Cryptography-Digest Digest #130, Volume #9 Wed, 24 Feb 99 09:13:02 EST
Contents:
Re: Testing Algorithms ("Tim Woodall")
Re: Unicity of English, was Re: New high-security 56-bit DES: Less-DES (Bryan Olson)
Re: Define Randomness ("Trevor Jackson, III")
Re: Crypt for FTP Protocol ([EMAIL PROTECTED])
Re: Testing Algorithms (Steven Runyeard)
Re: Another extension to CipherSaber (Paul Crowley)
Re: Testing Algorithms (Paul Crowley)
Re: Block cipher in the smallest PIC (Paul Crowley)
Re: Randomness based consciousness?. (Was: Re: *** Where Does The Randomness Come
From ?!? *** ) (R. Knauer)
Re: True Randomness (R. Knauer)
Re: Randomness of coin flips (R. Knauer)
Re: Randomness of coin flips (R. Knauer)
Re: Define Randomness (R. Knauer)
Re: Define Randomness (R. Knauer)
ICS Toolkit (Yikes1010)
Re: Define Randomness (Patrick Juola)
Re: Quantum Cryptography (Patrick Juola)
Re: Testing Algorithms [moving off-topic] (Patrick Juola)
Re: What do you all think about the new cipher devised by a 16 year old? (Patrick
Juola)
Re: Testing Algorithms (Patrick Juola)
Re: Define Randomness (R. Knauer)
Re: True Randomness (Patrick Juola)
----------------------------------------------------------------------------
From: "Tim Woodall" <No Spam [EMAIL PROTECTED]>
Subject: Re: Testing Algorithms
Date: Wed, 24 Feb 1999 09:05:27 -0000
Steven Runyeard wrote in message <[EMAIL PROTECTED]>...
>Someone wrote:
>>There's no garantee that this growth rate will continue. In fact
>>everything points to the opposite.
>
>No, there is no quarantee of this. There is also no quarantee that the
>speed of light will be a barrier.
You really don't understand how big 2^256 is.
Consider a computer consisting of a single water molecule.
Consider that this computer can test 10^9 keys per second.
Now build a computer of a cubic light year of water (at 1g/cm3)
This is approximately 9e15^3 m3
Each cubic meter contains approximately 3e28 molecules of water.
So our computer can test 2e85 keys per second (2^256 keys).
This computer can, therefore, crack a 256 bit key in one second although it
will take a
year or so to distribute the test cases to the individual processors and get
the result back. (assuming a speed of light limitation)
Unfortunately, a cubic light year of water (even if you assume it to be
incompressible) will be contained within its own Schwarzchild radius (a
black hole) and you won't be able to get the result out anyway.
>It's your guess that we won't crack a 256 bit key. It's my guess that
>we will. Each guess is just as valid.
I don't think anyone would suggest that 256 bit will always be uncrackable -
breakthroughs in various areas of mathematics could cause different cipher
designs to fall. It is just that no reasonable person expects that a 256 bit
key will _ever_ fall to brute force.
Tim.
------------------------------
From: Bryan Olson <[EMAIL PROTECTED]>
Subject: Re: Unicity of English, was Re: New high-security 56-bit DES: Less-DES
Date: Wed, 24 Feb 1999 01:08:15 -0800
[EMAIL PROTECTED] wrote:
>
> In article <[EMAIL PROTECTED]>,
> Bryan Olson <[EMAIL PROTECTED]> wrote:
>
> > With no key there is no equivocation.
>
> "Equivocation" (better, conditional entropy) applies not only to the key but
> also to the message -- two different and quite independent concepts, which of
> course do not have to be zero at the same length of received text (otherwise,
> they would be dependent in that sense).
Different yes, independent no. See Shannon's theorem 7.
Note pages 693, 696 and 697. When Shannon talks about
the message equivocation curve, he is considering the
equivocation corresponding to the intercepted letters.
> You must also change the
> wording from "no key" to "one key of unity probability"
Fine.
> > This is the
> > "degenerate type of secrecy system" described by Shannon at the
> > bottom of page 663.
