December 2003 - cypherpunks-legacy

MS, IBM, Apple, EFF and DTB [was : TIS, SKE, & CyberCash Inc.
by Pat Farrell 17 Dec '03

17 Dec '03

tcmay(a)netcom.com (Timothy C. May) writes: > - The latest "Internet World" (Oct. '94, p. 11) confirms that > Microsoft is building Internet connectivity into upcoming releases of > Windows and Windows NT. ^^^^^^^^^^ this one, at least has been released and should be at your local computer store RSN. I've been on the NT beta test, and it is really nice. The built in SLIP/PPP will massivly increase the number of real internet hosts. It is easy to use and robust. They don't ship Cello/Mosaic, but that is trivial to add. > (The scenario I think is likely: SKE is put in at the OS level, > perhaps with these SLIP/PPP/TCP-IP protocols. > > And given the EFF's recent sell-out on Digital Telephony (which is of > course related to this, especially since the OS makers like Microsoft > and Apple are negotiating deals with the cable-telco companies, thus > presumably making the OS makers partners in the "wiretapping" > requirements), I would not be surprised to see similar deals being > arranged behind the scenes. Much more than working deals, Microsoft wants to be an Internet Serivce Provider (ISP), much like Apple and IBM have recently become. IBM's new OS/2 has a "one button" signon/configuration onto their service. Apple has been bundling eWorld for a while. But I don't see Tim's OS-oriented collusion. The EFF sell out clearly focused on defining service providors and then excluding then, specifically, from the burden of DTB. Doesn't look like they like GAK any more than Tim or me. Pat Pat Farrell Grad Student pfarrell(a)cs.gmu.edu Department of Computer Science George Mason University, Fairfax, VA Public key availble via finger #include <standard.disclaimer>

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PGP, remailer@rebma.mn.org
by Bill O'Hanlon 17 Dec '03

17 Dec '03

The remailer at rebma.mn.org was not using pgp 2.6, and it was having trouble with messages that used the newer versions. (I think it was running 2.3.) Anyway, I fixed it, but I imagine there's been some traffic that didn't get remailed. Sorry. -Bill

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Re: Data Fellows announces F-Secure SSH Tunnel&Terminal
by Petri Laakkonen 17 Dec '03

17 Dec '03

Hi guys, I'm afraid of that US sales has fallen off the tracks. We need to catch up ASAP. At 07:58 PM 7/24/97 +0200, Tom Helenius wrote: >FOR IMMEDIATE RELEASE >23 July, 1997 > >Data Fellows announces F-Secure SSH Tunnel&Terminal > What's this product all in all ? Has this now replaced F-Secure SSH or is this one additional derivative of SSH a'la ISP SSH ? Are the features same as for the most recent SSH clients/servers ? HOw does this product differ from SSH ? Any data sheets ? Is the software a) shipping b) downloadable from the web ? >The remote worker can use e-mail, Internet browser, database tools and all >the usual applications at home, on the road or in any place with Internet >access. The big difference, though invisible to the remote worker, is that >all data communication between the server in the office and the remote user >is flowing through an encrypted tunnel. > Does this configure itself automatically for most popular office apps as discussed some time earlier, or do admins still need to do the installation manually for each computer or count on users doing this themselves ? >F-Secure SSH Tunnel&Terminal provides strong encryption of data and thus >sets a new standard for secure remote working. Existing solutions like >Cisco Systems L2F, IETF L2TP and firewalls dont provide strong encryption >and authentication, which makes these solutions insecure against >eavesdropping and IP spoofing attacks. In addition to encrypted tunnels, >F-Secure Tunnel&Terminal also provides secure terminal connections to UNIX >hosts and secures UNIX X11 applications. > What would be F-Secure Tunnel's added value over MS pptp ? > >The automatic deployment tool enables straightforward company-wide >installation and updates. > Interesting. Tell us more about this ? > > >F-Secure SSH Tunnel&Terminal is available for win3.1, win95, winNT and UNIX >operating systems worldwide in the end of July, 1997. > How about our friends from Cupertino (e.g. Apple) ? > Thanks for the additional info in advance, Petri -------------------------------------------------------------------- Petri.Laakkonen(a)DataFellows.com, World Wide Web: http://www.DataFellows.com Data Fellows U.S headquarters has moved ! Our new contacts as of March 24th, 1997 are: Data Fellows 675 N. First Street, Suite 605 San Jose, CA 95112 phone (408) 938-6700, fax (408) 938-6701 ********************************************************************* * F-Secure * * Award-winning Security for Peace of Mind * * from the Desktop to the Internet * * * * http://www.DataFellows.com/ * ********************************************************************

