Cryptography-Digest Digest #281, Volume #14 Wed, 2 May 01 01:13:00 EDT
Contents:
Timing analysis attacks/Power analysis attacks ("Michael Scott")
Re: Timing analysis attacks/Power analysis attacks (Doug Stell)
Re: Intacta.Code ... ("Tom St Denis")
Re: RSA BRUTE FORCE ("Douglas A. Gwyn")
Re: What Is the Quality of Randomness? (John Wasser)
Re: What Is the Quality of Randomness? (Jim Gillogly)
Re: Re: What Is the Quality of Randomness? (those who know me have no need of my
name)
Re: Style of discussions ("Full Name")
Re: Best, Strongest Algorithm (jlcooke)
Re: Encryption and decryption in VHDL (jlcooke)
Re: RSA BRUTE FORCE (jlcooke)
Re: A Question Regarding Backdoors (nugatory)
Re: Intacta.Code ... (John Savard)
Re: DSA in GF(2^W)? (jlcooke)
Re: bogus speed claims (just wondering) ("Ben Hamilton")
Re: Intacta.Code ... (John Savard)
Re: Intacta.Code ... (John Savard)
Re: Rijndael Galois Field construction problem. (jlcooke)
Ecash via anonymous credentials without blinding (David Hopwood)
Re: Rijndael Galois Field construction problem. (David Wagner)
Re: Intacta.Code ... (newbie)
----------------------------------------------------------------------------
From: "Michael Scott" <[EMAIL PROTECTED]>
Subject: Timing analysis attacks/Power analysis attacks
Date: Tue, 1 May 2001 18:10:56 -0500
I don't know much about these attacks, but wouldn't PK systems be immune if
much-maligned Lucas exponentiation were used instead?
The optimal algorithm for Lucas exponentiation is described in
http://www.eskimo.com/~weidai/lucas.html
The bad news is that it is about 50% slower than "regular" modular
exponentiation. But there are two bits of good news.
First you can use smaller "half-sized" primes for example in Diffie-Hellman.
So 512 bit primes are fine, instead of 102-bit primes. Second the optimal
algorithm seems likely (to me) to take time/draw power independent of the
bit pattern used in the exponent.
Comments?
Mike Scott
------------------------------
From: [EMAIL PROTECTED] (Doug Stell)
Subject: Re: Timing analysis attacks/Power analysis attacks
Date: Tue, 01 May 2001 23:45:38 GMT
On Tue, 1 May 2001 18:10:56 -0500, "Michael Scott"
<[EMAIL PROTECTED]> wrote:
>I don't know much about these attacks, but wouldn't PK systems be immune if
>much-maligned Lucas exponentiation were used instead?
There are several countermeasures for these attacks that can be
applied to exponentiation in Diffie-Hellman, DSA and RSA based
systems.
BTW, the math engine of the Motorola Advanced INFOSEC Machine (AIM)
has just been proven to implement one of the key countermeasures. This
made the Agency quite happy.
doug
------------------------------
From: "Tom St Denis" <[EMAIL PROTECTED]>
Subject: Re: Intacta.Code ...
Date: Wed, 02 May 2001 00:41:47 GMT
"Thomas Christensen" <[EMAIL PROTECTED]> wrote in message
news:80HH6.926$[EMAIL PROTECTED]...
> > Sadly this is nothing more then Reed-Solomon codes and a B&W bitmap.
>
> Do you have some more information about the "Reed-Solomon codes" and how
it
> is converted into a "B&W bitmap" ..?
Nope, but from what I gather from the lack of knowledge on their site that's
all they are doing.
It's not special, it's not even remotely interesting.
Interesting is Xerox's vector code stuff. It's a similar idea if I am not
mistake except they use slashes (either / or \) to encode a message that
looks like anything the person wants (i.e a photo or just a random jumble).
The decoder can turn that back into the data required.
It's not more useful, just more keen.
Tom
------------------------------
From: "Douglas A. Gwyn" <[EMAIL PROTECTED]>
Subject: Re: RSA BRUTE FORCE
Date: Wed, 02 May 2001 00:50:54 GMT
[EMAIL PROTECTED] wrote:
> Even though you're factoring a number that has only two factors (presumably),
> that doesn't mean that you'll only see one pair of digits that will work.
How about in base 2 instead of base 10?
------------------------------
Subject: Re: What Is the Quality of Randomness?
