Cryptography-Digest Digest #817, Volume #9 Thu, 1 Jul 99 17:13:03 EDT
Contents:
Re: Secure link over Inet if ISP is compromized. (Patrick Juola)
Re: Windows PWL Files (JPeschel)
Re: Secure link over Inet if ISP is compromized. ("Else")
Re: Windows PWL Files ([EMAIL PROTECTED])
Reference Implementation of Quadibloc S
Re: Quantum Computers (Greg Ofiesh)
Re: Quantum Computers (Mok-Kong Shen)
Re: Quantum Computers (Greg Ofiesh)
Re: The One-Time Pad Paradox ("Robert C. Paulsen, Jr.")
Re: Quantum Computers (Greg Ofiesh)
Re: Quantum Computers (Greg Ofiesh)
Re: Quantum Computers (Patrick Juola)
Re: Quantum Computers (Patrick Juola)
Re: The One-Time Pad Paradox (Patrick Juola)
Re: The One-Time Pad Paradox ("Robert C. Paulsen, Jr.")
Re: The One-Time Pad Paradox ("Robert C. Paulsen, Jr.")
Re: The One-Time Pad Paradox (Patrick Juola)
Re: Quantum Computers (Patrick Juola)
Re: Quantum Computers ([EMAIL PROTECTED])
Re: Infinity: was Quantum Computers ("Tony T. Warnock")
----------------------------------------------------------------------------
From: [EMAIL PROTECTED] (Patrick Juola)
Subject: Re: Secure link over Inet if ISP is compromized.
Date: 1 Jul 1999 15:01:35 -0400
In article <7lgcjq$g5r$[EMAIL PROTECTED]>, Else <[EMAIL PROTECTED]> wrote:
>
>Patrick Juola wrote in message <7lfspi$mij$[EMAIL PROTECTED]>...
>>In article <7lfi2r$38f$[EMAIL PROTECTED]>,
>>Gene Sokolov <[EMAIL PROTECTED]> wrote:
>>> What do you think is the fraction of the Net users who exchange keys
>>>"out of band", i.e. not through their ISPs?
>>
>>My PGP public key is available through a half-dozen different sources,
>>including one in print (Proc. NeMLaP-2); if the FBI decides to tamper
>
>What do you think is the fraction of people who do likewise?
Anyone who signs up with the MIT key database, for one.
Anyone who *has* ever exchanged a key with someone prior to
the discussion at hand.
Anyone who makes backups of their system(s).
-kitten
------------------------------
From: [EMAIL PROTECTED] (JPeschel)
Subject: Re: Windows PWL Files
Date: 01 Jul 1999 19:06:41 GMT
>"Andrew Whalan" <[EMAIL PROTECTED]> writes:
>Anyone know about the method used to generate PWL files, thus, the method
>that could be used to crack PWL files.
Peter Gutmann did some work on this. I believe it was someone else, however,
who wrote the PWL cracking code called "Glide," which you'll find on my site.
Joe
__________________________________________
Joe Peschel
D.O.E. SysWorks
http://members.aol.com/jpeschel/index.htm
__________________________________________
------------------------------
From: "Else" <[EMAIL PROTECTED]>
Subject: Re: Secure link over Inet if ISP is compromized.
Date: Thu, 1 Jul 1999 22:55:56 +0400
Patrick Juola wrote in message <7lfspi$mij$[EMAIL PROTECTED]>...
>In article <7lfi2r$38f$[EMAIL PROTECTED]>,
>Gene Sokolov <[EMAIL PROTECTED]> wrote:
>> What do you think is the fraction of the Net users who exchange keys
>>"out of band", i.e. not through their ISPs?
>
>My PGP public key is available through a half-dozen different sources,
>including one in print (Proc. NeMLaP-2); if the FBI decides to tamper
What do you think is the fraction of people who do likewise?
------------------------------
From: [EMAIL PROTECTED]
Subject: Re: Windows PWL Files
Date: Thu, 01 Jul 1999 18:25:52 GMT
In article <7lfral$9ij$[EMAIL PROTECTED]>,
"Andrew Whalan" <[EMAIL PROTECTED]> wrote:
> Oh, this might target my required audience.
>
> Anyone know about the method used to generate PWL files, thus, the
method
> that could be used to crack PWL files.
They proably use their MD4 hash code (which goes with their RC4 code)
to hash the password.
If you want to cheat a passwd protected screen saver just delete
the .PWL files...