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Beach Clash first edition review
by merriman＠metronet.com 17 Dec '03

17 Dec '03

Yup. Pretty much a case of Beach Blanket American Gladiators; except that it's two "teams", each team consisting of HomeTown Folks and 2 each of the HardBodies (1 each male & female). Swimsuits on contestants are "sports" types (can't afford to have anything popping free on national TV, eh?). Bystanders/Audience, however, suffer no such limitations :-) Ditto on "personal interviews" with contestants (guys, too, for those so inclined). Alison wears normal street clothes (sorry Sandy!) Team names are Suitably Impressive and Beach-y: Tigersharks and Sea Otters Tonights program included: > two-pass swim/climb: guys come in from out at sea, girls climb rope. One guy rides paddleboard in, tags girl who climbs rope to release flag, which signals other guy to swim in from raft - said guy then tags same girl who releases additional flag. > hill climb: guys & girls climb wet plastic fake hills, run back to beginning, tag another team member who climbs, until all have gone over the hills. > raft drag: guy team member on jet ski pulls girl team member hanging onto inflatable raft. > VolleySmash: 4-person/team volleyball on a giant airmattress > BungeeBall: contestants try to run against restraint of bungee cord, getting close enough to make freethrows. > BeachBout: contestants try to knock each other off horizontal pole using foam bats. > King of the Raft: male/female contestants paddle out to raft to join other members to try to climb pyramid and displace ball. > Walk the Plank: team members walk across the horizontal pole from BeachBout while opposing team throws "dodge balls" at them. > Surf War: tug-o-war in the surf. > Crash and Burn: obstacle course through/in the surf and beach. I'm sure there are crypto/privacy issues here, but I'm too thick to see them :-) Mildly amusing, but not something I'm going to stay up 'till midnight for next week. Dave Merriman - - - - - - - - - - - - - - - - - - - - - - - - - - Finger merriman(a)metronet.com for PGP/RIPEM public keys and fingerprints. Unencrypted Email may be ignored without notice to sender. PGP preferred. Remember: It is not enough to _obey_ Big Brother; you must also learn to *love* Big Brother.

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Re: Chomsky (Thread from Hell)
by blancw＠pylon.com 17 Dec '03

17 Dec '03

Responding to msg by James A. Donald: >He implies that democratic control of speech and ideas >would be a vast improvement in our civil liberties, >that it would make us more free. But who pays attention to what Chomsky thinks (say, by comparison to others similarly inclined). >In other words he is perverting the language so that >for him "freedom of speech" is democratic control of >speech and ideas by the people. Then who is going to understand what he really means? >He continually describes (and wildly exaggerates) the >problem using language that implies that only a >collective, rather than individual, response to >misinformation can make us free. He isn't the only one who ever has, or ever will, advocate such things. He's not on the board of directors of the NII, is he; or how does he exert influence? >. . . .Chomsky fans show a notable lack of >tolerance for other forms of speech, as is most >noticeable on the net. So is it Chomsky, or his fans who are the problem? And how do they succeed in making themselves influential? >Since there are clearly a great many people who seek >and desire totalitarianism, with their group at the >top, we should hardly be surprised to see large >number of people seeking to achieve this through means >that are workable and feasible, rather than through >means that are absurd and impossible. This type of person is interchangeable: they could follow someone (like Chomsky) today or someone else tomorrow. It should always be possible to recognize the difference between one thing and another - one kind of idea or social system or another - just as you have, by seeing the contradictions and actual relations in the expressed statements, proposals, methodologies, etc. It looks as though you are simply fighting the ideas which many people have always found to their advantage to believe, but I can't see where Chomsky is the only & most important reason why they are willing to think as they do. So - those are my comments on Chomsky, about which I will write no more, as he doesn't sound interesting at all to pursue. Blanc

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An Attempt to Hobble SAFE Crypto Bill
by Declan McCullagh 17 Dec '03

