CN112039653B - Cloud outsourcing data encryption and decryption method based on neural network activation unit - Google Patents

Cloud outsourcing data encryption and decryption method based on neural network activation unit Download PDF

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CN112039653B
CN112039653B CN202010881848.5A CN202010881848A CN112039653B CN 112039653 B CN112039653 B CN 112039653B CN 202010881848 A CN202010881848 A CN 202010881848A CN 112039653 B CN112039653 B CN 112039653B
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李芙蓉
王保仓
陈艳格
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Xidian University
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Abstract

The invention discloses a cloud outsourcing data encryption and decryption method based on a neural network activation unit, which is characterized in that a homomorphic DT-PKC encryption algorithm is used for carrying out privacy protection on cloud outsourcing data of a user requesting service, a cloud server CP interacts with a service provider SP, polynomial approximate fitting of a segmented point Taylor series is adopted for the activation unit, a homogeneous thought is adopted for ciphertext generation of the activation unit, and an accurate and privacy-protected corrected ciphertext of the cloud outsourcing data in the activation unit is generated. According to the cloud outsourcing data encryption method, the homomorphic DT-PKC encryption algorithm is used for encrypting the cloud outsourcing data of the user requesting service, the privacy of results generated by the cloud outsourcing data and the cloud outsourcing data in the activation unit is protected, the cipher text to be corrected of the activation unit is generated by the SAC protocol, the corrected cipher text of the activation unit is generated by the homogeneous algorithm, and the accuracy of the results generated by the cloud outsourcing data in the activation unit is protected.

Description

Cloud outsourcing data encryption and decryption method based on neural network activation unit
Technical Field
The invention belongs to the technical field of computers, and further relates to a cloud outsourcing data encryption and decryption method based on a neural network activation unit in the technical field of electric digital data processing. The method can be used for encrypting and decrypting the cloud outsourced data.
Background
The user cloud outsourcing data refers to privacy type inquiry service data, for example, data of a user personal privacy data inquiry service in the field of medical disease prediction neural network service. When cloud outsourced data uploaded by a user is transmitted to a neural network service provider, in order to solve the problem that local data storage and computing resources are limited, the service provider usually migrates part of computing to an untrusted cloud server, and the cloud server may curiously or even utilize privacy data in the cloud outsourced data to expose the privacy data to an illegal merchant, so that secret leakage is caused. The homomorphic password technology is a common technology for realizing privacy protection of cloud outsourced data, and an encryption scheme with homomorphic property can operate the cloud outsourced data on a ciphertext, so that the privacy data of a user are prevented from being leaked.
A method for encrypting Cloud outsourcing data by using a DT-PKC encryption method is disclosed in a paper published by Xindi Ma et al, "PDLM: Privacy-presetting Deep Learning Model on Cloud with Multiple Keys" (IEEE Transactions on Services Computing (Early Access), 05 September 2018, Page(s): 1-1). In the method, users respectively encrypt outsourcing data by using own secret keys, the outsourcing data are uploaded to a service provider to train a model, a cloud server assists the service provider to calculate, the cloud outsourcing data are generated in an activation unit by adopting an approximate polynomial of a zero point Taylor series, then corresponding homomorphic calculation is carried out through a ciphertext of the cloud outsourcing data, and finally a ciphertext result generated by the cloud outsourcing data in the activation unit is obtained. Although the method realizes the privacy of the output result of the cloud outsourcing data in the activation function unit, the method still has two defects: firstly, approximate polynomial fitting of a zero-point Taylor series is used for processing the activation unit in the method, and the Taylor series can be accurately fitted only in a small range of the zero point in zero-point expansion and cannot adapt to the range of the whole input cloud outsourcing data. Secondly, the homomorphic encryption algorithm only supports encryption with plaintext as an integer, the input cloud outsourcing data of the activation unit is encrypted and uploaded to the cloud server after being expanded into the integer, the approximate polynomial coefficient of the activation unit has decimal and the independent variable is not the expanded integer value, so that when the corresponding activation unit homomorphic generation of the ciphertext is carried out, even if the coefficient is subjected to integer processing encryption, the generated corresponding ciphertext result has errors due to the existence of high-order power of the polynomial independent variable. It can be seen that the above two disadvantages directly result in the accuracy of the result generated by the cloud outsourced data in the activation unit.
Korean patent document "method for establishing a medical intelligent diagnosis system for neurological diseases" (patent application No. 2020102813308, application publication No. CN111383760A) discloses a user cloud outsourcing data method based on neural network disease diagnosis. According to the method, sensitive cloud outsourcing data containing physical health conditions are directly uploaded to a service provider without being preprocessed by a user, early screening and diagnosis are carried out on the cloud outsourcing data of the user through big data disease screening service provided by a neural network, and finally the privacy result generated by the cloud outsourcing data in the neural network is directly returned to the user without being processed by the service provider. Although the method realizes that the cloud outsourcing data accurately generates the result in the neural network activation unit. However, this method still has two disadvantages: first, the user's graphical data, which contains sensitive data of the user's physical health status and which the user may not want to expose to the privacy information, is uploaded directly to the service provider without any pre-processing. Secondly, the generation result of the neural network is also a transparent diagnosis result, the information privacy of the user can be influenced by directly exposing the diagnosis result, and the intermediate generation result can also expose partial information privacy as the generation of the important activation unit of the neural network. The two defects can cause the privacy of the uploading process of the cloud outsourced data and the privacy of the result generated by the cloud outsourced data in the neural network activation unit.
