Thread: CADO
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Old 2008-11-06, 12:35   #5
akruppa's Avatar
Aug 2002

246710 Posts

I found that with two 30-bit primes (so that the product fits in one word), ECM is almost as fast as Kleinjung's MPQS. Often one prime is a smaller than the other, which gives ECM an advantage. If their product is a little bigger than the word size, MPQS should have a noticeable advantage. If the composite needs to have 3 factors to be smooth, ECM with an early abort strategy will perform far better than MPQS which doesn't tell anything about likely smoothness until it found the actual factors. All in all, an implementation with only P-1, P+1 and ECM can perform quite well, although for some particular cases it would be worthwhile to have MPQS around as a fall-back.

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