A new method of large integer prime decomposition for network public key cryptosystem Online publication date: Tue, 01-Oct-2024
by Wenbo Sun; Wei Wang; Chenguang Bai
International Journal of Security and Networks (IJSN), Vol. 19, No. 3, 2024
Abstract: This paper takes prime numbers as the research object. Firstly, a dynamic password authentication scheme based on prime modulus is proposed by using prime modulus as an identity identifier, combined with the Chinese remainder theorem in number theory and RSA public key system, and its security is analysed. Secondly, this paper establishes prime-base linear spaces and corresponding positive rational logarithmic linear spaces. It obtains the matrix of natural logarithmic function linear isomorphism mapping under the corresponding basis through logarithmic isomorphism linear mapping between spaces based on the important role that prime numbers play in theory. Thirdly, by transforming the problem of large integer prime factorisation into the problem of factorisation over polynomial rings, several new methods of large integer prime factorisation based on the theory of polynomial rings are proposed. It provides a theoretical basis for further improving the security of network public key encryption systems.
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