Cryptography-Digest Digest #27, Volume #10       Wed, 11 Aug 99 09:13:05 EDT

Contents:
  Re: brute force crackers unethical? ("Douglas A. Gwyn")
  Re: Why does MS-Visual C++ ABSOLUTELY REQUIRE . . . (Pretty Boy Mohandas)
  Re: brute force crackers unethical? (JPeschel)
  Re: Why does MS-Visual C++ ABSOLUTELY REQUIRE . . . (Lee Winter)
  SSL/SGC - Is 3DES (168bit) Available? ("Goll, David M")
  Re: Why does MS-Visual C++ ABSOLUTELY REQUIRE . . . (Lee Winter)
  Re: Why does MS-Visual C++ ABSOLUTELY REQUIRE . . . (Lee Winter)
  Re: Why does MS-Visual C++ ABSOLUTELY REQUIRE . . . (Lee Winter)
  Re: Between Silk & Cyanide - two questions (Jim Gillogly)
  Re: Why does MS-Visual C++ ABSOLUTELY REQUIRE . . . (Lee Winter)
  Re: Why does MS-Visual C++ ABSOLUTELY REQUIRE . . . ("Paul Lutus")
  Re: Why does MS-Visual C++ ABSOLUTELY REQUIRE . . . ("Paul Lutus")
  Re: Why does MS-Visual C++ ABSOLUTELY REQUIRE . . . ("Paul Lutus")
  My web site is up! (Greg)
  Re: What's first? (Gabriel Belingueres)
  Re: NIST AES FInalists are.... ([EMAIL PROTECTED])
  Re: brute force crackers unethical? (Volker Hetzer)
  Re: AES finalists to be announced (Mike Just)
  Re: frequency of prime numbers? (DJohn37050)
  Re: frequency of prime numbers? (Paul Crowley)

----------------------------------------------------------------------------

From: "Douglas A. Gwyn" <[EMAIL PROTECTED]>
Subject: Re: brute force crackers unethical?
Date: Wed, 11 Aug 1999 06:16:01 GMT

Andrew Whalan wrote:
> Anyhow, in a nutshell, I would just like to be reassured that I am not
> acting in an unethical fashion to write a brute force cracker, as IMHO at
> least, it is a valid (but annoyingly time consuming) method of
> cryptanalysis.

But was it your job to crack the passwd file?  There is nothing new
about UNIX passwd cracking, so it had no intellectual value.
Presumably, you had agreed to conditions of use that forbid your
engaging in such activity.  So it is understandable that not keeping
your promise was viewed as evidence that you wouldn't set a good
example for students of ethics.

Basically, one would need a *lot* more information to form a valid
judgment of the merits of your case, essentially work for an
independent investigator, not a newsgroup.

P.S. The UNIX system should be using a shadow password file, with a
low-bandwidth query port, which would render passwd cracking
infeasible.

------------------------------

From: Pretty Boy Mohandas <[EMAIL PROTECTED]>
Crossposted-To: comp.lang.c++
Subject: Re: Why does MS-Visual C++ ABSOLUTELY REQUIRE . . .
Date: Tue, 10 Aug 1999 14:12:23 +0600

Bruce Wheeler wrote:
> Very off-topic here, but you can change it in the 'accessibility' options
> under IE4. 
Never knew. Thanks, I'll check it out.

> Apparently, we're visually handicapped if we want to customize
> our envirnoments.
Oh yeah. We're the stupid ones. We need to be kept by the hand.

> Note, however, this is a global change for IE, not just for InfoViewer.
Isn't it another piece of cretinism? Btw, same relates to the fonts. I
guess to everything.

-- 
len
if you must email, reply to:
len bel at world net dot att dot net (no spaces, ats2@, dots2.)

------------------------------

From: [EMAIL PROTECTED] (JPeschel)
Subject: Re: brute force crackers unethical?
Date: 11 Aug 1999 06:29:18 GMT

>"Andrew Whalan" <[EMAIL PROTECTED]> writes:

>I would just like to be reassured that I am not
>acting in an unethical fashion to write a brute force cracker, as IMHO at
>least, it is a valid (but annoyingly time consuming) method of
>cryptanalysis.

Brute-force cracking isn't cryptanalysis, and writing a brute-force
cracker isn't unethical.  Reassured?

