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Large prime number generation method and apparatus in an RSA encryption algorithm

An encryption algorithm and a technology for generating devices, which are applied in secure communication devices, digital transmission systems, public keys for secure communications, etc., can solve problems such as the difficulty of large prime numbers, time-consuming generation, and the possibility of generating only a close-to-prime number, etc. , to achieve the effects of improving detection efficiency, shortening time, and improving generation efficiency

Inactive Publication Date: 2018-07-10
GUANGDONG KINGPOINT DATA SCI & TECH CO LTD
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  • Summary
  • Abstract
  • Description
  • Claims
  • Application Information

AI Technical Summary

Problems solved by technology

[0004] In the RSA encryption algorithm, it is necessary to generate a large number of prime numbers. At present, it can be predicted that the length of the RSA key that is safe enough before 2030 is 2048bit, but it is very difficult to generate a large prime number of this length (that is, a large number of orders of magnitude). difficult things
At present, there are mainly two methods of generating prime numbers: probabilistic prime number generation and deterministic prime number generation; however, probabilistic prime number generation is time-consuming due to the uncertainty of prime number distribution, and the generated prime numbers are likely to be only close to prime numbers. Pseudo-prime numbers: deterministically generated prime numbers can guarantee that the generated numbers must be prime numbers, but the prime numbers generated by this method have certain rules, and the attacker can use a small cost to deduce the rules of prime number generation

Method used

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  • Large prime number generation method and apparatus in an RSA encryption algorithm
  • Large prime number generation method and apparatus in an RSA encryption algorithm
  • Large prime number generation method and apparatus in an RSA encryption algorithm

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Embodiment 1

[0062] Such as figure 2Shown, it is the flowchart of the large prime number generation method in the RSA encryption algorithm of the present invention, wherein, the large prime number generation method in the described RSA encryption algorithm comprises:

[0063] Step S1, searching for a large prime number to generate a pseudo-prime number;

[0064] The distribution of large prime numbers is uneven and the density is small. In order to improve the detection efficiency of prime numbers, it is necessary to choose a better search method. At present, the common search methods mainly include random incremental search and random search. However, the number of random incremental searches is smaller than that of the random search method. Therefore, the random incremental search method is used in the present invention to search for large prime numbers.

[0065] Random incremental search method, that is, randomly generate a number, and test the numbers starting from this number in tu...

Embodiment 2

[0071] As the method for generating large prime numbers in the RSA encryption algorithm described above, the present embodiment is different from it in that, as image 3 As shown, the step S2 includes:

[0072] Step S22, using the small prime number division method to exclude the numbers divisible by small prime numbers in the pseudo prime numbers;

[0073] The small prime number division method is to divide the pseudo prime number by the small prime number in 100, if a certain small prime number can divide a certain pseudo prime number, it shows that the pseudo prime number is not a prime number, and it is excluded.

[0074] Step S23, using the Miller-Rabin algorithm to perform 5 detections on the pseudo-prime numbers, and keep the pseudo-prime numbers that pass the detection.

[0075] The Miller-Rabin algorithm is a probability-based primality testing algorithm. It is a probability algorithm in essence. There is a possibility of misjudgment, but the probability of error is ...

Embodiment 3

[0093] As the method for generating large prime numbers in the RSA encryption algorithm described above, the present embodiment is different from it in that, as Figure 4 As shown, the step S2 also includes:

[0094] Step S21, using an even number exclusion method to exclude even numbers in the pseudo prime numbers;

[0095] Using the even number exclusion method, you only need to test about 0.5lnn integers, which further improves the generation efficiency of large prime numbers; first use the even number exclusion method, then only need to test the remaining about 0.5lnn in the small prime number exclusion method Integers can be divided and excluded by small prime numbers, which reduces the number of integers that need to be tested, greatly improves the detection efficiency, and further improves the production efficiency of large prime numbers.

[0096] In this way, the specific process of preprocessing is as follows: Figure 5 Shown:

[0097] (1) First filter out the even...

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Abstract

The present invention discloses a large prime number generation method and apparatus in an RSA encryption algorithm, and the method comprises: step S1, performing a search of large prime numbers, generating a pseudo-prime; step S2, preprocessing the pseudo-prime by a pre-processing unit 2; step S3, detecting the primality of the probably prime number after preprocessing by a detecting unit 3, resulting in a large prime number. The apparatus includes a corresponding search unit, a pre-processing unit, and a detection unit. In this way, the large prime number generation method and apparatus havethe advantages of quick generating of a large prime number, short time and high efficiency.

Description

technical field [0001] The invention relates to the field of encryption technology, in particular to a method and device for generating a large prime number in an RSA encryption algorithm. Background technique [0002] With the rapid development of the Internet and the wide application of computer technology, it is very important to ensure information security in the network age. Information encryption technology is one of the most important and basic measures to ensure data security in the network. Among them, the RSA encryption algorithm is considered to be the best, most perfect, and also the most widely used algorithm. [0003] The RSA encryption algorithm is a typical public key cryptographic algorithm, which has two related but different keys, an encryption key and a decryption key. In public-key cryptography, the encryption key can be made public as a public key, and the decryption key as a secret private key. In the RSA encryption algorithm, both the public key and...

Claims

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): H04L9/30
CPCH04L9/302H04L9/3033
Inventor 吴剑文何伟潮单小红麻建
Owner GUANGDONG KINGPOINT DATA SCI & TECH CO LTD