Disclosure of Invention
The invention aims to provide a cloud outsourced data encryption and decryption method based on a neural network activation unit aiming at the defects of the prior art, and the method is used for solving the problems of privacy of the cloud outsourced data uploading process and the accuracy and privacy of the cloud outsourced data generated result in the neural network activation unit in the prior art.
In order to achieve the purpose, the method includes the steps of using a homomorphic DT-PKC encryption algorithm to carry out privacy protection on cloud outsourcing data of a user requesting service, dividing a main key into a first decryption part main key and a second decryption part main key, respectively distributing the first decryption part main key and the second decryption part main key to a cloud server SP and a service provider CP, interacting the cloud server CP and the service provider SP, carrying out approximate fitting on an activation unit by adopting a piecewise point Taylor series polynomial, adopting a homogeneous thought on ciphertext generation of the activation unit, and generating an accurate and privacy-protected corrected ciphertext of the cloud outsourcing data in the activation unit by using the property of DT-PKC homomorphic encryption.
The method comprises the following specific steps:
(1) generating a public and private key of an encryption system:
(1a) the key generation center generates a public and private key pair { pk ] of a user requesting service by using a homomorphic DT-PKC key generation algorithmz,skz}；
(1b) Key generation center assigns pk to each user through key generation centerz,skzGiving users requesting service;
(1c) the key generation center generates a master key lambda by using a homomorphic DT-PKC key generation algorithm, and divides the master key lambda into a first decryption part master key lambda1And a second decryption part master key lambda2；
(1d) The key generation center transmits the first decryption part master key lambda through a key channel1Is assigned to the service provider SP and the second decryption part master key lambda is assigned2Distributing the data to a cloud server CP;
(2) requesting a service user to upload encrypted cloud outsourcing data:
(2a) requesting service user to utilize its public key pkzEncrypting cloud outsourced data X and random integer R, in accordance with
Figure GDA0003147976480000031
Generating a ciphertext CXZAnd CR(ii) a Wherein, | | · | represents an encryption operation, X ═ X1,x2,...xi,...xn＞，xiOrdinals representing cloud outsourced data, n representing a total number of cloud outsourced data requesting service users, R ∈ ZN，ZNA residual class ring representing modulo N;
(2b) request service user to upload cipher text CXZAnd CRProviding the service provider SP;
(3) the service provider SP collects and uploads data:
(3a) service provider SP calculates joint public key pk according to public key of each userψUsing the joint public key pkψEncrypting the model parameters W and B of the basic neural network in accordance with
Figure GDA0003147976480000032
Formula C of connection weight between neuron h and neuron in previous layer of basic neural networkWCiphertext and threshold ciphertext C of neuron hB；
(3b) C is to beXZConnecting the weight ciphertext CWSum threshold ciphertext CBUploading the cloud server CP together;
(4) an activation unit input ciphertext for generating cloud outsourcing data:
(4a) the cloud server CP receives the user data ciphertext CXZRespectively calculating the public key pk of each service requesting user according to the public key of the userzConversion to federated public key pkψThe part h to be multipliedψ'According to CX＝{C1·hψ',C2Formula, using hψ'Cipher text C for completing user cloud outsourcing data encryption by joint public keyXConverting; wherein, C1Is represented by CXZThe first part of the ciphertext, C2Is represented by CXZThe second portion of ciphertext;
(4b) the cloud server CP receives the connection weight ciphertext CWSum threshold ciphertext CBBy utilizing an SMP protocol, through interaction between a cloud server CP and a service provider SP, a ciphertext A (A) of a connection weight and a corresponding cloud outsourcing data inner product is generated1,A2,...,Ak,...,Au>; wherein A iskRepresenting the connecting weight and the kth inner product ciphertext of the corresponding cloud outsourcing data, and u representing the total number of the inner product ciphertexts;
(4c) the cloud server CP compares the obtained u inner product ciphertexts according to D ═ A1·A2···Ak···AuA formula is adopted, multiplication operation is carried out, and a ciphertext D of the inner product sum is obtained;
(4d) the cloud server CP combines the inner product and the ciphertext D with the threshold ciphertext C of the neuron hBAccording to
Figure GDA0003147976480000041
Obtaining the input ciphertext C of the neuron activation unitOWherein o represents the input plaintext of the activation unit;
(5) generating a ciphertext to be corrected of the activation unit:
the cloud server CP inputs a ciphertext C to the generated activation unitOGenerating a ciphertext C to be corrected of the activation unit by using a SAC protocol through interaction between a cloud server CP and a service provider SPOU；
(6) And generating a modified ciphertext of the activated unit:
service provider SP generates activation unit to-be-corrected ciphertext COUGenerating a modified ciphertext C of the activation unit by using a homogeneous algorithm through interaction between the cloud server CP and the service provider SPf；
(7) Decryption of the ciphertext generated by the activation unit:
(7a) service provider SP utilizes random number cipher text C of requesting service userRAnd the activation unit generates a ciphertext CfAccording to
Figure GDA0003147976480000042
