NEW PRACTICAL ATTACK ON RSA MODULUS OF TYPE $N=p^{2}q$
Normahirah Nek Abd Rahman, Muhammad Rezal Kamel Ariffin · International Journal of Pure and Apllied Mathematics · 2016
This paper proposes three new attacks on RSA with the modulus N = p 2 q.The first attack is based on the equation eX -N Y = (p 2 u + q 2 v)Z such that u is an integer multiple of 2 and v is an integer multiple of 3 with |p 2 uq 2 v| < N 1/2 and gcd(X, Y ) = 1.If X|Z| < N 2|p 2 u+q 2 v| , then N can be factored in polynomial time using continued fractions expansion.For the second and third attack, this paper proposes new vulnerabilities in k RSA cryptosystem moduli Ni = p 2 i qi for k ≥ 2 and i = 1, ..., k.The attacks work when k RSA public keys (Ni, ei) are related through eix-Niyi = (p 2 i u+q 2 i v)zi or eixi -Niy = (p 2 i u+q 2 i v)zi where the parameters x, xi, y, yi and zi are suitably small.