Paper 2015/071

Factoring N=p^r q^s for Large r and s

Jean-Sebastien Coron, Jean-Charles Faugere, Guenael Renault, and Rina Zeitoun


Boneh et al. showed at Crypto 99 that moduli of the form N=p^r q can be factored in polynomial time when r=log p. Their algorithm is based on Coppersmith's technique for finding small roots of polynomial equations. In this paper we show that N=p^r q^s can also be factored in polynomial time when r or s is at least (log p)^3; therefore we identify a new class of integers that can be efficiently factored. We also generalize our algorithm to moduli N with k prime factors; we show that a non-trivial factor of N can be extracted in polynomial-time if one of the k exponents is large enough.

Available format(s)
Public-key cryptography
Publication info
Published elsewhere. Major revision. CT-RSA 2016
Factoring N=p^r q^sCoppersmith's AlgorithmLLLRSA.
Contact author(s)
jean-sebastien coron @ uni lu
2015-11-24: last of 2 revisions
2015-02-10: received
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Creative Commons Attribution


      author = {Jean-Sebastien Coron and Jean-Charles Faugere and Guenael Renault and Rina Zeitoun},
      title = {Factoring N=p^r q^s for Large r and s},
      howpublished = {Cryptology ePrint Archive, Paper 2015/071},
      year = {2015},
      note = {\url{}},
      url = {}
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