Formula calculation, and generating ciphertext C added with noise by homomorphic propertya；
(7b) The service provider SP uses the first decryption part master key lambda1Partially decrypted noisy ciphertext CaObtaining an intermediate result C of the partially decrypted noisy ciphertextmAnd C isaAnd CmTransmitted to the CP together;
(7c) cloud server CP receives CaAnd CmUsing the second decryption part master key lambda2Intermediate result C for noisy ciphertextmContinuing to decrypt to obtain the plaintext M of the activation unit added with random number noisea；
(7d) Cloud server CP utilizes public key pkzEncrypting random number noise added activation unit plaintext MaObtaining the ciphertext C which can be decrypted only by the user requesting the serviceOZReturning to the service requesting user;
(7e) the request service user receives a ciphertext C generated by the cloud outsourcing data which can be decrypted only by the request service user in the activation unitOZBy means of its private key skzDecrypting by a factor of 10 by removing random number noise Rα+3βTo obtainPlaintext f generated by cloud outsourcing data of modified request service user in activation unitV(o)。
Compared with the prior art, the invention has the following advantages:
firstly, the cloud outsourced data of the service requesting user is encrypted by using a homomorphic DT-PKC encryption algorithm, so that the problems of privacy of the uploading process of the cloud outsourced data and privacy of the result generated by the cloud outsourced data in the neural network activation unit in the prior art are solved, and the cloud outsourced data encryption method has the advantages of high privacy and high safety of the result generated by the cloud outsourced data of the service requesting user and the cloud outsourced data in the activation unit.
Secondly, the method and the device have the advantages that the SAC protocol is used for generating the ciphertext to be corrected of the activation unit, the homogenization algorithm is used for generating the corrected ciphertext of the activation unit, the problem of accuracy of a result generated by the cloud outsourced data in the activation unit in the prior art is solved, and the method and the device have the advantage of high accuracy of the result generated by the cloud outsourced data in the activation unit.
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FIG. 1 is a flow chart of the present invention.
Detailed Description
The present invention will be described in further detail with reference to fig. 1.
And step 1, generating a public key and a private key of an encryption system.
The key generation center generates a public and private key pair { pk ] of a user requesting service by using a homomorphic DT-PKC key generation algorithmz,skz}。
The public and private key pair { pk ] of the user requesting the service is generated by utilizing a homomorphic DT-PKC key generation algorithmz,skzThe steps of are as follows:
step 1, a safety parameter k is given, two safety big prime numbers p and q with the bit length of k are uniformly and randomly selected, wherein safety refers to that intermediate parameters p 'and q' which satisfy the following formula and are calculated by p and q are also prime numbers:
p'＝(p-1)/2
q'＝(q-1)/2
and 2, calculating the modulus N of the homomorphic DT-PKC cipher key generation algorithm according to the N ═ pq.
Step 3, randomly selecting thetaz∈[1,N/4]Generating a partial public key h for the requesting user zz：
Figure GDA0003147976480000051
Wherein g represents in the remaining ring class ZNSelecting a random number with the order of 2p 'q', mod represents a modular operation, a left expression of a symbol is identical to a right expression of the symbol, and N is equal to2The modulus is indicated.
Step 4, generating public and private key pair pk of user requesting servicez＝{N,g,hz}，skz＝θz。
Key generation center assigns pk to each user through key generation centerz,skzTo the user requesting the service.
The key generation center generates a master key lambda by using a homomorphic DT-PKC key generation algorithm, and divides the master key lambda into a first decryption part master key lambda1And a second decryption part master key lambda2。
The method comprises generating a master key lambda by using a homomorphic DT-PKC key generation algorithm, and dividing the master key lambda into a first decryption part master key lambda1And a second decryption part master key lambda2The method comprises the following steps:
and step 1, calculating a master key lambda of a homomorphic DT-PKC password generation algorithm according to the lambda being 2p 'q'.
Step 2, according to the following formula, dividing the main key into two partial keys which are respectively the first decryption partial main key lambda1And a second decryption part master key lambda2：
Figure GDA0003147976480000061
Wherein mod represents a modulo operation, and ≡ represents that the left expression of the symbol is congruent with the right expression of the symbol, and N is2Representing the modulus of the DT-PKC key generation algorithm.
The key generation center transmits the first decryption part master key lambda through a key channel1Is assigned to the service provider SP and the second decryption part master key lambda is assigned2And distributing to the cloud server CP.
And 2, requesting the service user to upload the encrypted cloud outsourcing data.
Requesting service user to utilize its public key pkzEncrypting cloud outsourced data X and random integer R, in accordance with
Figure GDA0003147976480000062
Generating a ciphertext CXZAnd CR(ii) a Wherein, | | · | represents an encryption operation, X ═ X1,x2,...xi,...xn＞，xiOrdinals representing cloud outsourced data, n representing a total number of cloud outsourced data requesting service users, R ∈ ZN，ZNThe remaining class rings of modulo N are represented.
