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Paper 2016/551
Improved Factorization of $N=p^rq^s$
Jean-Sebastien Coron and Rina Zeitoun
Abstract
Bones et al. showed at Crypto 99 that moduli of the form $N=p^rq$ can be factored in polynomial time when $r \geq \log p$. Their algorithm is based on Coppersmith's technique for finding small roots of polynomial equations. Recently, Coron et al. showed that $N=p^rq^s$ can also be factored in polynomial time, but under the stronger condition $r \geq \log^3 p$. In this paper, we show that $N=p^rq^s$ can actually be factored in polynomial time when $r \geq \log p$, the same condition as for $N=p^rq$.
Metadata
- Available format(s)
- Category
- Public-key cryptography
- Publication info
- Preprint. MINOR revision.
- Keywords
- FactoringCoppersmith's techniquelattice reduction
- Contact author(s)
-
jean-sebastien coron @ uni lu
r zeitoun @ oberthur com - History
- 2016-06-02: received
- Short URL
- https://ia.cr/2016/551
- License
-
CC BY