Cryptography-Digest Digest #127, Volume #9 Tue, 23 Feb 99 18:13:04 EST
Contents:
What do you all think about the new cipher devised by a 16 year old? ("H. Cheng")
Re: Define Randomness (Darren New)
Re: Define Randomness (R. Knauer)
Re: Quantum Cryptography (R. Knauer)
Re: Quantum Cryptography (fungus)
Re: Interesting DES results (fungus)
Re: paper on all 15 AES candidates ?? (Christopher Jobmann)
Re: Bruce's Feb. "CRYPTO-GRAM" (Matt Curtin)
Re: Another extension to CipherSaber (Darren New)
Re: Testing Algorithms (Darren New)
Re: Define Randomness ("Tony T. Warnock")
Re: Randomness of coin flips (R. Knauer)
Re: Randomness of coin flips (Darren New)
Re: What do you all think about the new cipher devised by a 16 year old? (Darren New)
Re: Define Randomness (R. Knauer)
Re: Define Randomness
Re: random number generator??? ("karl malbrain")
Re: Define Randomness (R. Knauer)
Re: Bigger variables... ("D")
Testing Algorithms [moving off-topic] (Withheld)
----------------------------------------------------------------------------
From: "H. Cheng" <[EMAIL PROTECTED]>
Reply-To: [EMAIL PROTECTED]
Subject: What do you all think about the new cipher devised by a 16 year old?
Date: Tue, 23 Feb 1999 03:26:47 GMT
Its supposed to be as strong as RSA but 10 times as fast. Well, I think
a lot of it is media hyped. I don't even know if its a public key
system. Anyhow, can anyone give me some info on this new cipher, such
as its strength and its principle. It seems pretty simple. It uses a
2X2 matrices. I wonder how on earth can something so simple been
overlooked?
http://www.msnbc.com/news/231690.asp
------------------------------
From: Darren New <[EMAIL PROTECTED]>
Subject: Re: Define Randomness
Date: Tue, 23 Feb 1999 20:55:54 GMT
> We would all probably agree that the Keno games in Reno or Lake Tahoe or
> Las Vegas, Nevada, produce the twenty numbers used in the game at
> random, by encasing eighty uniquely numbered ping pong balls in that
> plastic sphere and driving them into a tumult with a continuous stream
> of modestly compressed air.
Just as an aside, there was someone in Atlantic City who won the
million-dollar Keno game three times in six months. It turns out the
PRNG in the computer generating the numbers got initialized with the
same value after every power failure, so when he saw the same sequence
of numbers coming up, he knew what games were next.
I think he even won the court case.
--
Darren New / Senior Software Architect / MessageMedia, Inc.
San Diego, CA, USA (PST). Cryptokeys on demand.
"Be.... the email."
------------------------------
From: [EMAIL PROTECTED] (R. Knauer)
Subject: Re: Define Randomness
Date: Tue, 23 Feb 1999 19:28:37 GMT
Reply-To: [EMAIL PROTECTED]
On Tue, 23 Feb 1999 10:25:50 -0800, Anthony Stephen Szopa
<[EMAIL PROTECTED]> wrote:
>Define Randomness
"A random number is one which cannot be described."
Oops, that's the Berry Paradox. Oh, well - it sounded good.
>So, unreproducibility and equal probability of outcome are two essential
>characteristics of randomness. I am not an expert but are there other
>characteristics or do they all derive from these two?
I think you mean "independent" and equidistributed". Both concepts are
contained in the term "equiprobable".
>Let us use the Keno game analogy but define our significant factors. We
>will leave out quantum factors because the device is too large for these
>effects to effect the outcome of each game.
Don't assume that the size of a device has anything to do with whether
it is classical or quantum. A liter of liquid helium near zero degrees
Kelvin is quite large yet also quite quantum mechanical in many
respects.
>But we do not have a perfect Keno machine, or perfect information, or a
>sufficiently powerful computer to process this data and give us our
>predictable outcome. But if we had, we could predict the outcome!