Said requesting service user utilizes its public key pkzEncrypted cloud outsourced data and random integer generation ciphertext CXZAnd CRThe method comprises the following steps:
step 1, for xiSelecting a random integer ri∈[1,N/4]For the random number R, a random integer R is selectedR∈[1,N/4]。
Step 2, according to the following formula, the service requesting user encrypts the cloud outsourcing data by using a homomorphic DT-PKC cryptographic algorithm to generate pkzEncrypted cloud outsourced data ciphertext and random number ciphertext:
Figure GDA0003147976480000071
Figure GDA0003147976480000072
Figure GDA0003147976480000073
Figure GDA0003147976480000074
wherein, C1Representing a first part, C, of the encrypted ciphertext of the cloud outsourced data2A second portion representing encrypted ciphertext of the cloud outsourced data,
Figure GDA0003147976480000075
representing a first portion of the random integer encrypted ciphertext,
Figure GDA0003147976480000076
representing a second portion of the random integer encrypted ciphertext.
Request service user to upload cipher text CXZAnd CRTo the service provider SP.
And 3, the service provider SP collects and uploads the data.
Service provider SP calculates joint public key pk according to public key of each userψUsing the joint public key pkψEncrypting the model parameters W and B of the basic neural network in accordance with
Figure GDA0003147976480000077
Formula C generating connection weights between neurons h and neurons of the previous layer of the basic neural networkWCiphertext and threshold ciphertext C of neuron hB。
Said joint public key pkψThe calculation method of the model parameters W and B of the encryption basic neural network is as follows:
step 1, the service provider SP uses the public key pk of the requesting service userzThe joint public key pk is calculated according to the following formulaψ：
Figure GDA0003147976480000078
Wherein h isψRepresenting a federated public key pkψE represents the total number of requesting service subscribers,
Figure GDA0003147976480000079
partial public key h representing each requesting service userzThe product of (a).
Step 2, for wihE.g. W, the service provider SP randomly selects an integer rih∈[1,N/4]Calculating the ciphertext C of the join weight according tow∈CW：
Figure GDA0003147976480000081
Wherein, wihRepresenting the connection weight between neuron h and the preceding layer of neurons i.
Step 3, for the model parameter B, the service provider SP randomly selects an integer rh∈[1,N/4]. Calculate the ciphertext C of the threshold value according to the following formulaB：
Figure GDA0003147976480000082
C is to beXZConnecting the weight ciphertext CWSum threshold ciphertext CBUploading the cloud server CP together.
And 4, generating an activation unit input ciphertext of the cloud outsourcing data.
The cloud server CP receives the user data ciphertext CXZRespectively calculating the public key pk of each service requesting user according to the public key of the userzConversion to federated public key pkψThe part h to be multipliedψ'According to CX＝{C1·hψ',C2Formula, using hψ'Cipher text C for completing user cloud outsourcing data encryption by joint public keyXConverting; wherein, C1Is represented by CXZThe first part of the ciphertext, C2Is represented by CXZThe second portion of ciphertext.
The ciphertext C for encrypting the cloud outsourcing dataXThe conversion steps are as follows:
step 1, cloud server CP utilization requestService user public key pkzMiddle part public key hzH is calculated according to the following formulaψ'：
Figure GDA0003147976480000083
Step 2, the cloud server CP receives the user data ciphertext CXZAccording to CX＝{C1·hψ',C2Formula, ciphertext C for encrypting cloud outsourcing dataXThe conversion of (1).
The cloud server CP receives the connection weight ciphertext CWSum threshold ciphertext CBBy utilizing an SMP protocol, through interaction between a cloud server CP and a service provider SP, a ciphertext A (A) of a connection weight and a corresponding cloud outsourcing data inner product is generated1,A2,...,Ak,...,Au>; wherein A iskAnd u represents the total number of inner product ciphertexts.
The steps of the SMP protocol are as follows:
step 1, the cloud server CP selects a random integer rwih∈ZNW is calculated according to the following formulaihAdding random noise rwihThe ciphertext of (a):
Figure GDA0003147976480000091
step 2, the cloud server CP selects a random integer rxi∈ZNCalculating the request service user outsourcing data adding noise r according to the following formulaxiThe ciphertext of (a):
Figure GDA0003147976480000092
step 3, the cloud server CP uses the second decryption part of the master key lambda2According to the following formula, to dwihPartial decryption to obtain a partial decrypted intermediate result d'wihTo d is pairedxiPartial decryption to obtain a partial decrypted intermediate result d'xi：
d'wih＝PMDec'(dwih)d'xi＝PMDec'(dxi)
Where PMDec' (-) represents a partial decryption operation.
Step 4, the cloud server CP will d'wih，dwih，d'xi，dxiTo the service provider SP.
Step 5, the service provider SP uses its first decryption part master key λ1Continuing to decrypt the decrypted intermediate result to obtain a plaintext e according to the following formulawihAnd exi：
ewih＝PMDec”(dwih,d'wih)＝wih+rwih
exi＝PMDec”(dxi,d'xi)＝xi+rxi
Where PMDec "(-) represents a full decryption operation.
Step 6, the service provider SP will get the plaintext ewihAnd exiMultiplying, according to the following formula, obtaining a multiplied plaintext result e, and utilizing the joint public key pkψAnd E is encrypted to obtain a ciphertext E:
e＝ewih·exi＝(wih+rwih)(xi+rxi)
and 7, the service provider SP sends the ciphertext E to the cloud server CP.
