International Association for Cryptologic Research

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Paper: A New Class of Unsafe Primes

Authors:
Qi Cheng
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URL: http://eprint.iacr.org/2002/109
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Abstract: In this paper, a new special-purpose factorization algorithm is presented, which finds a prime factor $p$ of an integer $n $ in polynomial time, if $4p-1$ has the form $d b^2$ where $d \in \{3, 11, 19, 43, 67, 163\}$ and $b$ is an integer. Hence such primes should be avoided when we select the RSA secret keys. Some generalizations of the algorithm are discussed in the paper as well.
BibTeX
@misc{eprint-2002-11632,
  title={A New Class of Unsafe Primes},
  booktitle={IACR Eprint archive},
  keywords={public-key cryptography / RSA, integer factoring, elliptic curve factorization},
  url={http://eprint.iacr.org/2002/109},
  note={ qcheng@cs.ou.edu 11902 received 3 Aug 2002},
  author={Qi Cheng},
  year=2002
}