Cryptography-Digest Digest #978, Volume #12      Sun, 22 Oct 00 14:13:01 EDT

Contents:
  Re: Help ,Does anybody know ??? (SCOTT19U.ZIP_GUY)
  Re: A new paper claiming P=NP (Eric Cordian)
  Re: ---- As I study Rinjdael... (SCOTT19U.ZIP_GUY)
  Re: ---- As I study Rinjdael... (John Savard)
  Re: ---- As I study Rinjdael... (John Savard)
  Re: Huffman stream cipher. (Richard Heathfield)
  Re: Rijndael implementations (Tim Tyler)
  Re: ---- As I study Rinjdael... (John Savard)
  Re: Rijndael implementations (Tim Tyler)
  Re: Huffman stream cipher. (SCOTT19U.ZIP_GUY)
  Re: Rijndael implementations (Tim Tyler)

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

From: [EMAIL PROTECTED] (SCOTT19U.ZIP_GUY)
Subject: Re: Help ,Does anybody know ???
Date: 22 Oct 2000 17:10:11 GMT

[EMAIL PROTECTED] wrote in <8suute$2m7$[EMAIL PROTECTED]>:

>Does anybody know where i can find the program or " C " component
>
>about use the RSA to encrypt the "file" directly.
>
> Please help me ,thanks so much.
>
>
>Sent via Deja.com http://www.deja.com/
>Before you buy.

  It is not that hard to code your self. But it
is not considered a strong method of encryption. It
has lots of weaknesses. The main use of it is for
key exchanges in public key cipher. But one would not
in gerneral try not to do file encryption with it.

David A. Scott
-- 
SCOTT19U.ZIP NOW AVAILABLE WORLD WIDE
        http://www.jim.com/jamesd/Kong/scott19u.zip
Scott famous encryption website **now all allowed**
        http://members.xoom.com/ecil/index.htm
Scott LATEST UPDATED source for scott*u.zip
        http://radiusnet.net/crypto/  then look for
  sub directory scott after pressing CRYPTO
Scott famous Compression Page
        http://members.xoom.com/ecil/compress.htm
**NOTE EMAIL address is for SPAMERS***
I leave you with this final thought from President Bill Clinton:

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

From: Eric Cordian <[EMAIL PROTECTED]>
Subject: Re: A new paper claiming P=NP
Crossposted-To: comp.theory,sci.math,sci.op-research
Date: Sun, 22 Oct 2000 17:19:01 GMT

In comp.theory Douglas A. Gwyn <[EMAIL PROTECTED]> wrote:

> Eric Cordian wrote:

>> However, if it does contain a working algorithm for solving an
>> NP-Complete problem in polynomial time, I would rather have it now,
>> as opposed to two years from now.

> Are you too young to remember the "cold fusion" fiasco?
> If so, there are books that describe it, which might help
> you understand why such an attitude is dangerous.

I am a great believer in end-user filtering.  I wish I had been able to
review Plotnikov's algorithm in 1992, when he first thought of it.

Cold Fusion was a fiasco because the PR department at the University of
Utah acted like the National Enquirer.  The same guy sold Cold Fusion to
the public that sold the plastic stroke-producing heart attached to the
300 lb console to Barney Clark.

Once people were expecting a practical battery-sized device that powered
their whole house to be engineered instantly, anything else was a great
disappointment, and the Pons and Fleischmann weenie roast was the natural
consequence.

There is quite a bit of evidence to suggest that nuclear reactions can
sometimes occur in the solid state, and Cold Fusion, now renamed
"Low-Energy Nuclear Reactions," continues to be an area of research.

-- 
Eric Michael Cordian 0+
O:.T:.O:. Mathematical Munitions Division
"Do What Thou Wilt Shall Be The Whole Of The Law"

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

From: [EMAIL PROTECTED] (SCOTT19U.ZIP_GUY)
Subject: Re: ---- As I study Rinjdael...
Date: 22 Oct 2000 17:16:21 GMT

[EMAIL PROTECTED] (Mok-Kong Shen) wrote in <39F31EFA.3C0A6996@t-
online.de>:

