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Re: Making the Agora Vanish
by Declan McCullagh 19 Apr '01

19 Apr '01

On Tue, Apr 17, 2001 at 10:16:53AM +0300, Sampo Syreeni wrote: > Agreed, to a degree. But it isn't very difficult to outlaw crypto, and to > effectively control its use for online anonymity - to get a workable > anonymity infrastructure, you need common protocols, participants to create It is trivial to pass a law banning crypto. (If you ignore the political considerations. There was a proposal in the House a few years back that banned nonescrowed crypto, see the archives for my report, heh.) It is nontrivial to pass a law that *succeeds* in banning crpto. -Declan

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RE: Making the Agora Vanish
by Greg Broiles 19 Apr '01

19 Apr '01

At 10:16 AM 4/17/2001 +0300, Sampo Syreeni wrote: >Agreed, to a degree. But it isn't very difficult to outlaw crypto, and to >effectively control its use for online anonymity - to get a workable >anonymity infrastructure, you need common protocols, participants to create >the mixnets and a certain amount of publicity to make your effort matter. It >is extremely difficult to run such a usable setup without being detected by >a determined TLA. Unlike with IP, porn, prostitution and drug trade, control >of online activities can largely be automated. You're still thinking like a nice middle-class person with a normal job. People who are serious about participating in black markets use human and technological cutouts to do their business, as well as good old-fashioned graft and corruption. In some criminal cultures, prison time is a badge of honor. In many criminal cultures, it's low-level disposable people who commit the actual crimes - it's the John Gottis and the Pablo Escobars and the Dick Nixons back sleeping in their beds who profit from it. If it was easy to stop crime by passing laws, we'd have done it already. Consider Jim Bell in light of your objections above - do you consider him "controlled"? If so, then the control you speak of is hardly sufficient to prevent forbidden activity. If not, then what makes you think that other, more clueful people can be controlled? -- Greg Broiles gbroiles(a)well.com "Organized crime is the price we pay for organization." -- Raymond Chandler

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Fwd: ~400 bits - New Discrete Log Record due to Joux and Lercier
by Bill Stewart 19 Apr '01

