Small secret exponent attack on RSA variant with modulus $$N=p^rq$$ N = p r q

Abstract

We consider an RSA variant with Modulus $$N=p^rq$$ N = p r q . This variant is known as Prime Power RSA. In PKC 2004, May proved when decryption exponent $$d<N^{ \frac{r}{(r+1)^2}}$$ d < N r ( r + 1 ) 2 or $$d< N^{\left( \frac{r-1}{r+1}\right) ^2}$$ d < N r - 1 r + 1 2 , one can factor $$N$$ N in polynomial time. In this paper, we improve this bound when $$r \le 5$$ r ≤ 5 . We provide detailed experimental results to justify our claim.