>
>
>Greggy wrote:
>> 
>> As I study Rijndael, I am constantly haunted by the question I hope
>> someone can answer:
>> 
>> If Rijndael is so strong, why does the US government choose NOT to use
>> it for ANY (not all) classified information?
>
>I am not aware that the US government 'chooses' not to use
>Rijndael for any classified information. Why should it tell
>you what it uses to encrypt classified information? By
>definition, classified information doesn't concern you
>as normal citizen at all. (You are not supposed to care 
>about it.)
>
>M. K. Shen

  Actually every concerned citizen should care about what
the government ecnrypts otherwise we will go down the same
path as the soviets. The amount and type of information the
government tries to hide should be closely watched unless one
wants to be taken care of cradle to grave with little contorl
over ones life. The govenment assumes it knows more than
every one else so they use internal methods that have an additional
security feature of the algorithms being kept secret. Rijndael
fails since the method is not secret. I also suspect it may fail
since there is a gook chance the NSA can already break it. Unless
one uses a chaining mod like "wrapped PCBC" and those kind of
modes will not be approved for use.


David A. Scott
-- 
SCOTT19U.ZIP NOW AVAILABLE WORLD WIDE
        http://www.jim.com/jamesd/Kong/scott19u.zip
Scott famous encryption website **now all allowed**
        http://members.xoom.com/ecil/index.htm
Scott LATEST UPDATED source for scott*u.zip
        http://radiusnet.net/crypto/  then look for
  sub directory scott after pressing CRYPTO
Scott famous Compression Page
        http://members.xoom.com/ecil/compress.htm
**NOTE EMAIL address is for SPAMERS***
I leave you with this final thought from President Bill Clinton:

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

From: [EMAIL PROTECTED] (John Savard)
Subject: Re: ---- As I study Rinjdael...
Date: Sun, 22 Oct 2000 17:23:24 GMT

On Thu, 19 Oct 2000 17:20:52 -0700, Eric Lee Green <[EMAIL PROTECTED]>
wrote, in part:
>[EMAIL PROTECTED] wrote:

>> That narrows the choice to a) use Rijndael, and provide advesaries
>> with complete documentation of the algorithm, and test vectors. Or b)
>> use an equally strong system and make advesaries guess the algorithm.

>Or c), say nothing, and make adversaries guess as to what algorithm they're
>using. Could you tell, just by looking at a file, whether it was encrypted via
>Rijndael, 3DES, IDEA, or NSA256?

But if adversaries happen to have a Rijndael cracker (and an IDEA
cracker, and a 3-DES cracker) handy, why make it easy? With an
in-house designed algorithm from the ground up, the chance of a lucky
guess is much smaller.

John Savard
http://home.ecn.ab.ca/~jsavard/crypto.htm

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

From: [EMAIL PROTECTED] (John Savard)
Subject: Re: ---- As I study Rinjdael...
Date: Sun, 22 Oct 2000 17:21:12 GMT

On Thu, 19 Oct 2000 00:05:14 GMT, Greggy <[EMAIL PROTECTED]>
wrote, in part:

>IBM today
>announced the immediate availability of its MARS encryption algorithm
>under a royalty-free license, worldwide from Tivoli Systems Inc.

Except for that announcement, however, the license conditions don't
seem to be visible anywhere on the provided Tivoli web site; perhaps
there isn't a written "license" any more than there was for DES, but
that is unclear.

John Savard
http://home.ecn.ab.ca/~jsavard/crypto.htm

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

Date: Sun, 22 Oct 2000 18:37:54 +0100
From: Richard Heathfield <[EMAIL PROTECTED]>
Subject: Re: Huffman stream cipher.

