CN104660400A - RSA modular exponentiation calculation method and device - Google Patents
RSA modular exponentiation calculation method and device Download PDFInfo
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- CN104660400A CN104660400A CN201310608764.4A CN201310608764A CN104660400A CN 104660400 A CN104660400 A CN 104660400A CN 201310608764 A CN201310608764 A CN 201310608764A CN 104660400 A CN104660400 A CN 104660400A
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Abstract
The invention provides a RSA modular exponentiation calculation method and device. The RSA modular exponentiation calculation method comprises the following steps: acquiring a random number r, a public key e and a private key d; calculating a first value, wherein the first value is a value that the product of the public key e and the private key d minus 1; calculating a second value, wherein the second value is the product of the random number r and the first value; calculating a third value, the third value is the sum of the second value and the private key d; performing RSA modular exponentiation calculation by taking the third value as an index of RSA modular exponentiation calculation. By adopting the method and the device, the data security can be improved.
Description
Technical field
The present invention relates to the technical field of data security, particularly a kind of RSA modular exponentiation operation method and device.
Background technology
In the prior art, assailant generally can by gather the hardware device such as cryptographic system, encryption chip being encrypted, decipher or signature operation time the reveal information such as the power consumption that produces, utilize cryptography, probability, Principle of Statistics, analysis and decoding key information.Such as, in the Montgomery Algorithm method of RSA public key encryption algorithm, when key d directly carries out computing as the index of Montgomery Algorithm, assailant just can directly obtain described key d by above-mentioned analysis, and decodes encrypted data by described key d.
Therefore, need to propose a kind of new RSA modular exponentiation operation method and device, to improve the fail safe of data.
Summary of the invention
The problem that the present invention solves proposes a kind of new RSA modular exponentiation operation method and device, to improve the fail safe of data.
The embodiment provides a kind of RSA modular exponentiation operation method, described method comprises: obtain random number r, PKI e and private key d; Calculate the first value, described first value is that the product of PKI e and private key d deducts the value after 1; Calculate the second value, described second value is the product of described random number r and described first value; Calculate the 3rd value, described 3rd value for described second value and private key d with; Described 3rd value is carried out described RSA modular exponentiation computing as the index of RSA modular exponentiation computing.
Embodiments of the invention additionally provide a kind of RSA modular exponentiation arithmetic unit, and described device comprises: acquiring unit, for obtaining random number r, PKI e and private key d; First arithmetic element, for calculating the first value, described first value is that the product of PKI e and private key d deducts the value after 1; Second arithmetic element, for calculating the second value, described second value is the product of described random number r and described first value; 3rd arithmetic element, for calculating the 3rd value, described 3rd value for described second value and private key d with; Montgomery Algorithm unit, for carrying out described RSA modular exponentiation computing using described 3rd value as the index of RSA modular exponentiation computing.
Compared with prior art, embodiments of the invention have the following advantages:
In technique scheme, private key d is the direct index as RSA modular exponentiation computing not, but by adding random number r, described private key d is hidden, thus the corresponding relation between the median eliminated in algorithm implementation and reveal information, that is assailant is difficult to directly obtain private key d, is therefore also just not easy to crack enciphered data, therefore can improves the fail safe of data.
Accompanying drawing explanation
Fig. 1 is the flow chart of RSA modular exponentiation operation method in the embodiment of the present invention;
Fig. 2 is the structural representation of RSA modular exponentiation arithmetic unit in the embodiment of the present invention.
Embodiment
By describing technology contents of the present invention, structural feature in detail, being realized object and effect, below in conjunction with accompanying drawing, the specific embodiment of the present invention is described in detail.Set forth a lot of detail in the following description so that fully understand the present invention, but the present invention can also adopt other to be different from alternate manner described here to implement, therefore the present invention is not by the restriction of following public specific embodiment.
Fig. 1 is the flow chart of RSA modular exponentiation operation method in the embodiment of the present invention.As shown in Figure 1, described method comprises step S101 to S105.
Step S101, obtains random number r, PKI e and private key d.
In an embodiment of the present invention, described random number r is variable random number, and that is, in each RSA modular exponentiation calculating process, described random number r can change.The object adding described random number r is to make the follow-up index carrying out RSA modular exponentiation computing be a randomized result, which eliminate the corresponding relation between median (private key d) in algorithm implementation and reveal information (information of the correlation of indices after randomization), thus make assailant be difficult to directly obtain private key d, be therefore also just not easy to crack enciphered data.
The index of the RSA modular exponentiation computing after randomization will be obtained below by step S102 to S104.
Step S102, calculate the first value, described first value is that the product of PKI e and private key d deducts the value after 1.
By step S102, the first value of acquisition is ed-1.
Step S103, calculates the second value, and described second value is the product of described random number r and described first value.