From: John Wasser <[EMAIL PROTECTED]>
Date: Wed, 02 May 2001 00:54:19 GMT
[[ This message was both posted and mailed. ]]
Is it sufficient to just find a "pattern" in a cyphertext? If I were
to tell you that the following data was a cyphertext, what could you
tell me about the plaintext or OTP?
83 FB C1 0A 67 80 F0 7D B3 02
3E CD 15 E4 7D 55 81 3F D7 74
76 B3 8C FB A1 0A 66 81 C0 FD
40 05 13 60 E8 BE 59 C1 A0 A0
E5 BE C1 94 42 78 E6 3E 57 30
19 38 7B 1F 15 9A FE 74 3F 07
One pattern I see is that all of the bytes with 8 as the first nibble
are in the first half of the message. What does that tell you about
the plaintext or the OTP?
------------------------------
From: Jim Gillogly <[EMAIL PROTECTED]>
Subject: Re: What Is the Quality of Randomness?
Date: Tue, 01 May 2001 18:27:59 -0700
John Wasser wrote:
>
> [[ This message was both posted and mailed. ]]
>
> Is it sufficient to just find a "pattern" in a cyphertext? If I were
> to tell you that the following data was a cyphertext, what could you
> tell me about the plaintext or OTP?
>
> 83 FB C1 0A 67 80 F0 7D B3 02
> 3E CD 15 E4 7D 55 81 3F D7 74
> 76 B3 8C FB A1 0A 66 81 C0 FD
> 40 05 13 60 E8 BE 59 C1 A0 A0
> E5 BE C1 94 42 78 E6 3E 57 30
> 19 38 7B 1F 15 9A FE 74 3F 07
>
> One pattern I see is that all of the bytes with 8 as the first nibble
> are in the first half of the message. What does that tell you about
> the plaintext or the OTP?
Given a few million ciphertexts produced by the same process you used
to create this sample, what is the shortest program that would produce
them all? Would that program also predict the next million ciphertexts?
As Doug Gwyn is fond of pointing out, randomness is not a property of
a particular purported ciphertext, but of the process used to produce it.
--
Jim Gillogly
Mersday, 11 Thrimidge S.R. 2001, 01:25
12.19.8.3.6, 1 Cimi 4 Uo, Third Lord of Night
------------------------------
From: those who know me have no need of my name <[EMAIL PROTECTED]>
Subject: Re: Re: What Is the Quality of Randomness?
Date: 02 May 2001 01:12:38 GMT
<[EMAIL PROTECTED]> divulged:
>Is it sufficient to just find a "pattern" in a cyphertext?
when generated by an otp? no, at least not so far as anyone has been
able to discover. it may mean quite a lot for other ciphers.
>If I were to tell you that the following highly patterned data was a
>cyphertext, what could you tel me about the plaintext or OTP?
firstly, that a miracle had occurred. second, nothing else, provided
an otp really was used. (which the former makes highly unlikely.)
--
okay, have a sig then
------------------------------
From: "Full Name" <[EMAIL PROTECTED]>
Subject: Re: Style of discussions
Date: Tue, 01 May 2001 12:26:21 -0700
Unlike those of some individuals that frequent this forum, your postings
are always a model of prudence and good manners. I, for one, certainly second
the proposal implicit in your posting below.
In article <[EMAIL PROTECTED]>, "Mok-Kong Shen"
<[EMAIL PROTECTED]> wrote:
> Time and again I read articles that contain, in my opinion, more or less
> heavy personal attacks of some writers on the others. I surmise that the
> underlying purpose of these is not to express any private hostility but
> to give certain emphasis to other sentences of the articles that form
> the proper scientific topics being discussed. If that is indeed the
> case, I wonder whether it wouldn't be feasible to find some non-personal
> expressions in the language to convey same/equivalent emphasis without
> causing negative psychological effects on the part of the persons
> addressed. Though being a foreigner with yet rather humble language
> competency, I am quite sure that English is rich/universal enough to
> enable such reformulations without much difficulty in all concievable
> situations of scientific debates. Wouldn't it be a nice thing that we
> all try a bit to keep the atmosphere of the group as agreeable as
> possible (not only for ourselves but also for persons who occasionally
> visit our group)?