Your fellow data security student likely mentioned your cracker
to the administration. Words like cracker, crack, hacker, and the
like tend to send administrators (and the public) into a panic.
You did inform them that there are faster and better UNIX pwd 
crackers already freely available, and that that they are useful
for finding weak passwords, didn't you?

Joe


__________________________________________

Joe Peschel 
D.O.E. SysWorks                                 
http://members.aol.com/jpeschel/index.htm
__________________________________________


------------------------------

Date: Thu, 12 Aug 1999 02:50:58 -0400
From: Lee Winter <[EMAIL PROTECTED]>
Crossposted-To: comp.lang.c++
Subject: Re: Why does MS-Visual C++ ABSOLUTELY REQUIRE . . .



wtshaw wrote:

> In article <7onr9j$onb$[EMAIL PROTECTED]>, "Rosimildo DaSilva"
> <[EMAIL PROTECTED]> wrote:
>
> > >
> > >Unless you need to use the debugger...
>
> > Well, debugger is for programmers that writes buggy code !!! < g >.
> >
> > Rosimildo.
>
> Come off it! One way of programming is to crawl through the steps of what
> you want to do, a surefire way of knowing what is going on in each snippit
> of code that you add, and correct if needed.
>
> While it may seem that the fastest way to write source code is to put all
> of it down at one, I realize that the parts must all be verified at one
> time or another before you can rely on the end result.  Once you have
> established good functions, only then should you can copy them to new
> projects.

This is the classic model of code reuse that nobody follows.  In reality you
look at the source of the model, and if it scares you, you copy it.  If it is
well designed, clearly documented, etc., you "improve" it to make it fit your
new app.  Thus the worst code is copied verbatim and the best code gets hacked
up.

>
>
> The biggest headache that I see in some of the MS offerings is the
> tendency to not allow you to do simple mods and easily rerun the same
> file, while add and remarking out real-time variable monitoring
> procedures, something that I do lots of as I whittle out new applications.
>
> Working and working well are too different things.
> --
> Sometimes you have to punt, and hope for the best.




------------------------------

From: "Goll, David M" <[EMAIL PROTECTED]>
Subject: SSL/SGC - Is 3DES (168bit) Available?
Date: Wed, 11 Aug 1999 15:48:24 +1000

Where a foreign organisation is granted an SGC certificate by VeriSign
or Thawte, does this allow 3DES (168bit) on browser / server dialogues,
or are they limited to 128 bit RC2/4?

I would appreciate any assistance.

Regards

David



------------------------------

Date: Thu, 12 Aug 1999 02:44:56 -0400
From: Lee Winter <[EMAIL PROTECTED]>
Crossposted-To: comp.lang.c++
Subject: Re: Why does MS-Visual C++ ABSOLUTELY REQUIRE . . .



Paul Lutus wrote:

> << Nope. I installed MS C++ 6.0 without MSDN, so I don't get the help
> system. >>
>
> <off-topic>
>
> You don't get the *complete* help system. You still have help screens,
> abbreviated ones. They are in HTML. This requires MSIE.

Why?  What is special about IE that any other HTML viewer does not have>

>
>
> </off-topic>
>
> --
>
> Paul Lutus
> www.arachnoid.com
>
> Roger Schlafly <[EMAIL PROTECTED]> wrote in message
> news:7ol69h$ha0$[EMAIL PROTECTED]...
> > Douglas A. Gwyn wrote in message <[EMAIL PROTECTED]>...
> > >Guenther Brunthaler wrote:
> > >> On 7 Aug 1999 18:41:27 GMT, [EMAIL PROTECTED] () wrote:
> > >> >     Why does Microsoft ABSOLUTELY REQUIRE me to install and use their
> > >> >Internet Explorer (IE) before I can even install their Visual C++
> > compiler?
> > >> Haven't you have heard of all those rumours about the various built-in
> > >> backdoors of IE?
> > >Don't be ridiculous!  The main reason IE is required is that the
> > >Visual Studio help system is now based on HTML, and IE contains
> > >the modules needed to support that.
> >
> > Nope. I installed MS C++ 6.0 without MSDN, so I don't get the
> > help system. There must be some other reason for the IE
> > requirement.
> >
> > Other possibilities:
> >
> > 1. MS management issued an order to make products dependent
> > on IE, either as a way of pressuring people to use IE or to give
> > evidence that IE is part of the OS.
> > 2. Some sloppy MS programmer created an IE dependency,
> > and the project manager didn't want to bother fixing the bug
> > for some reason.
> >
> >
> >




------------------------------

Date: Thu, 12 Aug 1999 02:47:26 -0400
From: Lee Winter <[EMAIL PROTECTED]>
Crossposted-To: comp.lang.c++
Subject: Re: Why does MS-Visual C++ ABSOLUTELY REQUIRE . . .



