Paper 2015/398

Factoring RSA moduli with weak prime factors

Abderrahmane Nitaj and Tajjeeddine Rachidi

Abstract

In this paper, we study the problem of factoring an RSA modulus $N=pq$ in polynomial time, when $p$ is a weak prime, that is, $p$ can be expressed as $ap=u_0+M_1u_1+\ldots+M_ku_k$ for some $k$ integers $M_1,\ldots, M_k$ and $k+2$ suitably small parameters $a$, $u_0,\ldots u_k$. We further compute a lower bound for the set of weak moduli, that is, moduli made of at least one weak prime, in the interval $[2^{2n},2^{2(n+1)}]$ and show that this number is much larger than the set of RSA prime factors satisfying Coppersmith's conditions, effectively extending the likelihood for factoring RSA moduli. We also prolong our findings to moduli composed of two weak primes.

Metadata
Available format(s)
PDF
Publication info
Published elsewhere. C2SI-Berger2015
Keywords
RSA
Contact author(s)
abderrahmane nitaj @ unicaen fr
History
2015-05-01: received
Short URL
https://ia.cr/2015/398
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2015/398,
      author = {Abderrahmane Nitaj and Tajjeeddine Rachidi},
      title = {Factoring RSA moduli with weak prime factors},
      howpublished = {Cryptology ePrint Archive, Paper 2015/398},
      year = {2015},
      note = {\url{https://eprint.iacr.org/2015/398}},
      url = {https://eprint.iacr.org/2015/398}
}
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