[Resource Topic] 2016/551: Improved Factorization of $N=p^rq^s$

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Title:
Improved Factorization of N=p^rq^s

Authors: Jean-Sebastien Coron, 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.

ePrint: https://eprint.iacr.org/2016/551

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