And 8, the cloud server CP receives the ciphertext E, calculates the ciphertext according to the following formula, and generates a ciphertext A of a connection weight and a corresponding cloud outsourcing data inner producti∈A：
Figure GDA0003147976480000101
Wherein A ═ A1,A2,...,Ak,...,Au＞，
Figure GDA0003147976480000102
Representing a federated public key pkψTo-rxirwihThe encrypted ciphertext.
The cloud server CP compares the obtained u inner product ciphertexts according to D ═ A1·A2···Ak···AuAnd (4) performing multiplication operation to obtain a ciphertext D of the inner product sum.
The cloud server CP combines the inner product and the ciphertext D with the threshold ciphertext C of the neuron hBAccording to
Figure GDA0003147976480000103
Obtaining the input ciphertext C of the neuron activation unitOWhere o denotes the input plaintext of the activation unit.
And 5, generating a ciphertext to be corrected of the activation unit.
The cloud server CP inputs a ciphertext C to the generated activation unitOGenerating a ciphertext C to be corrected of the activation unit by using a SAC protocol through interaction between a cloud server CP and a service provider SPOU。
Generating ciphertext C to be corrected of activation unit by using SAC protocolOUThe steps are as follows:
step 1, the cloud server CP selects a random integer r1∈ZNThe added random noise r is calculated according to the following formula1And partial decryption result t' of ciphertext input t and t of the activation unit of (1):
Figure GDA0003147976480000104
t'＝PMDec'(t)
where PMDec' (-) represents a partial decryption operation.
Step 2, the cloud server CP selects a random integer r2,r3∈ZNThe added random noise r is calculated as follows2And r3And the partial decryption result s' of the ciphertext input s and s of the activation unit of (1):
Figure GDA0003147976480000105
s'＝PMDec'(s)
step 3, the cloud server CP generates an approximate polynomial table T of the activation unit and stores, adds a random integer r to each index value in the table T2Then multiplied by a random integer r3Obtaining a table T' corresponding to the new index value; the table T represents an approximate polynomial table generated by the cloud server CP expanding the activating unit through the segmentation point 4-level Taylor series with the interval of 0.5 according to the plaintext integer range of the data uploaded by the service requesting user.
Step 4, the cloud server CP sends t, t', COS, s ', T' to the service provider SP.
Step 5, the service provider SP receives t, t', COS, s ', T', using the joint public key pkψEncrypting, and generating random noise r according to the following formula1Plaintext input square sum cubic ciphertext L of activated unit1And L2And decrypting s yields the additive random noise r2And r3Activation unit plaintext input:
l1＝(PMDec”(t,t”))2＝(o+r1)2l2＝(PMDec”(t,t'))3＝(o+r1)3
Figure GDA0003147976480000111
v＝PMDec”(s,s')＝r3(o+r2)
where PMDec "(-) represents a full decryption operation.
Step 6, the service provider SP generates V, a corresponding table T', selects the approximate polynomial f corresponding to the index V nearest to VV(x) And mixing L1，L2And sending the data to the cloud server CP.
Step 7, the cloud server CP receives the L1，L2Then, to L1，L2Calculating according to the following formula, and generating ciphertext
Figure GDA0003147976480000112
And
Figure GDA0003147976480000113
sending to the service provider SP:
Figure GDA0003147976480000114
Figure GDA0003147976480000115
wherein the content of the first and second substances,
Figure GDA0003147976480000116
representing a federated public key pkψEncrypted-r1The ciphertext of (a) may be encrypted,
Figure GDA0003147976480000117
representing a federated public key pkψEncrypted-2 r1The ciphertext of o is then encrypted,
Figure GDA0003147976480000118
representing a federated public key pkψEncrypted-2 r1·o2The ciphertext of (a) may be encrypted,
Figure GDA0003147976480000119
representing a federated public key pkψEncrypted-r1 2The ciphertext of o.
Step 8, the service provider SP combines the ciphertext CO，
Figure GDA00031479764800001110
And the selected corresponding approximate polynomial fV(x) Generating a ciphertext output result C of the active unitOU。
And 6, generating a corrected ciphertext of the activation unit.
The service provider SP waits for the generated activation unitModified ciphertext COUGenerating a modified ciphertext C of the activation unit by using a homogeneous algorithm through interaction between the cloud server CP and the service provider SPf。
The modified ciphertext C of the activation unit is generated by utilizing the homogeneous algorithmfThe steps are as follows:
step 1, the service provider SP pairs the approximate polynomial fV(x) Replacing x with y to obtain an approximate polynomial
Figure GDA0003147976480000121
Multiplying both sides of the approximate polynomial by 10 simultaneouslyαTo obtain polynomial coefficients
Figure GDA0003147976480000122
An equation that expands exactly to an integer:
Figure GDA0003147976480000123
therein, 10αCoefficients representing the coefficients of the approximation polynomial such that they all exactly extend to integers [ ·]Representing the sign of an expansion of a floating-point number to an integer.
