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arXiv · 1004.3366

Some integer factorization algorithms using elliptic curves

Richard P. Brent
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Abstract

Lenstra's integer factorization algorithm is asymptotically one of the fastest known algorithms, and is 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.

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Richard P. Brent. 2010-04-20. Some integer factorization algorithms using elliptic curves. https://arxiv.org/abs/1004.3366

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