Tom
--
PGP key is at:
'http://mypage.goplay.com/tomstdenis/key.pgp'.
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------------------------------
From: [EMAIL PROTECTED] ()
Subject: Reference Implementation of Quadibloc S
Date: 1 Jul 99 19:15:02 GMT
There is a post with this title in alt.sources.crypto, containing a BASIC
program. It is for generating test vectors.
Quadibloc S is a block cipher with a 64-bit block, very similar to the
original QUADIBLOC. The program illustrates the version with four rounds.
The intent of this is to provide a cipher "weak" enough to be subjected to
cryptanalysis.
My web page will include a description of Quadibloc S tomorrow afternoon.
Quadibloc S differs from QUADIBLOC in its original form in two important
respects.
The f-function includes a final key-dependent S-box, after the manner in
which S8 is used in the f-function of Quadibloc II.
The key schedule involves subjecting the key (with a byte equal to the
inverse of the XOR sum of the key added, so the key can't be zero) to
chain addition, and then using a buffer to scramble the order of the chain
addition output (in a degenerate form of the MacLaren-Marsaglia generator,
as alternating bytes from the same chain addition generator are placed in
the buffer and are used as pointers to the buffer).
The algorithm for generating a permutation is much simpler than the one
used in Quadibloc II as well.
Incidentally, today is the national holiday of Canada, now known as
"Canada Day".
John Savard
------------------------------
From: Greg Ofiesh <[EMAIL PROTECTED]>
Subject: Re: Quantum Computers
Date: Thu, 01 Jul 1999 19:29:24 GMT
In article <[EMAIL PROTECTED]>,
[EMAIL PROTECTED] wrote:
> Greg Ofiesh <[EMAIL PROTECTED]> wrote:
>
> > Let us begin with the following assertion that I think you will all
> > agree with. If a quantum computer exists, then the only form of
> > encryption that cannot be broken by it, or at least has half a
chance
> > to survive an attack, is OTP.
>
> I won't.
>
> Quantum Computers are not some magical devices that can do anything.
There
> are some problems that *can* be made much more tractable on them (for
> example, factoring which can be used to crack RSA). There are problems
> which cannot be handled.
>
> I don't know (enough) of Quantum computation to give or be able to
prove
> that certain problems are not made easy using a QC ... but what would
make
> you think that, for example the symmetric ciphers, would be
approachable
> using one?
>
in a word: parallelism.
to be more specific - extremely massive parallelism.
to be even more specific, and even I have trouble with this, you don't
necessarily attack the key space, but the algorithm. I keep hearing
that and yet I can't conceive of it either.
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------------------------------
From: Mok-Kong Shen <[EMAIL PROTECTED]>
Subject: Re: Quantum Computers
Date: Thu, 01 Jul 1999 20:46:18 +0200
Douglas A. Gwyn wrote:
>
> One does need to keep in mind that the normal laws of
> arithmetic need to be modified for infinities, and in
> particular, infinity/infinity is indefinite, not 1.
> The floating-point implementations are responsible for getting
> such details right.
I tend to think that the application of infinity is to cater for cases
such as where something is divided by sin(x) where x becomes 0 due
to rounding errors which could in turn be due to using some
bad parameters in the algorithm or other causes in input values.
Cases where some values become exactly 0 should appropriately
be considered as such, since they very often have special meanings
associated with them. Lumping that together with the normal
case simply because the availability of 'infinity' allows one to do
that so that codes can be shorter is something I personally wouldn't
recommend to others who program.
M. K. Shen
------------------------------
From: Greg Ofiesh <[EMAIL PROTECTED]>
Subject: Re: Quantum Computers
Date: Thu, 01 Jul 1999 19:50:05 GMT
> Again, you're not looking for information; you're looking for sock
> puppets to confirm your prejudices.
Well, you can make that claim, but don't forget that I have yet to have
one person point me to a document that "proves" I am wrong. I have had
someone suggest that I look at the QC literature. Where is it? Who
has it? What on earth is he talking about?
And who has been studying QCs on this forum? I read a lot of people's
opinions going back and forth (and it is fun to read the responses,
don't get me wrong), but I have no clue who has what background or
expertise, or who has done ANY in depth studying in this field like my
brother has.
So give me a break. And give me the facts. That's all I ask. Give me
the facts that counter my brother and I will throw them back into his
face. Arm me! I want to counter my brother! PLEASE! (If you can.)