>
> M. K. Shen
> ------------------------------
> http://home.t-online.de/home/mok-kong.shen
------------------------------
From: jlcooke <[EMAIL PROTECTED]>
Subject: Re: Best, Strongest Algorithm
Date: Wed, 02 May 2001 03:25:35 GMT
"Leonard R. Budney" wrote:
> > ...and since the NSA chose it...
>
> You might as well leave the NSA out of your calculations. Nobody knows what
> they can and can't do. The penalty for choosing under-examined ciphers is
> much higher than for choosing ciphers that the NSA and hostile martians
> might be able to break. (Just take my advice: don't overthrow the US or
> assasinate the President. The NSA will leave you alone.)
Rules of thumb:
1. The NSA, CSE (Canada), and the grand children of Bl'y Park (UK)
can decrypt anything
2. The same folk can not decrypt everything
3. Mega-corps can pay for the hardware to break a few things
4. The wise know rules 1-3
I've ranted to people before about the thermodynamic limits of real
world cryptography so I'll spare you all. Basically you can have a
'perfect' block cipher but it doesn't really help you because a PK
cipher has to be used to talk to someone/something you've never
exchanged securely with before. The laws of thermodynamics forbid the
existence of a 'perfect' PK algorithm (even Quantum Crypto can't break
these rules).
This PK cipher is what governments spend their time on breaking when
'observing' the public.
So it's in the their best interests to choose the best block cipher to
assure everyone they can be trusted, why didn't they do this with
DES? We didn't have globally deployed PKIs at that point. The
paranoid would claim that I work for 'them' at this point, so I'll
stop here.
JLC
------------------------------
From: jlcooke <[EMAIL PROTECTED]>
Subject: Re: Encryption and decryption in VHDL
Date: Wed, 02 May 2001 03:32:39 GMT
The NIST site (http://www.nist.gov/aes) has lots of goodies for
newbies. (I know I should have gone into English :))
Specifically:
http://csrc.nist.gov/encryption/aes/round2/r2anlsys.htm#NSA
But the NSA did this work. If you're paranoid you can do it all
yourself and realize that they did a better job and many people do.
Cheers.
JLC
Mike Rosing wrote:
>
> kris wrote:
> >
> > Newbie poster (sorry) :-)
> >
> > Does anybody have any recommendations for sites, or references
> > for simple encryption of serial data in VHDL ? This would be for
> > a serial bitstream, and would need some kind of shared key, and
> > there woudl need to be a method for synchronising the two data
> > streams.
> >
> > Does anyone have any experience of this ?
> >
> > Can anyone offer any advice ?
>
> Check out this:
> http://www.ece.wpi.edu/People/faculty/cxp.html
>
> There's papers on Serpent in FPGA, I'm sure it was done in VHDL.
> One of Christof's students is doing his defense on hyperelliptic curves
> done in an FPGA. Should be lots of things for you to dig thru :-)
>
> Patience, persistence, truth,
> Dr. mike
------------------------------
From: jlcooke <[EMAIL PROTECTED]>
Subject: Re: RSA BRUTE FORCE
Date: Wed, 02 May 2001 03:51:26 GMT
Ahh. Flashback to when I taught myself number theory before I knew I
could have paid $2.75 in late fees at the library instead of 6months
rediscovering Euclid, Fermat and Larange. Then I got and education...
Here's your problem Eric the following will eventually happen:
iter{1}: A_1 * B_1 = too small
...
iter{n}: A_n * B_n = too small
iter{n+1}: A_{n+1} * B_{n+1} = too big
iter{n+2}: A_n * B_n = too small
Because:
7 * 11 = 77
3 * 23 = 69 = too big
3 * 29 = 87 = too small
Your bubble search technique works on single variables. What do you
do when you reach a point described above? Which (A or B) do you
change? Increase or decrease is clear, but which variable and by how
much?
I believe that if a solution to RSA exists, it will be simple to
implement. But our understanding of this problem is not very deep
(relatively).
JLC
"Douglas A. Gwyn" wrote:
>
> [EMAIL PROTECTED] wrote:
> > Even though you're factoring a number that has only two factors (presumably),
> > that doesn't mean that you'll only see one pair of digits that will work.
>
> How about in base 2 instead of base 10?
------------------------------
From: nugatory <[EMAIL PROTECTED]>
Subject: Re: A Question Regarding Backdoors
Date: Wed, 02 May 2001 03:35:55 GMT
Tom St denis wrote:
> Oh gotcha. What form of a backdoor would he *want* to put in there? The
> whole point of AES was to make a new more secure cipher that is std.
