Journal of Applied Mathematics and Computation

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Article http://dx.doi.org/10.26855/jamc.2020.12.014

Polynomial Time Attacks for Modulus N = p^2 q^2

Sadiq Shehu, Saidu Isah Abubakar*, Zaid Ibrahim

Department of Mathematics, Faculty of Science, Sokoto State University, Sokoto, Nigeria.

*Corresponding author: Saidu Isah Abubakar

Published: December 18,2020

Abstract

This research proposes three polynomial time attacks on prime power modulus  In the first attack, we show that if ,then the decryption exponent  can be found from the convergent of te continued fraction expansion of where approximation of φ(N) is prove to be  . We present second and third attacks on j multi prime power moduli  by transforming system of equation and into simultaneous Diophantine approximation problem from which we apply lattice basis reduction techniques to find unknown integers and , which leads to successful factorization of j moduli in polynomial time for  .

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How to cite this paper

Polynomial Time Attacks for Modulus N = p^2 q^2

How to cite this paper: Sadiq Shehu, Saidu Isah Abubakar, Zaid Ibrahim. (2020) Polynomial Time Attacks for Modulus N = p^2 q^2. Journal of Applied Mathematics and Computation, 4(4), 230-240.

DOI: http://dx.doi.org/10.26855/jamc.2020.12.014