A Fast Generation Method of Prime Number Family Applicable to the Application of Information Encryption Technology

A prime number family, fast technology, applied in the fields of information security and cryptography, it can solve the problems of long computing time, no invention, and inability to provide more choices for key algorithms, so as to achieve rapid generation and enhanced optionality. Effect

Active Publication Date: 2011-12-14
刘诗章 +1
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  • Abstract
  • Description
  • Claims
  • Application Information

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Problems solved by technology

Its disadvantage is that the number generated is not necessarily a prime number, and it is often necessary to operate this algorithm multiple times to reduce the probability of error
[0009] The common disadvantages of these two types of methods are: the overall operation time is too long, and only a single p

Method used

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  • A Fast Generation Method of Prime Number Family Applicable to the Application of Information Encryption Technology
  • A Fast Generation Method of Prime Number Family Applicable to the Application of Information Encryption Technology
  • A Fast Generation Method of Prime Number Family Applicable to the Application of Information Encryption Technology

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Embodiment Construction

[0036] A kind of prime number family rapid generation method applicable to the application of information encryption technology of the present invention is realized by adopting the following technical scheme:

[0037] Step 1, compress positive integers, and establish a reduced residual system modulo M=30. Choose M=30 as the modulus, seek its congruence class for positive integers, and make its reduced remainder system, by the Euler function

[0038]

[0039] have to

[0040] Thus, eight arithmetic progressions can be formed;

[0041] Step 2, establish the family of possible prime numbers. Take a representative number a from each of the eight categories that are mutually prime with the modulus M=30 1 ,...,a 8 , which in turn are

[0042] 1, 7, 11, 13, 17, 19, 23, 29

[0043] Therefore, the prime numbers p above 7 can be represented by the contracted residual system modulo M=30, that is

[0044] P = ...

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Abstract

The invention discloses a method for quickly generating a prime number group applicable to an information encryption technology. The method comprises the following steps of: establishing a probable prime number group by selecting a shrinkage residual system of a modulus M which is equal to 30; and according to the distribution rule and characteristics of composite numbers in the probable prime number group, screening out all composite numbers in the probable prime number group so as to accurately, quickly and completely generate all prime numbers of any section in a storage limitation range of a computer. In the field of information safety and cryptology, the acquisition and providing of large prime numbers are necessary flows in a public key algorithm. The convention method has the defects that: a single prime number can be provided at each time; most of the prime numbers are required to be subjected to primality detection; and operation time is over-long. The method provided by the invention has the advantages that: the primer number group can be generated by adopting computer software through simple screening operation, so that quick generation without complicated operation is realized on the computer; and a primality detection link is eliminated, and limitation of a prime number generation technology can be avoided, so that one-time pad can be realized, and related public key systems can perfectly work.

Description

technical field [0001] The invention relates to the fields of information security and cryptography, in particular to a method for rapidly generating prime numbers suitable for the application of information encryption technology. Background technique [0002] Since Diffie and Hellman proposed the new concept of public key cryptography in 1976, various public key systems have been widely used in people's daily life and work in the real world, and play an important role in ensuring information and network security. In public-key algorithms, such as RSA, EL Gamal, Schnorr, and Fint Schamir, one or more large prime number operations are required to obtain the key in the algorithm protocol. For example, the RSA public-key cryptosystem is based on this assumption: find two large prime numbers The prime numbers of are not very difficult, but it is extremely difficult to decompose a large composite number into its prime factor form. The system works as follows: [0003] C=M e (m...

Claims

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Application Information

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IPC IPC(8): G06F17/10H04L9/30
Inventor 刘诗章陈豫生
Owner 刘诗章
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