Cryptography-Digest Digest #977, Volume #13      Fri, 23 Mar 01 07:13:01 EST

Contents:
  Re: RC4 test vectors after gigabyte output?. ("Scott Fluhrer")
  Re: Latin Squares (Richard Bean)
  Re: What the Hell...Here's what my system can do at it's best... (wtshaw)
  Re: AES - which block/key size to use? ([EMAIL PROTECTED])
  Open Source Implementations of PGP (Peter Harrison)
  Re: Speed of factoring (Panu =?iso-8859-1?Q?H=E4m=E4l=E4inen?=)
  Re: cryptography using the method of elliptic curve. (Frank Gerlach)
  Re: Fill-in-the-blank codes (similar to Error-correcting codes) (glen herrmannsfeldt)
  Re: Pike stream cipher (Terry Ritter)
  Re: redodancy ("dexMilano")
  Re: Multiple encryption, more secure ciphers (Mok-Kong Shen)
  Re: Pike stream cipher (Mok-Kong Shen)
  Re: What happens when RSA keys don't use primes? ("Jakob Jonsson")
  Re: cryptography using the method of elliptic curve. (Mok-Kong Shen)
  Re: Pike stream cipher (Terry Ritter)
  SecFTP 0.95.6 ("Henrick Hellstr�m")
  the classified seminal 1940 work of Alan Turing? ([EMAIL PROTECTED] (j ))
  Re: Open Source Implementations of PGP (Jonathan Thornburg)
  Re: SecFTP 0.95.6 (Arturo)
  Re: Self Enforcing Protocol (Slightly OT and Long!) (Jim Farrand)

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

From: "Scott Fluhrer" <[EMAIL PROTECTED]>
Subject: Re: RC4 test vectors after gigabyte output?.
Date: Thu, 22 Mar 2001 23:05:53 -0800


Luis Yanes <[EMAIL PROTECTED]> wrote in message
news:=LC6OtScf+MW84Ho2A7VI3YEWtgU@wingate...
> On 21 Mar 2001 21:32:32 -0800 [EMAIL PROTECTED] (Gregory G Rose) wrote:
>
> >In article <u5C3OpCcF7b2VNiAEyPmh3csFGJy@wingate>,
> >Luis Yanes  <[EMAIL PROTECTED]> wrote:
> >>There is any RC4 test vectors after gigabyte output?.
> >
> >Well, not a gigabyte.
>
> But better than just 512 bytes. Thanks!.
>
> >Initialise RC4 (or equivalent) with the 8 byte key
> >"test key". Then the first 44 output bytes are:
>
> unsigned char testkey[] = {
>     't', 'e', 's', 't', ' ', 'k', 'e', 'y'
> };
>
> >unsigned char expected[] = {
> >    0xbd, 0xe9, 0x5c, 0xb5, 0x2b, 0x8d, 0xf8, 0xfb,
> >    0xf2, 0xb7, 0x51, 0xf6, 0x5b, 0xe1, 0xdf, 0x3e,
> >    0xd7, 0x4b, 0x45, 0x7a, 0xe9, 0x76, 0x4d, 0x26,
> >    0x2f, 0x43, 0xa4, 0x70, 0x9a, 0x2a, 0xc9, 0x4e,
> >    0x11, 0x23, 0x89, 0x7b, 0x02, 0x2a, 0x4f, 0x07,
> >    0x80, 0x98, 0xa1, 0xa0,
> >};
>
> But I get:
>
> unsigned char expected[] = {
>     0x01, 0x94, 0x79, 0x6b, 0xfc, 0xc7, 0xb9, 0xa8,
>     0xc2, 0xed, 0x96, 0x77, 0x64, 0x2c, 0x80, 0xe9,
>     0x65, 0x90, 0x4e, 0x6c, 0xab, 0x72, 0xf9, 0x84,
>     0x93, 0x84, 0xf4, 0x34, 0x7d, 0x27, 0xb2, 0x8b,
>     0xf0, 0x1f, 0x08, 0x3b, 0x86, 0xc1, 0xc5, 0x91,
>     0xb0, 0x1e, 0x4b, 0x1f
> };

That's what I get too.  Greg, can you double check your test?