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------------------------------
From: "Robert C. Paulsen, Jr." <[EMAIL PROTECTED]>
Subject: Re: The One-Time Pad Paradox
Date: Thu, 01 Jul 1999 14:49:22 -0500
Patrick Juola wrote:
> >
> >Can we say that scenario two didn't reveal the secret?
>
> Yes. Because it didn't happen.
>
Not much to discuss if you won't grant me my hypothetical.
--
____________________________________________________________________
Robert Paulsen http://paulsen.home.texas.net
If my return address contains "ZAP." please remove it. Sorry for the
inconvenience but the unsolicited email is getting out of control.
------------------------------
From: Greg Ofiesh <[EMAIL PROTECTED]>
Subject: Re: Quantum Computers
Date: Thu, 01 Jul 1999 19:40:40 GMT
In article <[EMAIL PROTECTED]>,
"Douglas A. Gwyn" <[EMAIL PROTECTED]> wrote:
> Greg Ofiesh wrote:
> > Let us begin with the following assertion that I think you will all
> > agree with. If a quantum computer exists, then the only form of
> > encryption that cannot be broken by it, or at least has half a
> > chance to survive an attack, is OTP. All other forms of encryption
> > are deterministic in nature and are not "cracked" but simply
> > "translated" (to convey the ease with which cryptanalysis is
> > performed) by a quantum computer.
>
> No, only certain types of algorithm are candidates for quantum
> computing. You might as well have said that parallel processing
> would magically crack every non-OTP cryptosystem, but of course
> it didn't.
>
> > Now let me make my assertion - The US government, most likely the
> > NSA, has operational quantum computers.
>
> No, nothing more than laboratory experiments.
>
> > Contrary to a point raised earlier, the quantum computer is not
> > used by the NSA. It is simply left running - translating everything
> > it sees on the internet into plain text and then passing it off to
> > storage devices.
>
> You've been watching too many movies.
>
> > God I wish this were not true, but I have strong reasons to believe
> > it is. My brother was studying how to build a quantum computer at
> > UC Berkeley in the early to mid 80's and talked with people from
> > around the country on this subject. He has little doubt that a
> > quantum computer exists today. In fact, talking to him, I see that
> > the biggest obstacle is not hardware but software, because it takes
> > near genius to understand the potential that exists with a quantum
> > computer.
>
> Just because it takes more intelligence than that exhibited by you
> and your brother doesn't mean that it takes a "near genius".
>
> > If a quantum computer is not operational today, it is due to the
> > fact that an operating system is still being developed- I am
> > convinced that it is not the hardware keeping it from working.
>
> To the contrary, the "hardware" issues are so severe that there is
> no point in trying to build an operational quantum computer today.
>
> > Can anyone provide any additional insight.
>
> Sure; why don't you simply go read the QC literature?
>
> > And please don't say I am nuts, or kook, or anything else.
>
> "Why on Earth not?"
> - from "A Fish Called Wanda"
>
Are you familiar with the "difficulties" in building a QC? My brother
was telling me that he would have (back then)built one given the right
funding and people. When I asked him how much, it was on the order of
hundreds of millions, and in less than a year.
The problem he stated was the extreme ineffeciencies the QC would
exhibit due to the fact that there is no software and that could take a
decade to develop (just the OS and a useful application).
Now back up 15 years ago, what is to say that the government has not
already accomplished all this? And if you want to tell me that I am
wrong, please give me the details. I would love my brother to get into
this forum, but he is too busy. I have to almost stand in line to get
a phone call to him. But I will certainly pass on anything you have to
counter with.
And can you give me directions to the QC literature?
And, finally, I stated not to call me a kook because only losers have
no life that they spend it responding in the extreme negative. That is
"why not".
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------------------------------
From: Greg Ofiesh <[EMAIL PROTECTED]>
Subject: Re: Quantum Computers
Date: Thu, 01 Jul 1999 19:41:51 GMT
In article <[EMAIL PROTECTED]>,
Mok-Kong Shen <[EMAIL PROTECTED]> wrote:
> Douglas A. Gwyn wrote:
> >
>
> > > Can anyone provide any additional insight.
> >
> > Sure; why don't you simply go read the QC literature?
>
> There is recently published in the Springer Lecture Notes a
proceedings
> of a conference on quantum computing. It should reflect the state
> of the art quite well.
In the public sector?
