CN106599715A - File encryption method, file decryption method and device - Google Patents
File encryption method, file decryption method and device Download PDFInfo
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- CN106599715A CN106599715A CN201611078988.9A CN201611078988A CN106599715A CN 106599715 A CN106599715 A CN 106599715A CN 201611078988 A CN201611078988 A CN 201611078988A CN 106599715 A CN106599715 A CN 106599715A
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F21/00—Security arrangements for protecting computers, components thereof, programs or data against unauthorised activity
- G06F21/60—Protecting data
- G06F21/62—Protecting access to data via a platform, e.g. using keys or access control rules
- G06F21/6209—Protecting access to data via a platform, e.g. using keys or access control rules to a single file or object, e.g. in a secure envelope, encrypted and accessed using a key, or with access control rules appended to the object itself
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2221/00—Indexing scheme relating to security arrangements for protecting computers, components thereof, programs or data against unauthorised activity
- G06F2221/21—Indexing scheme relating to G06F21/00 and subgroups addressing additional information or applications relating to security arrangements for protecting computers, components thereof, programs or data against unauthorised activity
- G06F2221/2107—File encryption
Abstract
The invention discloses a file encryption method, a file decryption method and a device, relating to the field of security technology. The method comprises the following steps: receiving an encryption instruction for encrypting an original file; obtaining a key pair (e, N) for encrypting the original file according to the encryption instruction; encrypting the original file by using the key pair (e, N) to obtain an encrypted file; and transmitting the encrypted file to a target device, wherein the target device is used for decrypting the encrypted file by using a key pair (d, N); the parameter N is a public parameter, one of the parameter e and the parameter d is a public parameter, and the other one is not a public parameter. According to the file encryption method, the file decryption method and the device disclosed by the invention, the problem that the encryption efficiency is low because the prime number with larger values is difficult to obtain can be solved; and the effects of guaranteeing the security of the encrypted file, reducing the time of obtaining the parameter N before file encryption, and increasing the efficiency of file encryption can be achieved.
Description
Technical field
The present invention relates to security technology area, more particularly to a kind of file encrypting method, file decryption method and device.
Background technology
With the high speed development of electronic information technology, increasingly popularized using network transmission file, in order to ensure that file exists
Safety in network transmission, needs to be encrypted file.
In prior art, generally it is encrypted using rivest, shamir, adelman.Specifically, public key and private key are generated by A ends,
And invent public key；B ends are obtained after public key, and the original document for needing encryption is encrypted using public key, obtain encrypting file,
And to A ends transmission encryption file；A ends receive the encryption file of B ends transmission, and are decrypted using private key, obtain original document.
However, with the development of quantum information science, the development of quantum computer has been achieved for breakthrough progress, profit
Encryption file is enough more easily cracked with quantum computer capacity, the safety for encrypting file receives threat.
The content of the invention
In order to solve to ensure before encryption that the safety for encrypting file needs to obtain larger parameter N of numerical value, numerical value compared with
Big prime number is difficult to obtain, the problem for causing encryption efficiency not high, and the present invention provides a kind of file encryption, decryption method and dress
Put.The technical scheme is as follows：
First aspect according to embodiments of the present invention, there is provided a kind of file encrypting method, methods described includes：
Receive the encrypted instruction for encrypting original document；
Key for encrypting the original document is obtained to (e, N) according to the encrypted instruction；
(e, N) is encrypted to the original document using the key, obtains encrypting file；
The encryption file is transmitted to target device, the target device is used to add (d, N) to described using key
Ciphertext part is decrypted；
Wherein, parameter N is the parameter of external disclosure, N=p1·p2·......·pn, n >=3,1≤i ≠ j≤n, piIt is
Prime number and piIt is confidential parameter；
A parameter in parameter e and parameter d is the parameter of external disclosure, and another parameter is confidential ginseng
Number, ed=1mod ((p1-1)·(p2-1)·......·(pn-1))。
Optionally, it is described (e, N) is encrypted to the original document using the key, obtain encrypting file, bag
Include：
The original document is encrypted using equation below, obtains the encryption file：
AeMod N=B,
Wherein, A represents the original document, and B represents the encryption file.
