Speeding up the Lattice Factoring Method

Shigenori UCHIYAMA  Naoki KANAYAMA  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E84-A   No.1   pp.146-150
Publication Date: 2001/01/01
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Cryptography and Information Security)
factoring problem,  LLL-algorithm,  lattice factoring method,  

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Recently, Boneh et al. proposed an interesting algorithm for factoring integers, the so-called LFM (Lattice Factoring Method). It is based on the techniques of Coppersmith and Howgrave-Graham, namely, it cleverly employs the LLL-algorithm. The LFM is for integers of the form N = pr q, and is very effective for large r. That is, it runs in polynomial time in log N when r is on the order of log p. We note that for small r, e.g. N =pq, p2q, it is an exponential time algorithm in log N. In this paper, we propose a method for speeding up the LFM from a practical viewpoint. Also, theoretical considerations and experimental results are provided that show that the proposed algorithm offers shorter runing time than the original LFM.