CN104980271B - Multiplying method and system based on Batch RSA in a kind of cloud computing - Google Patents
Multiplying method and system based on Batch RSA in a kind of cloud computing Download PDFInfo
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- CN104980271B CN104980271B CN201410142505.1A CN201410142505A CN104980271B CN 104980271 B CN104980271 B CN 104980271B CN 201410142505 A CN201410142505 A CN 201410142505A CN 104980271 B CN104980271 B CN 104980271B
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Abstract
The invention belongs to the communications field, there is provided the multiplying method and system based on Batch RSA in a kind of cloud computing, the described method includes：Data consumer calculates function F to k multiplicationiA corresponding public key is produced respectively, and public key is respectively sent to corresponding multiplication calculates function FiIn included data set provider；Data consumer calculates function F using public key to multiplicationiIn the data of required data consumer be encrypted, form corresponding multiplication and calculate function FiThe encryption data of required data consumer is sent to high in the clouds；Data set provider calculates function F using public key to multiplicationiIn the data row encryption of required data set provider send to high in the clouds；The high in the clouds carries out multiplying to encryption data and sends to data consumer, and the data consumer decrypts k multiplication and calculates function F at the same timeiCryptographic calculation as a result, obtain decryption operation result.Decryption speed of the data consumer to multiple cryptographic calculation results returned from high in the clouds is improved, improves computational efficiency.
Description
Technical field
The invention belongs to a kind of multiplying method in the communications field, more particularly to cloud computing based on Batch RSA and
System.
Background technology
With the progressively popularization being showing improvement or progress day by day with network application of information technology, cloud computing technology has obtained unprecedented development
And research, but it also gives while service efficiency is improved and realizes that user information safety brings great difficulty with secret protection
With challenge.Safety just becomes the major issue that field of cloud calculation is urgently broken through, its importance and urgency can not be ignored.And
Continuous with cloud computing is popularized, and the importance of cloud computing safety problem, which is presented, gradually rises trend, it has also become restricts
An important factor for it develops.Homomorphic cryptography technology provides a kind of key technology for the data safety of cloud computing and secret protection,
To carry out complicated computing and operation to the encryption data being stored in Cloud Server.Homomorphic cryptography technology can
Satisfaction operates ciphertext data, and does not allow operator to decrypt to obtain data message, while ensures computational efficiency, can be very
Solve the above problems in big degree.Existing homomorphic encryption scheme is the RSA systems based on factoring difficulty, to any time
Multiplication meets homomorphism speciality, but when client calculates function there are multiple multiplication and needs to be put into high in the clouds calculating, existing RSA bodies
System, which exists, decrypts the shortcomings that slow.
The content of the invention
The purpose of the embodiment of the present invention is in a kind of multiplying method in cloud computing is provided based on Batch RSA and is
System, it is intended to solve the problems, such as that RSA decryption is slow when multiple multiplication calculating function needs to be put into high in the clouds calculating in the prior art.
An embodiment of the present invention provides the multiplying method based on Batch RSA, the method bag in a kind of cloud computing
Include following steps：
Data consumer User calculates function F to k multiplicationiA corresponding RSA public keys (e is produced respectivelyi, Ni), by institute
State RSA public keys (ei, Ni) it is respectively sent to corresponding multiplication calculating function FiIn included data set provider, wherein, k, i,
J, n are natural number, ei≠eiAnd 1≤i, j≤k；
The data consumer User utilizes public key (ei, Ni) function F is calculated to multiplicationiIn the required data make
The data of userIt is encrypted, forms corresponding multiplication and calculate function FiThe required data consumer
Encryption data, multiplication is calculated into function FiAnd its corresponding required described data consumer
Encryption dataSend to high in the clouds；
The data set providerUtilize public key (ei, Ni) function F is calculated to multiplicationiIn the required data carry
The data of donorIt is encrypted, forms corresponding multiplication and calculate function FiThe required data set provider adds
Ciphertext data, multiplication is calculated into function FiThe encryption data of the required data set providerSend to high in the clouds；
Function F is calculated according to the multiplicationi, the high in the clouds carries out multiplying to encryption data, obtains k multiplication and calculate
Function FiCryptographic calculation result RSA (Fi(result)), by the k cryptographic calculation result RSA (Fi(result)) send extremely
The data consumer, the encryption data include the encryption data of the data consumerWith
The encryption data of the data set provider
K multiplication, which is received, in the data consumer calculates function FiCryptographic calculation result RSA (Fi(result))
Afterwards, the data consumer decrypts k multiplication and calculates function F at the same timeiCryptographic calculation result RSA (Fi(result)), obtain every
A multiplication calculates function FiDecryption operation result.