"SCOTT19U.ZIP_GUY" wrote:
> 
> [EMAIL PROTECTED] (Richard Heathfield) wrote in
> <[EMAIL PROTECTED]>:
> 
> >"SCOTT19U.ZIP_GUY" wrote:
> >>
> >> [EMAIL PROTECTED] (Benjamin Goldberg) wrote in
> >> <[EMAIL PROTECTED]>:
> >>
> >> >SCOTT19U.ZIP_GUY wrote:
> >> >[snip]
> >> >>   As for the fact a stream is not a file in one sense of the word
> >> >> you seemed to use it in other senses like in the case in adding
> >> >> an integer to a stream. In reading that problem I took it as a file
> >> >> and you did not object. Also I give you an example for that other
> >> >> thread. WHere you capaple of following it or what?
> >> >
> >> >I have not, and do not plan to, look at your DSC program.  If you can
> >> >explain the algorithm in clear english, I would be happy, but I am not
> >> >going to look at your shitty source code.
> >>
> >>   You sound like the kind of Jerk that is never happy so why
> >> pretend that if I did a little more FREE work for your lazy
> >> ass that you would be happy. I can see by your comment you
> >> obviously lacked the ability to even follow the simple example I
> >> did for you.
> >>
> >> ... rest of his nonsense dropped.
> >
> >I had a quick look at your source code. He's right. It's hard to read,
> >it's non-portable (I'd guess it's for DJGPP, but that's just a guess)
> >and in at least one place it's incorrect. I couldn't look at it for long
> >because it was so tiring.
> >
> 
>   Thats rude of you. Are you another one of Toms's idenites.

Wise up, brainless. If you'd tried a Deja search before making such an
asinine observation, you'd know that the likelihood of Tom St Denis and
I being the same person is zero minus. For one thing, I can regularly
type two words together without a letter transposition (sorry, Tom, if
you're reading...).

> If you found a mistake at least be honest and say what it is
> so we can tell if your full of shit or not.

Now who's being rude? If you want a flame war, I think it should be
taken to email so that other people aren't exposed to your obscene
language.

But as for the mistakes, please notice that I said:

"I had a quick look at your source code. He's right. It's hard to read,
it's non-portable (I'd guess it's for DJGPP, but that's just a guess)
and in at least one place it's incorrect. I couldn't look at it for long
because it was so tiring."

The "at least one place" is:

void
main()
{

In C, main returns int, and any other return type invokes undefined
behaviour.

> Just becasue you
> don't like the form tough shit.

In my opinion, it's hard to read. If you want people to help you out by
cryptanalysing your algorithms, it makes sense to help them out by
making the code easy to read. If you can't be bothered to take the
trouble to do that, you shouldn't be surprised if people don't bother to
analyse your algorithms.

> Many people say there are mistakes
> but most are wrong.

I can provide a citation from the C Standard if need be, which shows
that main returns int.

> LIke I am not god but you contrubute nothing
> by prestending you found something in the code.

I don't pretend. I don't need to. Your program is broken, not for any
cryptographic reason (I didn't have to look that far and I lack the
expertise to do so anyway, because I'm not an expert cryptographer and
don't pretend to be) but because it breaks the rules of the language.

> Even h2com.exe
> had a few sneaky mistakes that people found after years of use
> with no failings.

Furthermore, your program is non-portable. Here's what my compiler had
to say about it:

Borland C++ 5.3 for Win32 Copyright (c) 1993, 1998 Borland International
SCOTT19U.C:
Error SCOTT19U.C 4: Unable to open include file 'unistd.h'
Error SCOTT19U.C 5: Unable to open include file 'pc.h'
Error SCOTT19U.C 6: Unable to open include file 'keys.h'
Error dstypes.h 2: Too many types in declaration
Error bit19.h 15: Declaration missing ;
Error bit19.h 16: Declaration missing ;
Error bit19.h 17: Declaration missing ;
Error bit19.h 18: Declaration missing ;
Error bit19.h 19: Declaration missing ;
Error bit19.h 20: Declaration missing ;
Error bit19.h 21: Declaration missing ;
Error bit19.h 22: Declaration missing ;
Error bit19.h 23: Declaration missing ;
Error bit19.h 24: Declaration missing ;
Error bit19.h 25: Declaration missing ;
Error bit19.h 26: Declaration missing ;
Error bit19.h 27: Declaration missing ;
Error bit19.h 28: Declaration missing ;
Error bit19.h 29: Declaration missing ;
Error bit19.h 30: Declaration missing ;
Error bit19.h 31: Declaration missing ;
Error bit19.h 32: Declaration missing ;
Error bit19.h 33: Declaration missing ;
Error bit19.h 34: Declaration missing ;
Error bit19.h 35: Declaration missing ;
Error bit19.h 35: Too many error or warning messages
*** 26 errors in Compile ***

So much for "years of use with no failings"! Now either go wash your
mouth out and then apologise, or join yet another killfile (for I
suspect that you are already killfiled by most right-thinking people).