Second aspect according to embodiments of the present invention, there is provided a kind of file decryption method, methods described includes：Receive encryption
File, the encryption file is the file being encrypted to (e, N) using key；
Receive the decryption instructions for decrypting the encryption file；
According to the decryption instructions, (d, N) is decrypted to the encryption file using key, obtains original document；
Wherein, parameter N is the parameter of external disclosure, N=p1·p2·......·pn, n >=3,1≤i ≠ j≤n, piIt is
Prime number and piIt is confidential parameter
A parameter in parameter e and parameter d is the parameter of external disclosure, and another parameter is confidential ginseng
Number, ed=1mod ((p1-1)·(p2-1)·......·(pn-1))。
Optionally, it is described according to the decryption instructions (d, N) to be decrypted to the encryption file using key, obtain
To original document, including：
According to the decryption instructions, the encryption file is decrypted using equation below, obtains the original document：
BdMod N=A,
Wherein, A represents the original document, and B represents the encryption file.
The third aspect according to embodiments of the present invention, there is provided a kind of document encrypting apparatus, described device includes：
Receiver module, for receiving the encrypted instruction for encrypting original document；
Key to acquisition module, for obtaining the key pair for encrypting the original document according to the encrypted instruction
(e,N)；
Encrypting module, for being encrypted the original document (e, N) using the key, obtains encrypting file；
Transport module, for the encryption file to be transmitted to target device, the target device is used to utilize key pair
(d, N) is decrypted to the encryption file；
Wherein, parameter N is the parameter of external disclosure, N=p1·p2·......·pn, n >=3,1≤i ≠ j≤n, piIt is
Prime number and piIt is confidential parameter；
A parameter in parameter e and parameter d is the parameter of external disclosure, and another parameter is confidential ginseng
Number, ed=1mod ((p1-1)·(p2-1)·......·(pn-1))。
Optionally, the encrypting module, specifically for：
The original document is encrypted using equation below, obtains the encryption file：
AeMod N=B,
Wherein, A represents the original document, and B represents the encryption file.
Fourth aspect according to embodiments of the present invention, there is provided a kind of file deciphering device, described device includes：
First receiver module, for receiving encryption file, the encryption file is that (e, N) is encrypted using key
File；
Second receiver module, for receiving the decryption instructions for decrypting the encryption file；
Deciphering module, for according to the decryption instructions, being decrypted to the encryption file to (d, N) using key,
Obtain original document；
Wherein, parameter N is the parameter of external disclosure, N=p1·p2·......·pn, n >=3,1≤i ≠ j≤n, piIt is
Prime number and piIt is confidential parameter；
A parameter in parameter e and parameter d is the parameter of external disclosure, and another parameter is confidential ginseng
Number, ed=1mod ((p1-1)·(p2-1)·......·(pn-1))。
Optionally, the deciphering module, specifically for：
According to the decryption instructions, the encryption file is decrypted using equation below, obtains the original document：
BdMod N=A,
Wherein, A represents the original document, and B represents the encryption file.
The technical scheme that embodiments of the invention are provided can include following beneficial effect：
By first terminal according to encrypted instruction, obtain encrypting file to (e, N) encryption original document using key, and to
Second terminal sends encryption file, and second terminal is received after encryption file, according to decryption instructions (d, N) decrypted using key
Encryption file, wherein, parameter N is the parameter of external disclosure, and parameter N is multiplied by least three prime numbers and is obtained, N=p1·
p2·......·pn, n >=3, piIt is confidential parameter, the relation between parameter e and parameter d meets ed=1mod
((p1-1)·(p2-1)·......·(pn- 1)), by the less p of several numerical valueiMultiplication be just obtained in that one it is larger
Parameter N, it is ensured that the safety of encryption file, reduce and got parms time of N before encryption file, improve encryption file
Efficiency.
Further, since do not know that the key for decryption is not aware that how parameter N obtains to the user of (d, N),
Only know the numerical value of parameter N, if it is desired to decryption encryption file, then need to carry out factorization to parameter N, just can be decrypted
When the key pair that uses, and carry out that factorization is relatively difficult to parameter N, therefore ensure that the safety of encryption file.
It should be appreciated that the general description of the above and detailed description hereinafter are only exemplary, this can not be limited
Invention.
Description of the drawings
Accompanying drawing herein is merged in description and constitutes the part of this specification, shows the enforcement for meeting the present invention
Example, and be used to together explain the principle of the present invention in description.