Step 2, the service provider SP multiplies both sides of the above equation by 10 at the same time3βThe right side of the equation is 10 as xβy treatment of, 10βCoefficients representing the expansion of the input plaintext of the activation unit to integers:
Figure GDA0003147976480000124
and 3, the service provider SP performs homomorphic equation conversion on the equation to generate a corresponding ciphertext equation:
Figure GDA0003147976480000125
wherein the content of the first and second substances,
Figure GDA0003147976480000126
representing a federated public key pkψTo pair
Figure GDA0003147976480000127
The encrypted ciphertext of the message is encrypted with the key,
Figure GDA0003147976480000128
representing a federated public key pkψTo pair
Figure GDA0003147976480000129
The encrypted ciphertext of the message is encrypted with the key,
Figure GDA00031479764800001210
representing a federated public key pkψTo pair
Figure GDA00031479764800001211
The encrypted ciphertext.
Step 4, the service provider SP sends CO，
Figure GDA00031479764800001212
Substituting the above cipher text equation to generate a modified cipher text C of the cloud outsourcing data in the activation unitf：
Figure GDA0003147976480000131
Where f' (o) indicates that the expanded activation cell generates plaintext.
And 7, the activation unit generates decryption of the ciphertext.
Service provider SP utilizes random number cipher text C of requesting service userRAnd the activation unit generates a ciphertext CfAccording to
Figure GDA0003147976480000132
Formula calculation, and generating ciphertext C added with noise by homomorphic propertya。
The service provider SP uses the first decryption part master key lambda1According to Cm＝PMDec'(Ca) Formula, partial decryption of noisy ciphertext CaObtaining an intermediate result C of the partially decrypted noisy ciphertextmAnd C isaAnd CmAre transmitted to the CP together.
Cloud server CP receives CaAnd CmUsing the second decryption part master key lambda2According to Ma＝PMDec”(Cm,Ca) Intermediate result C for noisy ciphertext, R + f' (o) formulamContinuing to decrypt to obtain the plaintext M of the activation unit added with random number noisea。
Cloud server CP utilizes public key pkzAccording to
Figure GDA0003147976480000133
Formula, encryption of random number noise added activation unit plaintext MaObtaining the ciphertext C which can be decrypted only by the user requesting the serviceOZAnd returning to the requesting service user.
The request service user receives a ciphertext C generated by the cloud outsourcing data which can be decrypted only by the request service user in the activation unitOZAccording to fV(o)＝(Dec(COZ)-R)/10α+3βFormula, using its own private key skzDecrypting by a factor of 10 by removing random number noise Rα+3βObtaining a plaintext f generated by the cloud outsourcing data of the corrected request service user in the activation unitV(o), where Dec (-) denotes a decryption operation.

Claims (3)

1. A cloud outsourcing data encryption and decryption method based on a neural network activation unit is characterized in that a homomorphic DT-PKC encryption algorithm is used for encrypting cloud outsourcing data of a user requesting service, a ciphertext to be corrected of the activation unit is generated by a SAC protocol, and a corrected ciphertext of the activation unit is generated by a homogeneous algorithm; the encryption and decryption method comprises the following steps:
(1) generating a public and private key of an encryption system:
(1a) the key generation center generates a public and private key pair { pk ] of a user requesting service by using a homomorphic DT-PKC key generation algorithmz,skz}；
(1b) Key generation center assigns pk to each user through key generation centerz,skzGiving users requesting service;
(1c) the key generation center generates a master key lambda by using a homomorphic DT-PKC key generation algorithm, and divides the master key lambda into a first decryption part master key lambda1And a second decryption part master key lambda2；
(1d) The key generation center transmits the first decryption part master key lambda through a key channel1Is assigned to the service provider SP and the second decryption part master key lambda is assigned2Distributing the data to a cloud server CP;
(2) requesting a service user to upload encrypted cloud outsourcing data:
(2a) requesting service user to utilize its public key pkzEncrypting cloud outsourced data X and random integer R, in accordance with
Figure FDA0003147976470000011
Generating a ciphertext CXZAnd CR(ii) a Wherein, | | · | represents an encryption operation, X ═ X1,x2,...xi,...xn＞，xiOrdinals representing cloud outsourced data, n representing a total number of cloud outsourced data requesting service users, R ∈ ZN，ZNA residual class ring representing modulo N;
said requesting service user utilizes its public key pkzEncrypted cloud outsourced data and random integer generation ciphertext CXZAnd CRThe method comprises the following steps:
first step, for xiSelecting a random integer ri∈[1,N/4]For the random number R, a random integer R is selectedR∈[1,N/4]；
Secondly, according to the following formula, the service requesting user z encrypts the cloud outsourcing data by using a homomorphic DT-PKC cryptographic algorithm to generate pkzEncrypted cloud outsourced data ciphertext and random number ciphertext:
Figure FDA0003147976470000021
Figure FDA0003147976470000022
Figure FDA0003147976470000023
Figure FDA0003147976470000024
wherein, C1Representing a first part, C, of the encrypted ciphertext of the cloud outsourced data2A second portion representing encrypted ciphertext of the cloud outsourced data,
Figure FDA0003147976470000025
representing a first portion of the random integer encrypted ciphertext,
