i ∈ [1, l]), wherein riIt is the column vector of dimension s × 1, l values are big It is small to be randomly choosed by authentication module.
5.2 authentication modules verify X ' × (Y ' × ri) whether it is equal to Z ' × ri。
If 5.3 is equal, expression is verified, and authentication module receives result of calculation Z ', turns the 6th step；Otherwise, refusal is calculated As a result Z ', turns the 4th step.
6th step, deciphering module decrypts final result of calculation.
6.1 according to key P1, P3With the result of calculation Z ' by verifying, deciphering module calculating Z=P1 -1×Z′×P3, obtain Result of calculation Z.
Found out by the 3rd step 3.1 and 3.2, this matrix multiplication outsourcing scheme only protects non-zero entry in input matrix X and Y The privacy of element, have ignored the protection of neutral element number, result in data-privacy leakage.
The content of the invention
The technical problem to be solved in the present invention is to overcome the shortcomings of prior art leak data privacy, there is provided it is a kind of towards Safe encryption method during the matrix multiplication of cloud computing is safely outsourced, compared to currently existing scheme, can preferably protect Matrix Multiplication Method input data privacy.
The present invention is towards safe encryption method in the matrix multiplication sub-contract management of cloud computing by improving background technology matrix Matrix multiplication outsourcing software is completed in the safely outsourced computational algorithm of multiplication.Matrix multiplication outsourcing software after improvement is also by key mould Block, encrypting module, computing module, authentication module, deciphering module composition.Wherein cipher key module, encrypting module, authentication module, solution Close module is arranged on user terminal.Computing module is arranged on cloud server end.
The technical scheme is that：
The first step, improves matrix multiplication outsourcing software, and the matrix multiplication outsourcing software after improvement is also by cipher key module, encryption Module, computing module, authentication module, deciphering module composition, wherein computing module, authentication module do not change, cipher key module, plus Close module, deciphering module are all different from the corresponding module in background technology matrix multiplication outsourcing software.Cipher key module, encryption mould Block, authentication module, deciphering module are arranged on user terminal, and computing module is arranged on cloud server end.Encrypting module utilizes key pair The matrix multiplication problem of matrix multiplication problem encryption generation encryption, and the matrix multiplication problem of encryption is sent to computing module. Computing module receives the matrix multiplication problem of encryption, calculates the matrix multiplication problem of encryption, and result of calculation is sent into checking mould Block.Authentication module is verified to the result of calculation that computing module is returned, if result of calculation sends result of calculation by checking To deciphering module, otherwise, return to computing module and recalculate.Deciphering module is using key to the result of calculation solution by verifying It is close to obtain final result of calculation.Being read in from input file will carry out the matrix X and matrix Y of matrix multiplication calculating.
Second step, cipher key module generates key according to matrix size.
2.1 cipher key modules select a positive integer k according to the value of the dimension m, n, s of matrix, the scope of k values be 2≤k≤ 0.01 × min (m, n, s), wherein min (m, n, s) represent m, n, the minimum value in s.
The generation of 2.2 cipher key modules is raw using random function (srand the and rand functions such as in Matlab language and C language) Into 4k random vector a1,…,ak, b1,…,bk, c1,…,ck, d1,…,dk, wherein a1,…,akFor dimension for m × 1 row to Amount, b1,…,bk, c1,…,ckFor dimension is the column vector of n × 1, d1,…,dkFor dimension is the column vector of s × 1.Generate above Vector constitute key SK={ a1,…,ak,b1,…,bk,c1,…,ck,d1,…,dk}。
3rd step, encrypting module utilizes key scrambled matrix multiplication problem.
3.1 encrypting module generator matrix Z1And Z2：
3.2 encrypting modules calculate X '=X+Z1, wherein matrix X ' i-th6Row jth6Column element is X ' (i6,j6)=X (i6,j6) +Z1(i6,j6)(1≤i6≤m,1≤j6≤ n), that is to say, that i-th6Row jth6Column element is matrix X i-th6Row jth6Column element adds Upper matrix Z1I-th6Row jth6Column element is obtained.
