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RSA public key password cracking method

A technology of public key cryptography and prime numbers, which is applied in the field of cracking RSA public key cryptography, to achieve the effect of reducing the number of comparisons and the amount of calculation

Active Publication Date: 2020-05-22
TAIYUAN UNIV OF TECH
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  • Summary
  • Abstract
  • Description
  • Claims
  • Application Information

AI Technical Summary

Problems solved by technology

However, the number field sieve method is a probabilistic integer decomposition method, which has certain randomness, so there are few breakthroughs in the field of integer decomposition.

Method used

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Embodiment Construction

[0041] The technical solutions of the present invention will be further described in more detail below in conjunction with specific embodiments. Apparently, the described embodiments are only some of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other embodiments obtained by persons of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0042] Such as figure 1 As shown, the present invention provides a kind of RSA public key password cracking method, comprises steps:

[0043] Divide natural numbers into different prime factorials as intervals, and establish a prime factorial table according to the size of the region and the boundary of the region; the construction principle of the prime factorial table is: the integer in the first row of each column represents the product of the first n prime factorials, denoted as P n ! , the numbers in the...

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Abstract

The invention discloses an RSA public key password cracking method. The method comprises the following steps: establishing a prime number factorial table in advance; a prime factor combination mode ofintegers of all 617 decimal digits (RSA-2048 is 617 digits) can be included only through a 234-column table, that is, decomposing the integer of the maximum 617 decimal digit only by traversing about132 columns of prime number multiplication tables at most, and finding and adding alternative numbers in each column. Compared with a traditional method that traversal of all trial division integersnot larger than traversal is needed, the comparison frequency and the calculation amount are reduced. A beneficial reference is provided for security analysis of an RSA encryption algorithm. The invention relates to a method capable of quickly decomposing a composite number with relatively close two-factor digits, which is mainly applied to an RSA large-modulus decomposition scene and has a promoting effect on an attack method for cracking an RSA cryptosystem by utilizing a decomposed large modulus.

Description

technical field [0001] The invention relates to the technical field of integer decomposition, in particular to a method for cracking RSA public key ciphers. Background technique [0002] With the introduction of prime numbers and the fundamental theorem of arithmetic, as early as 300 BC, the concept of integer decomposition also came into being. The early development of mathematics was mainly driven by daily life and business, and integer factorization did not play a significant role in these two fields, so the research on integer factorization can only rely on the drive of interest. Until the late 1970s, the study of public key cryptography became the main driving force for the study of integer factorization. Trial division is the earliest known integer factorization method. Fermat proposed some ideas about integer factorization in 1643, and these ideas are still at the core of integer factorization today. Fermat proposed writing an integer as the difference between two ...

Claims

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): H04L9/30
CPCH04L9/302H04L9/3033Y02D30/50
Inventor 张景刚薛星陈永乐王旭陈俊杰
Owner TAIYUAN UNIV OF TECH
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