Fig. 1 is a kind of schematic diagram of implementation environment that each embodiment of the invention is related to；
Fig. 2 is a kind of file encryption, the flow chart of decryption method according to an exemplary embodiment；
Fig. 3 is a kind of structural representation of the document encrypting apparatus according to an exemplary embodiment；
Fig. 4 is a kind of structural representation of the file deciphering device for implementing to exemplify according to another exemplary.
Specific embodiment
Here exemplary embodiment will be illustrated in detail, its example is illustrated in the accompanying drawings.Explained below is related to
During accompanying drawing, unless otherwise indicated, the same numbers in different accompanying drawings represent same or analogous key element.Following exemplary embodiment
Described in embodiment do not represent and the consistent all embodiments of the present invention.Conversely, they be only with it is such as appended
The example of the consistent apparatus and method of some aspects described in detail in claims, the present invention.
Fig. 1 is a kind of schematic diagram of the implementation environment involved by each embodiment of the invention, and the implementation environment can include
First terminal 110 and second terminal 120.
First terminal 110 and second terminal 120 are such as mobile phone, panel computer, E-book reader, MP3 player
(Moving Picture Experts Group Audio Layer III, dynamic image expert's compression standard audio frequency aspect 3),
MP4 (Moving Picture Experts Group Audio Layer IV, dynamic image expert's compression standard audio frequency aspect
4) electronic equipment of player, desk computer and portable computer etc.
First terminal 110 can to being stored in first terminal in file in 120 be encrypted or decrypt, and transmit encryption
File or receiving and deciphering file.Second terminal 120 has same or analogous function with first terminal 110.
First terminal 110 and second terminal 120 can set up communication connection by wireless network or cable network.
When actually realizing, the quantity of first terminal 110 can be multiple, and the quantity of second terminal 120 can also be many
Individual, Fig. 1 is only illustrated by taking a first terminal 110 and a second terminal 120 as an example.
Fig. 2 is a kind of file encryption, the flow chart of decryption method according to an exemplary embodiment.The present invention is with this
Method is applied to be illustrated in the implementation environment shown in above-mentioned Fig. 1.The method can include following step：
Step 201, first terminal receives the encrypted instruction for encrypting original document.
When user is input into encrypted instruction on first terminal, first terminal receives encrypted instruction.
Step 202, first terminal obtains key for encrypting original document to (e, N) according to encrypted instruction.
Optionally, encrypted instruction includes the mark of original document, and first terminal obtains former according to the mark of original document
Beginning file.
Optionally, the mark for encrypting the key pair of original document is also included in encrypted instruction, first terminal is according to close
The mark of key pair obtains the key for being used for encrypting original document to (e, N).
Wherein, parameter N is the parameter of external disclosure, N=p1·p2·......·pn, n >=3,1≤i ≠ j≤n, piIt is
Prime number and piIt is confidential parameter.
N is the product of at least 3 prime numbers.It should be noted that the concrete numerical value of N is only disclosed during external disclosure, and it is unjust
It is the N for obtaining that is multiplied by several prime numbers to open.
Step 203, first terminal is encrypted to (e, N) using key to original document, obtains encrypting file.
Specifically, using formula AeMod N=B are encrypted to original document, obtain encrypting file, wherein, A represents former
Beginning file, B represents encryption file.
Step 204, first terminal is transmitted file is encrypted to target device.
Optionally, first terminal is transmitted to target device by cable network or wireless network by file is encrypted.
Optionally, the quantity of target device is at least one.
In the embodiment of the present invention, using second terminal equipment as target device.It should be noted that the embodiment of the present invention pair
This is not construed as limiting.
Step 205, second terminal receives encryption file.
Encryption file is the file being encrypted to (e, N) using key.
Step 206, second terminal is received for the decryption instructions of decryption encryption file.
Step 207, according to decryption instructions, is decrypted to (d, N) using key to encrypting file, obtains original document.
Optionally, decryption instructions include the mark of the key pair for decryption encryption file, and second terminal is according to decryption
Mark in instruction obtains key to (d, N).
Specifically, using formula BdMod N=A are decrypted to encrypting file, obtain original document, wherein, A represents former
Beginning file, B represents encryption file.