The embodiment of the present invention provides the multiplying system based on Batch RSA, the system in a kind of cloud computing again
Including：
RSA public key generation units, for calculating function F to k multiplicationiA corresponding RSA public keys (e is produced respectivelyi,
Ni), by the RSA public keys (ei, Ni) it is respectively sent to corresponding multiplication calculating function FiIn included data set provider, its
In, k, i, j, n are natural number, ei≠eiAnd 1≤i, j≤k；
The DEU data encryption unit of data consumer, public key (e is utilized for the data consumer Useri, Ni) to multiplication meter
Calculate function FiIn the required data consumer dataIt is encrypted, forms corresponding multiplication and calculate letter
Number FiThe encryption data of the required data consumer, multiplication is calculated into function FiIt is and right
Answer the encryption data of its required data consumerSend to high in the clouds；
The DEU data encryption unit of data set provider, for the data set providerUtilize public key (ei, Ni) to multiplication meter
Calculate function FiIn the required data set provider dataIt is encrypted, forms corresponding multiplication and calculate function
FiThe encryption data of the required data set provider, multiplication is calculated into function FiRequired institute
State the encryption data of data set providerSend to high in the clouds；
Multiplying unit, for calculating function F according to the multiplicationi, the high in the clouds carries out multiplication fortune to encryption data
Calculate, obtain k multiplication and calculate function FiCryptographic calculation result RSA (Fi(result)), by the k cryptographic calculation result RSA
(Fi(result)) sending to the data consumer, the encryption data includes the encryption data of the data consumerWith the encryption data of the data set provider
Arithmetic element is decrypted, receiving k multiplication in the data consumer calculates function FiCryptographic calculation result RSA
(Fi(result)) after, the data consumer decrypts k multiplication and calculates function F at the same timeiCryptographic calculation result RSA (Fi
(result)), obtain each multiplication and calculate function FiDecryption operation result.
Multiplying method and system based on Batch RSA in a kind of cloud computing that the embodiment of the present invention is provided,
Data consumer in client calculates function according to each multiplication and produces corresponding public key, and calculates function using each multiplication
Transmission is encrypted to high in the clouds in the data that corresponding public key calculates each multiplication the required data consumer of function, counts at the same time
Also function corresponding public key is calculated using each multiplication the required data consumer of function is calculated to each multiplication according to supplier
Data transmission is encrypted to high in the clouds, high in the clouds, which according to each multiplication calculates the encrypted data of function pair computing is encrypted, to be sent
To the data consumer in client, data consumer after receiving all multiplication and calculating the cryptographic calculation result of function,
Synchronous decryption obtains all data.It disclosure satisfy that high in the clouds carries out multiplying operation to ciphertext data and cannot get the letter of data
Breath, while improve data consumer and multiple cryptographic calculation results returned from high in the clouds are decrypted at the same time, improve computational efficiency.
Brief description of the drawings
Fig. 1 is the flow chart of the multiplying method based on Batch RSA in cloud computing provided in an embodiment of the present invention；
Fig. 2 is that data consumer decrypts k multiplication calculating function F at the same time in the embodiment of the present inventioniCryptographic calculation method
In upwards filtration stage schematic diagram；
Fig. 3 is that data consumer decrypts k multiplication calculating function F at the same time in the embodiment of the present inventioniCryptographic calculation method
In downwards filtration stage schematic diagram；
Fig. 4 is the schematic diagram of the multiplying system based on Batch RSA in cloud computing provided in an embodiment of the present invention.