--
poncho




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

From: [EMAIL PROTECTED] (Richard Bean)
Subject: Re: Latin Squares
Date: 23 Mar 2001 07:17:15 GMT

"MarinaP" <[EMAIL PROTECTED]> writes:

>I am not a crypto specialist, so I hope somebody here can help me.
>Latin Squares are known to be widely used in cryptography.
>Where are Latin Squares used in cryptography?
>Where can I read about Latin Squares?

"Discrete Mathematics Using Latin Squares" by Laywine and Mullen,
Chapter 14, covers:

14.2 encryption based upon the theory of sets of MOLS
14.3 secret sharing schemes based on critical sets
14.4 Diffie-Hellman key exchange and RSA in the group of row-Latin squares

Some other crypto-related Latin squares ideas which aren't covered
in the above book are found in the papers:

* "DESV: A Latin square variation of DES" by Carter, Dawson, and Nielsen
(Proceedings of the Workshop on Selected Areas in Cryptography, Ottawa,
Canada, 1995)

* "Black box cryptanalysis of hash networks based on multipermutations"
by Schnorr and Vaudenay (Eurocrypt '94 pp47-57)

* "Strongbox secured secret sharing schemes", by Seberry and Street (Util.
Math. 57, pp147-163)

* "Cryptosystems based on Latin rectangles and generalized affine spaces"
by Angelo Sonnino (Radovi Matematicki 9, pp177-186)

* "A new authentication scheme based on Latin squares" by Denes & Keedwell
(Discrete Math. v106/107, pp157-161)

* "On Golomb-Posner codes and a remark of W. W. Wu about secret-sharing
schemes" (IEEE Trans. Comm. 38, pp261-262)

* "Resolvable designs applicable to cryptographic authentication schemes"
by Martin, Seberry and Wild (JCMCC v12, pp153-160)

You can read about Latin squares in the two Denes & Keedwell books
and in the Laywine & Mullen book but neither of them cover critical
sets in any depth - try MathSciNet for later papers.

For another angle on Latin squares try Sachkov, "Combinatorial
Methods in Discrete Mathematics".  There's a 1967 book by Vajda
but I don't think it will have anything not in Denes & Keedwell.

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

From: [EMAIL PROTECTED] (wtshaw)
Subject: Re: What the Hell...Here's what my system can do at it's best...
Date: Fri, 23 Mar 2001 01:09:49 -0600

In article <[EMAIL PROTECTED]>, Keill Randor
<[EMAIL PROTECTED]> wrote:
> 
> Hope that explains things alittle better.  I cannot say any more without
giving it away, which is something I do not wish to do until all other
avenues have been explored.
>
There is no line, so consider you wait ended.  Beyond some point, the
better crypto is, the more it will be savaged by those already on the
take..

> To be honest, I would prefer to sell what I have.  Whoever controls this
program will have so much power in the field of computing, communications
etc, that they will effectively be one of the most powerful people in the
world. (If they are ot already).

If they are already so, they will not want to share as much as a crumb with you.

(They would make Microsoft look like, well, crap....).
> 
MS have done a pretty good job of doing that to themselves already.
-- 
Most [cryptographic] algorithms are based on assumptions which
could turn out to be false. -- Ron Rivest

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

From: [EMAIL PROTECTED]
Subject: Re: AES - which block/key size to use?
Date: Fri, 23 Mar 2001 07:46:54 GMT

=====BEGIN PGP SIGNED MESSAGE=====
Hash: SHA1

Scott Fluhrer wrote:
> Fine.  You are aware that CFB mode allows bit flipping attacks in the last
> block, don't you?

I wasn't.
what does this means and how to defeat it ?

== <EOF> ==
Disastry  http://i.am/disastry/
http://disastry.dhs.org/pgp <----PGP plugins for Netscape and MDaemon
 ^-GPG for Win32 (supports loadable modules and IDEA)
 ^-PGP 2.6.3ia-multi02 (supports IDEA,CAST5,BLOWFISH,TWOFISH,AES,3DES,MD5,SHA1)
=====BEGIN PGP SIGNATURE=====
Version: Netscape PGP half-Plugin 0.14 by Disastry / PGPsdk v1.7.1

iQA/AwUBOrrjLjBaTVEuJQxkEQJqawCcCFPoPiy5NR8W4LkEltrEV50HuOMAnA2E
NsJlHLUJ1eQnlB1xoBm8qfpj
=icEi
=====END PGP SIGNATURE=====

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

From: [EMAIL PROTECTED] (Peter Harrison)
Subject: Open Source Implementations of PGP
Date: Fri, 23 Mar 2001 07:57:01 GMT

I am looking for people interested in writing or adapting open source
implementations of PGP in

- Delphi
- C
- Java

to be part of an Open Source business document exchange system.