>
> As I quoted, yes. As you quoted, no.
So if I grant that we describe unencrypted plaintext as having
a key space of one key rather than not having a key, then we're
in agreement? Granted.
> >Since there is only one key,
> >we can uniquely determine it
>
> You can uniquely determine *nothing* [...]
I'd be willing to rephrase as "the one key is uniquely
determined".
> > without intercepting any ciphertext, yielding a unicity
> > distance of zero.
>
> Non sequitur. Without intercepting any character, the message's conditional
> entropy is not zero.
See the graphs on pages 696 and 697 showing message and key
equivocation as a function of the number of intercepted
letters. The message equivocation curves start at the
point (0,0).
> Oh, but why, you may ask. Well, I would suggest you simply write down the
> formula!!! As often said, surprise and information are synonymous ;-)
The formula for the random cipher? H(k) is zero, and D, the
redundancy of English, is not zero, so H(k)/D is zero. I am
not surprised. (Granted the formula is undefined for languages
of zero redundancy since it yields 0/0.)
--Bryan
------------------------------
Date: Wed, 24 Feb 1999 04:12:00 -0500
From: "Trevor Jackson, III" <[EMAIL PROTECTED]>
Subject: Re: Define Randomness
Anthony Stephen Szopa wrote:
> "Tony T. Warnock" wrote:
>
> > 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
>
> My example is as subject to quantum effects effecting the outcome as is the
> firing of the pistons in a V-8 engine. We do not need to know the parameters of
> a real system (keno game) to this degree for my argument to be valid.
>
> Accurate predictions can be made and practicably so with no effect of outcome in
> such a system while ignoring quantum effects.
>
> For example, a moving body in space with constant velocity can be measured
> accurately enough such that for the next 50 million years we could predict its
> position.
Only within a specified accuracy. If the body is part of a collection of
interacting bodies, where the interaction might be gravitic, magnetic, or
electrically charged then the accuracy of the result decreases very quickly. To and
past therepoint where there is any predictable position.
>
>
> This is done every day with your quartz crystal watch. Over a years time it is
> accurate to less than 1 second deviation. So, within a years time we know what
> time it is within one second.
>
> It would be absurd to say we can only think we are close to knowing the exact
> time from a practicable view point.
>
> And we are all trying to be practicable. Cryptography is an applied technology.
------------------------------
From: [EMAIL PROTECTED]
Subject: Re: Crypt for FTP Protocol
Date: Wed, 24 Feb 1999 11:07:39 GMT
In article <7avfb2$o11$[EMAIL PROTECTED]>,
"Bjorn Wesen" <[EMAIL PROTECTED]> wrote:
> I just use scp instead of ftp. scp is of course the ssh analogue to rcp, the
> remote file copy program, which simply does an rsh/ssh to the server, does
> the equivalent of cat'ing the requested file, and the client side listens
> and put it on disk. Only an outbound connection, and it can do everything
> ftp protocol can.
Yeah I tend to use it myself when I move files between my accounts. But it
doesn't fit into the FTP protocol at all well (send's bytes, instead of
string commands) and yes you could do a FTP like extention to ssh (see sftp
in ssh2) but that too is not at all like FTP. I wanted to keep normal FTP
functionality, but add encryption, so that once FTP clients starts to put in
support too more and more people will start using it.
SRP looks good, and it's working now (ignore previous post:) ) and has a
nicely defined set of commands.
Lund
============= Posted via Deja News, The Discussion Network ============
http://www.dejanews.com/ Search, Read, Discuss, or Start Your Own
------------------------------
From: [EMAIL PROTECTED] (Steven Runyeard)
Subject: Re: Testing Algorithms
Date: Wed, 24 Feb 1999 11:39:14 GMT
>No. The guess is only as valid as the assumptions it is based upon.
>Since you have based yours on nothing concrete, your guess is pretty
>useless.
