International Association for Cryptologic Research

International Association
for Cryptologic Research


Paper: Simple backdoors to RSA key generation

Claude Crépeau
Alain Slakmon
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Abstract: We present extremely simple ways of embedding a backdoor in the key generation scheme of RSA. Three of our schemes generate two genuinely random primes $p$ and $q$ of a given size, to obtain their public product $n=pq$. However they generate private/public exponents pairs $(d,e)$ in such a way that appears very random while allowing the author of the scheme to easily factor $n$ given only the public information $(n,e)$. Our last scheme, similar to the PAP method of Young and Yung, but more secure, works for any public exponent $e$ such as $3,17,65537$ by revealing the factorization of $n$ in its own representation. This suggests that nobody should rely on RSA key generation schemes provided by a third party.
  title={Simple backdoors to RSA key generation},
  booktitle={IACR Eprint archive},
  keywords={public-key cryptography /},
  note={ 12017 received 26 Nov 2002},
  author={Claude Crépeau and Alain Slakmon},