Paul Lutus wrote:

> No. The original statement was, "Why do I have to install MSIE to have help
> display in VC++". The answer is:
>
> 1. The help files are HTML, and
> 2. MSIE is the only browser that can integrate into MSDev.
>
> One may try to access the help files without MSIE, but you lose
> context-access. You have to sort out the help files for yourself in an
> external browser.
>
> These are not details. MSDev doesn't work - cannot work -- as designed
> without a built-in browser.

That's a pretty strong statement.  One I doubt.


------------------------------

Date: Thu, 12 Aug 1999 02:43:35 -0400
From: Lee Winter <[EMAIL PROTECTED]>
Crossposted-To: comp.lang.c++
Subject: Re: Why does MS-Visual C++ ABSOLUTELY REQUIRE . . .



Douglas A. Gwyn wrote:

> Guenther Brunthaler wrote:
> > On 7 Aug 1999 18:41:27 GMT, [EMAIL PROTECTED] () wrote:
> > >     Why does Microsoft ABSOLUTELY REQUIRE me to install and use their
> > >Internet Explorer (IE) before I can even install their Visual C++ compiler?
> > Haven't you have heard of all those rumours about the various built-in
> > backdoors of IE?
>
> Don't be ridiculous!  The main reason IE is required is that the
> Visual Studio help system is now based on HTML, and IE contains
> the modules needed to support that.

Is there something specific about the HTML help files that requires IE or will any
HTML viewer suffice?




------------------------------

From: Jim Gillogly <[EMAIL PROTECTED]>
Subject: Re: Between Silk & Cyanide - two questions
Date: Tue, 10 Aug 1999 18:33:46 +0000

John Savard wrote:
> 
> [EMAIL PROTECTED] (Phoeper) wrote, in part:
> 
> >1.   Several times, Marks states that a MINIMUM message size is required -  why
> >should giving the cryptanalyst more text reduce the chances of breaking the
> >message?
> 
> One of the cipher systems discussed is a transposition cipher. For that one -
> not for the one-time-pad cipher - messages that are too small could give away
> some information.

In particular, short transposition messages can be anagrammed, and
the result can be tested to see whether it's a valid double transposition.
Courville shows how to do this in "Manual for Cryptanalysis of the
Columnar Double Transposition cipher".  If the messages are long
enough anagramming a single message becomes impractical.

-- 
        Jim Gillogly
        Highday, 18 Wedmath S.R. 1999, 18:30
        12.19.6.7.16, 8 Cib 4 Yaxkin, Third Lord of Night

------------------------------

Date: Thu, 12 Aug 1999 02:46:21 -0400
From: Lee Winter <[EMAIL PROTECTED]>
Crossposted-To: comp.lang.c++
Subject: Re: Why does MS-Visual C++ ABSOLUTELY REQUIRE . . .

Paul Lutus wrote:

> Non sequitur. Only MSIE can reside within MSDev as a component. I discovered
> the same thing in my program Arachnophilia, to my dismay. :)

This indicates that there is a dependency.  Is that any technical reason for
this or are we seeing the "chinese wall" in action?

>
>
> --
>
> Paul Lutus
> www.arachnoid.com
>
> Pete Becker <[EMAIL PROTECTED]> wrote in message
> news:[EMAIL PROTECTED]...
> > Paul Lutus wrote:
> > >
> > > You don't get the *complete* help system. You still have help screens,
> > > abbreviated ones. They are in HTML. This requires MSIE.
> > >
> >
> > Non sequitur. There are many applications other than MSIE that can
> > display HTML.
> >
> > --
> > Pete Becker
> > Dinkumware, Ltd.
> > http://www.dinkumware.com




------------------------------

Reply-To: "Paul Lutus" <[EMAIL PROTECTED]>
From: "Paul Lutus" <[EMAIL PROTECTED]>
Crossposted-To: comp.lang.c++
Subject: Re: Why does MS-Visual C++ ABSOLUTELY REQUIRE . . .
Date: Wed, 11 Aug 1999 00:42:52 -0700

MSIE reads some special Microsoft-proprietary compressed HTML files. The
help files are in this format.