Due to not knowing that key is not aware that how parameter N obtains to the user of (d, N), the number of parameter N is only known
Value, if it is desired to decryption encryption file, then need to carry out factorization to parameter N, can just obtain the key pair used when decrypting,
And carry out that factorization is relatively difficult to parameter N, therefore ensure that the safety of encryption file.
Further, since the secrecy timeliness of encryption file is time-consuming with decryption related with parameter N, parameter N is bigger, secrecy timeliness with
Decryption time is longer, in order to add the safety of strong encryption file, it will usually select parameter N that numerical value is larger；When parameter N is two
Prime number a1And a2Product when, to ensure parameter N it is very big, then need a1And a2Also it is very big, but the very big prime number of numerical value compares
Hardly possible is obtained, and needs to expend more times before encryption during selection parameter, and the efficiency of encryption is affected；When parameter N be to
During the product of few three prime numbers, even if piNumerical value it is less, to make parameter N numerical value need it is very big, it is only necessary to more using several pi
It is multiplied, the more time need not be expended during selection parameter before encryption, is conducive to improving encryption efficiency.
Wherein, a parameter in parameter e and parameter d is the parameter of external disclosure, and another parameter is not external disclosure
Parameter, ed=1mod ((p1-1)·(p2-1)·......·(pn-1))。
When parameter e external disclosure, parameter d not external disclosure；When parameter d external disclosure, parameter e not external disclosure.
When parameter e external disclosure, parameter d not external disclosure when, first terminal is entered to (e, N) using key to original document
Row encryption is obtained encrypting and sent after file to second terminal, and second terminal, to (d, N) decryption encryption file, obtains original using key
Beginning file, ensure that the safety of original document in transmitting procedure；When parameter e not external disclosure, during parameter d external disclosure,
First terminal is encrypted to original document to (e, N) using key and obtains encrypting file, and second terminal gets encryption file
Afterwards original document is obtained to (d, N) decryption encryption file using key, due to the user with bad motivation, such as hacker, no
Key is known to (e, N), even if having forged text document to second terminal, second terminal is decrypted also using key to (d, N)
Cannot get original document, therefore the purpose of authentication can be realized.
It should be noted that above-mentioned steps 201 to step 204 can be implemented separately the method enforcement for becoming first terminal side
Example, step 205 to step 207 can be implemented separately the embodiment of the method for becoming second terminal side.
It should be noted that the executive agent of step 201 to step 204 can also be second terminal, step 205 is to step
207 executive agent can also be first terminal, and the embodiment of the present invention is not limited this.
In sum, file encryption provided in an embodiment of the present invention, decryption method, first terminal is according to encrypted instruction, profit
(e, N) encryption original document is obtained with key encrypt file, and encryption file is sent to second terminal, second terminal is received
After encryption file, according to decryption instructions using key to (d, N) decryption encryption file, wherein, parameter N is the ginseng of external disclosure
Number, parameter N is multiplied by least three prime numbers and is obtained, N=p1·p2·......·pn, n >=3, piIt is confidential ginseng
Number, the relation between parameter e and parameter d meets ed=1mod ((p1-1)·(p2-1)·......·(pn- 1)), if by
The dry less pi of numerical value is multiplied and is just obtained in that larger parameter N, it is ensured that the safety of encryption file, reduces encryption
Get parms time of N before file, improves the efficiency of encryption file.
It is following for apparatus of the present invention embodiment, can be used for performing the inventive method embodiment.For apparatus of the present invention reality
The details not disclosed in example is applied, the inventive method embodiment is refer to.
Fig. 3 is refer to, the structural representation of the document encrypting apparatus provided in one embodiment of the invention is provided.Should
Device can pass through software, hardware or both be implemented in combination with become the first terminal in the example environment shown in Fig. 1.The dress
Put including：
Receiver module 310, for receiving the encrypted instruction for encrypting original document.
Key to acquisition module 320, for the key for encrypting original document to be obtained according to encrypted instruction to (e, N).
Encrypting module 330, for being encrypted original document (e, N) using key, obtains encrypting file.
Transport module 340, for encryption file to be transmitted to target device, target device is used for using key to (d, N)
It is decrypted to encrypting file.
