Preserving Confidentiality against Factorization Attacks using Fake Modulus ($\zeta$) Approach in RSA and its Security Analysis

In today's world, the most vital feature is the security of shared information. To achieve this, various algorithms are offered in cryptosystems, with RSA being one among them. RSA is a robust encryption method, however it can be cracked using a factorization attack. As a result, this work presents an improved RSA algorithm that emphasises RSA's security feature of giving immunity to factorization attacks. The algorithm provides a third variable, which is used as the public key in the network, replacing the common modulus n. The experimental end results, such as differential analysis, performance analysis, and statistical analysis, clearly demonstrated the efficacy of the proposed methodology for secure communication. In addition, the article examines various assaults that could be made against the proposed system and reflects on its effectiveness.