17 Dec '03

---------- Forwarded message ---------- Date: Fri, 25 Jul 1997 11:03:33 -0800 From: "--Todd Lappin-->" <telstar(a)wired.com> To: fight-censorship(a)vorlon.mit.edu http://www.wired.com/news/news/politics/story/5492.html An Attempt to Hobble House Crypto Bill by Rebecca Vesely 9:08am 25.Jul.97.PDT A Republican opponent of a House bill that would loosen controls on the use and export of encryption is circulating an amendment that would effectively cripple the legislation. The amendment, by Representative Benjamin Gilman (R-New York), who chairs the International Relations Committee, would make it unlawful to "manufacture, distribute, sell, or import any product within the United States that can be used to encrypt communications or information if the product does not permit the real-time decryption of such encrypted communications or information." This means that if law-enforcement officials could not crack an encrypted file within 24 hours - the time that FBI director Louis Freeh and other law enforcement officials say is reasonable for accessing information related to a crime - that strength of encryption would be illegal. The amendment set a civil penalty of US$100,000 for such violations. Currently, the most complex programs that can be cracked so quickly use 40-bit algorithms. The relative ease of breaking such code makes it nearly worthless on the marketplace, the high-tech industry has warned. Stronger encryption - 56-bit and 128-bit algorithms are being employed in many products now - is widely viewed as a cornerstone to the development of electronic commerce. Stronger code can safeguard data such as credit-card numbers as it travels over networks. Gilman had the amendment in hand earlier this week when his panel marked up the Security and Freedom through Encryption Act by Representative Bob Goodlatte (R-Virginia). The bill has been condemned by the government's chief law-enforcement and national-security officials because it would prevent domestic controls on encryption while relaxing export controls. The FBI and National Security Agency want a domestic key-recovery system to wiretap digital communications. Gilman was unsuccessful in trying to insert another provision during the mark-up - one to give the president the power to deny crypto export licenses on national-security grounds. "The second amendment was a staff proposal that basically was dependent on what happened to the first amendment," said Jerry Lipson, spokesman for the House International Relations Committee. "There was no sentiment that this one should be introduced when the first one failed." A staffer for a congressman who supports the Goodlatte bill said that the new amendment was a "scare tactic" meant to show committee members that law enforcement won't stand for a relaxed approach to encryption policy. Indeed, FBI director Freeh met one-on-one with 10 International Relations panel members for hour-long sessions in the days before the mark-up, the staffer said. Nine of the 10 voted for the bill anyway. Some staffers and observers suggest that the Gilman amendment could be introduced when the bill goes to the Select Committee on Intelligence. Although the legislation has 214 co-sponsors in the House, none are members of that panel. And the bill still must reach two other committees before it goes to a full House vote: Commerce and National Security. The deadline for all committees to address the bill is 5 September. "They don't draft amendments like this for the heck of it," said Alan Davidson, staff counsel for the Center for Democracy and Technology. "It's a glimpse at what could be a very frightening future." Copyright © 1993-97 Wired Ventures, Inc. and affiliated companies. All rights reserved.

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Fwd: Anonymous Long Distance Phone Calling
by unknown＠example.com 17 Dec '03

