Certicom ECC Challenge(s) Cracked

from TBoToday, 1998-02-09

TBTF for 1998-01-19

TBTF for 1997-12-24

TBTF for 1997-12-08

In order to gain exposure and to jumpstart the expert scrutiny that ECC will need if it is to be widely trusted, Certicom is sponsoring a multi-part crypto challenge.

This page records the achievements of the individuals and groups who crack the various challenges.

- On 1997-12-06 Robery Harley <Robert.Harley at inria dot fr> announced that he and Wayne Baisley had cracked one of two first-level warmup exercises, a 79-bit problem designated ECCp-79.
- On 1997-12-16 Harley's team (now numbering 21) did it again, announcing the fall of the second Certicom exercise, ECC2-79.
- On 1998-01-12 the same team (now numbering 56) completed a hat trick, announcing that the third Certicom exercise, ECCp-89, had been broken.
- On 1998-02-07 the same team (now numbering more than 66) announced that the fourth Certicom exercise, ECC2-89, had been broken.

The announcements below are all copyright 1997-1998 by Robert Harley.

To: certicom-ecc-challenge@certicom.com6th 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 `-'

Robert J. Harley,

Sevres, France,

16th of December, 1997.To: certicom-ecc-challenge@certicom.com

Dear Mr. Gallant,

There are two types of communications. On the one hand are secure communications, intelligible only to their intended recipient, and on the other are all the rest. Between them, as Louis Freeh would say, there is a "bright line". On what side of that line does Certicom stand?

The solution to your ECC2-79 problem is the residue class of 276856274258963891889538 modulo 302231454903954479142443. The work was led by a group of Alpha Linux enthusiasts, and the British Telecom Labs team joined in too. We used about 30 Alphas running Linux, from UDBs up to 600 MHz workstations. Jay Estabrook's new 21264 machine made a cameo appearance! There were also 4 Alphas running Digital Unix.

Contributors were:

Andries Brouwer Andries.Brouwer@cwi.nl Christopher Brown cbrown@alaska.net Zach Brown zab@zabbo.net Jay Estabrook Jay.Estabrook@digital.com Rick Gorton gorton@amt.tay1.dec.com Oleg Gusev oleg@usm.uni-muenchen.de Robert Harley Robert.Harley@inria.fr Richard Holmes holmes@lanl.gov Andy Isaacson adi@acm.org Greg Lindahl lindahl@cs.virginia.edu Jon Nathan jon@blading.com Dennis Opacki dopacki@mac-guru.com Vance Petree vwp@vancpower.com Tim Rowley tor@cs.brown.edu Michael Sandfort sandfort@post.cis.smu.edu Jason Shiffer jshiffer@home.com Aaron Spink spink@pa.dec.com B.T. Labs Team jcs@zoo.bt.co.uk Bart-Jan Vrielink bartjan@mail.de-boulevard.nl Marinos Yannikos nino@complang.tuwien.ac.at Xiaoguang Zhang xgz@mn.ms.ornl.govand some anonymous others.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 12:47 today. A total of 1737410165382 iterations were performed, finding 1617 "distinguished" points and one collision. Our source code can be downloaded from:

http://pauillac.inria.fr/~harley/ecdl/ We would like to thank Michael Wiener for sending his paper, co-authored with Paul van Oorschot, in which they suggest using distinguished points for discrete log calculations. We used this idea to simplify our client program.

Thanks also to John Sager who spotted a broken line of code in one version of the program. We were quickly able to verify that it had caused no harm.

If this is the first correct submission, then, well I don't really know what you should do with the prize! Perhaps hold a raffle among the contributors?

