CN106850212A - Key generation system and method based on rsa cryptosystem algorithm - Google Patents
Key generation system and method based on rsa cryptosystem algorithm Download PDFInfo
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- CN106850212A CN106850212A CN201710129114.XA CN201710129114A CN106850212A CN 106850212 A CN106850212 A CN 106850212A CN 201710129114 A CN201710129114 A CN 201710129114A CN 106850212 A CN106850212 A CN 106850212A
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
- H04L9/30—Public key, i.e. encryption algorithm being computationally infeasible to invert or user's encryption keys not requiring secrecy
- H04L9/3006—Public key, i.e. encryption algorithm being computationally infeasible to invert or user's encryption keys not requiring secrecy underlying computational problems or public-key parameters
- H04L9/302—Public key, i.e. encryption algorithm being computationally infeasible to invert or user's encryption keys not requiring secrecy underlying computational problems or public-key parameters involving the integer factorization problem, e.g. RSA or quadratic sieve [QS] schemes
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
- H04L9/08—Key distribution or management, e.g. generation, sharing or updating, of cryptographic keys or passwords
- H04L9/0861—Generation of secret information including derivation or calculation of cryptographic keys or passwords
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
- H04L9/32—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials
- H04L9/3247—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials involving digital signatures
- H04L9/3249—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials involving digital signatures using RSA or related signature schemes, e.g. Rabin scheme
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- Engineering & Computer Science (AREA)
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- Computer Networks & Wireless Communication (AREA)
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Abstract
The invention discloses a kind of key generation system based on rsa cryptosystem algorithm and method, present system includes：Multiplication module, random number module, pretreatment module, judging module, modulus value generation module, mould are against module, output module.The inventive method realizes step：(1) factor I of RSA modulus value is generated；(2) factor Ⅱ of RSA modulus value is generated；(3) RSA modulus value is generated；(4) RSA private key indexes are calculated；(5) RSA key is exported.The present invention effectively reduces the computation burden of RSA key generating process, improves RSA key generating rate, it is ensured that the security of rsa cryptosystem algorithm.
Description
Technical field
The invention belongs to communication technical field, a kind of public key cryptography body in field of information security technology is further related to
Key generation system and method based on rsa cryptosystem algorithm in system.The present invention is pre-processed by Big prime, with reference to
Miller-Rabin is detected, is that, using improved Euclidean algorithm, effectively prevent division problem, generation symbol private key is calculated
Close the key of RSA Algorithm requirement.
Background technology
With communication and the development of information security technology, public-key cryptosystem is increasingly valued by people.Numerous
Public key cryptography algorithm in, rsa cryptosystem algorithm is most ripe, is also a kind of most popular cryptographic algorithm.It is not only
With traditional information cryptographic capabilities, and can be used in the authenticity of checking information, completeness and efficiency, so as to receive
The favor of users, and have become the international standard of public key cryptography.But actually rsa cryptosystem algorithm also has it originally
The inevitable shortcoming of body, produces key pretty troublesome, is limited by prime number generation technology, it is difficult to accomplish one-time pad；Speed
Too slow, because the block length of RSA is too big, to ensure security, n is at least also wanted more than 600 bits, makes computing cost very high,
Especially speed is slower, compared with the slow several orders of magnitude of symmetric cryptographic algorithm.Therefore a large amount of RSA that meet how are produced to calculate in a short time
The key of method requirement turns into current study hotspot.
Paper " Improvement of generation of large prime method in public key algorithm " (the Yunnan University master that Long Jianchao is delivered at it
Academic dissertation, 2014) in propose a kind of generation method of Big prime in improved public key algorithm.The method is in Big prime tradition
On the basis of generation method, searched for using random increase, with reference to the characteristic of quasi- Mersenne Prime, pre-filtering is increased after generation random number
Process, then carry out test for primality and obtain Big prime, reduce the generation time of Big prime.The method exist weak point be,
Test for primality result is that the probability of prime number is not big enough, causes rsa cryptosystem algorithm dangerous.
Patent document " a kind of improved method for quickly generating Big prime " (patent Shen that Nanjing Univ. of Posts and Telecommunications applies at it
Please number：201510814574.1, application publication number：CN1015770A a kind of improved Big prime that quickly generates is disclosed in)
Method.The method can quickly generate Big prime, be to be based on Miller-Rabin test for primality algorithms, and use Montgomery
Algorithm is optimized to former Miller-Rabin algorithms detection prime number.Montgomery algorithm uses mould and adds the side for moving to right
Method, efficiently avoid in modulus computing than relatively time-consuming division arithmetic, reduce the number of times of Montgomery Algorithm in former algorithm, so that
Improve the detection speed to prime number.But, the weak point that the method is still present is to calculate the mould inverse time, it is necessary to circulate
Cause for 1024 times to calculate practical application that is complicated and influenceing rsa cryptosystem.