17 Dec '03

-----BEGIN PGP SIGNED MESSAGE----- > HOW TO PURCHASE YOUR CALLING CARD: >You send a $50 or $100 blank Cashier's check, or cash, to the address >stated below. I have purchased a pile of PIN cards and I randomly select >and send it to you. The company I buy these cards from, keeps no records, >if they did, all records of sales are to me in my name unfortunately. >keep no records of addresses or PIN numbers who I am sending to. After yo >receive your card you go about making your calls and then when you want to >add more time to your calling card (recharge the card), This is where yo >gain another level of privacy, because I step out of the loop and you will >communicate with Traceless, the providing company, directly. You send a >money order or cash and your PIN number to the address provided on the car >and they will recharge the anonyous PIN number with the amount sent. You >no name or return address on the envelope. Since all they did was send a >pile of cards to me and I sent them out they have no way of knowing who wh >or where the cards went to. Alternatively, for those who have an offsho >Visa, MasterCard or American Express accounts, you can set it up so t >your PIN account can be credited by certain amounts when you hit a certai >key while making phone calls to the special 800 number. If this option i >appealing to you, let me know and I can send some more information. Also >for those that need voice encryption that option is available. Again >you want more info on this let me know. I wonder how anonymous this will be once the subpoenas start flying. I think that this is still traceable via this method: 1) The authorities have you under physical surveillance (A tail) 2) Since they know where you've been they pull the phone records and see all of the outgoing calls. 3) They get the records from this company and match the time or the number that the call was placed from. (800 billing records have this) 4) Now they know where you called. You are relying on this unknown company to NOT cave in when subpoenas are flying around. I wouldn't, especially at 30+ cents a minute. - -----BEGIN PGP PUBLIC KEY BLOCK----- Version: 2.6.1 mQCNAy5pUekAAAEEAKrDj64Zj9AJU+gC7/Ivdk8b1ef6a1T9K5CGFeu1yFDSXLyD DLIdGunZR/4ilosLMxdlZcNqPwZ3HgxL+Gk3y2SwYfqKpeWExWPgb696lgzf2BRC tED15ZAwi3UDIkcouv2PBiDwPNUUmnLb5diDXdA3qtALb+XzlwpnimeWAf3FAAUT tCFTYW11ZWwgS2FwbGluIDwrMSAoNjEyKSA1MzAtNzMxNj6JAJUCBRAuaVLjQqfV nzRSzxkBAcXuA/47yIN+sltMyIRqCgUZz/gubdI6LUcpFsTcXsFWppROpAWFPJv0 J9z/UoP1kjJ+nrAAizuKuhmC5eg5OOxUE+tUgSPl6hAtu2xJYmKtCbQpxF0sG8ni 4e8I8Zsk5vcopO5Vub96CiVgPjI5vITCb32kcLKI1yyFaztbHdtOasUthrQuU2Ft dWVsIEthcGxpbiA8c2FtdWVsLmthcGxpbkB3YXJlaG91c2UubW4ub3JnPg== =J2S+ - -----END PGP PUBLIC KEY BLOCK----- ----------------------------------------------------------------------------- Fido: Sam Kaplin 1:282/1018 | "...vidi vici veni" - Overheard Compuserve: 75240,131 | outside a Roman brothel. samuel.kaplin(a)warehouse.mn.org | 75240,131(a)compuserve.com | Change is the only constant in the For confidential communications use PGP | Universe..."Four quarters, please." ----------------------------------------------------------------------------- -----BEGIN PGP SIGNATURE----- Version: 2.6.1 iQCVAgUBLoUKLwpnimeWAf3FAQHfCAQAlCNoT0syIxVnHp+IqQpXRsrwRmOpWBk3 pB+GLBSwBgz9Vyl/unPj8PsxekkN6O5j+3eLAvVLQvluC1Ab0bAwkK44ta1ltRnz 3nXb4SQmNeLieKk+42iEXDNTUoplDhrf4FyoNew+k/NT3DzdlQi3rGA7SHUzfsZ2 4DqqXx6f/pc= =iXgU -----END PGP SIGNATURE-----

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Jim Bidzos
by unknown＠example.com 17 Dec '03