By step S103, described second value is the product of described random number r and described first value ed-1, that is: described second value is r (ed-1).
Step S104, calculate the 3rd value, described 3rd value for described second value and private key d with.
By step S104, described 3rd value for described second value r (ed-1) and private key d and, that is: described 3rd value be d+r (ed-1).
Step S105, carries out described RSA modular exponentiation computing using described 3rd value as the index of RSA modular exponentiation computing.
In an embodiment of the present invention, by step S104, using the 3rd value d+r(ed-1) as the index of RSA modular exponentiation computing.So, the value that the RSA modular exponentiation computing being index with described 3rd value obtains is: S=m
d+r(ed-1)mod N.
As previously mentioned, on the one hand, with described 3rd value for index, with random number r in described index, which eliminate the corresponding relation between median (private key d) in algorithm implementation and reveal information (information of the correlation of indices after randomization), thus make assailant be difficult to directly obtain private key d.
On the other hand, according to the intrinsic property of RSA enciphering and deciphering algorithm: m
ed) mod N=m, can derive as follows:,
S＝m
d+r（ed-1）mod N＝(m
dm
redm
-r)mod N＝(m
dm
rm
-1)mod N＝m
dmod N，
Shifted onto from above-mentioned, the RSA modular exponentiation operation result after described exponential random and the RSA modular exponentiation operation result before randomization are still consistent.
Embodiments of the invention additionally provide a kind of RSA modular exponentiation arithmetic unit.Please refer to Fig. 2, described kind of RSA modular exponentiation arithmetic unit 200 comprises:
Acquiring unit 210, for obtaining random number r, PKI e and private key d;
First arithmetic element 220, for calculating the first value, described first value is that the product of PKI e and private key d deducts the value after 1;
Second arithmetic element 230, for calculating the second value, described second value is the product of described random number r and described first value;
3rd arithmetic element 240, for calculating the 3rd value, described 3rd value for described second value and private key d with;
Montgomery Algorithm unit 250, for carrying out described RSA modular exponentiation computing using described 3rd value as the index of RSA modular exponentiation computing.
In an embodiment of the present invention, described first arithmetic element 220 can comprise multiplier and subtracter, described second arithmetic element 230 can be multiplier, and described 3rd arithmetic element 240 can be adder, and described Montgomery Algorithm unit 250 can be Montgomery Algorithm device.
One of ordinary skill in the art will appreciate that all or part of step in the various methods of above-described embodiment is that the hardware that can carry out instruction relevant by program has come, this program can be stored in a computer-readable recording medium, and storage medium can comprise: ROM, RAM, disk or CD etc.
Although the present invention discloses as above, the present invention is not defined in this.Any those skilled in the art, without departing from the spirit and scope of the present invention, all can make various changes or modifications, and therefore protection scope of the present invention should be as the criterion with claim limited range.
Claims (2)
1. a RSA modular exponentiation operation method, is characterized in that, comprising:
Obtain random number r, PKI e and private key d;
Calculate the first value, described first value is that the product of PKI e and private key d deducts the value after 1;
Calculate the second value, described second value is the product of described random number r and described first value;
Calculate the 3rd value, described 3rd value for described second value and private key d with;
Described 3rd value is carried out described RSA modular exponentiation computing as the index of RSA modular exponentiation computing.
2. a RSA modular exponentiation arithmetic unit, is characterized in that, comprising:
Acquiring unit, for obtaining random number r, PKI e and private key d;
First arithmetic element, for calculating the first value, described first value is that the product of PKI e and private key d subtracts
Go the value after 1;
Second arithmetic element, for calculating the second value, described second value is described random number r and described first
The product of value;
3rd arithmetic element, for calculating the 3rd value, described 3rd value for described second value and private key d with;
Montgomery Algorithm unit, for carrying out described RSA using described 3rd value as the index of RSA modular exponentiation computing
Montgomery Algorithm.
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Cited By (5)
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| CN106685661A (en) * | 2015-11-07 | 2017-05-17 | 上海复旦微电子集团股份有限公司 | Method and device for public key verification |
| CN106685643A (en) * | 2015-11-07 | 2017-05-17 | 上海复旦微电子集团股份有限公司 | Method and device for verifying public key in CRT mode |
| CN108599951A (en) * | 2018-08-10 | 2018-09-28 | 北京奇虎科技有限公司 | Encryption method and device |
| CN108933670A (en) * | 2018-10-18 | 2018-12-04 | 北京云测信息技术有限公司 | A kind of digital signature method, device, mobile device and storage medium |
| CN110492998A (en) * | 2019-08-14 | 2019-11-22 | 郑州大学 | The method of encryption and decryption data |
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| CN108933670B (en) * | 2018-10-18 | 2021-02-26 | 北京云测信息技术有限公司 | Digital signature method and device, mobile device and storage medium |
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Application publication date: 20150527 |