3.3 encrypting modules calculate Y '=Y+Z2, wherein matrix Y ' i-th7Row jth7Column element is Y ' (i7,j7)=Y (i7,j7) +Z2(i7,j7)(1≤i7≤n,1≤j7≤ s), that is to say, that matrix Y ' i-th7Row jth7Column element is matrix Y i-th7Row jth7Row Element adds matrix Z2I-th7Row jth7Column element is obtained.
3.4 encrypting modules are sent to the matrix X ' and Y ' of encryption the computing module of cloud server end.
4th step, computing module calculates the matrix multiplication problem of encryption.
After matrix X ' and Y ' that 4.1 computing modules receive encryption from the encrypting module of user terminal, Z '=X ' × Y ' is calculated.
4.2 authentication modules that result of calculation Z ' is sent to user terminal.
5th step, authentication module checking result of calculation.
5.1 authentication modules generate l random vector ri(i ∈ [1, l]), wherein riIt is the column vector of dimension s × 1, l values are big It is small to be randomly choosed by authentication module.
5.2 authentication modules verify X ' × (Y ' × ri) whether it is equal to Z ' × ri。
If 5.3 is equal, expression is verified, and authentication module receives result of calculation Z ', turns the 6th step；Otherwise, refusal is calculated As a result Z ', turns the 4th step.
6th step, deciphering module decrypts final result of calculation.
6.1 deciphering module calculating matrix S：
6.2 deciphering modules calculate Z=Z '-S, obtain result of calculation Z.
Following technique effect can be reached using the present invention：
In order to protect the privacy of input matrix, the present invention is in the 3rd step 3.3 and 3.4 encrypting modules to input matrix X, Y point Jia Shang not matrix Z1And Z2, encrypted each element in matrix X, Y, protect the privacy of each element, including neutral element Number, preferably protects the privacy of input data.
Brief description of the drawings
Fig. 1 is the building-block of logic of background technology matrix multiplication outsourcing software.
Fig. 2 is flow chart of the invention.
Specific embodiment
Specific embodiment of the invention is described below.As shown in Fig. 2 the present invention is comprised the following steps：
The first step, improves matrix multiplication outsourcing software, and the matrix X and matrix Y to be calculated are read in from input file.
Second step, cipher key module generates key according to matrix size：
2.1, cipher key module determines positive integer k.
2.2, cipher key module generates 4k vector a at random1,…,ak, b1,…,bk, c1,…,ckAnd d1,…,dk。
3rd step, encrypting module is encrypted to matrix multiplication problem：
3.1, encrypting module is according to the key SK of second step 2.2={ a1,…,ak,b1,…,bk,c1,…,ck,d1,…,dkRaw Into matrix Z1And Z2。
3.2, matrix X add matrix Z1, realize the encryption to matrix X.
3.3, matrix Y add matrix Z2, realize the encryption to matrix Y.
3.4, encrypting module is sent to the matrix X ' and Y ' of encryption the computing module of cloud server end.
4th step, computing module calculates the matrix multiplication problem of encryption：
4.1, the computing module of Cloud Server performs the calculating to Z '=X ' × Y '.
4.2, Z ' is sent to the authentication module of user terminal.
5th step, authentication module checking result of calculation：
5.1, authentication module generates l random vector ri。
5.2, authentication module checking X ' × (Y ' × ri) whether it is equal to Z ' × ri。
5.3, if equal, expression is verified, and authentication module receives result of calculation Z ', turns the 6th step；Otherwise, refusal is calculated As a result Z ', turns the 4th step.
6th step, deciphering module decrypts final result of calculation：
6.1, deciphering module is according to the key SK of second step 2.2={ a1,…,ak,b1,…,bk,c1,…,ck,d1,…,dkMeter Calculate matrix S.
6.2, Z=Z '-S are calculated, obtain final result of calculation Z.