Classical chaotic processes cannot be used to generate *true* random
numbers, precisely because the events are not completely independent.
Even a very chaotic system, the weather, can be predicted for a few
days in advance.
You must have complete indeterminancy for *true* randomness. Quantum
systems supply needed indeterminancy, classical systems do not.
>So, for our discussion, randomness all comes down to knowledge and
>programming: measurement and technology. What we call randomness is
>nothing more than a measure of our own ignorance and lack of ability.
There are many definitions of randomness, as a reading of books like
Li & Vitanyi's book on Kolmogorov Complexity will show. For purposes
of crytpo-grade randomness, which is suitable for use with the OTP
cryptosystem, a true random number is one which is produced by a
process which is capable of generating all possible finite sequences
equiprobably. In such manner, the cryptoanalyst will not have any
information upon which ti base his attack.
As a practical matter, since actual TRNGs are not perfectly random, it
is sufficient for the random numbers to leak only insignificant
amounts of information in the ciphers they produce. The level of
insignificance depends on your anticipated usage. If you plan to send
only one small message in a lifetime, like with the Washington-Moscow
hotline, the requirements for information leakage are much different
from what would be the case if you were filing a multi-megabyte report
each business day.
>So the argument is twofold: first randomness is relative. What is
>random for some is predictable and non random for others. And secondly,
>computer programs can produce genuinely true random numbers.
Computer programs cannot generate true random numbers because computer
programs are deterministic. But they can generate numbers that mimic
the essential characteristics of true random numbers, which we have
been calling "crypto-grade random numbers". The problem is how do you
decide if computer programs are actually doing that.
The digit expansion for pi looks random in terms of statistical tests,
but it is hardly random, since the bits are generated by a relatively
simple algorithmic procedure.
One example of a true random number is Chaitin's Halting probabiltiy,
Omega. Each bit of Omega is completely independent of all the others
and Omega is normal in the Borel sense. That gives Omega the
independence and equidistribution of bits that a true random number
must have.
>And may you rest in peace trying to refute what I have described and
>concluded because you will surely die trying.
One could in principle use your pseudo-random numbers to build test
ciphers with real messages and then try to break those ciphers,
looking for information leakage using inference techniques. If they
find a significant amount of such information leakage, they can use it
to break your system. Remember that stream ciphers are vulnerable to
known plaintext attacks and correlation attacks. If there are any
regularities in your ciphers, they can be broken in principle.
Bob Knauer
"If experience teaches us anything at all, it teaches us this: That a good
politician, under democracy, is quite as unthinkable as an honest burglar."
--H.L. Mencken
------------------------------
From: [EMAIL PROTECTED] (R. Knauer)
Subject: Re: Quantum Cryptography
Date: Tue, 23 Feb 1999 19:30:03 GMT
Reply-To: [EMAIL PROTECTED]
On Wed, 24 Feb 1999 01:24:24 +0100, fungus
<[EMAIL PROTECTED]> wrote:
>Is this the same government who funded research into "remote viewing"
>as a means of espionage???
If it is a form of criminal activity, you can be certain that the govt
has engaged in it.
Bob Knauer
"If experience teaches us anything at all, it teaches us this: That a good
politician, under democracy, is quite as unthinkable as an honest burglar."
--H.L. Mencken
------------------------------
From: fungus <[EMAIL PROTECTED]>
Subject: Re: Quantum Cryptography
Date: Wed, 24 Feb 1999 01:24:24 +0100
"R. Knauer" wrote:
>
> +++++
> "Moreover, the United States govternment is quietly funding research
> in code-breaking, using quantum computers".
> --Preface, p. xii.
> +++++
>
> Hmm...
>
Is this the same government who funded research into "remote viewing"
as a means of espionage???
--
<\___/>
/ O O \
\_____/ FTB.