Figure FDA0003147976470000026
representing a second portion of the random integer encrypted ciphertext;
(2b) request service user to upload cipher text CXZAnd CRProviding the service provider SP;
(3) the service provider SP collects and uploads data:
(3a) service provider SP calculates joint public key pk according to public key of each userψUsing the joint public key pkψEncrypting the model parameters W and B of the basic neural network in accordance with
Figure FDA0003147976470000027
Formula C of connection weight between neuron h and neuron in previous layer of basic neural networkWCiphertext and threshold ciphertext C of neuron hB；
(3b) C is to beXZConnecting the weight ciphertext CWSum threshold ciphertext CBUploading the cloud server CP together;
(4) an activation unit input ciphertext for generating cloud outsourcing data:
(4a) the cloud server CP receives the user data ciphertext CXZRespectively calculating the public key pk of each service requesting user according to the public key of the userzConversion to federated public key pkψThe part h to be multipliedψ'According to CX＝{C1·hψ',C2Formula, using hψ'Cipher text C for completing user cloud outsourcing data encryption by joint public keyXConverting; wherein, C1Is represented by CXZThe first part of the ciphertext, C2Is represented by CXZThe second portion of ciphertext;
(4b) the cloud server CP receives the connection weight ciphertext CWSum threshold ciphertext CBBy utilizing an SMP protocol, through interaction between a cloud server CP and a service provider SP, a ciphertext A (A) of a connection weight and a corresponding cloud outsourcing data inner product is generated1,A2,...,Ak,...,Au>; wherein A iskRepresenting the connecting weight and the kth inner product ciphertext of the corresponding cloud outsourcing data, and u representing the total number of the inner product ciphertexts;
(4c) the cloud server CP compares the obtained u inner product ciphertexts according to D ═ A1·A2···Ak···AuMultiplying by a formula to obtain a ciphertext D of the inner product sum:
(4d) the cloud server CP combines the inner product and the ciphertext D with the threshold ciphertext C of the neuron hBAccording to
Figure FDA0003147976470000031
Obtaining the input ciphertext C of the neuron activation unitOWherein o represents the input plaintext of the activation unit;
(5) generating a ciphertext to be corrected of the activation unit:
the cloud server CP inputs a ciphertext C to the generated activation unitOGenerating a ciphertext C to be corrected of the activation unit by using a SAC protocol through interaction between a cloud server CP and a service provider SPOU；
The to-be-repaired activating unit is generated by utilizing the SAC protocolPositive and negative text COUThe steps are as follows:
first, the cloud server CP selects a random integer r1∈ZNThe added random noise r is calculated according to the following formula1And partial decryption result t' of ciphertext input t and t of the activation unit of (1):
Figure FDA0003147976470000032
t'＝PMDec'(t)
wherein PMDec' (·) represents a partial decryption operation;
secondly, the cloud server CP selects a random integer r2,r3∈ZNThe added random noise r is calculated as follows2And r3And the partial decryption result s' of the ciphertext input s and s of the activation unit of (1):
Figure FDA0003147976470000033
s'＝PMDec'(s)
third, the cloud server CP generates an approximate polynomial table T of the activation unit and stores, adds a random integer r to each index value in the table T2Then multiplied by a random integer r3Obtaining a table T' corresponding to the new index value;
fourthly, the cloud server CP sends t, t' and COS, s ', T' to the service provider SP;
fifthly, the service provider SP receives t, t', COS, s ', T', using the joint public key pkψEncrypting, and generating random noise r according to the following formula1Plaintext input square sum cubic ciphertext L of activated unit1And L2And decrypting s yields the additive random noise r2And r3Activation unit plaintext input:
l1＝(PMDec”(t,t”))2＝(o+r1)2l2＝(PMDec”(t,t'))3＝(o+r1)3
Figure FDA0003147976470000041
v＝PMDec”(s,s')＝r3(o+r2)
wherein PMDec "(-) represents a decryption operation;
sixthly, the service provider SP generates V, a corresponding table T', and selects an approximate polynomial f corresponding to the index V closest to VV(x) And mixing L1，L2Sending the data to a cloud server CP;
seventhly, the cloud server CP receives the L1，L2Then, to L1，L2Calculating according to the following formula, and generating ciphertext
Figure FDA0003147976470000042
And
Figure FDA0003147976470000043
sending to the service provider SP:
Figure FDA0003147976470000044
Figure FDA0003147976470000045
wherein the content of the first and second substances,
Figure FDA0003147976470000046
representing a federated public key pkψEncrypted-r1The ciphertext of (a) may be encrypted,
Figure FDA0003147976470000047
representing a federated public key pkψEncrypted-2 r1The ciphertext of o is then encrypted,
Figure FDA0003147976470000048
representing a federated public key pkψEncrypted-2 r1·o2The ciphertext of (a) may be encrypted,
Figure FDA0003147976470000049
representing a federated public key pkψEncrypted
Figure FDA00031479764700000410
The ciphertext of (1);
eighth, the service provider SP combines the ciphertext CO，
Figure FDA00031479764700000411
And the selected corresponding approximate polynomial fV(x) Generating a ciphertext output result C of the active unitOU；
(6) And generating a modified ciphertext of the activated unit:
service provider SP generates activation unit to-be-corrected ciphertext COUGenerating a modified ciphertext C of the activation unit by using a homogeneous algorithm through interaction between the cloud server CP and the service provider SPf；
