New attacks on RSA with Moduli $N=p^rq$, by Abderrahmane Nitaj and Tajjeeddine Rachidi

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|