My Open Source project pages are at 
http://idtrans.sourceforge.net

or send to

[EMAIL PROTECTED]

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

From: Panu =?iso-8859-1?Q?H=E4m=E4l=E4inen?= <[EMAIL PROTECTED]>
Subject: Re: Speed of factoring
Date: Fri, 23 Mar 2001 10:04:29 +0200

Frank Gerlach wrote:

> For example, O(n) for a search algorithm means that search time
> increases with the length n linearly.

No. It means that the search time (or whatever you happen to measure) is bounded
by a linear function f(n) from above, i.e., even though n increases, the search
time never reaches f(n) after n > some N. The time can be constant but still it
is limited by a linear function.

-- Panu H�m�l�inen

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

From: Frank Gerlach <[EMAIL PROTECTED]>
Subject: Re: cryptography using the method of elliptic curve.
Date: Fri, 23 Mar 2001 09:25:03 +0100

Mauro wrote:
> 
> How can i find information about cryptography using the method of elliptic
> curve.
> 
> thanks
> Mauro Pace
> http://web.tiscalinet.it/theflynet/
maybe through altavista.com or google.com

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

From: [EMAIL PROTECTED] (glen herrmannsfeldt)
Crossposted-To: sci.math,comp.dsp
Subject: Re: Fill-in-the-blank codes (similar to Error-correcting codes)
Date: 23 Mar 2001 08:33:07 GMT

Bob Harris <[EMAIL PROTECTED]> writes:

>> The idea is to have a code that includes two redundant bits, and be able to
>> 'correct' any two errors, with the additional knowledge of which two bits
>> might be errant. ...
(snip)
>So, for example, I might have a 5 bits message, add two bits to it
>(according to my yet-undefined code), and transmit the 7 bits through
>separate channels.  Think of the channels as couriers.  Five couriers make
>it to the receiver, two never show up.  The receiver knows which courier is
>which, knows which haven't shown up (maybe they will, but why wait once we
>have five), and then (I hope) can fill in the bits that the two missing
>couriers would have.

When I first heard this story, it was in the days of distributing 
software on floppy disks.  The person bought the box with n disks,
and while installing it found one was bad.  If one additional disk
was supplied holding, in each bit position, the XOR of the bits on
all other disks, one could recreate the bad disk.  Codes to do this
for more than one bad disk were described.  I believe this uses the
same theory as other error correcting codes, though in different ways.
The same reference sources should be consulted.

-- glen

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

From: [EMAIL PROTECTED] (Terry Ritter)
Subject: Re: Pike stream cipher
Date: Fri, 23 Mar 2001 08:48:12 GMT


On Fri, 23 Mar 2001 05:02:26 GMT, in
<CNAu6.111020$[EMAIL PROTECTED]>, in sci.crypt "Tom
St Denis" <[EMAIL PROTECTED]> wrote:

>"Terry Ritter" <[EMAIL PROTECTED]> wrote in message
>news:[EMAIL PROTECTED]...
>>
>> On 22 Mar 2001 16:43:24 -0800, in <99e67c$[EMAIL PROTECTED]>, in
>> sci.crypt [EMAIL PROTECTED] (Gregory G Rose) wrote:
>>
>> >[...]
>> >Please note that neither Knuth nor anyone else
>> >reputable has ever claimed that Algorithm M is a
>> >good stream cipher. There are reasons to believe
>> >it might not be. It generates good psuedo-random
>> >numbers though.
>>
>> Almost every time this comes up, I post the successful attack
>> references.  For example, start at:
>>
>>    http://www.io.com/~ritter/RES/COMBCORR.HTM#B4
>>
>> and follow the links to the article summaries and exact literature
>> references.
>>
>> There is every reason to believe that MacLaren-Marsaglia is
>> fundamentally weak.
>
>Yes, MLM is weak, but that's not technically Algorithm M.  Algorithm M
>specifies two PRNGs are used not two LCGs

The whole point of Algorithm M is to mix two PRNG sources to get a
stronger sequence than is available from a single PRNG.
Unfortunately, that does not happen.  

