Quoth Schroeppel, Richard:

I'd like to encourage Math-Funsters to postpone discussing on the list the algorithms omitted from this paper for a month, till March 15.

Are you going to request DJB to withdraw his 2004 paper that describes how to do this too? The other team who've repeated Lenstra's results apparently used DJB's algorithm. Paul Leyland (see acknowledgements in the Lenstra paper) unwittingly squeezed an alternative algorithm with a very similar Big-Oh out of me today, again in a public forum. So there are at least 2 cats roaming around not in a bag any more. Phil