Wherein, parameter N is the parameter of external disclosure, N=p1·p2·......·pn, n >=3,1≤i ≠ j≤n, piIt is
Prime number and piIt is confidential parameter；
A parameter in parameter e and parameter d is the parameter of external disclosure, and another parameter is confidential ginseng
Number, ed=1mod ((p1-1)·(p2-1)·......·(pn-1))。
In sum, document encrypting apparatus provided in an embodiment of the present invention, according to encrypted instruction, using key to (e, N)
Encryption original document obtains encrypting file, and sends encryption file to second terminal, wherein, parameter N is the parameter of external disclosure,
Parameter N is multiplied by least three prime numbers and is obtained, N=p1·p2·......·pn, n >=3, piIt is confidential parameter, ginseng
Relation between number e and parameter d meets ed=1mod ((p1-1)·(p2-1)·......·(pn- 1)), by several
The less pi of numerical value is multiplied and is just obtained in that larger parameter N, it is ensured that the safety of encryption file, reduces encryption file
Before get parms time of N, improve the efficiency of encryption file.
Optionally, encrypting module 330, specifically for：
Original document is encrypted using equation below, obtains encrypting file：
AeMod N=B,
Wherein, A represents original document, and B represents encryption file.
Fig. 4 is refer to, the structural representation of the file deciphering device provided in one embodiment of the invention is provided.Should
Device can pass through software, hardware or both be implemented in combination with become the second terminal in the example environment shown in Fig. 1.The dress
Put including：
First receiver module 410, for receiving encryption file, encryption file is that (e, N) is encrypted using key
File；
Second receiver module 420, for receiving for the decryption instructions of decryption encryption file；
Deciphering module 430, for according to decryption instructions, being decrypted to encrypting file to (d, N) using key, obtains original
Beginning file；
Wherein, parameter N is the parameter of external disclosure, N=p1·p2·......·pn, n >=3,1≤i ≠ j≤n, piIt is
Prime number and piIt is confidential parameter；
A parameter in parameter e and parameter d is the parameter of external disclosure, and another parameter is confidential ginseng
Number, ed=1mod ((p1-1)·(p2-1)·......·(pn-1))。
In sum, file deciphering device provided in an embodiment of the present invention, after receiving encryption file, according to decryption instructions
Using key to (d, N) decryption encryption file, wherein, parameter N is the parameter of external disclosure, and parameter N is by least three prime number phases
It is multiplied to arrive, N=p1·p2·......·pn, n >=3, piIt is confidential parameter, the relation between parameter e and parameter d
Meet ed=1mod ((p1-1)·(p2-1)·......·(pn- 1)), by the less p of several numerical valueiIt is multiplied with regard to energy
Enough obtain larger parameter N, it is ensured that the safety of encryption file, reduce the time of the N that gets parms before encryption file, carry
The high efficiency of encryption file.
Optionally, deciphering module, specifically for：
According to decryption instructions, it is decrypted to encrypting file using equation below, obtains original document：
BdMod N=A,
Wherein, A represents original document, and B represents encryption file.
With regard to the device in above-described embodiment, wherein modules perform the concrete mode of operation in relevant the method
Embodiment in be described in detail, explanation will be not set forth in detail herein.
Those skilled in the art will readily occur to its of the present invention after the invention that description and practice are invented here is considered
Its embodiment.The application is intended to any modification of the present invention, purposes or adaptations, these modifications, purposes or
The common knowledge in the art that person's adaptations follow the general principle of the present invention and do not invent including the present invention
Or conventional techniques.Description and embodiments are considered only as exemplary, and true scope and spirit of the invention are by following
Claim is pointed out.
It should be appreciated that the precision architecture for being described above and being shown in the drawings is the invention is not limited in, and
And can without departing from the scope carry out various modifications and changes.The scope of the present invention is only limited by appended claim.
Claims (8)
1. a kind of file encrypting method, it is characterised in that methods described includes：
Receive the encrypted instruction for encrypting original document；
Key for encrypting the original document is obtained to (e, N) according to the encrypted instruction；
(e, N) is encrypted to the original document using the key, obtains encrypting file；
The encryption file is transmitted to target device, the target device is used for using key to (d, N) to described plus ciphertext
Part is decrypted；
Wherein, parameter N is the parameter of external disclosure, N=p1·p2·......·pn, n >=3,1≤i ≠ j≤n, piBe prime number and
piIt is confidential parameter；
A parameter in parameter e and parameter d is the parameter of external disclosure, and another parameter is confidential parameter, e
D=1mod ((p1-1)·(p2-1)·......·(pn-1))。
2. method according to claim 1, it is characterised in that it is described using the key to (e, N) to the original text
Part is encrypted, and obtains encrypting file, including：
The original document is encrypted using equation below, obtains the encryption file：
AeModN=B,
Wherein, A represents the original document, and B represents the encryption file.