--

Paul Lutus
www.arachnoid.com


Lee Winter <[EMAIL PROTECTED]> wrote in message news:[EMAIL PROTECTED]...
>
>
> Douglas A. Gwyn wrote:
>
> > Guenther Brunthaler wrote:
> > > On 7 Aug 1999 18:41:27 GMT, [EMAIL PROTECTED] () wrote:
> > > >     Why does Microsoft ABSOLUTELY REQUIRE me to install and use
their
> > > >Internet Explorer (IE) before I can even install their Visual C++
compiler?
> > > Haven't you have heard of all those rumours about the various built-in
> > > backdoors of IE?
> >
> > Don't be ridiculous!  The main reason IE is required is that the
> > Visual Studio help system is now based on HTML, and IE contains
> > the modules needed to support that.
>
> Is there something specific about the HTML help files that requires IE or
will any
> HTML viewer suffice?
>
>
>



------------------------------

Reply-To: "Paul Lutus" <[EMAIL PROTECTED]>
From: "Paul Lutus" <[EMAIL PROTECTED]>
Crossposted-To: comp.lang.c++
Subject: Re: Why does MS-Visual C++ ABSOLUTELY REQUIRE . . .
Date: Wed, 11 Aug 1999 00:41:18 -0700

<< This indicates that there is a dependency.  Is that any technical reason
for this or are we seeing the "chinese wall" in action? >>

MSIE is available as a class, easily integrable into an application. This
makes it unique.



--

Paul Lutus
www.arachnoid.com


Lee Winter <[EMAIL PROTECTED]> wrote in message news:[EMAIL PROTECTED]...
> Paul Lutus wrote:
>
> > Non sequitur. Only MSIE can reside within MSDev as a component. I
discovered
> > the same thing in my program Arachnophilia, to my dismay. :)
>
> This indicates that there is a dependency.  Is that any technical reason
for
> this or are we seeing the "chinese wall" in action?
>
> >
> >
> > --
> >
> > Paul Lutus
> > www.arachnoid.com
> >
> > Pete Becker <[EMAIL PROTECTED]> wrote in message
> > news:[EMAIL PROTECTED]...
> > > Paul Lutus wrote:
> > > >
> > > > You don't get the *complete* help system. You still have help
screens,
> > > > abbreviated ones. They are in HTML. This requires MSIE.
> > > >
> > >
> > > Non sequitur. There are many applications other than MSIE that can
> > > display HTML.
> > >
> > > --
> > > Pete Becker
> > > Dinkumware, Ltd.
> > > http://www.dinkumware.com
>
>
>



------------------------------

Reply-To: "Paul Lutus" <[EMAIL PROTECTED]>
From: "Paul Lutus" <[EMAIL PROTECTED]>
Crossposted-To: comp.lang.c++
Subject: Re: Why does MS-Visual C++ ABSOLUTELY REQUIRE . . .
Date: Wed, 11 Aug 1999 00:41:40 -0700

So try it, see what happens.

--

Paul Lutus
www.arachnoid.com


Lee Winter <[EMAIL PROTECTED]> wrote in message news:[EMAIL PROTECTED]...
>
>
> Paul Lutus wrote:
>
> > No. The original statement was, "Why do I have to install MSIE to have
help
> > display in VC++". The answer is:
> >
> > 1. The help files are HTML, and
> > 2. MSIE is the only browser that can integrate into MSDev.
> >
> > One may try to access the help files without MSIE, but you lose
> > context-access. You have to sort out the help files for yourself in an
> > external browser.
> >
> > These are not details. MSDev doesn't work - cannot work -- as designed
> > without a built-in browser.
>
> That's a pretty strong statement.  One I doubt.
>



------------------------------

From: Greg <[EMAIL PROTECTED]>
Subject: My web site is up!
Date: Wed, 11 Aug 1999 08:47:22 GMT

Thanks to the patience of people at this forum, I feel confident that
many of my previous beliefs are really not of such great concern as I
once thought.  So I have decided to go ahead and get my web site fully
launched.  Please let me know what you think of it, even the artistic
aspects of it.

www.ciphermax.com

Thanks again...

