CN104980271A - Multiplication operation method and system in cloud computing and based on Batch RSA - Google Patents

Abstract

The invention relates to the field of communication, and provides a multiplication operation method and a multiplication operation system in cloud computing and based on Batch RSA. The method comprises: a data user creates a public key corresponding to multiplication operation function Fi, the number of which is k, and the public keys are respectively sent to data providers included in the corresponding multiplication operation function Fi; the data user encrypts data needed by the data user in the multiplication operation function Fi with the help of the public keys, and enciphered data belonging to the data user and needed by the corresponding multiplication operation function Fi is sent to the cloud; the data providers encrypt the data needed by the multiplication operation function Fi and belonging to the data provider with the help of the public keys; the enciphered data is subject to multiplication operation through the cloud and sent to the data user. The data user deciphers the enciphered operation results from k multiplication operation functions Fi at the same time and gains deciphered operation results. Thus, deciphering speed of enciphered operation results returned from the cloud by the data user is improved, and calculation efficiency is developed.

Description

Based on the multiplying method and system of Batch RSA in a kind of cloud computing

Technical field

The invention belongs to the communications field, particularly relate to the multiplying method and system based on Batch RSA in a kind of cloud computing.

Background technology

Along with being showing improvement or progress day by day and the progressively popularization of network application of information technology, cloud computing technology obtains unprecedented development and research, but it is while raising service efficiency, also to realize user information safety and secret protection bring greatly difficulty with challenge.Safety is just becoming the major issue that field of cloud calculation urgently breaks through, and its importance and urgency can not be ignored.And along with constantly popularizing of cloud computing, the importance of cloud computing safety problem presents progressively ascendant trend, become the key factor of its development of restriction.Homomorphic cryptography technology is that the data security of cloud computing and secret protection provide a kind of key technology, makes to carry out complex calculations to the enciphered data be stored in Cloud Server and operation becomes possibility.Homomorphic cryptography technology can meet and operates encrypt data, does not allow again operator decipher and obtains data message, ensure computational efficiency simultaneously, can solve the problem to a great extent.Existing homomorphic encryption scheme is the RSA system based on factoring difficulty, meets homomorphism speciality to any time multiplication, but when client exist multiple multiplication computing function need to be put into high in the clouds calculate time, existing RSA system exists deciphers slow shortcoming.

Summary of the invention

The object of the embodiment of the present invention is to provide the multiplying method and system based on Batch RSA in a kind of cloud computing, is intended to need to be put into RSA when high in the clouds calculates at multiple multiplication computing function in solution prior art and deciphers slow problem.

Embodiments provide a kind of multiplying method based on Batch RSA in cloud computing, described method comprises the steps:

Data consumer User is to k multiplication computing function F _irSA PKI (the e that generation one is corresponding respectively _i, N _i), by described RSA PKI (e _i, N _i) be sent to corresponding multiplication computing function F respectively _iin included data set provider , wherein, k, i, j, n are natural number, e _i≠ e _iand 1≤i, j≤k;

Described data consumer User utilizes PKI (e _i, N _i) to multiplication computing function F _iin the data of required described data consumer be encrypted, form corresponding multiplication computing function F _ithe enciphered data of required described data consumer , by multiplication computing function F _iand the enciphered data of corresponding described data consumer required for it be sent to high in the clouds;

Described data set provider utilize PKI (e _i, N _i) to multiplication computing function F _iin the data of required described data set provider be encrypted, form corresponding multiplication computing function F _ithe enciphered data of required described data set provider , by multiplication computing function F _ithe enciphered data of required described data set provider be sent to high in the clouds;

According to described multiplication computing function F _i, multiplying is carried out to enciphered data in described high in the clouds, obtains k multiplication computing function F _icryptographic calculation result RSA (F _i(result)), by k described cryptographic calculation result RSA (F _i(result)) be sent to described data consumer, described enciphered data comprises the enciphered data of described data consumer with the enciphered data of described data set provider

K multiplication computing function F is received described data consumer _icryptographic calculation result RSA (F _i(result)), described data consumer deciphers k multiplication computing function F simultaneously _icryptographic calculation result RSA (F _i(result)), each multiplication computing function F is obtained _idecrypt operation result.

