Computational Difficulty of Factoring Large Integers Using Generalize System Equations

Samaila Abdullahi, Sadiq Shehu and Tukur Shehu
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Samaila Abdullahi: Department of Mathematics, Faculty of Science, Sokoto State University, Sokoto Nigeria
Sadiq Shehu: Department of Mathematics, Faculty of Science, Sokoto State University, Sokoto Nigeria
Tukur Shehu: Department of Mathematics, School of Science, Shehu Shagari College of Education, Sokoto Nigeria

International Journal of Research and Innovation in Applied Science, 2023, vol. 8, issue 1, 81-94

Abstract: The RSA algorithm is the foundation of a cryptosystem, which permits public key encryption and is frequently used to establish a secure connection, particularly when it is delivered over an unprotected network such as the internet. Let and be unbalance prime, we offer two novel attacks in this paper using prime power modulus N = prqs. Our first results are based on the RSA equation ex2-φ(N)y2= 1 e,N and x,p,q,φ(N) are public key and private key tuples respectively. If P ≤q ≤λ1/r+1N1/r+1, then x

Date: 2023
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