Thank you, Rob. .-. Robert.Harley@inria.fr .-. / \ .-. .-. / \ / \ / \ .-. _ .-. / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / `-' `-' \ / \ / \ \ / `-' `-' \ / `-' Linux + 500MHz Alpha + 256MB SDRAM = heaven `-'

To: certicom-ecc-challenge@certicom.comRobert 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:

Zach Brown Jon Reeves Dragisa Duric Tim Rowley Martin Edu John Sager Adrian Escott Michael Sandfort Douglas Frank Mike Schloss Rick Gorton Alex Selkirk Oleg Gusev Al Simons Robert Harley Aaron Spink David Hauan Murray Stokely Dave Hill Adrian En-Wei Sun Richard Holm Peter Swardes Chatchai Janta Greg Thomasraprim Olav Kongas Dimitris Tsapakidis Mika Kortela Jeff Uphoffinen Edward Lee Marko Vendelin Greg Lindah Carlos Vidall Brian Lund Bart-Jan Vrielink Rob Millner Tom Woodburn Francois Morai Berndt Josef Wulfn Pete Murray Marinos Yannikos Jon Nathan Paul Youngand 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 `-'

To: certicom-ecc-challenge@certicom.com

Robert J. Harley,

Sèvres, France,

7th of February, 1998.Dear Mr. Gallant,

The solution to Certicom's ECC2-89 problem is the residue class of 41871609686648820507900581 modulo 309485009821357445894232317. The calculation was carried out in 26 days by a group of 70 people in 17 countries. 95% of the work was done on Alpha workstations running Linux and Digital Unix and the remaining 5% was done on various 32-bit machines.

The fastest, naturally, were 600 MHz Alpha systems doing 241 K elliptic curve operations per second each. The fastest 32-bit systems were 233 MHz StrongARM NCs running NetBSD at 55 K each. Several other systems contributed too including a bunch of Pentium and Pentium Pro machines with Linux, a few Sparcs with SunOS, a 150 MHz SGI MIPS with Irix, an old 80 Mhz HP PA with NextStep and a Cyrix 486 DX2. Last and definitely least were my trusty old 8 MHz ARM 2's running RISC OS (hey, they seemed fast ten years ago :).

The people involved were:

Wayne Baisley Greg Lindahl Miguel Barreir Brian Lundo Paz Uri Blument Preda Mihailescuhal Spider Boardma Francois Morainn Alvin Brattli Pete Murray Bill Broadle Jon Nathany Andries Brouwer Burkhard Neidecker-Lutz Zach Brown Wieger Opmeer Bruce Dawson Vance Petree Dr. Sven Dietric Guillaume Pierreh Einar Doerum Martin Radford Dragisa Duric Jon Reeves Martin Edu Brian Romansky Gwyn Evans Geordy Rostad Douglas Frank Tim Rowley Megan Gentry Andrew Sapozhnikov Rick Gorton Aaron Sawyer Thomas Gschwin Mike Schlossd Oleg Gusev Al Simons Mikolaj Habryn Mikko Siren Robert Harley Chris Smith David Hauan Mark Smith Mike Iglesia Murray Stokelys Chatchai Jantara Adrian En-Wei Sunprim Travis Johnson Peter Sward Martin Kahlert Marko Vendelin Asim Kepkep Paul Verwer Rohit Khare Bill Viggers Mika Kortela Bart-Jan Vrielinkinen Andreas Krall Dan Weeks Edward Lee Michael Wins Dr. Hiankiat Lee Tom Woodburn Leon Lessing Gregory Woodburyand the British Telecom team, some students of the Ecole Centrale de Lille 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 16:21 today.

A total of 18161819582507 iterations i.e., over 18000 billion, were performed finding 17543 "distinguished" points. Two of the points, found by Guillaume Pierre of INRIA and Bill Broadley of U.C.Davis, were in fact equal allowing us to compute the final answer. Since an ECC2-89 iteration took close to twice as long as an ECCp-89 iteration, this was the most difficult calculation we have done so far.

Participants at INRIA found 3653 points using machines belonging to the following projects: Air, Algo, Codes, Coq, Cristal, Méval, Para, Sor and Sosso. Those at Digital found 4591 points, and others found 9299.

Our source code can be downloaded from:

http://pauillac.inria.fr/~harley/ecdl3/ We invite anyone interested in working on the next calculation to point their Web browsers at:

http://pauillac.inria.fr/~harley/ecdl4/ Bye, Rob. .-. Robert.Harley@inria.fr .-. / \ .-. .-. / \ / \ / \ .-. _ .-. / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / `-' `-' \ / \ / \ \ / `-' `-' \ / `-' Linux + 500MHz Alpha + 256MB SDRAM = heaven `-' ------------------------------------------------------------------------------

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