Embodiment
In order to make the purpose , technical scheme and advantage of the present invention be clearer, with reference to the accompanying drawings and embodiments, it is right
The present invention is further elaborated.It should be appreciated that the specific embodiments described herein are merely illustrative of the present invention, and
It is not used in the restriction present invention.
Fig. 1 shows the flow chart of the multiplying method based on Batch RSA in cloud computing.As shown in Figure 1, the side
Method includes the following steps：
In step S101, data consumer User calculates function F to k multiplicationiA corresponding RSA public key is produced respectively
(ei, Ni), by the RSA public keys (ei, Ni) it is respectively sent to corresponding multiplication calculating function FiIn included data set provider
, wherein, k, i, j, n are natural number, ei ≠ ejAnd 1≤i, j≤k；
In the present embodiment, data consumer User calculates function F to k multiplicationiIt is public that a corresponding RSA is produced respectively
Key (ei, Ni) method, include the following steps：Function F is calculated to the multiplicationi(1≤i≤k) chooses two Big prime pi, qi, meter
Calculate Ni=Piqi,Randomly select an integer ei, wherein, ei≠ej, 1≤i, j≤k
And i ≠ j, and meet Obtain RSA public keys (ei, Ni)。
In the present embodiment, data consumer User calculates function F to k multiplicationiIt is public that a corresponding RSA is produced respectively
Key (ei, Ni) method, further include generation one and RSA public keys (ei, Ni) key each other RSA private keys (di, Ni), specifically include as
Lower step：Function F is calculated to the multiplicationi(1≤i≤k) chooses two Big prime pi, qi, calculate Ni=piqi,Randomly select an integer ei, wherein, ei≠ej, 1≤i, j≤k and i ≠ j, it is and full
Foot According to
Try to achieve di, obtain RSA private keys (di, Ni)。
In step S102, the data consumer User utilizes public key (ei, Ni) function F is calculated to multiplicationiIn it is required
The data of the data consumerIt is encrypted, forms corresponding multiplication and calculate function FiThe required number
According to the encryption data of userMultiplication is calculated into function FiAnd its corresponding required described number
According to the encryption data of userSend to high in the clouds；
For example, if multiplication calculates function F1The data of data consumer need to be used, then (e is used1, N1) plus
Close multiplication calculates function F1The data of required data consumer；If multiplication calculates function FkUse need to be used
The data of person, then (e is usedk, Nk) encryption multiplication calculating function FkThe data of the required data consumer used。
In step S103, the data set providerUtilize public key (ei, Ni) function F is calculated to multiplicationiIn it is required
The data of the data set providerIt is encrypted, forms corresponding multiplication and calculate function FiThe required data
The encryption data of supplier, multiplication is calculated into function FiThe encryption of the required data set provider
DataSend to high in the clouds；
Such as：If multiplication calculates function FiData set provider need to be usedWithData, then data set providerWith
Utilize public key (ei, Ni) encryption each possesses and multiplication calculates function FiThe data needed.
In step S104, function F is calculated according to the multiplicationi, the high in the clouds carries out multiplying to encryption data, obtains
K multiplication calculates function FiCryptographic calculation result RSA (Fi(result)), by the k cryptographic calculation result RSA (Fi
(result)) sending to the data consumer, the encryption data includes the encryption data of the data consumerWith the encryption data of the data set provider
Such as：If multiplication calculates function F1It is that requirement calculates data set providerData, data set provider
Data(data) and data consumer dataProduct, then high in the clouds calculate data set provider,
The product of rear data is encrypted with user's data：
, and by cryptographic calculation result RSA (Fi(result)) data consumer is returned to.Wherein,Expression belongs to data and carries
DonorAnd multiplication calculates function F1Required data；Represent that belonging to data using rsa encryption provides
PersonAnd multiplication calculates function F1Encryption data after required data；Represent that multiplication calculates function F1Institute
Data that are needing and belonging to data consumer.