Claims (2)

1. safe encryption method in a kind of matrix multiplication sub-contract management towards cloud computing, the method is by matrix multiplication outsourcing software Complete, matrix multiplication outsourcing software is made up of cipher key module, encrypting module, computing module, authentication module, deciphering module, wherein Cipher key module, encrypting module, authentication module, deciphering module are arranged on user terminal, and computing module is arranged on cloud server end；It is special Levy is that safe encryption method is comprised the following steps in a kind of matrix multiplication sub-contract management towards cloud computing：
The first step, improves cipher key module, encrypting module, the deciphering module of matrix multiplication outsourcing software, and being read in from input file will The matrix X and matrix Y, X for carrying out matrix multiplication calculating are dimension m * n matrixes, and Y is dimension n × s matrixes, and m, n, s are positive integers；
Second step, cipher key module generates key according to matrix size, and method is：
2.1 cipher key modules select a positive integer k according to the value of the dimension m, n, s of matrix；
2.2 cipher key modules generate 4k random vector a using random function1,…,ak, b1,…,bk, c1,…,ck, d1,…,dk, Wherein a1,…,akFor dimension is the column vector of m × 1, b1,…,bk, c1,…,ckFor dimension is the column vector of n × 1, d1,…,dk For dimension is the column vector of s × 1；This 4k random vector constitutes key SK={ a1,…,ak,b1,…,bk,c1,…,ck, d1,…,dk}；
3rd step, encrypting module utilizes key scrambled matrix multiplication problem, and method is：
3.1 encrypting module generator matrix Z1And Z2：
Z 1 = a 1 ... a k b 1 t . . . b k T , Z 2 = c 1 ... c k d 1 T . . . d k T ;
3.2 encrypting modules calculate X '=X+Z1, wherein matrix X ' i-th6Row jth6Column element is X ' (i6,j6)=X (i6,j6)+Z1 (i6,j6),1≤i6≤m,1≤j6≤ n, i.e. matrix X ' i-th6Row jth6Column element is matrix X i-th6Row jth6Column element adds square Battle array Z1I-th6Row jth6Column element；
3.3 encrypting modules calculate Y '=Y+Z2, wherein matrix Y ' i-th7Row jth7Column element is Y ' (i7,j7)=Y (i7,j7)+Z2 (i7,j7),1≤i7≤n,1≤j7≤ s, i.e. matrix Y ' i-th7Row jth7Column element is matrix Y i-th7Row jth7Column element adds square Battle array Z2I-th7Row jth7Column element；
3.4 encrypting modules are sent to the matrix X ' and Y ' of encryption the computing module of cloud server end；
4th step, computing module calculates the matrix multiplication problem of encryption, and method is：
After matrix X ' and Y ' that 4.1 computing modules receive encryption from the encrypting module of user terminal, Z '=X ' × Y ' is calculated；
4.2 authentication modules that result of calculation Z ' is sent to user terminal；
5th step, authentication module verifies result of calculation, and method is：
5.1 authentication modules generate l random vector ri(i ∈ [1, l]), wherein riBe the column vector of dimension s × 1, l values size by Authentication module is randomly choosed；
5.2 authentication modules verify X ' × (Y ' × ri) whether it is equal to Z ' × ri；
If 5.3 is equal, expression is verified, and authentication module receives result of calculation Z ', turns the 6th step；Otherwise, result of calculation is refused Z ', turns the 4th step；
6th step, deciphering module decrypts final result of calculation, and method is：
6.1 deciphering module calculating matrix S：
S = ( X + Z 1 ) Z 2 + Z 1 Y = ( X ′ c 1 ... c k ) d 1 T . . . d k T + a 1 ... a k ( b 1 T . . . b k T Y ) ;
6.2 deciphering modules calculate Z=Z '-S, obtain result of calculation Z.
2. safe encryption method, its feature in a kind of matrix multiplication sub-contract management towards cloud computing as claimed in claim 1 It is that the scope of the k values is 2≤k≤0.01 × min (m, n, s), wherein min (m, n, s) represents m, n, the minimum value in s.
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CN109450625A (en) * 2018-11-12 2019-03-08 青岛大学 The safely outsourced method of extensive Polynomial Expansion Euclidean algorithm
CN109460536A (en) * 2018-11-16 2019-03-12 青岛大学 The safely outsourced algorithm of extensive matrix operation
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CN110309674A (en) * 2019-07-04 2019-10-08 浙江理工大学 A kind of sort method based on full homomorphic cryptography
CN110309674B (en) * 2019-07-04 2021-10-01 浙江理工大学 Ordering method based on fully homomorphic encryption
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CN112995189A (en) * 2021-03-08 2021-06-18 北京理工大学 Method for publicly verifying matrix multiplication correctness based on privacy protection
CN113271293A (en) * 2021-04-09 2021-08-17 上海大学 Verifiable constrained quadratic programming security outsourcing calculation method and system

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