The embodiment of the present invention further provides the multiplying system based on Batch RSA in a kind of cloud computing, and described system comprises:

RSA public key generation unit, for k multiplication computing function F _irSA PKI (the e that generation one is corresponding respectively _i, N _i), by described RSA PKI (e _i, N _i) be sent to corresponding multiplication computing function F respectively _iin included data set provider , wherein, k, i, j, n are natural number, e _i≠ e _iand 1≤i, j≤k;

The DEU data encryption unit of data consumer, utilizes PKI (e for described data consumer User _i, N _i) to multiplication computing function F _iin the data of required described data consumer be encrypted, form corresponding multiplication computing function F _ithe enciphered data of required described data consumer , by multiplication computing function F _iand the enciphered data of corresponding described data consumer required for it be sent to high in the clouds;

The DEU data encryption unit of data set provider, for described data set provider utilize PKI (e _i, N _i) to multiplication computing function F _iin the data of required described data set provider be encrypted, form corresponding multiplication computing function F _ithe enciphered data of required described data set provider , by multiplication computing function F _ithe enciphered data of required described data set provider be sent to high in the clouds;

Multiplying unit, for according to described multiplication computing function F _i, multiplying is carried out to enciphered data in described high in the clouds, obtains k multiplication computing function F _icryptographic calculation result RSA (F _i(result)), by k described cryptographic calculation result RSA (F _i(result)) be sent to described data consumer, described enciphered data comprises the enciphered data of described data consumer with the enciphered data of described data set provider

Decrypt operation unit, receives k multiplication computing function F described data consumer _icryptographic calculation result RSA (F _i(result)), described data consumer deciphers k multiplication computing function F simultaneously _icryptographic calculation result RSA (F _i(result)), each multiplication computing function F is obtained _idecrypt operation result.

Based on the multiplying method and system of Batch RSA in a kind of cloud computing that the embodiment of the present invention provides, data consumer in the client produces corresponding PKI according to each multiplication computing function, and utilize the data of PKI corresponding to each multiplication computing function to the data consumer required for each multiplication computing function to be encrypted to be sent to high in the clouds, data set provider also utilizes the data of PKI corresponding to each multiplication computing function to the data consumer required for each multiplication computing function to be encrypted and is sent to high in the clouds simultaneously, high in the clouds is encrypted computing according to the data of each multiplication computing function to encryption and sends to data consumer in client, data consumer is after the cryptographic calculation result receiving all multiplication computing functions, synchronous deciphering obtains all data.High in the clouds can be met carry out multiplying operation to encrypt data and can not get the information of data, improve data consumer simultaneously and multiple cryptographic calculation results returned from high in the clouds is deciphered simultaneously, improve computational efficiency.

Accompanying drawing explanation

Fig. 1 is the flow chart based on the multiplying method of Batch RSA in the cloud computing that provides of the embodiment of the present invention;

Fig. 2 is that in the embodiment of the present invention, data consumer deciphers k multiplication computing function F simultaneously _icryptographic calculation method in the schematic diagram of upwards filtration stage;

Fig. 3 is that in the embodiment of the present invention, data consumer deciphers k multiplication computing function F simultaneously _icryptographic calculation method in the schematic diagram of downward filtration stage;

Fig. 4 is the schematic diagram based on the multiplying system of Batch RSA in the cloud computing that provides of the embodiment of the present invention.

Embodiment

In order to make object of the present invention, technical scheme and advantage clearly understand, below in conjunction with drawings and Examples, the present invention is further elaborated.Should be appreciated that specific embodiment described herein only in order to explain the present invention, be not intended to limit the present invention.

Fig. 1 shows the flow chart based on the multiplying method of Batch RSA in cloud computing.As shown in Figure 1, described method comprises the steps:

In step S101, data consumer User is to k multiplication computing function F _irSA PKI (the e that generation one is corresponding respectively _i, N _i), by described RSA PKI (e _i, N _i) be sent to corresponding multiplication computing function F respectively _iin included data set provider , wherein, k, i, j, n are natural number, ei ≠ e _jand 1≤i, j≤k;

In the present embodiment, data consumer User is to k multiplication computing function F _irSA PKI (the e that generation one is corresponding respectively _i, N _i) method, comprise the steps: described multiplication computing function F _i(1≤i≤k) chooses two Big prime p _i, q _i, calculate N _i=P _iq _i, random selecting integer e _i, wherein, e _i≠ e _j, 1≤i, j≤k and i ≠ j, and to meet obtain RSA PKI (e _i, N _i).