------------------------------
From: fungus <[EMAIL PROTECTED]>
Subject: Re: Interesting DES results
Date: Wed, 24 Feb 1999 01:19:13 +0100
bill johnson wrote:
>
> The second test was to measure the + or - difference from one byte to
> the next. This was an eye opener. The plot looks like a nearly perfect
> inverted 'V'. In fact amazingly so.
>
> I've tried this on two different sources and I get the same result.
>
> Any comments from the grouop? I have the data and source files if
> anyone is interested.
>
This is what I would expect.
It's a bit like throwing two dice and adding the result. In the long
term you'll get a lot of sevens but this doesn't mean there's anything
wrong with the dice.
--
<\___/>
/ O O \
\_____/ FTB.
------------------------------
From: Christopher Jobmann <[EMAIL PROTECTED]>
Subject: Re: paper on all 15 AES candidates ??
Date: Tue, 23 Feb 1999 19:59:31 +0100
Somniac wrote:
> Yes. There are papers already written that answer your questions. You
> will have to wait until March 22, 1999 when they will be made public.
> Most of these papers will not be published before that date for reasons
> which are involved with marketing, advertising, proprietary interests,
> expectations of rejection upon pre-publication, bureaucratic approval
> processes, and a desire to maximize profit. It will only be 4 weeks to
> wait, so try to enjoy this quiet period for the AES process with other
> pursuits.
I guess that'll be mostly considerations of security and speed - I am
not
looking for cryptanalysis that much, but (for now at least) for basic
descryption of the different algorithms - Feistel-network with so many
rounds ... etc. Giving me an idea of the algorithm without having to
read
the full documentaiotn ;-)
But I am interested in those that have been broken - does anyone know
where
I can get information on those ?
Chris
------------------------------
From: Matt Curtin <[EMAIL PROTECTED]>
Subject: Re: Bruce's Feb. "CRYPTO-GRAM"
Date: 23 Feb 1999 15:40:50 -0500
[EMAIL PROTECTED] (Bruce Schneier) writes:
> > he could even be sued by someone unhappy with his
> > pronouncements
>
> Indeed, the author of the Snake Oil FAQ (a first, and an excellent,
> essay on the warnings of snake oil) had been afraid to name names for
> just that reason.
I used to have people threaten to sue me over the Snake Oil FAQ at the
rate of about once per month during its early development and postings
of the first revision. Some were under the impression that it was
possible to take some of the warning signs, compare it to their
marketing copy, figure that the FAQ was obviously talking about them,
and therefore be libelous and/or slanderous.
I solved this problem by stating that anyone threatening any legal
action against me would have their threats published in their entirety
on my web site, and I would link to them from the FAQ.
No one made any threats after that.
--
Matt Curtin [EMAIL PROTECTED] http://www.interhack.net/people/cmcurtin/
------------------------------
From: Darren New <[EMAIL PROTECTED]>
Subject: Re: Another extension to CipherSaber
Date: Tue, 23 Feb 1999 20:13:09 GMT
> Also, regarding the earlier suggestion of ASCII armoring, we already have
> universal standards (like binhex or UUEncode) which accomplish this.
Neither of which is actually universal. Stick with base64 or just hex if
you want guaranteed-to-work or trivial-to-implement, respectively. There
are lots of versions of binhex and uuencode which are incompatible and
which don't go thru gateways like you'd like.
--
Darren New / Senior Software Architect / MessageMedia, Inc.
San Diego, CA, USA (PST). Cryptokeys on demand.
"Be.... the email."
------------------------------
From: Darren New <[EMAIL PROTECTED]>
Subject: Re: Testing Algorithms
Date: Tue, 23 Feb 1999 20:19:54 GMT
> 56-bit DES was once considered unbreakable but was recently broken in
Was it really? I thought the DES spec was published with a lifetime set
to expire in the mid 1970's or something?
--
Darren New / Senior Software Architect / MessageMedia, Inc.
San Diego, CA, USA (PST). Cryptokeys on demand.
"Be.... the email."