17 Dec '03

-----BEGIN PGP SIGNED MESSAGE----- - ->:My humble opinion: Jim is not really the enemy, nor is he really a - ->:friend. He is a businessman trying to make a buck via the intellectual - ->:property laws. Sometimes this works out in our favor, sometimes it - ->:doesn't. He sends out letters defending his intellectual property - ->:rights that tend to be full of innuendo and that border on - ->:prevarication, but always stay on the proper side of the line; this is - ->:such a standard practice among people in businesses like his that I - ->:can't fault him for it. Overall, I'd say that anger towards him is - ->:misplaced. Unfortunately Herr Bizdos is not dealing with the business community, he is dealing with the INTERNET community. While all the sabre rattling may be acceptable within the business community, it is not acceptable within the INTERNET community. In effect Bizdos created his own problem. If the code was stolen, he should have had better physical security on it. If a licensee anonymously posted it, he should have included a means of tracing the code back to the source of the leak, then pursue that individual, not the whole INTERNET crypto community. If the code was reverse engineered, that's one of the risks in not patenting it. Personally I'm tiring of the whole affair. - -----BEGIN PGP PUBLIC KEY BLOCK----- Version: 2.6.1 mQCNAy5pUekAAAEEAKrDj64Zj9AJU+gC7/Ivdk8b1ef6a1T9K5CGFeu1yFDSXLyD DLIdGunZR/4ilosLMxdlZcNqPwZ3HgxL+Gk3y2SwYfqKpeWExWPgb696lgzf2BRC tED15ZAwi3UDIkcouv2PBiDwPNUUmnLb5diDXdA3qtALb+XzlwpnimeWAf3FAAUT tCFTYW11ZWwgS2FwbGluIDwrMSAoNjEyKSA1MzAtNzMxNj6JAJUCBRAuaVLjQqfV nzRSzxkBAcXuA/47yIN+sltMyIRqCgUZz/gubdI6LUcpFsTcXsFWppROpAWFPJv0 J9z/UoP1kjJ+nrAAizuKuhmC5eg5OOxUE+tUgSPl6hAtu2xJYmKtCbQpxF0sG8ni 4e8I8Zsk5vcopO5Vub96CiVgPjI5vITCb32kcLKI1yyFaztbHdtOasUthrQuU2Ft dWVsIEthcGxpbiA8c2FtdWVsLmthcGxpbkB3YXJlaG91c2UubW4ub3JnPg== =J2S+ - -----END PGP PUBLIC KEY BLOCK----- ----------------------------------------------------------------------------- Fido: Sam Kaplin 1:282/1018 | "...vidi vici veni" - Overheard Compuserve: 75240,131 | outside a Roman brothel. samuel.kaplin(a)warehouse.mn.org | 75240,131(a)compuserve.com | Change is the only constant in the For confidential communications use PGP | Universe..."Four quarters, please." ----------------------------------------------------------------------------- -----BEGIN PGP SIGNATURE----- Version: 2.6.1 iQCVAgUBLoW8JwpnimeWAf3FAQHSpQP+ONtJQFljElHW+cZqVS2Ad7qikN+58A/w SpUHb6jhkSjuQoEHMUxM54vpTPiPgaE+TGCvBt5u2d4zqJVeF52FYbS+MUvoT6rs 3pYuF0DxR23MBElthtJUdaLUOW6w2pSXk7bcCL5bgCiB9zHe+V/KmzvRdSX8y9xf ttke5IXHBeA= =QGMi -----END PGP SIGNATURE-----

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List of reliable remailers
by Raph Levien 17 Dec '03