In the present embodiment, data consumer User is to k multiplication computing function F _irSA PKI (the e that generation one is corresponding respectively _i, N _i) method, also comprise generation one and RSA PKI (e _i, N _i) the RSA private key (d of key each other _i, N _i), specifically comprise the steps: described multiplication computing function F _i(1≤i≤k) chooses two Big prime p _i, q _i, calculate N _i=p _iq _i, random selecting integer e _i, wherein, e _i≠ e _j, 1≤i, j≤k and i ≠ j, and to meet according to try to achieve d _i, obtain RSA private key (d _i, N _i).

In step S102, described data consumer User utilizes PKI (e _i, N _i) to multiplication computing function F _iin the data of required described data consumer be encrypted, form corresponding multiplication computing function F _ithe enciphered data of required described data consumer by multiplication computing function F _iand the enciphered data of corresponding described data consumer required for it be sent to high in the clouds;

Such as, if multiplication computing function F ₁the data of data consumer need be used , then (e is used ₁, N ₁) encryption multiplication computing function F ₁the data of required data consumer ; If multiplication computing function F _kthe data of user need be used , then (e is used _k, N _k) encryption multiplication computing function F _kneeded for the data of data consumer used .

In step S103, described data set provider utilize PKI (e _i, N _i) to multiplication computing function F _iin the data of required described data set provider be encrypted, form corresponding multiplication computing function F _ithe enciphered data of required described data set provider , by multiplication computing function F _ithe enciphered data of required described data set provider be sent to high in the clouds;

Such as: if multiplication computing function F _idata set provider need be used with data, then data set provider with utilize PKI (e _i, N _i) encryption have separately and multiplication computing function F _ithe data needed.

In step S104, according to described multiplication computing function F _i, multiplying is carried out to enciphered data in described high in the clouds, obtains k multiplication computing function F _icryptographic calculation result RSA (F _i(result)), by k described cryptographic calculation result RSA (F _i(result)) be sent to described data consumer, described enciphered data comprises the enciphered data of described data consumer with the enciphered data of described data set provider

Such as: if multiplication computing function F ₁requirement calculated data supplier data , data set provider data and the data of data consumer (data) product, then high in the clouds calculated data supplier , the product of rear data is encrypted with user's data: , and by cryptographic calculation result RSA (F _i(result)) data consumer is returned to.Wherein, represent and belong to data set provider and multiplication computing function F ₁required data; representing utilizes rsa encryption to belong to data set provider and multiplication computing function F ₁enciphered data after required data; represent multiplication computing function F ₁required and belong to the data of data consumer.

In step S105, receive k multiplication computing function F described data consumer _icryptographic calculation result RSA (F _i(result)), described data consumer deciphers k multiplication computing function F simultaneously _icryptographic calculation result RSA (F _i(result)), each multiplication computing function F is obtained _idecrypt operation result.

In the present embodiment, as Fig. 2 and Fig. 3, described data consumer deciphers k multiplication computing function F simultaneously _ifor described data consumer deciphers based on Batch RSA technology simultaneously, Batch RSA technology is batch process RSA technology, specifically comprises the steps:

Upwards filtration stage: construct Batch tree from bottom to top, the branch of each leaf node is a PKI, and public exponent is E ← e _i, the public exponent value of interior nodes is the product E ← E of its left and right child's public exponent value _le _r, each encrypted cipher text c _icorresponding PKI e _ileaf node on, and each interior nodes $c\←c_L^{E_R}\·c_R^{E_L};$

The exponentiation stage: calculate root node $c={\mathrm{\Π}}_{i=1}^k{c}_i^{e/e_i},e={\mathrm{\Π}}_{i=1}^k{e}_i,A=c^{1/e}=$ ${\mathrm{\Π}}_{i=1}^k{c}_i^{1/e_i};$

Downward filtration stage: get X and make it meet: X=0 (mod E _l) and X=1 (mod E _r), push away to obtain X according to Chinese remainder theorem CRT, make X _l=X/E _land X _r=(X-1)/E _r, each interior nodes m ^xbe equivalent to utilize and m _l← m/m _rrecurrence, tries to achieve each plaintext $m_i=\frac{A^{{\mathrm{\α}}_i}}{c_i^{({\mathrm{\α}}_i-1)\·d_i}x{\mathrm{\Π}}_{j=1,j\≠i}^k{c}_i^{{\mathrm{\α}}_i\·d_i}}\left(\mathrm{mod}N\right),$ Wherein ${\mathrm{\α}}_i=\left\{\begin{array}{c}1\mathrm{mod}{e}_i\\ 0\mathrm{mod}{e}_j,(j\≠i)\end{array}\right..$ M _irepresent the plaintext after i-th deciphering.