The cited articles show that mixing two LCG's by MacLaren-Marsaglia
still allows the two sources to be distinguished and one LCG attacked
fairly independently of the other.  The mixed result is said to be
perhaps twice as strong as an unmixed LCG.  This difference is
strength attributable to the mixing process itself.  

But in cryptography, a factor of two in strength is almost
meaningless.  The articles thus give us some of the clearest
demonstrations known of the lack of strength in a particular mixing
process.  

Based on this evidence -- as opposed to hearsay, wishes, hopes or
claims -- we see the MacLaren-Marsaglia mixing process not producing
significant (e.g., exponential) additional cryptographic strength.

---
Terry Ritter   [EMAIL PROTECTED]   http://www.io.com/~ritter/
Crypto Glossary   http://www.io.com/~ritter/GLOSSARY.HTM


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

From: "dexMilano" <[EMAIL PROTECTED]>
Subject: Re: redodancy
Date: Fri, 23 Mar 2001 09:55:28 +0100

if you have "A" you can use "!" to transcode.
in this way if you have "AAAA" you can use "!!!!". this is
transcodification.
if you have "AAAA" and you can manage "4A" this is compression (without
transcodification).

I hope this make sense.

dex

"amateur" <[EMAIL PROTECTED]> ha scritto nel messaggio
news:[EMAIL PROTECTED]...
> Transcodification eliminate redundancy.
> So, what is a difference?
>
>
> dexMilano wrote:
> >
> > This doesn't remove redodancy. It's a transcodification.
> > dex
> > "amateur" <[EMAIL PROTECTED]> ha scritto nel messaggio
> > news:[EMAIL PROTECTED]...
> > > Simple. You assign specific code to every character.
> > > It's easy.
> > >
> > >
> > > dexMilano wrote:
> > > >
> > > > Is there some simple algoritm to remove redodancy in text?
> > > > I tried ZIP but it's too heavy.
> > > >
> > > > Thx
> > > >
> > > > dex



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

From: Mok-Kong Shen <[EMAIL PROTECTED]>
Subject: Re: Multiple encryption, more secure ciphers
Date: Fri, 23 Mar 2001 10:20:01 +0100



David Wagner wrote:
> 
> John Savard wrote:
> >Concatenate the key with "01", and then hash it ten times, to make
> >KHA1, KHA2, KHA3 ... KHA10.
> 
> Personally, I prefer Knudsen's TEMK construction: it is simpler,
> doesn't require you to have a hash function available, and has some
> provable security guarantees as well.  But I don't see any reason
> why your scheme couldn't be used, if you prefer it.

Could you please give a reference? Does TEMK gives strictly 
greater strength? Thanks.

M. K. Shen

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

From: Mok-Kong Shen <[EMAIL PROTECTED]>
Subject: Re: Pike stream cipher
Date: Fri, 23 Mar 2001 10:38:16 +0100



Terry Ritter wrote:
> 
[snip]
> Based on this evidence -- as opposed to hearsay, wishes, hopes or
> claims -- we see the MacLaren-Marsaglia mixing process not producing
> significant (e.g., exponential) additional cryptographic strength.

I think that Knuth mentioned that it is difficult to
investigate this shuffling theoretically. On the other
hand, I guess that the effect depends on the materials
that are being shuffled and that its contribution
as a component to a whole system may under circumstances
not merely be 'additive'/'multiplicative'.

M. K. Shen

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

From: "Jakob Jonsson" <[EMAIL PROTECTED]>
Subject: Re: What happens when RSA keys don't use primes?
Date: Thu, 22 Mar 2001 10:05:41 +0100


"Paul Schlyter" <[EMAIL PROTECTED]> skrev i meddelandet
news:99c9vp$cq6$[EMAIL PROTECTED]...
> ...
> So then you just test your RSA key on some data, and if it
> correctly encrypts and decrypts, then you'll know p and q
> are actually primes?