In step S105, receive k multiplication in the data consumer and calculate function FiCryptographic calculation result RSA (Fi
(result)) after, the data consumer decrypts k multiplication and calculates function F at the same timeiCryptographic calculation result RSA (Fi
(result)), obtain each multiplication and calculate function FiDecryption operation result.
In the present embodiment, as Fig. 2 and Fig. 3, the data consumer decrypt k multiplication and calculate function F at the same timeiTo be described
Data consumer is based on Batch RSA technologies and decrypt at the same time, and Batch RSA technologies are batch processing RSA technologies, specific bag
Include following steps：
Upward filtration stage：Batch trees built bottom-up, the branch of each leaf node are a public key, public exponent
For E ← ei, the public exponent value of interior nodes is product E ← E of its left and right child's public exponent valueL·ER, each encrypted cipher text ci
Corresponding public key eiLeaf node on, and each interior nodes
The exponentiation stage：Root node is calculated
Downward filtration stage：X is taken to make its satisfaction：X=0(mod EL) and X=1 (mod ER), according to Chinese remainder theorem CRT
X is pushed away to obtain, makes XL=X/ELAnd XR=(X-1)/ER, each interior nodes mXIt is equivalent toUtilizeAnd mL← m/mRRecurrence, tries to achieve each plaintext
WhereinmiRepresent the plaintext after i-th of decryption.
Data consumer in the client calculates function according to each multiplication and produces corresponding public key, and is multiplied using each
Method calculates the corresponding public key of function and transmission is encrypted extremely to the data of each multiplication calculating required data consumer of function
High in the clouds, while data set provider is also required to each multiplication calculating function using the corresponding public key of each multiplication calculating function
Transmission is encrypted to high in the clouds in the data of data set provider, and high in the clouds calculates the encrypted data of function pair according to each multiplication and added
Close computing is sent to the data consumer in client, and data consumer calculates the encryption fortune of function receiving all multiplication
After calculating result, synchronous decryption obtains all data.It disclosure satisfy that high in the clouds carries out ciphertext data multiplying operation and cannot get
The information of data, while improve data consumer and multiple cryptographic calculation results returned from high in the clouds are decrypted at the same time, improve
Computational efficiency.
Fig. 4 shows the principle of the multiplying system based on Batch RSA in cloud computing provided in an embodiment of the present invention
Figure, the system comprises：RSA public key generation units 41, the DEU data encryption unit 42 of data consumer, the data of data set provider
Encryption unit 43, multiplying unit 44 and decryption arithmetic element 45.It is described in detail below：
RSA public key generation units 41 are used to calculate function F to k multiplicationiA corresponding RSA public keys (e is produced respectivelyi,
Ni), by the RSA public keys (ei, Ni) it is respectively sent to corresponding multiplication calculating function FiIn included data set provider, its
In, k, i, j, n are natural number, ei≠eiAnd 1≤i, j≤k.
The RSA public key generation units to the multiplication by calculating function Fi(1≤i≤k) chooses two Big prime pi,
qi, calculate Ni=piqi,Randomly select an integer ei, wherein, ei≠ej, 1≤i, j
≤ k and i ≠ j, and meet Obtain RSA public keys (ei, Ni)。
The RSA public key generation units include producing one and RSA public keys (ei, Ni) key each other RSA private keys (di,
Ni), by calculating function F to the multiplicationi(1≤i≤k) chooses two Big prime pi, qi, calculate Ni=piqi,Randomly select an integer ei, wherein, ei≠ej, 1≤i, j≤k and i ≠ j, and meetAccording to
Try to achieve di, obtain RSA private keys (di, Ni)。
The DEU data encryption unit 42 of data consumer utilizes public key (e for the data consumer Useri, Ni) to multiplication
Calculate function FiIn the required data consumer dataIt is encrypted, forms corresponding multiplication and calculate
Function FiThe encryption data of the required data consumer, multiplication is calculated into function FiAnd
The encryption data of its corresponding required data consumerSend to high in the clouds.