Data consumer in the client produces corresponding PKI according to each multiplication computing function, and utilize the data of PKI corresponding to each multiplication computing function to the data consumer required for each multiplication computing function to be encrypted to be sent to high in the clouds, data set provider also utilizes the data of PKI corresponding to each multiplication computing function to the data set provider required for each multiplication computing function to be encrypted and is sent to high in the clouds simultaneously, high in the clouds is encrypted computing according to the data of each multiplication computing function to encryption and sends to data consumer in client, data consumer is after the cryptographic calculation result receiving all multiplication computing functions, synchronous deciphering obtains all data.High in the clouds can be met carry out multiplying operation to encrypt data and can not get the information of data, improve data consumer simultaneously and multiple cryptographic calculation results returned from high in the clouds is deciphered simultaneously, improve computational efficiency.

Fig. 4 shows the schematic diagram based on the multiplying system of Batch RSA in the cloud computing that the embodiment of the present invention provides, and described system comprises: the DEU data encryption unit 42 of RSA public key generation unit 41, data consumer, the DEU data encryption unit 43 of data set provider, multiplying unit 44 and deciphering arithmetic element 45.Specifically describe as follows:

RSA public key generation unit 41 is for k multiplication computing function F _irSA PKI (the e that generation one is corresponding respectively _i, N _i), by described RSA PKI (e _i, N _i) be sent to corresponding multiplication computing function F respectively _iin included data set provider , wherein, k, i, j, n are natural number, e _i≠ e _iand 1≤i, j≤k.

Described RSA public key generation unit passes through described multiplication computing function F _i(1≤i≤k) chooses two Big prime p _i, q _i, calculate N _i=p _iq _i, random selecting integer e _i, wherein, e _i≠ e _j, 1≤i, j≤k and i ≠ j, and to meet obtain RSA PKI (e _i, N _i).

Described RSA public key generation unit comprises generation one and RSA PKI (e _i, N _i) the RSA private key (d of key each other _i, N _i), by described multiplication computing function F _i(1≤i≤k) chooses two Big prime p _i, q _i, calculate N _i=p _iq _i, random selecting integer e _i, wherein, e _i≠ e _j, 1≤i, j≤k and i ≠ j, and to meet according to try to achieve d _i, obtain RSA private key (d _i, N _i).

The DEU data encryption unit 42 of data consumer utilizes PKI (e for described data consumer User _i, N _i) to multiplication computing function F _iin the data of required described data consumer be encrypted, form corresponding multiplication computing function F _ithe enciphered data of required described data consumer , by multiplication computing function F _iand the enciphered data of corresponding described data consumer required for it be sent to high in the clouds.

Such as, if multiplication computing function F ₁the data of data consumer need be used , then (e is used ₁, N ₁) data of data consumer needed for encryption multiplication computing function F1 ; If multiplication computing function F _kthe data of user need be used then use (e _k, N _k) encryption multiplication computing function F _kneeded for the data of data consumer used

The DEU data encryption unit 43 of data set provider is for described data set provider utilize PKI (e _i, N _i) to multiplication computing function F _iin the data of required described data set provider be encrypted, form corresponding multiplication computing function F _ithe enciphered data of required described data set provider by multiplication computing function F _ithe enciphered data of required described data consumer be sent to high in the clouds.

Such as: if multiplication computing function F _idata set provider need be used with data, then data set provider with utilize PKI (e _i, N _i) encryption have separately and multiplication computing function F ₁the data needed.

Multiplying unit 44 is for according to described multiplication computing function F _i, multiplying is carried out to enciphered data in described high in the clouds, obtains k multiplication computing function F _icryptographic calculation result RSA (F _i(result)), individual for k listening is stated cryptographic calculation result RSA (F _i(result)) be sent to described data consumer, described enciphered data comprises the enciphered data of described data consumer with the enciphered data of described data set provider

Such as: if multiplication computing function F ₁requirement calculated data supplier data data set provider data with the data of data consumer product, then high in the clouds calculated data supplier the product of rear data is encrypted with user's data: and by cryptographic calculation result RSA (F _i(result)) data consumer is returned to.Wherein, represent and belong to data set provider and multiplication computing function F ₁required data; representing utilizes rsa encryption to belong to data set provider and multiplication computing function F ₁enciphered data after required data; represent multiplication computing function F ₁required and belong to the data of data consumer.

