New weak findings upon RSA modulo of type N = p2 q

This paper proposes new attacks on RSA with the modulus N = p2 q. The first attack is based on the equation eX −NY = p2 u+q2 v +Z such that u is an integer multiple of 2 and v is an integer multiple of 3. If |p2 u − q2 v| < N1/2, |Z| ■(|p^2 - q^2 | @3(p^2 + q^2)) < N1/3 and X < ▁((■(N@3(p^2 u + q^2 v))) ̅ ) then N can be factored in polynomial time using continued fractions. For the second and third attacks, this paper proposes new vulnerabilities in k RSA Moduli Ni = p_i^2 qi for k ≥ 2 and i = 1,...,k. The attacks work when k RSA public keys (Ni, ei) are related through eix − Niyi = p_i^2 u + q_i^2 v + zi or eixi − Niy = p_i^2 u + q_i^2 v + zi where the parameters x, xi, y, yi and zi are suitably small.

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