Quick large number decomposition method based on cryptographic technology application

Abstract

The invention discloses a quick large number decomposition method based on cryptographic technology application. The creative quick large number decomposition method organically combining the congruence theory and the composite number distribution rule includes the steps of compressing positive integers, setting up an almost prime number group, selecting a maximum dereferencing range, generating the almost prime number group, decomposing a large number, setting digits, deleting composite numbers and the like. The method different from traditional large number decomposition methods can be used for quick factorization of any large number selected from n without depending on computing speed, and quick decomposition can be realized by using computer software for simple identification processing instead of a great amount of time-consuming complex operations. Therefore, evaluation and improvement of relevant public key system safety can be greatly promoted, and the quick large number decomposition method is widely applicable to the field of information safety and cryptographic technology application.

Description

Technical field [0001] The invention relates to the fields of information security and application of cryptography technology, in particular to a large number fast decomposition method based on application of cryptography technology. Background technique [0002] In modern cryptography, the security of passwords comes first. The complexity of algorithmic solutions to mathematical problems can be described by computational complexity theory, which can provide practical measurement methods for deciphering codes and computational complexity. Therefore, most of today's cryptographic systems often boil down to solving a certain mathematical problem. Some typical mathematical problems in computational complexity theory provide the basis for designing practical and safe high-strength cryptosystems. For example, the public key cryptosystem designed based on the knapsack problem in NPC class, the RSA public key cryptosystem based on the large number factorization problem of NP prob...

AI Technical Summary

Problems solved by technology

Although the above-mentioned attempts to decompose the factors have been successful, the complexity and difficulty of its cracking can also be seen from this

However, at present, there is no algorithm that can completely solve the problem of large number decomposition. Most of the above-mentioned algorithms use the specific composition of large numbers to try to decompose large numbers. In many cases, they cannot be successful. Therefore, , for the password designer, as long as the assumptions of these algorithms can be avoided, theoretically speaking, the password he designed is relatively safe

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