Decrypt operation unit 45 receives k multiplication computing function F described data consumer _icryptographic calculation result RSA (F _i(result)), described data consumer deciphers k multiplication computing function F simultaneously _icryptographic calculation result RSA (F _i(result)), each multiplication computing function F is obtained _idecrypt operation result.

Data consumer in the client produces corresponding PKI according to each multiplication computing function, and utilize the data of PKI corresponding to each multiplication computing function to the data consumer required for each multiplication computing function to be encrypted to be sent to high in the clouds, data set provider also utilizes the data of PKI corresponding to each multiplication computing function to the data set provider required for each multiplication computing function to be encrypted and is sent to high in the clouds simultaneously, high in the clouds is encrypted computing according to the data of each multiplication computing function to encryption and sends to data consumer in client, data consumer is after the cryptographic calculation result receiving all multiplication computing functions, synchronous deciphering obtains all data.High in the clouds can be met carry out multiplying operation to encrypt data and can not get the information of data, improve data consumer simultaneously and multiple cryptographic calculation results returned from high in the clouds is deciphered simultaneously, improve computational efficiency.

The foregoing is only preferred embodiment of the present invention, not in order to limit the present invention, all any amendments done within the spirit and principles in the present invention, equivalent replacement and improvement etc., all should be included within protection scope of the present invention.

Claims (7)

1. in cloud computing based on a multiplying method of Batch RSA, it is characterized in that, described method comprises the steps:

Data consumer User is to k multiplication computing function F _irSA PKI (the e that generation one is corresponding respectively _i, N _i), by described RSA PKI (e _i, N _i) be sent to corresponding multiplication computing function F respectively _iin included data set provider , wherein, k, i, j, n are natural number, e _i≠ e _iand 1≤i, j≤k;

Described data consumer User utilizes PKI (e _i, N _i) to multiplication computing function F _iin the data of required described data consumer be encrypted, form corresponding multiplication computing function F _ithe enciphered data of required described data consumer , by multiplication computing function F _iand the enciphered data of corresponding described data consumer required for it be sent to high in the clouds;

Described data set provider utilize PKI (e _i, N _i) to multiplication computing function F _iin the data of required described data set provider be encrypted, form corresponding multiplication computing function F _ithe enciphered data of required described data set provider , by multiplication computing function F _ithe enciphered data of required described data set provider be sent to high in the clouds;

According to described multiplication computing function F _i, multiplying is carried out to enciphered data in described high in the clouds, obtains k multiplication computing function F _icryptographic calculation result RSA (F _i(result)), by k described cryptographic calculation result RSA (F _i(result)) be sent to described data consumer, described enciphered data comprises the enciphered data of described data consumer with the enciphered data of described data set provider ;

K multiplication computing function F is received described data consumer _icryptographic calculation result RSA (F _i(result)), described data consumer deciphers k multiplication computing function F simultaneously _icryptographic calculation result RSA (F _i(result)), each multiplication computing function F is obtained _idecrypt operation result.

2. the method for claim 1, is characterized in that, described data consumer User is to k multiplication computing function F _irSA PKI (the e that generation one is corresponding respectively _i, N _i) method, comprise the steps:

To described multiplication computing function F _i(1≤i≤k) chooses two Big prime p _i, q _i, calculate N _i=P _iq _i,

Random selecting integer e _i, wherein, e _i≠ e _j, 1≤i, j≤k and i ≠ j, and to meet obtain RSA PKI (e _i, N _i).

3. the method for claim 1, is characterized in that, described data consumer User is to k multiplication computing function F _irSA PKI (the e that generation one is corresponding respectively _i, N _i) method, also comprise generation one and RSA PKI (e _i, N _i) the RSA private key (d of key each other _i, N _i), specifically comprise the steps:

To described multiplication computing function F _i(1≤i≤k) chooses two Big prime p _i, q _i, calculate N _i=P _iq _i,

Random selecting integer e _i, wherein, e _i≠ e _j, 1≤i, j≤k and i ≠ j, and to meet

According to try to achieve d _i, obtain RSA private key (d _i, N _i).

