Method for quickly generating prime number group applicable to information encryption technology

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 number families 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 they have played an important role in ensuring information and network security. In public key algorithms, such as RSA, EL Gamal, Schnorr and Fint Schamir, all require one or more large prime operations to obtain the key in the algorithm protocol. For example, the RSA public key cryptosystem is based on this assumption: find two large numbers The prime number of is relatively not difficult, but it is extremely difficult to decompose a large composite number into its prime factor form. The system operates as follows: [0003] C=M ...

AI Technical Summary

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 prime number can be provided each time, which cannot provide more choices for the key algorithm

[0011] In 1986, I theoretically discussed the idea and idea of ​​establishing a large prime number family in a paper "Possible Prime Number Table and Its Application", but no similar invention has been seen so far.

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