-- 
Richard Heathfield
"Usenet is a strange place." - Dennis M Ritchie, 29 July 1999.
C FAQ: http://www.eskimo.com/~scs/C-faq/top.html
66 K&R Answers: http://users.powernet.co.uk/eton/kandr2/index.html (31
to go)

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

From: Tim Tyler <[EMAIL PROTECTED]>
Subject: Re: Rijndael implementations
Reply-To: [EMAIL PROTECTED]
Date: Sun, 22 Oct 2000 17:34:59 GMT

Douglas A. Gwyn <[EMAIL PROTECTED]> wrote:

: Why aren't you agitating for "word" to denote some standardized
: size such as 32 bits?

"Word" has much less strong connotations of 32 bits than byte has of 8
bits.  Nor is information commonly measured in words - there is no
KiloWord - or MegaWord.

There are other differences as well.  I do think a fixed size 32-bit unit
is a desirable thing to have a term for.  I would rather strongarm "int"
into this service than "word" (although "int" comes with baggage of its
own).  Perhaps there's an existing technical term for 32-bit units.

: Is it because you have experience of other word sizes (but apparently
: not of other byte sizes)?

Differing word sizes are more widespread than differing byte sizes.
This is a factor in the strength with which "word" denotes 32-bit units -
and is certainly a factor.

:> This is what I think should happen to definitions of bytes - ones
:> that vary in size depending on location should be discarded as
:> being of low utility when attempting to communicate with others.

: That's why those of us who know better are careful about the
: terms we use.

Well, I think the current situation is a mess.  If given a blank slate,
I'd have "byte" nailed down to meaning "8 bits" - and some more obscure
technical term meaning "the volume of information used to represent a
character".

:> If you want a term that denotes "small chunk of information, of
:> architecture dependent size", then you're welcome to it - but I
:> don't see that the need for such a term justifies polluting a
:> common information storage metric with architecture-dependent
:> considerations.

: You're misusing "architecture-dependent" here, but the important
: point is that one could just as well complain than you want to
: "pollute" a long-established term that denotes sub-word contiguous
: bit field by burdening it with additional constraints.

The motiviation for my view is clear enough.  As it stands byte means
"sub-word bitfield" - but it /also/ means "8 bits" - as in Kbyte and
Mbyte. This is confusing, and needlessly so.
-- 
__________  Lotus Artificial Life  http://alife.co.uk/  [EMAIL PROTECTED]
 |im |yler  The Mandala Centre   http://mandala.co.uk/  Florist: Petal pusher.

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

From: [EMAIL PROTECTED] (John Savard)
Subject: Re: ---- As I study Rinjdael...
Date: Sun, 22 Oct 2000 17:39:46 GMT

On 17 Oct 2000 17:33:19 -0700, Paul Rubin <[EMAIL PROTECTED]>
wrote, in part:
>Greggy <[EMAIL PROTECTED]> writes:

>> If Rijndael is so strong, why does the US government choose NOT to use
>> it for ANY (not all) classified information?

>What makes you think they don't?  I don't think they'd tell you if they did.

True.

But why *would* they? They have so many talented and experienced
cryptographers available, and having a secret algorithm is in itself
an advantage, even if for most people it has disadvantages that far
outweigh that advantage.

Actually, Rijndael is likely stronger than SKIPJACK, and it has been
publicly noted that SKIPJACK was considered adequate for SECRET but
not TOP SECRET information several years ago. So there is some data on
whether or not it is "good enough".

Also, from various comments appearing in this newsgroup and other
things that have appeared in print, because Rijndael is "key agile" -
it's key schedule runs as quickly, or more quickly, than encipherment
- one could, using Rijndael, throw together something that may even
possibly vaguely resemble some techniques actually used on classified
information, and which is likely to be comparable in security.

1) Generate 256 bits of true random information. Use this as the first
256 bits of your ciphertext.

2) For each 128 bits of your plaintext, do the following:

- encipher the preceding 256 bits of ciphertext using Rijndael with a
256-bit block size, and with the actual message key.

- using the 256-bit result of that encipherment as the key, and a
128-bit block size, encipher your 128-bit plaintext block.

- the result of this encryption is the next 128 bits of your
ciphertext.

