I'm enclosing two messages from sci.crypt: Peter Trei ------------------------------------------------------------------------ First message On sci.crypt Volker Mueller <vmueller@cdc.informatik.tu-darmstadt.de> wrote:
[...] Maybe the problem is not so easy. The biggest DL computation for an elliptic curve was a 19 digit prime order computation (up to my knowledge). The first Certicom "exercise" has 79 bits or 24 decimal digits.
Cheers, Volker
You're right, the so-called "exercise" was not so easy! However a few Alphas and some optimised code got through it eventually. I just posted the following to Certicom... -- Rob. PS: Any volunteers willing to dedicate Alpha CPU time for cracking the next challenge? With a bunch of machines it would be a piece of cake! ------------------------------------------------------------------------ ------ This message is copyright Robert J. Harley, 1997. If you wish to quote more than one sentence, please quote the whole thing. To: certicom-ecc-challenge@certicom.com Robert J. Harley, Se`vres, France, 6th of December, 1997. Dear Anonymous, Certicom's professed aim in setting its ECC challenge is to encourage research into secure cryptosystems based on elliptic curve discrete logarithms. Yet Certicom is a member of the Key Recovery Alliance, a lobby group whose purpose is to promote the use of back-doors allowing supposedly secure communications to be intercepted. How are these contradictory positions reconciled? The solution to your ECCp-79 problem is the residue class of 92221507219705345685350 modulo 466597814831947642887217. It was found by Wayne Baisley and myself using several Digital Alpha workstations running Linux and Digital Unix at the Institut National de Recherche en Informatique et Automatique (INRIA), at Fermi National Accelerator Laboratory and at the California Institute of Technology C.S. Department. The method used was a "birthday paradox" algorithm iterating from a random initial point (one per machine) with a random function (the same on all machines) until a collision was detected at 17:58 today at INRIA, Rocquencourt, France by a 500MHz Linux machine. This machine did 25 billion elliptic curve operations per day. The peak rate of all machines was approximately 6 six times as much. A total of about 1400 billion iterations were performed. If this is the first correct submission, please send the prize (a copy of "Handbook of Applied Cryptography" and Maple software) to the following address: Robert Harley, c/o Sylvie Loubressac, Projet CRISTAL, INRIA, Domaine de Voluceau - Rocquencourt, 78153 Le Chesnay, France. Thank you, Rob. .-. Robert.Harley@inria.fr .-. / \ .-. .-. / \ / \ / \ .-. _ .-. / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / `-' `-' \ / \ / \ \ / `-' `-' \ / `-' Linux + 500MHz Alpha + 256MB SDRAM = heaven `-' ------------------------------------------------------------------------ ------ ------------------------------------------------------------------------ ---------------------------------------------- Second message: From: Dimitris Tsapakidis <dimitris@alien.bt.co.uk> Date: 1997/12/08 Message-ID: <348BDD10.B5B2E641@alien.bt.co.uk> Newsgroups: sci.crypt [More Headers] Hello Robert, Congratulations on your effort. We would like to post some information on our attempt at BT Labs. We found the private key after you at 19:58 GMT on Sunday the 7th. We only completed 481 billion ECC operations at a peak rate of 84 billion per day using 170 to 210 machines. A couple of months ago we contributed 180-250 machines to the distributed.net/Bovine group attack on RC5-56, peaking at 60 million keys/sec. Dimitris