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Improved method for quickly generating big prime number

A technology of large prime numbers and prime numbers, applied in the field of improved rapid generation of large prime numbers, can solve problems such as increasing the length of RSA keys, and achieve the effect of reducing the number of modular exponentiation operations, increasing the length, and ensuring confidentiality

Inactive Publication Date: 2016-04-20
NANJING UNIV OF POSTS & TELECOMM
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Problems solved by technology

[0006] The purpose of the present invention is to provide a method that can quickly generate a large prime number, which solves the problem of increasing the length of the RSA key to improve the security of the RSA encryption algorithm, and ensures the security and security of data stored in the cloud storage system. The efficiency of generating large prime numbers and the efficiency of RSA encryption and decryption

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  • Improved method for quickly generating big prime number
  • Improved method for quickly generating big prime number
  • Improved method for quickly generating big prime number

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Embodiment Construction

[0035] The invention will be described in further detail below in conjunction with the accompanying drawings.

[0036] like figure 1 As shown, at the beginning of the present invention, corresponding large integers will be generated according to the specified number of digits (i.e., taking 1024 bits as an example), and PrimeTableB[N] is similar to PrimeTableA[M], both of which are one-dimensional arrays, except that the number of dimensions N is greater than that of M large, as shown in Table 1.

[0037] Table 1

[0038] PrimeTableA[M]=

[0039] 3 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251

[0040] Concrete flow process of the present invention is as figure 2 shown, including:

[0041] (1) First of all, it is necessary to define an array Array of unsignedlong type...

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Abstract

The invention discloses an improved method for quickly generating a big prime number, and the method can quickly generate the big prime number, is based on a Miller-Rabin prime number detection algorithm, has an additional preprocessing process, and employs a Montgomery modular multiplication algorithm to optimize the original detection of the prime number through the Miller-Rabin prime number detection algorithm. The Montgomery modular multiplication algorithm employs a method of modular addition right shift, effectively avoids the time-consuming division operation in a modular solving operation, reduces the number of times of modular exponentiation operation in an original algorithm, and greatly improves the detection speed of the prime number.

Description

technical field [0001] The invention relates to an improved method for quickly generating large prime numbers, which belongs to the technical field of information security. Background technique [0002] Asymmetric encryption system is also called public key encryption system, which is proposed to solve the defects of symmetric encryption system. In a public key encryption system, encryption and decryption are relatively independent, and two different keys are used for encryption and decryption. One of the keys is public, called the public key (referred to as the public key), used for encryption; the other key is dedicated to the user, so it is kept secret, called the secret key (referred to as the secret key) , for decryption. Therefore, the public-key cryptosystem is also called the dual-key cryptosystem, which completely changes the original encryption principle, and truly makes it possible for two parties who do not know each other to communicate securely on an insecure...

Claims

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Application Information

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IPC IPC(8): H04L9/30H04L9/08
CPCH04L9/302H04L9/0869
Inventor 叶宁梁成良林巧民王汝传
Owner NANJING UNIV OF POSTS & TELECOMM
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