------------------------------------------------------------------------------ This message is copyright (c) Robert J. Harley, 1998. If you wish to quote more than one sentence, please quote the whole thing. To: certicom-ecc-challenge@certicom.com Robert J. Harley, Rocquencourt, France, 12th of January, 1998. Dear Mr. Gallant, Please note that this submission, like the previous two, carries a copyright notice. If you wish to quote it on your Web pages, or anywhere else, you may not strip off the copyright notice nor replace it with "Copyright Certicom Corp." or any similar notice. The solution to your ECCp-89 problem is the residue class of 333373190151749761757285479 modulo 416363315556124458285894983. The calculation was carried out in 24 days by a group of 57 people using Alpha workstations running Linux, Digital Unix, VMS and NetBSD: Chris Adams Scott Appleton Wayne Baisley Spider Boardman Alvin Brattli Bill Broadley Andries Brouwer Zach Brown Dragisa Duric Martin Edu Adrian Escott Douglas Frank Rick Gorton Oleg Gusev Robert Harley David Hauan Dave Hill Richard Holmes Chatchai Jantaraprim Olav Kongas Mika Kortelainen Edward Lee Greg Lindahl Brian Lund Rob Millner Francois Morain Pete Murray Jon Nathan Burkhard Neidecker-Lutz Dennis Opacki Wieger Opmeer Miguel Barreiro Paz Vance Petree Guillaume Pierre Martin Radford Jon Reeves Tim Rowley John Sager Michael Sandfort Mike Schloss Alex Selkirk Al Simons Aaron Spink Murray Stokely Adrian En-Wei Sun Peter Sward Greg Thomas Dimitris Tsapakidis Jeff Uphoff Marko Vendelin Carlos Vidal Bart-Jan Vrielink Tom Woodburn Berndt Josef Wulf Marinos Yannikos Paul Young and a person who prefers to remain anonymous. The method we used was a "birthday paradox" algorithm iterating from a random initial point (one per machine) with a pseudo-random function (the same on all machines) until a collision was detected at 15:33 today. A total of 24249418904337 iterations were performed, finding 36345 "distinguished" points and one collision. The British Telecom team found 11333 of the points, people from Digital found 7853, people from INRIA found 4680 and individuals in more than a dozen countries found 12479. Our source code can be downloaded from: http://pauillac.inria.fr/~harley/ecdl2/ Bye, Rob. .-. Robert.Harley@inria.fr .-. / \ .-. .-. / \ / \ / \ .-. _ .-. / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / `-' `-' \ / \ / \ \ / `-' `-' \ / `-' Linux + 500MHz Alpha + 256MB SDRAM = heaven `-' ------------------------------------------------------------------------------