19 Apr '01

120 digits is about 400 bits, and while the computer is respectably fast, it's just 4 processors. (Remember that Alpha MHz != Pentium MHz.) 10 weeks of preprocessing, plus about 12 hours per key afterwards. So 512-bit Diffie-Hellman is pretty close to toast, at least if you re-use the modulus, and likewise 512-bit El Gamal. >Date: Wed, 18 Apr 2001 01:09:38 -0400 (EDT) >From: dmolnar <dmolnar(a)hcs.harvard.edu> >To: cryptography(a)wasabisystems.com >Subject: New Discrete Log Record due to Joux and Lercier > > > >From the NMBRTHRY(a)LISTSERV.NODAK.EDU mailing list: > >Date: Tue, 17 Apr 2001 22:52:56 -0400 >From: Reynald LERCIER <lercier(a)mail.club-internet.fr> >Subject: Discrete logarithms in GF(p) > >Tuesday, April 17 2001. > >We are very pleased to announce a new record for the general discrete >logarithm problem. We were able to compute discrete logarithms modulo >a 120 digits prime. This was done in 10 weeks, on a unique 525MHz >quadri-processors Digital Alpha Server 8400 computer. > >The approach we followed for this computation is close to the approach >we used for computing discrete logarithms modulo a 110 digits prime >[JoLe01]. It is mostly based on algorithms described in [JoLe00]. > >Precisely, let > > p = \lfloor 10^{119} \pi \rfloor+ 207819, > = 314159265358979323846264338327950288419716939937510582097494\ > 459230781640628620899862803482534211706798214808651328438483, > > g = 2, > >and > > y = \lfloor 10^{119} e \rfloor, > = 271828182845904523536028747135266249775724709369995957496696\ > 762772407663035354759457138217852516642742746639193200305992. > >Then > > y = g^262112280685811387636008622038191827370390768520656974243035\ > 380382193478767436018681449804940840373741641452864730765082, > >and, similarly, > > y+1 = g^39657965519539238631090956325038481900751981791165229696297\ > 421520645832904710912189562251329527994908449750607046857937. > >This result was obtained using a now classical algebraic sieve as >explained, from a theoretical point of view, by Schirokauer >[Schi93]. So, it was done in three steps: > _ the sieving step, > _ the linear algebra, > _ the final computation of individual logarithms. > >Sieving: >-------- > >The sieving step consisted in finding couples (a,b) such that the >principal ideal (a+bt) is of smooth norm in the so-called ``right'' >number field defined by > > t^3-9*t^2-9*t+9 > >and such that (ac+bs) is of smooth norm in the so called ``left'' >number field defined by > > s^2 > -7374389167922711279538633461199308033087*s > -333238556260219119547406855509826713348*c > >where > > c = 1201639291188427271122019272295979872125. > >The Galois group of the degree 3 polynomial is of order 3. The >corresponding number field has 2 fundamental units, 1/12*t^2-t+1/4 and >-1/12*t^2+1/2*t+5/4, its class group is of order 1 and its index is >equal to 2^6*3^2. > >Nothing is really known about the degree 2 polynomial except, of >course, that the corresponding number field is a real quadratic field. > >The sieving was done efficiently following a now traditional ``sieving >by vector'' with ``special-q'' technique. It yields many linear >equations between ``logarithms of ideals'' of norms smaller than >15485870 (1000000-th prime) in the left number field and of norms >smaller than 3497870 (250000-th prime) in the right number field. > >After a 40 days computation on a quadri-processors alpha server 8400 >computer, we obtained 2685597 equations with 1242551 unknowns. > >At this point, it usually remains to add 5 Schirokauer maps to these >equations. Here, we added only 2 maps (for the left number field) and >prefer for the right number field, instead of what was done in >[JoLe01], to add explicitly fundamental units contribution taking >advantage that any ideal on the right number field is principal. > >This step (maps+units) took one day. > >Linear algebra: >--------------- > >The linear algebra was further divided in two phases. > >We first applied structured Gaussian eliminations to reduce our system >to 271654 equations in 271552 unknowns with 22690782 non null entries >[LaOd91, JoLe00]. Time needed for this on only one processor was less >than 1 day. > >Then, the critical phase was the final computation via Lanczos's >algorithm [GoLo89]. Our parallelized version of this algorithm took 30 >days over 4 processors. At the end, we had ``logarithms for ideals'' >of small norms. As a consequence, we had logarithms for small primes. > >For instance, > 3 = g ^ 28812588093314776509699010256332271205911219293533606948309\ > 244629961378102894412283315317373685769257402738003506902138, > > 5 = g ^ 21755718305811583829459340786707488931552080300620288049491\ > 6079418842612898727245046247623746814003335266081854116641401, > > 7 = g ^ 30620343436458977106289725314901617172209074240481960209355\ > 5007057950445875245076830599652008193628520847056151254242513, > > 11 = g ^ 26369065546060570062275123759054389628546695463387446804852\ > 2904503050215021182824543943461120732653168766053846377967922, > >etc ... > >Individual Logarithms: >---------------------- > >We take advantage of the Galois group of t^3-12*t^2-9*t+12 [JoLe00]. > >Precisely, we found in less than 6 hours, using our very crude >implementation, two algebraic integers > num = 136919628471533453465*t^2 > - 109185518772042207040*t > - 218010383119442982304 > >and > > den = 90752177247861263294*t^2 > + 5976502381138861785*t > + 161979899979266169279 > >such that > > 19^2*y = num/den modulo p > >and such that, > > in GP-PARI notation, the principal ideal (num) is equal to > >[[53, [7, 2, 0]~, 1, 1, [-18, 19, 12]~] 1] * >[[431, [-20, 2, 0]~, 1, 1, [168, 20, 12]~] 1] * >[[2179, [140, 2, 0]~, 1, 1, [-502, -300, 12]~] 1] * >[[16831, [-3928, 2, 0]~, 1, 1, [-1478, 7836, 12]~] 1] * >[[156781, [-45467, 2, 0]~, 1, 1, [15351, -65867, 12]~] 1] * >[[7691507, [-3118090, 2, 0]~, 1, 1, > [-1592322, -1455347, 12]~] 1] * >[[5847120361, [-944554227, 2, 0]~, 1, 1, > [-2613536996, 1889108434, 12]~] 1] * >[[7689099923, [-1979641955, 2, 0]~, 1, 1, > [-1763503409, -3729816033, 12]~] 1] * >[[14023824873312563677, [2910448673841826685, 2, 0]~, 1, 1, > [-4872413772263364932, -5820897347683653390, 12]~] 1] > > and the principal ideal (den) is equal to > >[[2, [2, 0, 0]~, 1, 3, [1, 0, 0]~] 1] * >[[3, [1, -1, 1]~, 3, 1, [2, 2, 0]~] 3] * >[[19, [8, 2, 0]~, 1, 1, [-3, 2, -7]~] 1] * >[[1873, [-237, 2, 0]~, 1, 1, [889, 454, 12]~] 1] * >[[110359, [36889, 2, 0]~, 1, 1, [-37268, 36561, 12]~] 1] * >[[2672473789, [-932319595, 2, 0]~, 1, 1, > [1125968488, -807834619, 12]~] 1] * >[[626844366559, [-255501920253, 2, 0]~, 1, 1, > [-211702090482, -115840526073, 12]~] 1] * >[[685495972547, [-197652881054, 2, 0]~, 1, 1, > [-276404069769, -290190210459, 12]~] 1] * >[[641614040507139551, [33835176915624305, 2, 0]~, 1, 1, > [159262188369356649, -67670353831248630, 12]~] 1] > >Then, using special-q descents, computing discrete ``logarithms for >the ideals'' of norms 7691507, 5847120361, 7689099923, >14023824873312563677 and 25465743776843, 160516256694037129 in the >right number field was (thanks to one hour computation for each ideal, >on a unique processor) equivalent to compute discrete ``logarithms for > ideals'' of norms larger than those of the factor basis in the >left number field. Time needed for computing the 31 corresponding >discrete logarithms was at most one hour for each on a unique >processor. > >So, as a conclusion, time that we need for computing discrete >logarithms modulo a 120 digit prime on a 525 MHz quadri-processor >alpha server 8400 computer is approximatively 12 hours for each, once >the sieving step (42 days) and the linear algebra steps (30 days) is >performed. > >Antoine JOUX (DCSSI, Issy les Moulineaux, France, Antoine.Joux(a)ens.fr) >Reynald LERCIER (CELAR, Rennes, France, lercier(a)celar.fr) > >References: >=========== > >[JoLe01] A. Joux and R. Lercier, ``Discrete logarithms in GF(p)'', > January 19 2001. Announce on the NMBRTHRY Mailing List. > Available at http://www.medicis.polytechnique.fr/~lercier. > >[JoLe00] A. Joux and R. Lercier, Improvements to the general Number > Field Sieve for discrete logarithms in prime fields, acceped > for publication at Math. of Comp., 2000. Preprint > available at http://www.medicis.polytechnique.fr/~lercier. > >[Schi93] O. Schirokauer, Discrete Logarithms and local units. Phil. > Trans. R. Soc Lond. A 345, pages 409-423, 1993. > >[LaOd91] B.A. Lamacchia and A.M. Odlyzko, Computation of discrete > logarithm in prime fields, Designs, Codes and Cryptography, > 1991, volume 1, pages 47-62. > >[GoLo89] G.H. Golub and C.F. van Loan, Matrix computations, chapter 9, > The John Hopkins University Press, 1989, Mathematical > Sciences. > >------------------------------ > >End of NMBRTHRY Digest - 16 Apr 2001 to 17 Apr 2001 (#2001-56) >************************************************************** > > > > >--------------------------------------------------------------------- >The Cryptography Mailing List >Unsubscribe by sending "unsubscribe cryptography" to >majordomo(a)wasabisystems.com