------------------------------
From: "Tony T. Warnock" <[EMAIL PROTECTED]>
Subject: Re: Define Randomness
Date: Tue, 23 Feb 1999 12:49:00 -0700
Reply-To: [EMAIL PROTECTED]
Actually, the future positions (and momenta) of the balls often depends in a
chaotic way on the initial conditions. It is possible (I haven't done the
computations.) that the initial conditions must be known so accurately that
quantum effects obtain. That is to say, if you have to know the initial
conditions to a greater degree of accuracy than QM allows, even large
systems can show random behavior. A simple example would be to have a ball
(the usual perfect weightless, frictionless, odorless, shameless, particle)
bouncing back and forth in a 1 dimensional space 1 meter long. If the ball's
velocity is 1 meter per second with an uncertainty of 1 part in 10000, then
by the next day one cannot say where the ball is. The same for an
uncertainty in position.
Tony
------------------------------
From: [EMAIL PROTECTED] (R. Knauer)
Subject: Re: Randomness of coin flips
Date: Tue, 23 Feb 1999 21:37:30 GMT
Reply-To: [EMAIL PROTECTED]
On Tue, 23 Feb 1999 20:34:18 GMT, Darren New <[EMAIL PROTECTED]>
wrote:
>Right. My confusion is that one talks about the uniform Bernouilli
>process with p=1/2, apparently calculating something about the bits of a
>number that are incalculable. I'm questioning where the "p=1/2" comes
>from? How does one know it's 1/2, and not 1/3, say?
You don't. According to what I read in Li & Vitanyi, which presumably
I will get to read more about in Feller, if p is not exactly 1/2, you
can get radical skew in the output, far more than you would imagine
for just a slight deviation of p from the exact value of 1/2.
Side note: I am getting into that book on Quantum Computing that I
cited the other day, and from what I have read thus far it is a must
read for people in crypto.
Bob Knauer
"Democracy is the theory that the common people know what they
want, and deserve to get it good and hard."
--H.L. Mencken
------------------------------
From: Darren New <[EMAIL PROTECTED]>
Subject: Re: Randomness of coin flips
Date: Tue, 23 Feb 1999 20:34:18 GMT
> You missed my point - you can examine *some* simple TMs, like the ones
> used to set the bounds on Omega.
No, I got that. I wasn't sure you got mine. Of course there are some
machines you can examine. The way you phrased it made me think you were
saying "there's no program that can look at all the TMs, but you can
look at any particular TM and see if it halts." I misunderstood what
you were saying.
> +++++
> The bits of Chaitin's Halting Probability, Omega, arise from a uniform
> Bernouilli process (p=1/2), namely from inspecting his exponential
> diaphantine equation, or equivalently, inspecting the halting behavior
> of universal Turing machines.
> +++++
>
> I did not mean to imply that one could actually inspect each and every
> entity, be it TM or EDE, and determine all the bits of Omega. I meant
> to say that the bits of Omega were dependent on the TMs and the EDEs
> in the sense that they arise from whether TMs halt or whether EDEs
> have a finite or infinite number of solutions. The term "inspect" is
> at fault, since it implied an effective construction - which is not
> possible for all bits of Omega with certainty.
Right. My confusion is that one talks about the uniform Bernouilli
process with p=1/2, apparently calculating something about the bits of a
number that are incalculable. I'm questioning where the "p=1/2" comes
from? How does one know it's 1/2, and not 1/3, say?
--
Darren New / Senior Software Architect / MessageMedia, Inc.
San Diego, CA, USA (PST). Cryptokeys on demand.
"Be.... the email."
------------------------------
From: Darren New <[EMAIL PROTECTED]>
Subject: Re: What do you all think about the new cipher devised by a 16 year old?
Date: Tue, 23 Feb 1999 20:43:16 GMT
> It's still a secret, until the "patents go through".
>
> This sounds like twaddle to me. Once a patent is filed, you can publish
> the algorithm, whether it finally gets granted or not.