For example, if multiplication calculates function F1The data of data consumer need to be used, then (e is used1, N1) plus
Close multiplication calculates the data of the data consumer needed for function F1；If multiplication calculates function FkUse need to be used
The data of personThen use (ek, Nk) encryption multiplication calculating function FkThe data of the required data consumer used
The DEU data encryption unit 43 of data set provider is used for the data set providerUtilize public key (ei, Ni) to multiplication meter
Calculate function FiIn the required data set provider dataIt is encrypted, forms corresponding multiplication and calculate function
FiThe encryption data of the required data set providerMultiplication is calculated into function FiRequired institute
State the encryption data of data consumerSend to high in the clouds.
Such as：If multiplication calculates function FiData set provider need to be usedWithData, then data set providerWith
Utilize public key (ei, Ni) encryption each possesses and multiplication calculates function F1The data needed.
Multiplying unit 44 is used to calculate function F according to the multiplicationi, the high in the clouds carries out multiplication fortune to encryption data
Calculate, obtain k multiplication and calculate function FiCryptographic calculation result RSA (Fi(result)), k are listened and states cryptographic calculation result RSA
(Fi(result)) sending to the data consumer, the encryption data includes the encryption data of the data consumerWith the encryption data of the data set provider
Such as：If multiplication calculates function F1It is that requirement calculates data set providerDataData
SupplierDataWith the data of data consumerProduct, then high in the clouds count
Calculate data set providerThe product of rear data is encrypted with user's data： And by cryptographic calculation result RSA (Fi(result)) data are returned to
User.Wherein,Expression belongs to data set providerAnd multiplication calculates function F1Required data；Represent to belong to data set provider using rsa encryptionAnd multiplication calculates function F1After required data
Encryption data；Represent that multiplication calculates function F1Data that are required and belonging to data consumer.
Decryption arithmetic element 45 receives k multiplication in the data consumer and calculates function FiCryptographic calculation result
RSA(Fi(result)) after, the data consumer decrypts k multiplication and calculates function F at the same timeiCryptographic calculation result RSA (Fi
(result)), obtain each multiplication and calculate function FiDecryption operation result.
Data consumer in the client calculates function according to each multiplication and produces corresponding public key, and is multiplied using each
Method calculates the corresponding public key of function and transmission is encrypted extremely to the data of each multiplication calculating required data consumer of function
High in the clouds, while data set provider is also required to each multiplication calculating function using the corresponding public key of each multiplication calculating function
Transmission is encrypted to high in the clouds in the data of data set provider, and high in the clouds calculates the encrypted data of function pair according to each multiplication and added
Close computing is sent to the data consumer in client, and data consumer calculates the encryption fortune of function receiving all multiplication
After calculating result, synchronous decryption obtains all data.It disclosure satisfy that high in the clouds carries out ciphertext data multiplying operation and cannot get
The information of data, while improve data consumer and multiple cryptographic calculation results returned from high in the clouds are decrypted at the same time, improve
Computational efficiency.
The foregoing is merely illustrative of the preferred embodiments of the present invention, is not intended to limit the invention, all essences in the present invention
All any modification, equivalent and improvement made within refreshing and principle etc., should all be included in the protection scope of the present invention.