Used _that_ way, I don't think there is too much problem with Rijndael
being "good enough" for _any_ purpose. I would be inclined, though, to
use a 352-bit key for the 256-bit encipherment, and then use only 224
bits of the result to encipher the 128-bit plaintext, discarding the
rest (since even using 160 bits would be adequate for security, given
that the key for that part changes with every block).

John Savard
http://home.ecn.ab.ca/~jsavard/crypto.htm

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

From: Tim Tyler <[EMAIL PROTECTED]>
Subject: Re: Rijndael implementations
Reply-To: [EMAIL PROTECTED]
Date: Sun, 22 Oct 2000 17:42:45 GMT

Douglas A. Gwyn <[EMAIL PROTECTED]> wrote:
: Tim Tyler wrote:
:> Richard Heathfield <[EMAIL PROTECTED]> wrote:

[C porting issues]

:> I believe the original issue about the byte was a terminological one
:> - a question of which term should refer to what.
:> No volume of terminology or naming of names will help with porting C
:> programs ...

: Understanding the terminology may well be *essential* to writing
: portable C code.  If you are one of the many who assume that C
: "char" type has to be represented with exactly 8 bits because
: you don't understand the meaning of the correspondence (imposed
: by the C standard) between "char" and "byte", then you provide
: an example of how portability problems can arise from not
: understanding the terminology.

I believe the issue under discussion is what terminology is desirable -
not whether people understand the existing terms.

Personally I think the existing terminology mixes two separate ideas
(unit that represents a character and "8 bit unit") together - and
is thus the source of confusion.

Clear terminology might help somewhat in understanding porting issues,
but it is not a magic bullet that makes issues involving the way Cs
primitive types are different sizes on different architectures vanish
overnight.
-- 
__________                  http://alife.co.uk/  http://mandala.co.uk/
 |im |yler  [EMAIL PROTECTED]  http://hex.org.uk/   http://atoms.org.uk/

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

From: [EMAIL PROTECTED] (SCOTT19U.ZIP_GUY)
Subject: Re: Huffman stream cipher.
Date: 22 Oct 2000 17:52:38 GMT

[EMAIL PROTECTED] (Richard Heathfield) wrote in
<[EMAIL PROTECTED]>: 

>"SCOTT19U.ZIP_GUY" wrote:
>> 
>> [EMAIL PROTECTED] (Richard Heathfield) wrote in
>> <[EMAIL PROTECTED]>:
>> 
>> >"SCOTT19U.ZIP_GUY" wrote:
>> >>
>> >> [EMAIL PROTECTED] (Benjamin Goldberg) wrote in
>> >> <[EMAIL PROTECTED]>:
>> >>
>> >> >SCOTT19U.ZIP_GUY wrote:
>> >> >[snip]
>> >> >>   As for the fact a stream is not a file in one sense of the
>> >> >>   word 
>> >> >> you seemed to use it in other senses like in the case in adding
>> >> >> an integer to a stream. In reading that problem I took it as a
>> >> >> file and you did not object. Also I give you an example for that
>> >> >> other thread. WHere you capaple of following it or what?
>> >> >
>> >> >I have not, and do not plan to, look at your DSC program.  If you
>> >> >can explain the algorithm in clear english, I would be happy, but
>> >> >I am not going to look at your shitty source code.
>> >>
>> >>   You sound like the kind of Jerk that is never happy so why
>> >> pretend that if I did a little more FREE work for your lazy
>> >> ass that you would be happy. I can see by your comment you
>> >> obviously lacked the ability to even follow the simple example I
>> >> did for you.
>> >>
>> >> ... rest of his nonsense dropped.
>> >
>> >I had a quick look at your source code. He's right. It's hard to
>> >read, it's non-portable (I'd guess it's for DJGPP, but that's just a
>> >guess) and in at least one place it's incorrect. I couldn't look at
>> >it for long because it was so tiring.
>> >
>> 
>>   Thats rude of you. Are you another one of Toms's idenites.
>
>Wise up, brainless. If you'd tried a Deja search before making such an
>asinine observation, you'd know that the likelihood of Tom St Denis and
>I being the same person is zero minus. For one thing, I can regularly
>type two words together without a letter transposition (sorry, Tom, if
>you're reading...).
>
>> If you found a mistake at least be honest and say what it is
>> so we can tell if your full of shit or not.
>
>Now who's being rude? If you want a flame war, I think it should be
>taken to email so that other people aren't exposed to your obscene
>language.
>
>But as for the mistakes, please notice that I said:
>
>"I had a quick look at your source code. He's right. It's hard to read,
>it's non-portable (I'd guess it's for DJGPP, but that's just a guess)
>and in at least one place it's incorrect. I couldn't look at it for long
>because it was so tiring."
>
>The "at least one place" is:
>
>void
>main()
>{
>

    I state that is written for DJGPP. If you have other compilers
you may have to change it. But the above is not an error it complies
and runs under DGJPP C.


