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Cryptanalysis of RSA with constrained keys

Authors:
Abderrahmane Nitaj
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URL: http://eprint.iacr.org/2006/092
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Abstract: Let $n=pq$ be an RSA modulus with unknown prime factors and $F$ any function for which there exists an integer $u\neq 0$ satisfying $F(u)\approx n$ and $pu$ or $qu$ is computable from $F(u)$ and $n$. We show that choosing a public key exponent $e$ for which there exist positive integers $X$, $Y$ such that $\left\vert eY-XF(u)\right\vert$ and $Y$ are suitably small, then the system is insecure.
BibTeX
@misc{eprint-2006-21585,
  title={Cryptanalysis of RSA with constrained keys},
  booktitle={IACR Eprint archive},
  keywords={RSA cryptosystem, Cryptanalysis, Continued fractions, Bl\"omer-May attack, Coppersmith's algorithm},
  url={http://eprint.iacr.org/2006/092},
  note={ nitaj@math.unicaen.fr 13216 received 9 Mar 2006},
  author={Abderrahmane Nitaj},
  year=2006
}