--
The US is not a democracy - US Constitution Article IV Section 4.
Democracy is the male majority legalizing rape.
UN Security Council is a Democracy.  NO APPEALS!  Welcome to the NWO.
Criminals=Crime.  Armies=Tyranny.  The 2nd amendment is about tyranny.


Sent via Deja.com http://www.deja.com/
Share what you know. Learn what you don't.

------------------------------

From: Gabriel Belingueres <[EMAIL PROTECTED]>
Subject: Re: What's first?
Date: Wed, 11 Aug 1999 12:00:41 GMT

In article <[EMAIL PROTECTED]>,
  [EMAIL PROTECTED] (John Savard) wrote:
> Gabriel Belingueres <[EMAIL PROTECTED]> wrote, in part:
>
> >I was wondering why is that when I send a ciphered message, I have to
do
> >the MAC computation from the plaintext, then the encryption of the
> >plaintext + MAC.
>
> >If I would do this in the reverse order (ie encrypt first, then
compute
> >the MAC from the ciphertext) I could save a decryption when the
message
> >is modified.
>
> Well, anyone can compute the MAC from the ciphertext.

Not anyone. You have to know the MAC secret key (usually called just
the MAC secret). Also, usually the array of bytes that you apply the MAC
is concatenated with the "security context" of the session, witch is
secret too. For example, in SSL you concatenate to the message the SSL
version number, the secuence number of the record, the message length,
the content type, etc.

> Hence, doing it
that way
> is good if the purpose of the MAC is to correct transmission errors.
If the
> purpose of the MAC is to authenticate the message, though, to prove it
came from
> its sender, then encrypting it with the secret key is required.

First, MACs are intented for message authentication. For correct
transmission errors are other kind of codes, like Hamming, CRCs, etc.
Second, this encryption is not necessary. If you don't generate the MAC
using the MAC secret key (and the security context), then any bit you
can flip is detected.

Regards,
Gabriel.


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Share what you know. Learn what you don't.

------------------------------

From: [EMAIL PROTECTED]
Subject: Re: NIST AES FInalists are....
Date: Wed, 11 Aug 1999 12:28:18 GMT

In article <7oqt5t$goi$[EMAIL PROTECTED]>,
  [EMAIL PROTECTED] (SCOTT19U.ZIP_GUY) wrote:
>   Yes just what we need a kid telling the NIST that 2 fish is good.
Just what
> the hell does this kid know about encryption or anything else for
that matter.
> Yes I see he is trying to kiss up to you and you think your a god. So
since
> there are no facts that 2 fish is any "good" let the kid write to
them. Heavan
> forbid that someone actually takes a real good look at it. By the way
in your
> phony contest did any one get the money. Or since there was no real
black
> and white problem to solve did you pay anyone.

I for one think NIST will only appreciate comments from people who are
objective.  I never say Twofish is the 'best' of AES but I think it's
among the top.

1.  Twofish is fast, compact and good for desktop/smartcard and
hardware.  It's portability means good multi-plaform protocals can be
installed easily.  It's also well designed by people who have 'broken
their share of algorithms'.

2.  RC6 is fast, compact and good for multiplatforms as well.  It's
based on the considerable strength of data dependant rotations.  It's
designed to stop ALL known attacks on RC5.  It's designed by a group of
compotent cryptgographers.

3.  Serpennt is slow but conservative.  Designed by people who have
also 'broken their share of algorithms'.  It's also well suited for
multiplatform.

4.  Rijndael is ok.  Nothing special about it above the others though.

That's my point of view.  I am not 'try to kiss' up to Bruce.  I have
never even met him.

Tom
--
PGP 6.0.2i Key
http://mypage.goplay.com/tomstdenis/key.pgp
PGP 2.6.2  Key
http://mypage.goplay.com/tomstdenis/key_rsa.pgp


Sent via Deja.com http://www.deja.com/
Share what you know. Learn what you don't.

