## Some integer factorization algorithms using elliptic curves (1986)

Venue: | Australian Computer Science Communications |

Citations: | 46 - 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}

}

### Years of Citing Articles

### OpenURL

### 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