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Swedish crypto & math mailinglist (fwd)
by Jim Choate 18 Apr '01

18 Apr '01

---------- Forwarded message ---------- Date: Thu, 19 Apr 2001 02:16:29 +0200 (CEST) From: "Bluefish (P.Magnusson)" <11a(a)gmx.net> To: cryptography(a)wasabisystems.com Subject: Swedish crypto & math mailinglist Hi I'd like to send announce a new mailinglist: http://www.ludd.luth.se/~bluefish/ciphermath/ Basicly it is a swedish mailinglist where anything which is math or cryptography is on topic. The list is very new and have few subscribers, so feel free to change that... Currently there have been some mails regarding designing cryptographic open source hardware blocks in VHDL, which I plan to participate in this summer, and some rather basic math. --------------------------------------------------------------------- The Cryptography Mailing List Unsubscribe by sending "unsubscribe cryptography" to majordomo(a)wasabisystems.com ____________________________________________________________________ The ultimate authority...resides in the people alone. James Madison The Armadillo Group ,::////;::-. James Choate Austin, Tx /:'///// ``::>/|/ ravage(a)ssz.com www.ssz.com .', |||| `/( e\ 512-451-7087 -====~~mm-'`-```-mm --'- --------------------------------------------------------------------

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CNN.com - Belgrade court pursues world leaders - April 18, 2001
by Jim Choate 18 Apr '01

18 Apr '01

http://www.cnn.com/2001/WORLD/europe/04/18/yugoslavia.warrents/index.html?s… -- ____________________________________________________________________ The ultimate authority...resides in the people alone. James Madison The Armadillo Group ,::////;::-. James Choate Austin, Tx /:'///// ``::>/|/ ravage(a)ssz.com www.ssz.com .', |||| `/( e\ 512-451-7087 -====~~mm-'`-```-mm --'- --------------------------------------------------------------------

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by Anonymous 18 Apr '01

18 Apr '01

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18 Apr '01

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18 Apr '01

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18 Apr '01

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