3. a kind of file decryption method, it is characterised in that methods described includes：
Encryption file is received, the encryption file is the file being encrypted to (e, N) using key；
Receive the decryption instructions for decrypting the encryption file；
According to the decryption instructions, (d, N) is decrypted to the encryption file using key, obtains original document；
Wherein, parameter N is the parameter of external disclosure, N=p1·p2·......·pn, n >=3,1≤i ≠ j≤n, piBe prime number and
piIt is confidential parameter；
A parameter in parameter e and parameter d is the parameter of external disclosure, and another parameter is confidential parameter, e
D=1mod ((p1-1)·(p2-1)·......·(pn-1))。
4. method according to claim 3, it is characterised in that described according to the decryption instructions, using key to (d, N)
The encryption file is decrypted, original document is obtained, including：
According to the decryption instructions, the encryption file is decrypted using equation below, obtains the original document：
BdModN=A,
Wherein, A represents the original document, and B represents the encryption file.
5. a kind of document encrypting apparatus, it is characterised in that described device includes：
Receiver module, for receiving the encrypted instruction for encrypting original document；
Key to acquisition module, for the key for encrypting the original document to be obtained according to the encrypted instruction to (e, N)；
Encrypting module, for being encrypted the original document (e, N) using the key, obtains encrypting file；
Transport module, for the encryption file to be transmitted to target device, the target device is used for using key to (d, N)
The encryption file is decrypted；
Wherein, parameter N is the parameter of external disclosure, N=p1·p2·......·pn, n >=3,1≤i ≠ j≤n, piBe prime number and
piIt is confidential parameter；
A parameter in parameter e and parameter d is the parameter of external disclosure, and another parameter is confidential parameter, e
D=1mod ((p1-1)·(p2-1)·......·(pn-1))。
6. device according to claim 5, it is characterised in that the encrypting module, specifically for：
The original document is encrypted using equation below, obtains the encryption file：
AeModN=B,
Wherein, A represents the original document, and B represents the encryption file.
7. a kind of file deciphering device, it is characterised in that described device includes：
First receiver module, for receiving encryption file, the encryption file is the text being encrypted to (e, N) using key
Part；
Second receiver module, for receiving the decryption instructions for decrypting the encryption file；
Deciphering module, for according to the decryption instructions, being decrypted to the encryption file to (d, N) using key, is obtained
Original document；
Wherein, parameter N is the parameter of external disclosure, N=p1·p2·......·pn, n >=3,1≤i ≠ j≤n, piBe prime number and
piIt is confidential parameter；
A parameter in parameter e and parameter d is the parameter of external disclosure, and another parameter is confidential parameter, e
D=1mod ((p1-1)·(p2-1)·......·(pn-1))。
8. device according to claim 7, it is characterised in that the deciphering module, specifically for：
According to the decryption instructions, the encryption file is decrypted using equation below, obtains the original document：
BdModN=A,
Wherein, A represents the original document, and B represents the encryption file.
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| WO2013095356A1 (en) * | 2011-12-20 | 2013-06-27 | Intel Corporation | File encryption, decryption and accessvia near field communication |
| CN102662628A (en) * | 2012-03-23 | 2012-09-12 | 山东大学 | Instruction optimization processor for RSA encryption algorithm |
| CN103067164A (en) * | 2013-01-17 | 2013-04-24 | 北京昆腾微电子有限公司 | Anti-attack method for electronic components using RSA public key encryption algorithm |
| CN104917611A (en) * | 2014-03-13 | 2015-09-16 | 航天信息股份有限公司 | Data encryption and decryption processing method and device for cloud computing |
| CN104811297A (en) * | 2015-04-23 | 2015-07-29 | 成都信息工程学院 | Method for modular multiplication remainder input side channel attacks aiming at M-ary implementation of RSA |
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