It takes a long time to file a patent. Many months just to do the
application.
> Another mystery is that a patent is being applied for when (according
> to the press) the girl in question says she's not interested in making
> money from it. Something doesn't add up...
You can patent something and then license it for free, to assure nobody
else patents it. Besides, it might not be her choice. Perhaps her
parents want her to patent it even if she doesn't want to make the money
from it.
No need for fishiness on *that* count.
(Note, this is from a US patent perspective. I have no idea about
Scottish patents, or whatever.)
--
Darren New / Senior Software Architect / MessageMedia, Inc.
San Diego, CA, USA (PST). Cryptokeys on demand.
"Be.... the email."
------------------------------
From: [EMAIL PROTECTED] (R. Knauer)
Subject: Re: Define Randomness
Date: Tue, 23 Feb 1999 22:07:31 GMT
Reply-To: [EMAIL PROTECTED]
On Tue, 23 Feb 1999 20:55:54 GMT, Darren New <[EMAIL PROTECTED]>
wrote:
>Just as an aside, there was someone in Atlantic City who won the
>million-dollar Keno game three times in six months. It turns out the
>PRNG in the computer generating the numbers got initialized with the
>same value after every power failure, so when he saw the same sequence
>of numbers coming up, he knew what games were next.
>I think he even won the court case.
How can someone sue him for being a smart guy? If that were allowed,
the state could renege on any winnings it wanted just by claiming that
the winner took advantage of something heretofore unknown.
Bob Knauer
"Democracy is the theory that the common people know what they
want, and deserve to get it good and hard."
--H.L. Mencken
------------------------------
From: <[EMAIL PROTECTED]>
Subject: Re: Define Randomness
Date: Tue, 23 Feb 1999 21:33:54 +0100
On Tue, 23 Feb 1999, Anthony Stephen Szopa wrote:
> Define Randomness
What about 'unpredictability'?
>
> We would all probably agree that the Keno games in Reno or Lake Tahoe or
> Las Vegas, Nevada, produce the twenty numbers used in the game at
> random, by encasing eighty uniquely numbered ping pong balls in that
> plastic sphere and driving them into a tumult with a continuous stream
> of modestly compressed air.
>
> We would agree to the randomness of the process in part because the
> outcomes are essentially non reproducible. Furthermore, we would agree
> to the randomness of the process because the outcome generally over long
> but modest runs would certainly demonstrate that each numbered ball has
> the same probability of being among the twenty chosen.
No: I don't know Keno, but other games like this show that the probability
is slightly different for every ball. The difference is too small to
become rich, but it exists.
>
> So, unreproducibility and equal probability of outcome are two essential
> characteristics of randomness. I am not an expert but are there other
> characteristics or do they all derive from these two?
What about random numbers with poor statistical qualities? The probability
is not equal for all of them, but nevertheless they are random.
>
> Now, let us define our object random process, the one we will consider
> to support my definition of randomness as it applies to computer
> software.
>
> Let us use the Keno game analogy but define our significant factors. We
> will leave out quantum factors because the device is too large for these
> effects to effect the outcome of each game.
I don't agree: Quantum effects may be very important in this game.
> We will set up a classical,
> in a physics sense, keno game.
...
>
> There is no reason that we could not do this given an ideal Keno
> machine, perfect information at one instant in time, and a powerful
> computer.
>
> But we do not have a perfect Keno machine, or perfect information, or a
^^^^^^^^^^^^^^^^^^^
> sufficiently powerful computer to process this data and give us our
> predictable outcome. But if we had, we could predict the outcome!
If you are able to get an exact description of a classic system you are
able to predict all states as well in the future as in the past.
That's all right, but if you try to calculate such a system you'll find
out that small changes will become more and more important if you are
moving info future or past.
You'll find a point where quantum effects become important even for
macroscopic systems.
Now what about our game? It seems to be very chaotic. This means: Very
small effects may cause very large changes within a very short time.
