For Full-Text PDF, please login, if you are a member of IEICE,|
or go to Pay Per View on menu list, if you are a nonmember of IEICE.
Speeding up the Lattice Factoring Method
Shigenori UCHIYAMA Naoki KANAYAMA
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Publication Date: 2001/01/01
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Cryptography and Information Security)
factoring problem, LLL-algorithm, lattice factoring method,
Full Text: PDF(201KB)>>
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.