>
> M. K. Shen
>
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------------------------------
From: [EMAIL PROTECTED] (Patrick Juola)
Subject: Re: Quantum Computers
Date: 1 Jul 1999 15:52:02 -0400
In article <7lgfi5$mj3$[EMAIL PROTECTED]>,
Greg Ofiesh <[EMAIL PROTECTED]> wrote:
>In article <[EMAIL PROTECTED]>,
> [EMAIL PROTECTED] wrote:
>> Greg Ofiesh <[EMAIL PROTECTED]> wrote:
>>
>> > Let us begin with the following assertion that I think you will all
>> > agree with. If a quantum computer exists, then the only form of
>> > encryption that cannot be broken by it, or at least has half a
>chance
>> > to survive an attack, is OTP.
>>
>> I won't.
>>
>> Quantum Computers are not some magical devices that can do anything.
>There
>> are some problems that *can* be made much more tractable on them (for
>> example, factoring which can be used to crack RSA). There are problems
>> which cannot be handled.
>>
>> I don't know (enough) of Quantum computation to give or be able to
>prove
>> that certain problems are not made easy using a QC ... but what would
>make
>> you think that, for example the symmetric ciphers, would be
>approachable
>> using one?
>>
>
>in a word: parallelism.
>
>to be more specific - extremely massive parallelism.
>
>to be even more specific, and even I have trouble with this, you don't
>necessarily attack the key space, but the algorithm. I keep hearing
>that and yet I can't conceive of it either.
So why don't you do some reading, instead of scare-mongering?
-kitten
------------------------------
From: [EMAIL PROTECTED] (Patrick Juola)
Subject: Re: Quantum Computers
Date: 1 Jul 1999 16:10:46 -0400
In article <7lgg9s$mtt$[EMAIL PROTECTED]>,
Greg Ofiesh <[EMAIL PROTECTED]> wrote:
>In article <[EMAIL PROTECTED]>,
> Mok-Kong Shen <[EMAIL PROTECTED]> wrote:
>> Douglas A. Gwyn wrote:
>> >
>>
>> > > Can anyone provide any additional insight.
>> >
>> > Sure; why don't you simply go read the QC literature?
>>
>> There is recently published in the Springer Lecture Notes a
>proceedings
>> of a conference on quantum computing. It should reflect the state
>> of the art quite well.
>
>In the public sector?
On what basis do you assert a difference between the public and
secret sectors? The public sector is better funded....
-kitten
------------------------------
From: [EMAIL PROTECTED] (Patrick Juola)
Subject: Re: The One-Time Pad Paradox
Date: 1 Jul 1999 16:08:27 -0400
In article <[EMAIL PROTECTED]>,
Robert C. Paulsen, Jr. <[EMAIL PROTECTED]> wrote:
>Patrick Juola wrote:
>
>> >
>> >Can we say that scenario two didn't reveal the secret?
>>
>> Yes. Because it didn't happen.
>
>Not much to discuss if you won't grant me my hypothetical.
But that's the *POINT*; your hypothetical won't happen.
More precisely, it's *LESS* likely than the following scenario :
You work on a cure for cancer and find nothing and submit a
lenthy report detailing your null finding. By a conspiracy of
the random numbers, the OTP converts your report of null finding
into an apparent scientific document detailing a correct and
complete method for curing cancer.
... and, equivalently, less likely than the following scenario :
You work on a cure for cancer and find nothing. Your opponent,
having nothing better to do, compresses tomorrow's Wall Street
Journal and finds that it compresses into an apparent scientific
document detailing a correct and complete method for curing cancer.
Why are you worried about the revealed-plaintext hypothetical, but
not about the compressing-WSJ or apparent-more-valuable-plaintext
scenarios?
-kitten
------------------------------
From: "Robert C. Paulsen, Jr." <[EMAIL PROTECTED]>
Subject: Re: The One-Time Pad Paradox
Date: Thu, 01 Jul 1999 15:11:33 -0500
"Douglas A. Gwyn" wrote:
>
> "Robert C. Paulsen, Jr." wrote:
> > Scenario 2: The signals department uses a OTP to encrypt the message but
> > in a one-in-a-gazillion chance, the encrypted text describes, perhaps in
> > different words, our cure.
> > Can we say that scenario two didn't reveal the secret?
>
> Yes, it does not reveal anything (other than surface characteristics
> such as the fact that a message was sent, its length, etc.).
Well, I contend that since the secret was sent in the clear (for
purposes of discussion, per my hypothesis) it was revealed. That was
supposed to be a rhetorical question!
>
> Why don't you ask the same kind of question about the much more
> likely scenario:
>
> Scenario 3: The account number of a billionaire's Swiss bank
> account is disclosed.