4. the method for claim 1, is characterized in that, described data consumer deciphers k multiplication computing function F simultaneously _ifor described data consumer deciphers based on Batch RSA technology simultaneously, specifically comprise the steps:

Construct Batch tree from bottom to top, the branch of each leaf node is a PKI, and public exponent is E ← e _i, the public exponent value of interior nodes is the product E ← E of its left and right child's public exponent value _le _r, each encrypted cipher text ci is on the leaf node corresponding PKI ei, and each interior nodes obtain root node $c={\mathrm{\Π}}_{i=1}^k{c}_i^{e/e_i},e={\mathrm{\Π}}_{i=1}^k{e}_i,A=c^{1/e}={\mathrm{\Π}}_{i=1}^k{c}_i^{1/e_i};$

Getting X makes it meet: X=0 (mod E _l) and X=1 (mod E _r), push away to obtain X according to Chinese remainder theorem CRT, make X _l=X/E _land X _r=(X-1)/E _r, each interior nodes m ^xbe equivalent to utilize and m _l← m/m _rrecurrence, tries to achieve each plaintext $m_i=\frac{A^{{\mathrm{\α}}_i}}{c_i^{({\mathrm{\α}}_i-1)\·d_i}x{\mathrm{\Π}}_{j=1,j\≠i}^k{c}_i^{{\mathrm{\α}}_i\·d_i}}\left(\mathrm{mod}N\right),$ Wherein ${\mathrm{\α}}_i=\left\{\begin{array}{c}1\mathrm{mod}{e}_i\\ 0\mathrm{mod}{e}_j,(j\≠i)\end{array}\right..$

5. in cloud computing based on a multiplying system of Batch RSA, it is characterized in that, described system comprises:

RSA public key generation unit, for k multiplication computing function F _irSA PKI (the e that generation one is corresponding respectively _i, N _i), by described RSA PKI (e _i, N _i) be sent to corresponding multiplication computing function F respectively _iin included data set provider , wherein, k, i, j, n are natural number, e _i≠ e _iand 1≤i, j≤k;

The DEU data encryption unit of data consumer, utilizes PKI (e for described data consumer User _i, N _i) to multiplication computing function F _iin the data of required described data consumer be encrypted, form corresponding multiplication computing function F _ithe enciphered data of required described data consumer , by multiplication computing function F _iand the enciphered data of corresponding described data consumer required for it be sent to high in the clouds;

The DEU data encryption unit of data set provider, for described data set provider utilize PKI (e _i, N _i) to multiplication computing function F _iin the data of required described data set provider be encrypted, form corresponding multiplication computing function F _ithe enciphered data of required described data set provider , by multiplication computing function F _ithe enciphered data of required described data consumer be sent to high in the clouds;

Multiplying unit, for according to described multiplication computing function F _i, multiplying is carried out to enciphered data in described high in the clouds, obtains k multiplication computing function F _icryptographic calculation result RSA (F _i(result)), by k described cryptographic calculation result RSA (F _i(result)) be sent to described data consumer, described enciphered data comprises the enciphered data of described data consumer with the enciphered data of described data set provider ;

Decrypt operation unit, receives k multiplication computing function F described data consumer _icryptographic calculation result RSA (F _i(result)), described data consumer deciphers k multiplication computing function F simultaneously _icryptographic calculation result RSA (F _i(result)), each multiplication computing function F is obtained _idecrypt operation result.

6. system as claimed in claim 5, is characterized in that, described RSA public key generation unit passes through described multiplication computing function F _i(1≤i≤k) chooses two Big prime p _i, q _i, calculate N _i=p _iq _i, random selecting integer e _i, wherein, e _i≠ e _j, 1≤i, j≤k and i ≠ j, and to meet obtain RSA PKI (e _i, N _i).

7. system as claimed in claim 5, is characterized in that, described RSA public key generation unit comprises generation one and RSA PKI (e _i, N _i) the RSA private key (d of key each other _i, N _i), by described multiplication computing function F _i(1≤i≤k) chooses two Big prime p _i, q _i, calculate N _i=P _iq _i, random selecting integer ei, wherein, ei ≠ ej, 1≤i, j≤k and i ≠ j, and meet according to try to achieve d _i, obtain RSA private key (d _i, N _i).