17 Dec '03

I have written and installed a remailer pinging script which collects detailed information about remailer features and reliability. To use it, just finger remailer-list(a)kiwi.cs.berkeley.edu There is also a Web version of the same information, at: http://www.cs.berkeley.edu/~raph/remailer-list.html Please let me know about any other remailers which I missed. I've only included remailers which can mail to arbitrary addresses, so I already know chop and twwells are missing. This information is used by premail, a remailer chaining and PGP encrypting client for outgoing mail, which is available at: fftp://soda.berkeley.edu/pub/cypherpunks/premail/premail-0.22.tar.gz For the PGP public keys of the remailers, as well as some help on how to use them, finger remailer.help.all(a)chaos.bsu.edu This is the current info: REMAILER LIST This is an automatically generated listing of remailers. The first part of the listing shows the remailers along with configuration options and special features for each of the remailers. The second part shows the 10-day history, and average latency and uptime for each remailer. You can also get this list by fingering remailer-list(a)kiwi.cs.berkeley.edu. $remailer{"chaos"} = "<remailer(a)chaos.bsu.edu> cpunk hash ksub"; $remailer{"vox"} = "<remail(a)vox.xs4all.nl> cpunk oldpgp. post"; $remailer{"avox"} = "<anon(a)vox.hacktic.nl> cpunk oldpgp post"; $remailer{"extropia"} = "<remail(a)extropia.wimsey.com> cpunk pgp special"; $remailer{"portal"} = "<hfinney(a)shell.portal.com> cpunk pgp hash"; $remailer{"alumni"} = "<hal(a)alumni.caltech.edu> cpunk pgp hash"; $remailer{"bsu-cs"} = "<nowhere(a)bsu-cs.bsu.edu> cpunk hash ksub"; $remailer{"rebma"} = "<remailer(a)rebma.mn.org> cpunk pgp hash"; $remailer{"jpunix"} = "<remailer(a)jpunix.com> cpunk pgp hash latent cut post"; $remailer{"wien"} = "<remailer(a)ds1.wu-wien.ac.at> cpunk pgp hash nsub"; $remailer{"c2"} = "<remail(a)c2.org> eric pgp hash"; $remailer{"soda"} = "<remailer(a)csua.berkeley.edu> eric pgp. post"; $remailer{"penet"} = "<anon(a)anon.penet.fi> penet post"; $remailer{"ideath"} = "<remailer(a)ideath.goldenbear.com> cpunk hash ksub"; $remailer{"usura"} = "<usura(a)xs4all.nl> cpunk pgp. hash latent cut post"; $remailer{"leri"} = "<remail(a)leri.edu> cpunk pgp hash"; $remailer{"desert"} = "<remail(a)desert.xs4all.nl> cpunk pgp. post"; $remailer{"underdog"} = "<lmccarth(a)ducie.cs.umass.edu> cpunk pgp hash latent cut post"; $remailer{"nately"} = "<remailer(a)nately.ucsd.edu> cpunk pgp hash latent cut"; catalyst(a)netcom.com is _not_ a remailer. Last ping: Mon 26 Sep 94 6:00:01 PDT remailer email address history latency uptime ----------------------------------------------------------------------- wien remailer(a)ds1.wu-wien.ac.at ++********#+ 5:08 99.99% c2 remail(a)c2.org *+*-*+**+-** 29:25 99.99% chaos remailer(a)chaos.bsu.edu #**#*****### 1:18 99.99% ideath remailer(a)ideath.goldenbear.com *-.++*+***** 31:44 99.99% leri remail(a)leri.edu *+*-*+****#* 13:43 99.99% bsu-cs nowhere(a)bsu-cs.bsu.edu ***+*--**# # 20:40 99.99% portal hfinney(a)shell.portal.com ********##*# 4:01 99.97% underdog lmccarth(a)ducie.cs.umass.edu **********+* 4:22 99.92% penet anon(a)anon.penet.fi ************ 34:17 99.81% jpunix remailer(a)jpunix.com * #*****-*#* 7:46 99.79% vox remail(a)vox.xs4all.nl -.- .-..-. 14:02:41 99.66% soda remailer(a)csua.berkeley.edu ...__..-.. 8:25:41 99.27% alumni hal(a)alumni.caltech.edu **** ******* 5:25 99.02% extropia remail(a)extropia.wimsey.com ++++-+-++ * 1:01:20 99.00% nately remailer(a)nately.ucsd.edu -+++* 54:21 98.17% rebma remailer(a)rebma.mn.org -+-_..--+-- 10:18:14 97.33% usura usura(a)xs4all.nl **+***+***+ 6:05 96.17% desert remail(a)desert.xs4all.nl -------.--- 24:51:16 82.67% Suggested path: chaos;c2;wien For more info: http://www.cs.berkeley.edu/~raph/remailer-list.html Options and features cpunk A major class of remailers. Supports Request-Remailing-To: field. eric A variant of the cpunk style. Uses Anon-Send-To: instead. penet The third class of remailers (at least for right now). Uses X-Anon-To: in the header. pgp Remailer supports encryption with PGP. A period after the keyword means that the short name, rather than the full email address, should be used as the encryption key ID. oldpgp Remailer does not like messages encoded with MIT PGP 2.6. Other versions of PGP, including 2.3a and 2.6ui, work fine. hash Supports ## pasting, so anything can be put into the headers of outgoing messages. ksub Remailer always kills subject header, even in non-pgp mode. nsub Remailer always preserves subject header, even in pgp mode. latent Supports Matt Ghio's Latent-Time: option. cut Supports Matt Ghio's Cutmarks: option. special Accepts only pgp encrypted messages. History key * # response in less than 5 minutes. * * response in less than 1 hour. * + response in less than 4 hours. * - response in less than 24 hours. * . response in more than 1 day. * _ response came back too late (more than 2 days). If you've got a Web page, please feel free to include a link to this page. If you think your Web page is relevant to the subject of remailers, let me know and I'll link it in. Comments and suggestions welcome! Note to remailer operators: this script generates hourly ping messages. If you don't want that, let me know and I will take your mailer off the list, or increase the interval between pings. Raph Levien

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(n!)modx ...
by Jim choate 17 Dec '03

17 Dec '03

Hi all, In a reply late last week concerning large values of x and x having many prime factors I made the comment that even pairs might be factored out by multiplying them and then finding a different way to factor the product. I as assuming that the product of two primes would not produce a product which in general could not be factored a different way. This seems to be in error. So far the vast majority of cases I have looked at have failed. This leaves the problem of large values of x which have many prime factors that appear either two or more times in n. At this point I don't see a way to use this relationship to further gain. Any ideas would be greatly appreciated. Side Note: I have lost the original post concerning this subject. I am still working on a paper concerning the behaviour of the mod function and would like to provide credit where credit is due. If you are the original author or can provide the e-mail address (please reply via e-mail) of the author it would be much appreciated. Take care.

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