>
I didn't ask that question because it wasn't pertinent to my point. I
was hypothesizing a secret that is inherently recognizable when
revealed. A Swiss bank account number isn't obviously correct just by
looking at it. Also, the likelihood of the situation is not pertinent to
the original question posed by John Savard.
> If you understand the relevance, or more accurately, lack of
> relevance, of the "message" supposedly revealed in scenario 3
> to the actual plaintext message, then you should understand
> the *same* relevance, i.e. lack of any, of the "message" of
> scenario 2. Only once in a zillion times will such a coherent,
> accidental message state something that is *true*; the rest of
> the time, it will be asserting some falsehood or another.
> (It will get the account number wrong almost all the time.)
> If the adversary mistakenly thinks it is a plaintext "bust",
> it will practically never work out to his advantage.
>
> It is precisely because there is no causal relationship
> between the actual message and the one supposedly seen in
> the ciphertext, that no information is conveyed to the
> interceptor.
OK, but still trying to see things from the Savard point-of-view (as I
understood his message) I think there is a possible case where a secret
can be revealed *through the use of a OTP* -- even if the message itself
is not revealed. I grant that if the *exact same wording* gets through
(because our OTP was all 1-bits, for example) the adversary has no way
of knowing this happened (although he is likely to assume that my
scenario 1 happened and the actual message was sent by mistake). In any
case he was exposed to the secret.
But if the secret is revealed, does this lead to the paradox John Savard
discussed?
One could counter argue that, since the message itself wasn't revealed
(although the underlying secret was), the OTP was successful 100% and
therefore there is no paradox -- the failure (and by definition there
was one since the secret was revealed) was not the OTP process itself.
--
____________________________________________________________________
Robert Paulsen http://paulsen.home.texas.net
If my return address contains "ZAP." please remove it. Sorry for the
inconvenience but the unsolicited email is getting out of control.
------------------------------
From: "Robert C. Paulsen, Jr." <[EMAIL PROTECTED]>
Subject: Re: The One-Time Pad Paradox
Date: Thu, 01 Jul 1999 15:34:53 -0500
Patrick Juola wrote:
>
> In article <[EMAIL PROTECTED]>,
> Robert C. Paulsen, Jr. <[EMAIL PROTECTED]> wrote:
> >Patrick Juola wrote:
> >
> >> >
> >> >Can we say that scenario two didn't reveal the secret?
> >>
> >> Yes. Because it didn't happen.
> >
> >Not much to discuss if you won't grant me my hypothetical.
>
> But that's the *POINT*; your hypothetical won't happen.
>
> More precisely, it's *LESS* likely than the following scenario :
...clip...
Maybe your point but not mine. I am trying to discuss John Savard's
"small, but finite, probability" that an unfortunate key is used. The
fact that the likelyhood of it happening is vanishingly small does not
necessarily invalidate the possible "paradox". It doesn't matter how
less likely it is than some other scenario.
--
____________________________________________________________________
Robert Paulsen http://paulsen.home.texas.net
If my return address contains "ZAP." please remove it. Sorry for the
inconvenience but the unsolicited email is getting out of control.
------------------------------
From: [EMAIL PROTECTED] (Patrick Juola)
Subject: Re: The One-Time Pad Paradox
Date: 1 Jul 1999 16:44:34 -0400
In article <[EMAIL PROTECTED]>,
Robert C. Paulsen, Jr. <[EMAIL PROTECTED]> wrote:
>Patrick Juola wrote:
>>
>> In article <[EMAIL PROTECTED]>,
>> Robert C. Paulsen, Jr. <[EMAIL PROTECTED]> wrote:
>> >Patrick Juola wrote:
>> >
>> >> >
>> >> >Can we say that scenario two didn't reveal the secret?
>> >>
>> >> Yes. Because it didn't happen.
>> >
>> >Not much to discuss if you won't grant me my hypothetical.
>>
>> But that's the *POINT*; your hypothetical won't happen.
>>
>> More precisely, it's *LESS* likely than the following scenario :
>
>...clip...
>
>Maybe your point but not mine. I am trying to discuss John Savard's
>"small, but finite, probability" that an unfortunate key is used. The
>fact that the likelyhood of it happening is vanishingly small does not
>necessarily invalidate the possible "paradox". It doesn't matter how
>less likely it is than some other scenario.
Do you actually bother to read the articles to which you respond?