Actually no. There are composites p that will not be caught by such an RSA
test, no matter how many integers you encrypt and decrypt. For example, if p
= 561, q is a prime, and e, d satisfy

e*d == 1 (mod lcm(p-1,q-1))  (lcm = least common multiple)

then x^(e*d) == x (mod pq) for every x. Namely, 561 = 3 * 11 * 17, so

lcm(3-1, 11-1, 17-1, q-1) = lcm(2, 10, 16, q-1) = lcm(80, q-1),

which divides

lcm(561-1, q-1) = lcm(560, q-1).

Background: If n = p_1 * p_2 * ... * p_r (distinct primes), then for all
integers x and k,

x^(kw+1) == x (mod n),

where

w = lcm(p_1 - 1, p_2 - 1, ..., p_r - 1).

Jakob



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

From: Mok-Kong Shen <[EMAIL PROTECTED]>
Subject: Re: cryptography using the method of elliptic curve.
Date: Fri, 23 Mar 2001 10:54:03 +0100



Tom St Denis wrote:
> 
[snip]
> No it's math prof's using sentences like "it's obvious that..." that really
> turn me off.  Yeah I am a "baby" and I have tons to learn, I admit that but
> honestly all too often people write papers assuming they are the target
> audience....

In all natural sciences, each book or journal has its
implicit assumption of the background of readers. (True
also elsewhere. If you step into certain exquisite
boutiques, the saleswomen assume that your bank account
is non-trivial.) You are not obliged to buy or subscribe 
these.

M. K. Shen

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

From: [EMAIL PROTECTED] (Terry Ritter)
Subject: Re: Pike stream cipher
Date: Fri, 23 Mar 2001 10:01:41 GMT


On Fri, 23 Mar 2001 10:38:16 +0100, in
<[EMAIL PROTECTED]>, in sci.crypt Mok-Kong Shen
<[EMAIL PROTECTED]> wrote:

>Terry Ritter wrote:
>> 
>[snip]
>> Based on this evidence -- as opposed to hearsay, wishes, hopes or
>> claims -- we see the MacLaren-Marsaglia mixing process not producing
>> significant (e.g., exponential) additional cryptographic strength.
>
>I think that Knuth mentioned that it is difficult to
>investigate this shuffling theoretically. On the other
>hand, I guess that the effect depends on the materials
>that are being shuffled and that its contribution
>as a component to a whole system may under circumstances
>not merely be 'additive'/'multiplicative'.

Maybe, maybe not.  The referenced literature gives us more evidence
than we have for most cryptographic constructions, and it is not
encouraging.

The whole point to using the MacLaren-Marsaglia construction in this
case is to add strength.  If we must have a strong sequence generator
before that will work, one might think there really is no point in
using that mixing.  A requirement for a strong sequence generator
would not help anyway, because we cannot guarantee such strength.

If we have to know the strength of the generator before we can
understand the contribution of the mixing, we are already out of our
depth.  We generally don't know these values even to orders of
magnitude.  The only time we need the mixing is when the generator
isn't strong, and the evidence we have is precisely about what can
happen in that case.

---
Terry Ritter   [EMAIL PROTECTED]   http://www.io.com/~ritter/
Crypto Glossary   http://www.io.com/~ritter/GLOSSARY.HTM


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

From: "Henrick Hellstr�m" <[EMAIL PROTECTED]>
Subject: SecFTP 0.95.6
Date: Fri, 23 Mar 2001 11:47:50 +0100

Skall fungera med drag-and-drop, samt att uppdatera fj�rrfilen. (L�ter som
en produkt fr�n NNP)

--
Henrick Hellstr�m  [EMAIL PROTECTED]
StreamSec HB  http://www.streamsec.com



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

From: [EMAIL PROTECTED] (j <[EMAIL PROTECTED]>)
Subject: the classified seminal 1940 work of Alan Turing?
Date: 23 Mar 2001 11:13:51 GMT

In Applied Cryptography by B.Schneier it says:
"Unfortunately, most literature on applying information theory to
cryptoanalysis remains classified, including the seminal 1940 work of
Alan Turing."

Who, where, why it is kept classified?
What are those other "most literature"?

