Some integer factorization algorithms using elliptic curves (1986)
| Venue: | Australian Computer Science Communications |
| Citations: | 41 - 13 self |
BibTeX
@ARTICLE{Brent86someinteger,
author = {Richard P. Brent},
title = {Some integer factorization algorithms using elliptic curves},
journal = {Australian Computer Science Communications},
year = {1986},
volume = {8},
pages = {149--163}
}
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Abstract
Lenstra’s integer factorization algorithm is asymptotically one of the fastest known algorithms, and is also ideally suited for parallel computation. We suggest a way in which the algorithm can be speeded up by the addition of a second phase. Under some plausible assumptions, the speedup is of order log(p), where p is the factor which is found. In practice the speedup is significant. We mention some refinements which give greater speedup, an alternative way of implementing a second phase, and the connection with Pollard’s “p − 1” factorization algorithm. 1