The "paradox" is merely that people can choose to interpret random
data; sometimes random data will carry an interpretable message;
sometimes the message will even be correct.
If your worry is that your competitors will paradoxically receive
the contents of your message via an unfortunate OTP, you should
also worry that your competitors will also be able to read the
content of your message in the snow on their TV screen.
-kitten
------------------------------
From: [EMAIL PROTECTED] (Patrick Juola)
Subject: Re: Quantum Computers
Date: 1 Jul 1999 16:22:49 -0400
In article <7lggp9$n3e$[EMAIL PROTECTED]>,
Greg Ofiesh <[EMAIL PROTECTED]> wrote:
>
>
>> Again, you're not looking for information; you're looking for sock
>> puppets to confirm your prejudices.
>
>Well, you can make that claim, but don't forget that I have yet to have
>one person point me to a document that "proves" I am wrong.
Of course not. You are quite accurate to put "proves" in quotes,
because it's obvious that your standards of proof are your own
and not to be related to rational argumentation or evidence.
>I have had
>someone suggest that I look at the QC literature. Where is it? Who
>has it? What on earth is he talking about?
Well, it took me literally ten seconds to find several dozen references
via AltaVista. Check _Science_, _Nature_, _J. Modern Optics_, the
xxx.lanl.gov preprint archives (there are over 100 references there
alone). The Oxford Center for Quantum Computation lists thirty-five
"important" research groups (three quarters of which are outside
the USA and thus independent of NSA and its tentacles) -- any of
them would no doubt be happy to send you copies of their tech
reports upon request.
So do some legwork.
>I have no clue who has what background or
>expertise, or who has done ANY in depth studying in this field like my
>brother has.
Obviously. And thirty seconds of legwork will give you more information
than you can possibly use.
-kitten
------------------------------
From: [EMAIL PROTECTED]
Subject: Re: Quantum Computers
Date: Thu, 01 Jul 1999 20:50:58 GMT
In article <7lfric$i48$[EMAIL PROTECTED]>,
[EMAIL PROTECTED] (SCOTT19U.ZIP_GUY) wrote:
> In article <7lf4l4$5uo$[EMAIL PROTECTED]>, Greg Ofiesh
<[EMAIL PROTECTED]> wrote:
> >Let us begin with the following assertion that I think you will all
> >agree with. If a quantum computer exists, then the only form of
> >encryption that cannot be broken by it, or at least has half a chance
> >to survive an attack, is OTP. All other forms of encryption are
> >deterministic in nature and are not "cracked" but simply "translated"
> >(to convey the ease with which cryptanalysis is performed) by a
quantum
> >computer.
> >
> >Now let me make my assertion - The US government, most likely the
NSA,
> >has operational quantum computers.
> >
>
> If one starts with that assumption and I think it is a good
assumption that
> the NSA has quantum computers and most likely has had them for many
> years. If one makes this assumption then the idea behind future
encryption
> system should be to make the entropy such that for an average english
text
> message one sends or encrypts. There should exist the possiblitlity of
more
> than one soultion. This would prevent a break since there would not be
a
> unique decryption to a given message. The problem with short key
methods
> like all the AES candidates is that for any resonable length message
the
> key is so short that there exists only one unique decription to a
english
> message and this is where the so called experts want the masses to
use.
> Try scott19u.zip its better.
Do you have any proof that your algorithm is better? I've never even
seen an analysis of your algorithm.
>
> David A. Scott
> --
> SCOTT19U.ZIP NOW AVAILABLE WORLD WIDE
> http://www.jim.com/jamesd/Kong/scott19u.zip
> http://members.xoom.com/ecil/index.htm
> NOTE EMAIL address is for SPAMERS
>
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Share what you know. Learn what you don't.
------------------------------
From: "Tony T. Warnock" <[EMAIL PROTECTED]>
Subject: Re: Infinity: was Quantum Computers
Date: Thu, 01 Jul 1999 14:41:05 -0600
Reply-To: [EMAIL PROTECTED]
Another use for a (signed) infinity in a computer is interval arithmetic.
An interval may have an infinite range and still be a useful interval.
Because one can not only do arithmetic, but also set operations on
intervals, even (-inf, +inf) is useful, after all it will include your
(real) answer.
There is a good argument for having two or even three zeroes. Plus zero is
used for things like (+0, 3) in an interval, zero is excluded, (-0, 3) has
zero included. The first interval has an inverse but the second does not.
(0,0) is just zero.
Tony
------------------------------
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