A Note on the Lattice Factoring Method

Tetsuya IZU  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E87-A   No.1   pp.221-223
Publication Date: 2004/01/01
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section LETTER (Special Section on Cryptography and Information Security)
integer factoring problem,  Lattice Factoring Method (LFM),  LLL-algorithm,  Uchiyama-Kanayama's improvement,  

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In 1999, Boneh et al. proposed the Lattice Factoring Method (LFM) for the integer factoring problem for a composite of the form N = prq by employing the LLL-algorithm. Time complexity of LFM is measured by the number of calls of the LLL-algorithm. In the worst case, the number is 2log p for a certain constant c. In 2001, Uchiyama and Kanayama introduced a novel criterion and provided an improved algorithm which runs (2k-p)/|p-Nr+1| times faster (for certain constants k, Nr+1). In this letter, we note another practical improvement applicable to the original and the improved LFM, which enables to provide about 2 times speed-up.