Quantum effects may change the result of the game.
>
> So, for our discussion, randomness all comes down to knowledge and
> programming: measurement and technology. What we call randomness is
> nothing more than a measure of our own ignorance and lack of ability.
Yes.
>
> But let us suppose that we could in fact model such an ideal Keno game
> to approach real conditions, in a simplistic manner, of course. We
> would make our ping pong balls unique in shape from one another but with
> specific irregularities and or flaws.
...
> They found out the hard way that their task was impossible.
>
> So, the cracker hackers found that their ignorance and lack of ability
> resulted in them trying to reproduce a truly random process.
>
> So the argument is twofold: first randomness is relative. What is
> random for some is predictable and non random for others.
I don't think so: If randomness means unpredictability there is true
randomness (the real mashine) and pseudo-randomness (the simulation).
The real mashine produces random numbers even if somebody is able to
measure and control whatever parameter he wants. Not so the simulation.
Your definition of randomness contained 'unreproducebility'. The
simulation can be reproduced once one knows all parameters.
> And secondly,
> computer programs can produce genuinely true random numbers.
Not the computer program produces the ramdomness but the person generating
the starting parameters.
This causes two problems:
1) You may use a fixed set of parameters and use it to produce more and more
random numbers.
This allows the attacker to calculate the internal state of your mashine
from a sufficiently large amount of random numbers and this way to
calculate all future and all previous random numbers.
2) What if the initial parameters weren't random?
This may allow to calculate the initial state of your mashine much earlier
and this way to break the RNG.
Andreas Enterrottacher
[EMAIL PROTECTED]
[EMAIL PROTECTED]
------------------------------
Reply-To: "karl malbrain" <[EMAIL PROTECTED]>
From: "karl malbrain" <[EMAIL PROTECTED]>
Subject: Re: random number generator???
Date: Tue, 23 Feb 1999 14:28:21 -0800
R. Knauer <[EMAIL PROTECTED]> wrote in message
news:[EMAIL PROTECTED]...
>(...) As it is now, only 30% of eligible voters
>actually vote, which tells the criminals in govt that they can get by
>with anything they want because 70% of the people don't care what they
>do.
People are MADE to care what criminals do when it affects them directly.
They won't do X or Y when they can't DETERMINE the CONSEQUENT of action X
over action Y, a state of affairs that is MADE by the fascist form in the
first place -- if you can't distinguish what cadre X are doing from what
cadre Y are doing, you are reduced to a RANDOM choice, a VULGARITY. I,
speaking personally, try harder not to engage vulgarity in the first place.
>(...) I can tell you that here in Texas the
>Waco incident is not over by any means.
The point is: for those who are dead, the incident is over -- under the
shielding provided by the Civil Rights Act of the 1960's that you've (did
someone else here already say: prematurely) LEAPED to.
>BTW, the people rotting in prison unjustly were not the "other half".
>And nobody who understands what really happened at Waco believes for
>one minute that the govt was justified in what it did. It was a rogue
>operation by a criminal element inside the govt, similar to the kinds
>of things that went on in Nazi Germany.
No, it's not some <<randomly determined/criminal element>> rogue group
operation that created either the National Socialist Workers Party in 1920's
Germany, nor the agents' actions at 1990's WACO. I believe that this is the
basis for your confusion on RANDOMNESS in general. These environments are
DETERMINED, not random outcomes.....
But, this is moving <<RANDOM=CHAOS/COMPLEXITY>> into POLITICS,
not-with-standing here. Karl M
------------------------------
From: [EMAIL PROTECTED] (R. Knauer)
Subject: Re: Define Randomness
Date: Tue, 23 Feb 1999 22:05:15 GMT
Reply-To: [EMAIL PROTECTED]
On Tue, 23 Feb 1999 21:33:54 +0100, <[EMAIL PROTECTED]>
wrote:
>> Define Randomness
>What about 'unpredictability'?