Also in Cryptography FAQ (08/10: Technical Miscellany):
< http://www.landfield.com/faqs/cryptography-faq/part08/ >
"
 Unfortunately, most literature on the application of information
 statistics to cryptanalysis remains classified, even the seminal
 1940 work of Alan Turing (see [KOZ84]). For some insight into the
 possibilities, see [KUL68] and [GOO83].
"


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

From: [EMAIL PROTECTED] (Jonathan Thornburg)
Subject: Re: Open Source Implementations of PGP
Date: 23 Mar 2001 12:36:17 +0100

In article <[EMAIL PROTECTED]>,
Peter Harrison <[EMAIL PROTECTED]> wrote:
>I am looking for people interested in writing or adapting open source
>implementations of PGP in
>- Delphi
>- C
>- Java

GNU Privacy Guard may already provide (some or all of) what you want:
   http://www.gnupg.org

>From that web page:
| Overview 
| 
| GnuPG is a complete and free replacement for PGP. Because it does
| not use the patented IDEA algorithm, it can be used without any
| restrictions. GnuPG is a RFC2440 (OpenPGP) compliant application.
| 
| The German Federal Ministry of Economics and Technology granted funds
| for the further development of GnuPG. See our press notice for details.

-- 
-- Jonathan Thornburg <[EMAIL PROTECTED]>
   http://www.thp.univie.ac.at/~jthorn/home.html
   Universitaet Wien (Vienna, Austria) / Institut fuer Theoretische Physik
   Q: Only 6 countries have the death penalty for children.  Which are they?
   A: Congo, Iran, Nigeria, (Pakistan[*]), Saudi Arabia, United States, Yemen
      [*] Pakistan reportedly ended it in July 2000. -- Amnesty International
                         http://www.web.amnesty.org/ai.nsf/index/AMR511392000 

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

From: Arturo <aquiranNO$[EMAIL PROTECTED]>
Subject: Re: SecFTP 0.95.6
Date: Fri, 23 Mar 2001 12:10:09 +0100

On Fri, 23 Mar 2001 11:47:50 +0100, "Henrick Hellstr�m" <[EMAIL PROTECTED]>
wrote:

>Skall fungera med drag-and-drop, samt att uppdatera fj�rrfilen. (L�ter som
>en produkt fr�n NNP)

        Unencrypted, please :-)

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

From: Jim Farrand <[EMAIL PROTECTED]>
Subject: Re: Self Enforcing Protocol (Slightly OT and Long!)
Date: Fri, 23 Mar 2001 12:03:27 GMT

John Joseph Trammell wrote:

> [protocol snipped for brevity]
> I like it.  Have you done any research on other SEPs in this genre?
> Maybe you (and I) are reinventing the wheel.

I'm not that sure where to look.  I did a search of the web but I didn't
get anything more interesting than definitions of SEPs.  

> One problem with this is that it would allow A to possibly mess with
> the contents of his library at this point. 

<Nod>

> A way around this is to
> work the "selection" like this:

[...snip...]

> Looks to me like this hides the values of H well enough to keep
> B from "recognizing" anything that was once played, then put back
> into the library.

Indeed it does.  The value of R' would have to be change each time a
card is selected (not that this is a problem).  Otherwise, if B knows
all H(i) and R', and the a L(i) associated with a particular H(i), he
can spot that card.

> Next question: what about the case of n players, n > 2?  What about
> when multiple players "gang up" on another?  Is there a way to keep
> this a SEP?  I think so.  :-)

Mmmm.  Okay...

When A draws a card, we need to involve B and C independently in the
choosing process.

So, when A selects a card:

1. A calculates H1(i)=hash(L(i) ++ R(i)) for all i.
2. B chooses a random number R'.
3. B calculates H2(i)=hash(H1(i) ++ R') for all i.
4. C chooses a H2(i).
5. B reveals R'.  A and C can verify H2(i) for all i.
6. (When the card is revealed) A reveals the appropriate L(i) and
R1(i).  A and C can now verify H1(i).

I *think* this works.  :)  If so that's pretty cool, IMHO.  :)

B and C can't cheat because however they collude they are still choosing
blindly.  A and B can't cheat because 1) they can't influence the choice
made by C and 2) C can verify that the choice he made matches the card
played.  A and C can't cheat by a symmetrical argument.

Actually.. B also needs to randomize the order in which the H2(i)'s are
presented.  Otherwise A and C can cheat - A could tell C to choose the
nth H2(i), which would correspond to the nth H1(i) which correspond to
the card A wants.

This all scales for more than 3 players by creating a chain of players,
each one computing a new hash except the last who chooses.

Any further comment appreciated.  :)

Thanks for your help!

Jim

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


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