" RSA key is generated the patent document that Shenzhen National Engineering Lab. for DTV Co., Ltd. applies at it
Method and device " (number of patent application：201410092851.3, application publication number：CN103812648A a kind of RSA is disclosed in)
Key generation method and device.Be transferred to outside credible platform for the calculating of the operand high needed for generating key by the device, subtracts
The light computation burden of credible platform module.But, the weak point that the device is still present is, when RSA key parameter is created,
The module not pre-processed to Big prime, causes system amount of calculation when prime number examination is carried out too big and influences that RSA's is close
Key formation speed.
The content of the invention
It is an object of the invention to overcome the shortcomings of above-mentioned prior art, a kind of key based on rsa cryptosystem algorithm is proposed
Generation method.The present invention is pre-processed by Big prime, with reference to Miller-Rabin detections, is used when private key is obtained and changed
The Euclid's method entered, effectively prevent division problem, further increase RSA key formation efficiency.
To achieve the above object, system of the invention includes multiplication module, random number module, pretreatment module, judgement
Module, modulus value generation module, mould against module, output module, wherein：
Described multiplication module, the product for calculating all prime numbers within 500；
Described random number module, for the integer of random generation one 512；
Described pretreatment module, for calculating the product of all prime numbers and the greatest common divisor for generating integer within 500；
Described judging module, for generated with 500 within all prime numbers the coprime integer of product carry out Miller-
Rabin's Miller-Rabin test for primality；
Described modulus value generation module, the modulus value for calculating RSA；
Described mould is against module, the private key index for calculating RSA；
Described output module, for exporting modulus value, factor I, factor Ⅱ, private key index.
The method of the present invention to implement step as follows：
(1) factor I of RSA modulus value is generated：
Using the generation method of the RSA modulus value factors, generation Peter Lonard Lee Vista, A Di Shamirs, Leonard
The factor I p of A Deman RSA modulus value；
(2) factor Ⅱ of RSA modulus value is generated：
Using the generation method of the RSA modulus value factors, generation Peter Lonard Lee Vista, A Di Shamirs, Leonard
The factor Ⅱ q of A Deman RSA modulus value；
(3) modulus value is generated：
With factor Ⅱ q be multiplied factor I p by modulus value generation module, obtains Peter Lonard Lee Vista, A Disa
More, the modulus value of Leonard A Deman RSA；
(4) the private key index of RSA is calculated：
After divide operations in traditional Euclidean algorithm are changed into shifting function by (4a), obtain improved Europe it is several in
Obtain algorithm；
(4b) utilizes improved Euclidean algorithm, and mould inverse operation is carried out to public exponent, and resulting mould reciprocal value is made
It is private key index；
(5) RSA key is exported：
Output module exports modulus value, factor I, factor Ⅱ, private key index respectively.
The present invention has advantages below compared with prior art：
3rd, due to using pretreatment module in system of the invention, before test for primality is carried out, calculate within 500
The product of all prime numbers with generate the greatest common divisor of integer, overcome prior art is due to lacking caused by pretreatment module
The amount of calculation when prime number examination is carried out of uniting influences greatly very much the key formation speed of RSA so that system of the invention has efficient
Quick advantage.
First, due to being carried out to Big prime using Miller-Rabin Miller-Rabin detection methods in the method for the present invention
Detection, overcome prior art due to test for primality result be prime number probability it is not big enough, cause the dangerous of rsa cryptosystem algorithm
Problem so that key of the invention has the advantages that safe.
Second, the inverse behaviour of mould is carried out to public exponent due to employing improved Euclidean algorithm in the method for the present invention
Make, overcome and calculate challenge caused by the mould inverse time is calculated, it is necessary to circulate 1024 times in the prior art, improve private key
Formation speed so that the present invention has the advantages that practicality is high.
Brief description of the drawings
Fig. 1 is the structured flowchart of present system；
Fig. 2 is the flow chart of the inventive method；
Fig. 3 is the flow chart of the private key index that step 4 of the present invention calculates RSA；
Specific embodiment
The invention will be further described below in conjunction with the accompanying drawings.
Referring to the drawings 1, system of the invention include multiplication module, random number module, pretreatment module, judging module,
Modulus value generation module, mould are against module, output module.
Described multiplication module, the product for calculating all prime numbers within 500.
Described random number module, for the integer of random generation one 512.
Described pretreatment module, for calculating the product of all prime numbers and the greatest common divisor for generating integer within 500.