Works for me, although I am sure the mathematicians will find
something to nitpick about it.
I like the definition that says that randomness is that for which
there is no reason why the number exists, but that is a bit
metaphysical. The reason pi exists is because I can calculate it from
an algorithm - that is, its reason for existing is the algorithm that
calculates it. That means that random numbers are uncomputable numbers
(when they are infinite in length). If you cannot compute them, there
is no reason for their existence. They just exist and that is all you
can say about them.
That means that the number 000...0 is random if there was no algorithm
that produced it, although it could certainly be produced by an
algorithm. That is what makes Kolmogorov Complexity not applicable to
crypto. A TRNG can produce the null sequnece 000...0 as one possible
sequence.
Perhaps the best mathematically pure description of randomness is that
it is undecideable how a number is generated. Therefore, using such
numbers as the keystream for an OTP cipher leaks absolutely no
information for the cryptanalyst. Even if you had a long run of 0s the
crypanalyst cannot decide if the cipher is the same as the plaintext,
or an coincidental English ciphertext.
Another definition (which I floated a year ago when we had the big
discussion on OTP random numbers) was that randomness is anything and
everything that is possible. Imagine you have this jar with each and
every possible number represented once, and you select one "at random"
to use with your cipher. Since the selection of any number is
completely indeterminant, the cryptanalyst cannot know which one it
is and therefore it could be anything. Therefore a random process
selects anything from everything that is possible.
But when all is said and done, cryptographers only need crypto-grade
random numbers which are produced by a TRNG, even one that is not
perfect, as long as the ciphers are not breakable. To decide that one
would have to subject test ciphers to attacks to see how much
information actually leaked out and if it is significant enough to
compromise future ciphers made using that TRNG.
This practical TRNG could possible be algorithmic (such as coming from
digit expansion of transcentental numbers or well-hashed text). I have
not seen a consensus on that issue which we discussed a few months
ago. The prevailing consensus is that with the proper selection of the
hash one can produce keystreams that leak little if any information.
>I don't think so: If randomness means unpredictability there is true
>randomness (the real mashine) and pseudo-randomness (the simulation).
The simulation comes from a calculation, and therefore involves
computable numbers, which cannot be truly random. You cannot simulate
a quantum process with a classical Turing machine, whether it is
deterministic or nondeterministic. That was demonstrated by Feynmann,
where he shows that the simulation slows down exponentially, which
means it can be exponentially long to get the next quantum state in
the simulation. Quantum entanglement is very costly to simulate
classically - exponentially costly.
Bob Knauer
"Democracy is the theory that the common people know what they
want, and deserve to get it good and hard."
--H.L. Mencken
------------------------------
From: "D" <[EMAIL PROTECTED]>
Subject: Re: Bigger variables...
Date: Tue, 23 Feb 1999 17:37:21 -0500
I have produced a working prototype. Where do I put it so as to not
become imprisioned or financially handicapped? I am sorry to say that it is
somewhat slow. Also, as to the bitwise operation restriction, I do not
believe that it is a big deal because xors are also bitwise, and the bits
that decide the operations to be preformed are not contiguous.
------------------------------
From: Withheld <[EMAIL PROTECTED]>
Subject: Testing Algorithms [moving off-topic]
Date: Tue, 23 Feb 1999 21:50:38 +0000
Reply-To: Withheld <[EMAIL PROTECTED]>
In article <[EMAIL PROTECTED]>, fungus
<[EMAIL PROTECTED]> writes
>
[cut]
>Only very recently have people been saying that "Moore's law cannot
>hold because of fundamental physical limitations" like the speed of
>light. There is no evidence whatsoever that Moore's law can hold
>beyond another 15-20 years or so. Electrons/photons simply don't
>move that fast...
>
>When this limit is reached, we'll have to move towards more
>parallelism in software to get things done (if we actually
>need *more* speed on the desktop...)
Or if we want to run Windows NT version 43.8 beta... :-)
--
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