> Why would they want to compromise it?
Ohmigod... some troll has hijacked our Tom.... Maybe if I
feed it, it'll relent and give him back to us
unharmed.... I hope so.....
OK. Original poster stated that he lived in the United States.
Therefore he is subject to United States export regulations.
You may not like these regulations. In fact, you may even share
my belief that they are aggressively stupid, but based on your
postings so far, it's more likely that you've never had to
deal with them. If so, count your blessings.
For a very long time as these things go, the US government
prohibited the export of any strong cryptography, and many
US software vendors were forced into the (idiotic, IMNHSO)
position of providing weak (40-bit keys, for example)
crypto in exported products, while still being allowed to ship
domestic versions with much stronger encryption. In other words,
the US government has a track record of *requiring* that exported
software be compromised. The original origin of the technology
is irrelevant - it's the export from the United States that's
at issue.
Of course, there was always an element of unclarity about
just exactly what forms of cryptography would be considered
weak enough to be granted an export license. So there have
been recurrent rumors that some companies have been told that
they would be granted an export license only if they built
sme sort of backdoor into their product. I am not aware of
any case in which someone has been willing to go on the record
as saying that they were required to do so in exchange for
being granted a license, but the rumors do circulate.
So original poster was asking a naive but not a stupid
question. OK troll, can you give us Tom back now?
------------------------------
From: [EMAIL PROTECTED] (John Savard)
Subject: Re: Intacta.Code ...
Date: Wed, 02 May 2001 04:02:08 GMT
On Mon, 30 Apr 2001 19:12:04 -0300, newbie <[EMAIL PROTECTED]>
wrote, in part:
>That is polite answer.
>Thank you.
Particularly since it appears to have been an insult he was answering.
John Savard
http://home.ecn.ab.ca/~jsavard/
------------------------------
From: jlcooke <[EMAIL PROTECTED]>
Subject: Re: DSA in GF(2^W)?
Date: Wed, 02 May 2001 04:01:37 GMT
Roger Schlafly wrote:
>
> The Sieve was a way of finding primes, not factoring. It does not give any
> theory for how hard factoring is.
>
> But it is a common misconception that the RSA problem is synonomous
> with factoring. Breaking RSA means solving
> y = x^e mod pq
> for x, given y, e, and pq. Typically this means finding cube roots mod pq.
>
> Factoring is one method, but there may be others. If the original poster
> was trying to argue that the RSA problem is 2000 years older than the
> discrete logarithm problem, then I disagree. It would be easier to make
> the case that the discrete logarithm problem is older.
You get at the message in 2 ways:
1. DL the message over the modulus (n=pq)
2. Factor the modulus to generate d (de = 1 mod (p-1)(q-1))
- this has been reduced to find x in 2^x = 1 mod n in a recent
claim of breaking RSA if I recall.
When people starting about how _hard_ factoring is...I do not know.
But I know that factoring is as old as arithmetic (Egyptian over
lords' accountants assigning plots of land. Agriculture and
arithmetic go hand in had in history.
Formalities of euler's totiant functions came latter with mass
literacy and the proliferation of academia. I'm curious if anyone
knows the first examples of factoring and DL problem analysis?
JLC
------------------------------
From: "Ben Hamilton" <[EMAIL PROTECTED]>
Subject: Re: bogus speed claims (just wondering)
Date: Wed, 2 May 2001 14:03:56 +1000
one word - marketing.
Not everyone in this sweet world is as straightforward as you Tom.
ben hamilton
"Tom St Denis" <[EMAIL PROTECTED]> wrote in message
news:TVvH6.105445$[EMAIL PROTECTED]...
> > If you see someone claiming a code size of 500 B when he needs a 256 B
> > table, that probably means the table is in ROM or EEPROM, and what he
> > means is "I can make this algorithm run on a microcontroller with 512 B
of
> > RAM".
> Then why don't they say that? Are they afraid it wouldn't seem so cool?
>
> Tom
------------------------------
From: [EMAIL PROTECTED] (John Savard)
Subject: Re: Intacta.Code ...
Date: Wed, 02 May 2001 04:03:10 GMT
On Wed, 2 May 2001 00:45:10 +0200, "Thomas Christensen"
<[EMAIL PROTECTED]> wrote, in part:
>Do you have some more information about the "Reed-Solomon codes" and how it
>is converted into a "B&W bitmap" ..?