Described judging module, for carrying out Miller-Rabin's Miller-Rabin test for primality to coprime integer.
Described modulus value generation module, the modulus value for calculating RSA.
Described mould is against module, the private key index for calculating RSA.
Described output module, for exporting modulus value, factor I, factor Ⅱ, private key index.
Referring to the drawings 2, implementation method of the invention is described further.
Step 1, generates the factor I of RSA modulus value.
(1) factor I of RSA modulus value is generated：
Using the generation method of the RSA modulus value factors, generation Peter Lonard Lee Vista, A Di Shamirs, Leonard
The factor I p of A Deman RSA modulus value.
The generation method of RSA modulus value factor Is is comprised the following steps that：
1st step, multiplication module calculates the product of all prime numbers within 500；
2nd step, random number module generates the integer of 512 at random；
3rd step, pretreatment module calculates the product of all prime numbers and the greatest common divisor for generating integer within 500；
4th step, judges whether greatest common divisor is 1, if so, within the integer for then being generated and 500 all prime numbers product
It is coprime, the 5th step is performed, otherwise, the product of all prime numbers is not coprime within the integer for being generated and 500, gives up this not coprime whole
Number, performs the 2nd step；
5th step, judging module to generated with 500 within the coprime integer of product of all prime numbers carry out Miller-Rabin
Miller-Rabin test for primality, if testing result is to close number, gives up the coprime integer, performs the 2nd step, otherwise, performs
6th step；
6th step, using the integer after test for primality as Peter Lonard Lee Vista, A Di Shamirs, Leonard Ah
The factor of the graceful RSA modulus value of moral.
Step 2, generates the factor Ⅱ of RSA modulus value.
(2) factor Ⅱ of RSA modulus value is generated：
Using the generation method of the RSA modulus value factors, generation Peter Lonard Lee Vista, A Di Shamirs, Leonard
The factor Ⅱ q of A Deman RSA modulus value.
The generation method of RSA modulus value factor Ⅱs is comprised the following steps that：
1st step, multiplication module calculates the product of all prime numbers within 500；
2nd step, random number module generates the integer of 512 at random；
3rd step, pretreatment module calculates the product of all prime numbers and the greatest common divisor for generating integer within 500；
4th step, judges whether greatest common divisor is 1, if so, within the integer for then being generated and 500 all prime numbers product
It is coprime, the 5th step is performed, otherwise, the product of all prime numbers is not coprime within the integer for being generated and 500, gives up this not coprime whole
Number, performs the 2nd step；
5th step, judging module to generated with 500 within the coprime integer of product of all prime numbers carry out Miller-Rabin
Miller-Rabin test for primality, if testing result is to close number, gives up the coprime integer, performs the 2nd step, otherwise, performs
6th step；
6th step, using the integer after test for primality as Peter Lonard Lee Vista, A Di Shamirs, Leonard Ah
The factor of the graceful RSA modulus value of moral.
Step 3, generates modulus value.
(3) modulus value is generated：
With factor Ⅱ q be multiplied factor I p by modulus value generation module, obtains Peter Lonard Lee Vista, A Disa
More, the modulus value of Leonard A Deman RSA.
Step 4, calculates the private key index of RSA.
(4) the private key index of RSA is calculated：
After divide operations in traditional Euclidean algorithm are changed into shifting function by (4a), obtain improved Europe it is several in
Obtain algorithm；
(4b) utilizes improved Euclidean algorithm, and mould inverse operation is carried out to public exponent, and resulting mould reciprocal value is made
It is private key index.
Step 5, exports RSA key.
(5) RSA key is exported：
Output module exports modulus value, factor I, factor Ⅱ, private key index respectively.
Referring to the drawings 3, the specific steps to improved Euclidean algorithm are further described.
1st step, makes (X1,X2,X3)=(1,0, e), (Y1,Y2,Y3)=(0,1, Φ (n)), wherein Φ (n) represents RSA moulds
The Euler's function of value n；
2nd step, judges X3Whether it is even number, if so, then performing the 3rd step, otherwise, performs the 6th step；
3rd step, judges X1And X2Whether be all even number, if so, then perform the 4th step, otherwise, perform the 5th step；
4th step, by X3The number at end 0 is designated as t, order
Perform the 6th step；
5th step, makes (X1,X2,X3)=(X1+Φ(n),X2-e,X3), perform the 3rd step；
6th step, judges Y3Whether it is even number, if so, then performing the 7th step, otherwise, performs the 10th step；
7th step, judges Y1And Y2Whether all it is even number, if so, then performing the 8th step, otherwise, performs the 9th step；
8th step, by Y3The number at end 0 is designated as s, order
Perform the 10th step；
9th step, makes (Y1,Y2,Y3)=(Y1+Φ(n),Y2-e,Y3), perform the 7th step；
10th step, compares X3With Y3Size, if X3>Y3, then the 11st step is performed, otherwise, perform the 12nd step；
11st step, makes (X1,X2,X3)=(X1-Y1,X2-Y2,X3-Y3), perform the 13rd step；
12nd step, makes (Y1,Y2,Y3)=(Y1-X1,Y2-X2,Y3-X3)；
13rd step, judges X3And Y3Value whether be equal to 1.If X3=1, then now X1It is exactly private key index d；If Y3=
1, then now Y1It is exactly private key index d；If X3And Y3Value be all not equal to 1, then perform the 2nd step.
