Welcome to the resource topic for 2015/399
Title:
New attacks on RSA with Moduli N=p^rq
Authors: Abderrahmane Nitaj, Tajjeeddine Rachidi
Abstract:We present three attacks on the Prime Power RSA with modulus N=p^rq. In the first attack, we consider a public exponent e satisfying an equation ex-\phi(N)y=z where \phi(N)=p^{r-1}(p-1)(q-1). We show that one can factor N if the parameters |x| and |z| satisfy |xz|<N^\frac{r(r-1)}{(r+1)^2} thereby extending the recent results of Sakar~\cite{SARKAR}. In the second attack, we consider two public exponents e_1 and e_2 and their corresponding private exponents d_1 and d_2. We show that one can factor N when d_1 and d_2 share a suitable amount of their most significant bits, that is |d_1-d_2|<N^{\frac{r(r-1)}{(r+1)^2}}. The third attack enables us to factor two Prime Power RSA moduli N_1=p_1^rq_1 and N_2=p_2^rq_2 when p_1 and p_2 share a suitable amount of their most significant bits, namely, |p_1-p_2|<\frac{p_1}{2rq_1q_2}.
ePrint: https://eprint.iacr.org/2015/399
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