------------------------------

From: Volker Hetzer <[EMAIL PROTECTED]>
Subject: Re: brute force crackers unethical?
Date: Wed, 11 Aug 1999 13:57:19 +0200

Andrew Whalan wrote:

> Anyhow, in a nutshell, I would just like to be reassured that I am not
> acting in an unethical fashion to write a brute force cracker, as IMHO at
> least, it is a valid (but annoyingly time consuming) method of
> cryptanalysis.
The writing of it in itself is certainly not unethical as it is probably done
in a lot of cases for scientific purpose.
Publishing it is not unethical either as it creates a big public demand for a
more secure solution and therefore prevents exploiting the security hole by
the bad guys.
Off hand I'd consider everything else unethical because it does not help to
increase security. (add a big IMHO to this)

Greetings!
Volker
-- 
Hi! I'm a signature virus! Copy me into your signature file to help me spread!

------------------------------

From: Mike Just <[EMAIL PROTECTED]>
Subject: Re: AES finalists to be announced
Date: Wed, 11 Aug 1999 12:56:38 GMT

<!doctype html public "-//w3c//dtd html 4.0 transitional//en">
<html>
Well, I hope that being "primarily" a designer does not exclude one from
being a good cryptanalyst as well.&nbsp; In any case, a complete list of
Serge's publications is available at <A 
HREF="http://www.dmi.ens.fr/~vaudenay/pub.html">http://www.dmi.ens.fr/~vaudenay/pub.html</A>
<p>Mike
<p>Bruce Schneier wrote:
<blockquote TYPE=CITE>On Mon, 09 Aug 1999 19:52:14 +0000, Helger Lipmaa
&lt;[EMAIL PROTECTED]>
<br>wrote:
<p>>Bruce Schneier wrote:
<br>>
<br>>> The most interesting thing to notice is that the five finalists
were
<br>>> designed by teams that have had strong cryptanalysts on them.&nbsp;
Almost
<br>>> all of the other algorithms (E2 being the only exception) were
<br>>> designed by teams that did not have strong cryptanalysts on them.&nbsp;
As
<br>>> I have said again and again, good ciphers are designed by good
<br>>> cryptanalysts.
<br>>
<br>>I can imagine the face of Serge Vaudenay when reading this posting.
<p>I meant no ill will, but my bibliography of Serge's work shows
<br>primarily design papers.
<p>Bruce
<br>**********************************************************************
<br>Bruce Schneier, President, Counterpane Systems&nbsp;&nbsp;&nbsp;&nbsp;
Phone: 612-823-1098
<br>101 E Minnehaha Parkway, Minneapolis, MN&nbsp; 55419&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
Fax: 612-823-1590
<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Free crypto
newsletter.&nbsp; See:&nbsp; <a 
href="http://www.counterpane.com">http://www.counterpane.com</a></blockquote>
</html>


------------------------------

From: [EMAIL PROTECTED] (DJohn37050)
Subject: Re: frequency of prime numbers?
Date: 11 Aug 1999 12:33:50 GMT

One always has to be careful in the reduction to absurdity proofs, as it only
means that at least one of your assumptions were invalid, and your assumptions
can be very subtle.  I have heard that some of these types of proofs were
actually invalid (at least later considered invalid) as all the assumptions
were not stated, and it could turn out that a different assumption might be the
invalid one.
Don Johnson

------------------------------

From: Paul Crowley <[EMAIL PROTECTED]>
Subject: Re: frequency of prime numbers?
Date: 11 Aug 1999 09:55:10 +0100

[EMAIL PROTECTED] (Don Dodson) writes:

> Sniggerfardimungus wrote:
> >  I ask this question here not because it necessarily relates to
> >cryptography, but to an interest of cryptographers, prime numbers; is
> >there any reason to believe that there are either a finite or an
> >infinite number of primes?  Even better, is there any proof either
> >way?
> 
> Assume for a moment that there was a finite number of primes.

This proof seems to cause terrible trouble.  Here's a way to put it
that avoids the trouble:

Let S be *any* finite set of natural numbers, and let n = 1 + PI(S)
(ie, the product of all the numbers in the set plus 1).  If n <= 2,
then either 2 is not a member of S or 0 is a member of S.  If n > 2, n
has no prime factors in S as argued in the usual way; therefore n's
prime factors must all be outside S.  In either of these cases, S is
not a complete set of primes.  Therefore *no* finite set is a complete
set of primes.

I'll be interested to see if this gets the Silverman Treatment.
Right, I'm off to see the eclipse.
-- 
  __
\/ o\ [EMAIL PROTECTED]     Got a Linux strategy? \ /
/\__/ Paul Crowley  http://www.hedonism.demon.co.uk/paul/ /~\

------------------------------


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