Claims (7)
1. a kind of multiplying method based on Batch RSA in cloud computing, it is characterised in that the described method includes following step
Suddenly：
Data consumer User calculates function F to k multiplicationiA corresponding RSA public keys (e is produced respectivelyi, Ni), by described in
RSA public keys (ei, Ni) it is respectively sent to corresponding multiplication calculating function FiIn included data set providerWherein, k, i, n are equal
For natural number and 1≤i≤k；
The data consumer User utilizes public key (ei, Ni) function F is calculated to multiplicationiIn the required data consumer
DataIt is encrypted, forms corresponding multiplication and calculate function FiThe encryption of the required data consumer
DataMultiplication is calculated into function FiAnd the encryption of its corresponding required data consumer
DataSend to high in the clouds；
The data set providerUtilize public key (ei, Ni) function F is calculated to multiplicationiIn the required data set provider
DataIt is encrypted, forms corresponding multiplication and calculate function FiThe encryption data of the required data set providerMultiplication is calculated into function FiThe encryption data of the required data set providerSend to high in the clouds；
Function F is calculated according to the multiplicationi, the high in the clouds carries out multiplying to encryption data, obtains k multiplication and calculate function
FiCryptographic calculation result RSA (Fi(result)), by the k cryptographic calculation result RSA (Fi(result)) send to described
Data consumer, the encryption data include the encryption data of the data consumerWith it is described
The encryption data of data set provider
K multiplication, which is received, in the data consumer calculates function FiCryptographic calculation result RSA (Fi(result)) after, institute
State data consumer and decrypt k multiplication calculating function F at the same timeiCryptographic calculation result RSA (Fi(result)) each multiply, is obtained
Method calculates function FiDecryption operation result.
2. the method as described in claim 1, it is characterised in that the data consumer User calculates function F to k multiplicationiPoint
Chan Sheng not a corresponding RSA public keys (ei, Ni) method, include the following steps：
Function F is calculated to the multiplicationi(1≤i≤k) chooses two Big prime pi, qi, calculate Ni=Piqi,
Randomly select an integer ei, meetObtain RSA public keys (ei,
Ni)。
3. the method as described in claim 1, it is characterised in that the data consumer User calculates function F to k multiplicationiPoint
Chan Sheng not a corresponding RSA public keys (ei, Ni) method, further include generation one and RSA public keys (ei, Ni) key each other RSA
Private key (di, Ni), specifically comprise the following steps：
Function F is calculated to the multiplicationi(1≤i≤k) chooses two Big prime pi, qi, calculate Ni=piqi,
Randomly select an integer ei, meet
According toTry to achieve di, obtain RSA private keys (di, Ni)。
4. the method as described in claim 1, it is characterised in that the data consumer decrypts the k multiplication received at the same time
Calculate function FiCryptographic calculation result RSA (Fi(result)), it is decrypted, is specifically included as follows based on Batch RSA technologies
Step：
Batch trees built bottom-up, the branch of each leaf node is a public key, and public exponent is E ← ej, internal node
Public exponent value is product E ← E of its left and right child's public exponent valueL·ER, wherein, ELFor the left child of the internal node
Public exponent, ERFor the public exponent of the right child of the internal node；Each encrypted cipher text ciCorresponding public key ei
Leaf node on, and the value of each internal node is CL ER.CR EL, wherein, CLFor the value of the left child of the internal node, CRFor
The value of the right child of the internal node；The value for obtaining root node isWherein,Pass through e and institute
The public exponent for stating root node obtains plaintext parameter：The A is used to represent filtering ginseng in downward filtration stage
Number；
According to Chinese remainder theorem CRT and X=0 (mod EL) and X=1 (mod ER), filtered index X is pushed away to obtain, makes XL=X/EL
And XR=(X-1)/ER, the filter value m of each internal nodeXIt is equivalent toUtilizeAnd mL←m/mR, try to achieve each plaintextIts
InWherein, j is natural number, ei≠ejAnd 1≤j≤k；M is filtration parameter, mLFor left filtration parameter,
mRFor right filtration parameter；XLFor left filtered index, XRFor right filtered index.