>Furthermore, your program is non-portable. Here's what my compiler had
>to say about it:
>
>Borland C++ 5.3 for Win32 Copyright (c) 1993, 1998 Borland International
>SCOTT19U.C:
>Error SCOTT19U.C 4: Unable to open include file 'unistd.h'
>Error SCOTT19U.C 5: Unable to open include file 'pc.h'
>Error SCOTT19U.C 6: Unable to open include file 'keys.h'
>Error dstypes.h 2: Too many types in declaration
>Error bit19.h 15: Declaration missing ;
>Error bit19.h 16: Declaration missing ;
>Error bit19.h 17: Declaration missing ;
>Error bit19.h 18: Declaration missing ;
>Error bit19.h 19: Declaration missing ;
>Error bit19.h 20: Declaration missing ;
>Error bit19.h 21: Declaration missing ;
>Error bit19.h 22: Declaration missing ;
>Error bit19.h 23: Declaration missing ;
>Error bit19.h 24: Declaration missing ;
>Error bit19.h 25: Declaration missing ;
>Error bit19.h 26: Declaration missing ;
>Error bit19.h 27: Declaration missing ;
>Error bit19.h 28: Declaration missing ;
>Error bit19.h 29: Declaration missing ;
>Error bit19.h 30: Declaration missing ;
>Error bit19.h 31: Declaration missing ;
>Error bit19.h 32: Declaration missing ;
>Error bit19.h 33: Declaration missing ;
>Error bit19.h 34: Declaration missing ;
>Error bit19.h 35: Declaration missing ;
>Error bit19.h 35: Too many error or warning messages
>*** 26 errors in Compile ***


   I can't help it if you use a poor compiler and don't
have the smarts to make it fit the tools you have. I write
for C in DGJPP. If you can't figure out how to mode it to
work with your complier thats to bad. ALso in case you
lack the brains to figure it out. THe code is targeted for
a PC so if you have a MAC to bad.

David A. Scott
-- 
SCOTT19U.ZIP NOW AVAILABLE WORLD WIDE
        http://www.jim.com/jamesd/Kong/scott19u.zip
Scott famous encryption website **now all allowed**
        http://members.xoom.com/ecil/index.htm
Scott LATEST UPDATED source for scott*u.zip
        http://radiusnet.net/crypto/  then look for
  sub directory scott after pressing CRYPTO
Scott famous Compression Page
        http://members.xoom.com/ecil/compress.htm
**NOTE EMAIL address is for SPAMERS***
I leave you with this final thought from President Bill Clinton:

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

From: Tim Tyler <[EMAIL PROTECTED]>
Subject: Re: Rijndael implementations
Reply-To: [EMAIL PROTECTED]
Date: Sun, 22 Oct 2000 17:51:18 GMT

Douglas A. Gwyn <[EMAIL PROTECTED]> wrote:
: Tim Tyler wrote:

:> C is trying to accomodate hardware variations too much.

: Not in the opinion of the people entrusted with developing
: the C standard.

Really?  I presume they're doing the best they can with a voluminous
legacy codebase.  They can't easily redefine the size of fundamental
types overnight.

If they think that using different sized primitive types on different
architectures is a /good/ thing, then they probably need their heads
examining - this has caused no end of headaches for developers all
over the planet.

If this is their view, practically no other modern language designers
agree with them - everyone else goes for portability.

C is a well out of date language for most practical purposes these days.
Writing code in C has too much in common with programming in assembler.
Programming in assembler used to be commonplace - but now is a relatively
specialised activity - and so I expect it will be with C.
-- 
__________  Lotus Artificial Life  http://alife.co.uk/  [EMAIL PROTECTED]
 |im |yler  The Mandala Centre   http://mandala.co.uk/  Surf against sewage.

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


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