Claims (3)
1. a kind of key generation system based on rsa cryptosystem algorithm, including multiplication module, random number module, pretreatment module,
Judging module, modulus value generation module, mould against module, output module, wherein：
Described multiplication module, the product for calculating all prime numbers within 500；
Described random number module, for the integer of random generation one 512；
Described pretreatment module, for calculating the product of all prime numbers and the greatest common divisor for generating integer within 500；
Described judging module, for generated with 500 within the coprime integer of product of all prime numbers carry out Miller-Rabin
Miller-Rabin test for primality；
Described modulus value generation module, the modulus value for calculating RSA；
Described mould is against module, the private key index for calculating RSA；
Described output module, for exporting modulus value, factor I, factor Ⅱ, private key index.
2. a kind of key generation method based on rsa cryptosystem algorithm, comprises the following steps that：
(1) factor I of RSA modulus value is generated：
Using the generation method of the RSA modulus value factors, generation Peter Lonard Lee Vista, A Di Shamirs, Leonard A De
The factor I p of graceful RSA modulus value；
(2) factor Ⅱ of RSA modulus value is generated：
Using the generation method of the RSA modulus value factors, generation Peter Lonard Lee Vista, A Di Shamirs, Leonard A De
The factor Ⅱ q of graceful RSA modulus value；
(3) modulus value is generated：
With factor Ⅱ q be multiplied factor I p by modulus value generation module, obtain Peter Lonard Lee Vista, A Di Shamirs,
The modulus value of Leonard A Deman RSA；
(4) the private key index of RSA is calculated：
After divide operations in traditional Euclidean algorithm are changed into shifting function by (4a), obtain improved Euclid and calculate
Method；
(4b) utilizes improved Euclidean algorithm, mould inverse operation is carried out to public exponent, using resulting mould reciprocal value as private
Key index；
(5) RSA key is exported：
Output module exports modulus value, factor I, factor Ⅱ, private key index respectively.
3. it is according to claim 2 based on rsa cryptosystem algorithm generate key method, it is characterised in that step (1), step
Suddenly RSA modulus value factor generation method described in (2) is comprised the following steps that：
The first step, multiplication module calculates the product of all prime numbers within 500；
Second step, random number module generates the integer of 512 at random；
3rd step, pretreatment module calculates the product of all prime numbers and the greatest common divisor for generating integer within 500；
4th step, judges whether greatest common divisor is 1, if so, the product of all prime numbers is mutual within the integer for then being generated and 500
Element, performs the 5th step, and otherwise, the product of all prime numbers is not coprime within the integer for being generated and 500, gives up this not coprime whole
Number, performs second step；
5th step, judging module to generated with 500 within the coprime integer of product of all prime numbers carry out Miller-Rabin
Miller-Rabin test for primality, if testing result is to close number, gives up the coprime integer, performs second step, otherwise, performs
6th step；
6th step, using the integer after test for primality as Peter Lonard Lee Vista, A Di Shamirs, Leonard A Deman
The factor of RSA modulus value.
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| CN108306730A (en) * | 2018-03-05 | 2018-07-20 | 飞天诚信科技股份有限公司 | A kind of implementation method and device generating key pair in embedded systems |
| CN112202562A (en) * | 2017-12-27 | 2021-01-08 | 数安时代科技股份有限公司 | RSA key generation method, computer device and medium |
| CN113077568A (en) * | 2021-04-16 | 2021-07-06 | 南京国电南自电网自动化有限公司 | Anti-misoperation locking method and system |
| CN114513306A (en) * | 2022-03-28 | 2022-05-17 | 北京石油化工学院 | Data encryption transmission method and system |
| CN114760055A (en) * | 2022-06-15 | 2022-07-15 | 山东区块链研究院 | Secret sharing method, system, storage medium and device based on Messen prime number |
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Application publication date: 20170613 |