A kind of 5. multiplying system based on Batch RSA in cloud computing, it is characterised in that the system comprises：
RSA public key generation units, for calculating function F to k multiplicationiA corresponding RSA public keys (e is produced respectivelyi, Ni), will
RSA public keys (the ei, Ni) it is respectively sent to corresponding multiplication calculating function FiIn included data set providerWherein, k,
I, n are natural number and 1≤i≤k；
The DEU data encryption unit of data consumer, public key (e is utilized for the data consumer Useri, Ni) letter is calculated to multiplication
Number FiIn the required data consumer dataIt is encrypted, forms corresponding multiplication and calculate function Fi
The encryption data of the required data consumerMultiplication is calculated into function FiAnd correspond to it
The encryption data of the required data consumerSend to high in the clouds；
The DEU data encryption unit of data set provider, for the data set providerUtilize public key (ei, Ni) letter is calculated to multiplication
Number FiIn the required data set provider dataIt is encrypted, forms corresponding multiplication and calculate function FiInstitute
The encryption data of the data set provider neededMultiplication is calculated into function FiThe required number
According to the encryption data of userSend to high in the clouds；
Multiplying unit, for calculating function F according to the multiplicationi, the high in the clouds carries out multiplying to encryption data, obtains
Function F is calculated to k multiplicationiCryptographic calculation result RSA (Fi(result)), by the k cryptographic calculation result RSA (Fi
(result)) sending to the data consumer, the encryption data includes the encryption data of the data consumerWith the encryption data of the data set provider
Arithmetic element is decrypted, receiving k multiplication in the data consumer calculates function FiCryptographic calculation result RSA (Fi
(result)) after, the data consumer decrypts k multiplication and calculates function F at the same timeiCryptographic calculation result RSA (Fi
(result)), obtain each multiplication and calculate function FiDecryption operation result.
6. system as claimed in claim 5, it is characterised in that the RSA public key generation units are by calculating the multiplication
Function Fi(1≤i≤k) chooses two Big prime pi, qi, calculate Ni=piqi,With
Machine chooses an integer ei, meet Obtain RSA public keys (ei, Ni)。
7. system as claimed in claim 6, it is characterised in that the RSA public key generation units include producing one and RSA public affairs
Key (ei, Ni) key each other RSA private keys (di, Ni), by calculating function F to the multiplicationi(1≤i≤k) chooses two big element
Number pi, qi, calculate Ni=piqi, Randomly select an integer ei, wherein, According to
Try to achieve di, obtain RSA private keys (di, Ni)。
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| CN106209371B (en) * | 2016-07-25 | 2019-05-03 | 青岛大学 | The outsourcing method of key is generated applied to RSA Algorithm |
| CN107124276B (en) * | 2017-04-07 | 2020-07-28 | 西安电子科技大学 | Safe data outsourcing machine learning data analysis method |
| CN107294698B (en) * | 2017-07-25 | 2019-11-26 | 西安电子科技大学 | The full homomorphic cryptography method that single ciphertext homomorphism calculates |
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| CN103095459A (en) * | 2013-01-17 | 2013-05-08 | 广东数字证书认证中心有限公司 | Operation method, device and server of modular exponentiation in public key cryptosystem |
| CN103209073A (en) * | 2013-01-17 | 2013-07-17 | 北京昆腾微电子有限公司 | Anti-attack method and device in electronic component using Rivest-Shamir-Adleman (RSA) public-key encryption algorithm |
| CN103401871A (en) * | 2013-08-05 | 2013-11-20 | 苏州大学 | Method and system for sequencing ciphertexts orienting to homomorphic encryption |
| CN103428299A (en) * | 2013-09-04 | 2013-12-04 | 安徽大学 | Cloud storage access control method |
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| CN103095459A (en) * | 2013-01-17 | 2013-05-08 | 广东数字证书认证中心有限公司 | Operation method, device and server of modular exponentiation in public key cryptosystem |
| CN103209073A (en) * | 2013-01-17 | 2013-07-17 | 北京昆腾微电子有限公司 | Anti-attack method and device in electronic component using Rivest-Shamir-Adleman (RSA) public-key encryption algorithm |
| CN103401871A (en) * | 2013-08-05 | 2013-11-20 | 苏州大学 | Method and system for sequencing ciphertexts orienting to homomorphic encryption |
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