Reed-Solomon codes are a form of error-correcting code. They're used
in the Compact Disc standard also.
John Savard
http://home.ecn.ab.ca/~jsavard/
------------------------------
From: [EMAIL PROTECTED] (John Savard)
Subject: Re: Intacta.Code ...
Date: Wed, 02 May 2001 04:11:40 GMT
On Mon, 30 Apr 2001 22:36:46 GMT, "Tom St Denis"
<[EMAIL PROTECTED]> wrote, in part:
>Sadly this is nothing more then Reed-Solomon codes and a B&W bitmap.
>A big problem with the intacta system is that you must scan and print at the
>same resolution or it won't work.
I've taken a look at the site, and it appears there's a bit more than
that.
For one thing, although it prints things as dots, if the printer is
high resolution, it isn't going to print single dots; the result would
have an impossibly high error rate. It will still be visibly like a
2-D barcode, the printout will be visible little squares. Maybe 60 to
the inch, not 300 to the inch.
So I don't think your statement about matched resolutions is correct.
They don't give out exact technical details, but apparently their
product standardizes all these things:
- optional encryption,
- compression,
- interleaving (or "randomization") of data,
- error correction
plus, there's a file format to it so that files can be encoded and
reconstructed.
John Savard
http://home.ecn.ab.ca/~jsavard/
------------------------------
From: jlcooke <[EMAIL PROTECTED]>
Subject: Re: Rijndael Galois Field construction problem.
Date: Wed, 02 May 2001 04:30:53 GMT
Yaniv Sapir wrote:
>
> Hi all.
>
> In the Rijndael algorithm, there is an extensive use of Finite Field (GF)
> arithmetic. The primitive polynomial chosen is 0x11B = 283, and the field is
> GF(256). Trying to construct this field I faced a problem when, instead of
> 255 distinct elements (1-255) I get 51 elements repeating five times (the
> 51'st element is 1 - while it should be element 255 - so the series repeats
> itself).
Try this code:
http://www.engsoc.carleton.ca/~jlcooke/c.c
You'll see everything is well. And the GF transform is irreducible,
which means _all_ (not just 0x02 and 0x03) elements of the field are
generators as you expect them to be otherwise things would be ugly
(weak cipher and decrypt would not work).
JLC
------------------------------
Date: Wed, 02 May 2001 05:54:24 +0100
From: David Hopwood <[EMAIL PROTECTED]>
Subject: Ecash via anonymous credentials without blinding
=====BEGIN PGP SIGNED MESSAGE=====
One of the obstacles to adopting anonymous e-cash protocols has been
the various patents on blind signatures, so I thought the group might
find this interesting.
- --- begin forwarded text
Date: Sun, 29 Apr 2001 15:34:19 -0600
From: Anonymous <[EMAIL PROTECTED]>
Comments: This message did not originate from the Sender address above.
It was remailed automatically by anonymizing remailer software.
Please report problems or inappropriate use to the
remailer administrator at <[EMAIL PROTECTED]>.
To: [EMAIL PROTECTED]
Subject: Ecash via anonymous credentials without blinding
Sender: [EMAIL PROTECTED]
One of the papers at Eurocrypt 2001 will be a new credential system by
Jan Camenisch and Anna Lysyanskaya. It is available from Jan's page
at http://www.zurich.ibm.com/~jca/publications.html.
Each player creates a numerical pseudonym with organization O, of the
form P = a_O^xu * b_O^s, mod n_O. (n_O is an RSA modulus belonging to
the organization, a_O and b_O are group elements < n_O, xu is the user's
secret identiy value, and s is a random blinding factor).
The idea is that the xu value is supposed to be the same for all the
user's pseudonyms. If so, then when the user gets a credential on one
of his pseudonyms, he can show it with regard to any of the others.
The credential is an RSA signature by O on P * d_O, where d_O is a
constant value chosen by O. The RSA signature uses a random exponent
e_O, different for each credential.
Using these values, a user with a credential on one of its pseudonyms
can show it on another by exhibiting a ZK proof. When he shows the
credential it is at another organization O' where he has a different
pseudonym P'. The user shows that he knows a value P such that both
P and P' are of the proper form above, and share the same xu value.
Furthermore, he knows an RSA signature on P' * d_O issued by O, with
some particular exponent e. All these proofs are zero knowledge and
the user does not actually reveal P or e or xu.