The modified ciphertext C of the activation unit is generated by utilizing the homogeneous algorithmfThe steps are as follows:
first, the service provider SP pairs the approximate polynomial fV(x) Replacing x with y to obtain an approximate polynomial
Figure FDA0003147976470000051
Multiplying both sides of the approximate polynomial by 10 simultaneouslyαTo obtain polynomial coefficients
Figure FDA0003147976470000052
An equation that expands exactly to an integer:
Figure FDA0003147976470000053
therein, 10αCoefficients representing the coefficients of the approximation polynomial such that they all exactly extend to integers [ ·]A symbol representing a floating point number scaled up to an integer;
in a second step, the service provider SP multiplies both sides of the above equation by 10 at the same time3βThe right side of the equation is 10 as xβy treatment of, 10βCoefficients representing the expansion of the input plaintext of the activation unit to integers:
Figure FDA0003147976470000054
thirdly, the service provider SP converts the equation into a homomorphic equation to generate a corresponding ciphertext equation:
Figure FDA0003147976470000055
wherein the content of the first and second substances,
Figure FDA0003147976470000056
representing a federated public key pkψTo pair
Figure FDA0003147976470000057
The encrypted ciphertext of the message is encrypted with the key,
Figure FDA0003147976470000058
representing a federated public key pkψTo pair
Figure FDA0003147976470000059
The encrypted ciphertext of the message is encrypted with the key,
Figure FDA00031479764700000510
representing a federated public key pkψTo pair
Figure FDA00031479764700000511
Encrypted ciphertext；
Fourth, the service provider SP sends CO，
Figure FDA00031479764700000512
Substituting the above cipher text equation to generate a modified cipher text C of the cloud outsourcing data in the activation unitf：
Figure FDA00031479764700000513
Wherein f' (o) indicates that the expanded activation unit generates plaintext;
(7) decryption of the ciphertext generated by the activation unit:
(7a) service provider SP utilizes random number cipher text C of requesting service userRAnd the activation unit generates a ciphertext CfAccording to
Figure FDA0003147976470000061
Formula calculation, and generating ciphertext C added with noise by homomorphic propertya；
(7b) The service provider SP uses the first decryption part master key lambda1Partially decrypted noisy ciphertext CaObtaining an intermediate result C of the partially decrypted noisy ciphertextmAnd C isaAnd CmTransmitted to the CP together;
(7c) cloud server CP receives CaAnd CmUsing the second decryption part master key lambda2Intermediate result C for noisy ciphertextmContinuing to decrypt to obtain the plaintext M of the activation unit added with random number noisea；
(7d) Cloud server CP utilizes public key pkzEncrypting random number noise added activation unit plaintext MaObtaining the ciphertext C which can be decrypted only by the user requesting the serviceOZReturning to the service requesting user;
(7e) the request service user receives a ciphertext C generated by the cloud outsourcing data which can be decrypted only by the request service user in the activation unitOZBy means of its private key skzDecryption by removalMachine-to-machine noise R, reduced by a factor of 10α+3βAnd obtaining a plaintext generated by the cloud outsourcing data of the modified request service user in the activation unit.
2. The encryption and decryption method for cloud outsourced data based on neural network activation unit as claimed in claim 1, wherein the step (1a) utilizes a homomorphic DT-PKC key generation algorithm to generate the user public and private key pair { pk ] of the requested servicez,skzThe steps of are as follows:
firstly, a safety parameter k is given, two safety big prime numbers p and q with the bit length of k are uniformly and randomly selected, wherein safety refers to that intermediate parameters p 'and q' which satisfy the following formula and are obtained by calculating p and q are also prime numbers:
p'＝(p-1)/2
q'＝(q-1)/2
secondly, calculating a modulus N of a homomorphic DT-PKC cipher key generation algorithm according to the N ═ pq;
third, randomly selecting thetaz∈[1,N/4]Generating a partial public key h for the requesting user zz：
Figure FDA0003147976470000071
Wherein g represents in the remaining ring class ZNSelecting a random number with the order of 2p 'q', mod represents a modular operation, a left expression of a symbol is identical to a right expression of the symbol, and N is equal to2Represents a modulus;
fourthly, generating public and private key pair pk of the user requesting servicez＝{N,g,hz}，skz＝θz。
3. The encryption and decryption method for cloud outsourced data based on neural network activation unit as claimed in claim 1, wherein the step (1c) generates the master key λ by using a homomorphic DT-PKC key generation algorithm, and divides the master key λ into the first decryption part master key λ1And a second decryption part master key lambda2The method comprises the following steps:
firstly, calculating a master key lambda of a homomorphic DT-PKC password generation algorithm according to lambda being 2p 'q';
second, the main key is divided into two partial keys, which are the first decrypted partial main key lambda according to the following formula1And a second decryption part master key lambda2：
Figure FDA0003147976470000072
Wherein mod represents a modulo operation, and ≡ represents that the left expression of the symbol is congruent with the right expression of the symbol, and N is2Representing the modulus of the DT-PKC key generation algorithm.
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