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

2 PolSys - Polynomial Systems
LIP6 - Laboratoire d'Informatique de Paris 6, Inria de Paris
Abstract : 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 with k prime factors N = \prod_{i=1}^k p_i^{r_i} ; we show that a non-trivial factor of N can be extracted in polynomial-time if one of the exponents r_i is large enough.
Type de document :
Communication dans un congrès
RSA Conference Cryptographers' Track , Feb 2016, San Francisco, United States. Topics in Cryptology – CT-RSA 2016. 〈10.1007/978-3-319-29485-8_26〉
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Littérature citée [14 références]

https://hal.inria.fr/hal-01250302
Contributeur : Guénaël Renault <>
Soumis le : vendredi 11 novembre 2016 - 15:01:58
Dernière modification le : jeudi 11 janvier 2018 - 06:28:03
Document(s) archivé(s) le : jeudi 16 mars 2017 - 11:42:36

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Copp16.pdf
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Jean-Sébastien Coron, Jean-Charles Faugère, Guénaël Renault, Rina Zeitoun. Factoring $N=p^r q^s$ for Large $r$ and $s$. RSA Conference Cryptographers' Track , Feb 2016, San Francisco, United States. Topics in Cryptology – CT-RSA 2016. 〈10.1007/978-3-319-29485-8_26〉. 〈hal-01250302〉

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