The net result is that he can convince O' that he has a credential issued
by O on another of his pseudonyms, while showing only his P' pseudonym
with O'.
The cool thing is that this can also be used as an ecash system, one that
doesn't use blind signatures. The pseudonym gets another term multiplied,
and information about that term is revealed openly during the credential
showing. This transforms the credential into a one-show credential,
in that any showing of the same credential must reveal that same value.
A one-show credential is essentially the same as an online ecash coin.
Issuing the credential is like issuing a coin, and showing the one-show
credential is like spending the coin. The revealed value during the
showing must be kept in a "spent coins" list as with other online ecash
systems.
Although it sounds complicated, the computation required is quite
practical. According to the authors, with an RSA modulus of 1024 bits,
a credential-pseudonym pair is about 4K bits, and showing possession of
a credential takes about 22 exponentiations total for both parties.
The paradigm of replacing blinding during withdrawal with ZK proof during
spending seems to be a promising alternative to the many blind signature
patents which cover electronic cash.
- --- end forwarded text
- --
David Hopwood <[EMAIL PROTECTED]>
Home page & PGP public key: http://www.users.zetnet.co.uk/hopwood/
RSA 2048-bit; fingerprint 71 8E A6 23 0E D3 4C E5 0F 69 8C D4 FA 66 15 01
Nothing in this message is intended to be legally binding. If I revoke a
public key but refuse to specify why, it is because the private key has been
seized under the Regulation of Investigatory Powers Act; see www.fipr.org/rip
=====BEGIN PGP SIGNATURE=====
Version: 2.6.3i
Charset: noconv
iQEVAwUBOu+S5jkCAxeYt5gVAQEmtQf+NMLllZvumhLUkGCFXPnhUqh6yMu2jnk5
A0G+halFSCygyHhMpR8sOMpksqrZ17Jenf/rLDwKMQwXGes+ilz9kraOcY3eyy5L
8Vp/rYCsmz9EzpsyR+4xcvtjzJr3SCYayiRT0CjvNWaAL+tQDP+n9YzbEBncyyrN
A3mANYK24KalgPphlG/71AZR+ry4KFBDsqRdVTtloSvrDTdrgwsfKLM6BMGK+LMd
/JGjaAs0q6AqnWn0C91kvLyZdmB9hBpPGbUrH9yB1L5bGmI7t062aGNzvlfD401Q
5zP+PWmgAG4PXjatC5wYb8gU5ENLijQ+F/ANxWTWgBG4KD3FbH+gOQ==
=Og7z
=====END PGP SIGNATURE=====
------------------------------
From: [EMAIL PROTECTED] (David Wagner)
Subject: Re: Rijndael Galois Field construction problem.
Date: 2 May 2001 05:03:38 GMT
jlcooke wrote:
>Yaniv Sapir wrote:
>> GF(256) [...]
>
>[...] And the GF transform is irreducible,
>which means _all_ (not just 0x02 and 0x03) elements of the field are
>generators as you expect them to be otherwise things would be ugly
>(weak cipher and decrypt would not work).
Maybe I don't understand finite field arithmetic well enough, but this
remark doesn't look right to me. In particular, the multiplicative group
GF(256)^* has 255 elements, which is not prime, so not all elements are
generators. If g is a generator, then g^3 and g^5 are not generators of
the multiplicative group (to give two examples) since 3 and 5 divide 255.
Also, 0 is not a generator. Did I misunderstand something?
------------------------------
From: newbie <[EMAIL PROTECTED]>
Subject: Re: Intacta.Code ...
Date: Wed, 02 May 2001 00:58:22 -0300
You have to read what he said before to understand.
It is long story.
He insults me first.
Read the previous posts, please before blaming me.
John Savard wrote:
>
> On Mon, 30 Apr 2001 19:12:04 -0300, newbie <[EMAIL PROTECTED]>
> wrote, in part:
>
> >That is polite answer.
> >Thank you.
>
> Particularly since it appears to have been an insult he was answering.
>
> John Savard
> http://home.ecn.ab.ca/~jsavard/
------------------------------
** FOR YOUR REFERENCE **
The service address, to which questions about the list itself and requests
to be added to or deleted from it should be directed, is:
Internet: [EMAIL PROTECTED]
You can send mail to the entire list by posting to sci.crypt.
End of Cryptography-Digest Digest
******************************