I don't agree. Because we are brought up in an environment with a
certain level of technology it's hard to imagine anything much
different. Let's look back at the technology surrounding Babbage in
the late 1800s. If anyone had suggested to him that within 100 years
someone could build a processor about an inch square that could
perform 2,000,000,000 instructions per second he would have sent them
to the nearest nut house. It would have taken a massive leap of faith
to believe it was possible. I feel that in another 100 years we would
have made an equally 'unbelievable' leap in technology. Don't limit
your thinking to the size of computers the size of melecules and
atoms. What about a computer made of super strings? Maybe even
smaller. Who knows? The point is we don't know what lies ahead of us.
My guess is no more worthless than yours.
Steve
------------------------------
From: Paul Crowley <[EMAIL PROTECTED]>
Subject: Re: Another extension to CipherSaber
Date: 24 Feb 1999 10:20:15 -0000
"Jay" <[EMAIL PROTECTED]> writes:
> I don't think this will help. To be useful, the discard count must be
> in a format that others can use, i.e. its location in the stream and
> function must be known, or it must be a shared secret. If it is part
> of the encrypted stream, the attacker can read it unambiguously for
> each possible key transaction so its primary benefit will be some
> slowdown in setup. If it is a shared secret, it is simply another form
> of key extension. A few bytes longer key will have more effect on
> security. It's true that the pass phrase has an eventual practical
> limit in Ciphersaber, but this is at a key length that is reasonably
> secure for the forseable future.
Making it a shared secret is certainly the Wrong Thing: as you say,
you would be better off putting it at the end of the pass phrase
Encrypting it at the start of the message is worse: an attacker's
plausible guess at the likely stretching you've employed will enable
them to discard passphrases much faster, and the benefit of stretching
is lost. Two useful approaches stand out:
a) include the amount of stretching in the message in plaintext
b) use my approach of prepending eight zero bytes to the message, so
you know when you've stretched it enough.
All this complicates a very simple cryptosystem quite a lot, of
course.
--
__
\/ o\ [EMAIL PROTECTED] http://www.hedonism.demon.co.uk/paul/ \ /
/\__/ Paul Crowley Upgrade your legacy NT machines to Linux /~\
------------------------------
From: Paul Crowley <[EMAIL PROTECTED]>
Subject: Re: Testing Algorithms
Date: 24 Feb 1999 10:11:12 -0000
Withheld <[EMAIL PROTECTED]> writes:
> 56-bit DES was once considered unbreakable
Simply false. DES's small key space was criticised the moment the
standard was made available for comment.
--
__
\/ o\ [EMAIL PROTECTED] http://www.hedonism.demon.co.uk/paul/ \ /
/\__/ Paul Crowley Upgrade your legacy NT machines to Linux /~\
------------------------------
From: Paul Crowley <[EMAIL PROTECTED]>
Subject: Re: Block cipher in the smallest PIC
Date: 24 Feb 1999 10:30:47 -0000
It sounds like you want this: Gideon Yuval, "Reinventing the Travois:
encryption/MAC in 30 ROM bytes", Proceedings of Fast Software
Encryption Workshop 1997. This system, designed for the 8051, uses an
eight-byte key and whatever program you happen to blow into the rest
of the PIC as an extra source of nonlinearity. I don't know if the
paper can still be found online.
--
__
\/ o\ [EMAIL PROTECTED] http://www.hedonism.demon.co.uk/paul/ \ /
/\__/ Paul Crowley Upgrade your legacy NT machines to Linux /~\
------------------------------
From: [EMAIL PROTECTED] (R. Knauer)
Crossposted-To:
sci.skeptic,sci.philosophy.meta,sci.psychology.theory,alt.hypnosis,sci.logic
Subject: Re: Randomness based consciousness?. (Was: Re: *** Where Does The Randomness
Come From ?!? *** )
Date: Wed, 24 Feb 1999 13:18:07 GMT
Reply-To: [EMAIL PROTECTED]
On Tue, 23 Feb 1999 14:31:44 GMT, [EMAIL PROTECTED] (tiger9) wrote:
>That's my point: a lot of theories and absolutely no proof! We will
>have to wait untill we die before any proof can or will be apparant,
>or we may just cease to exist and never find out anyway.
You are demanding the proof of a Positivist. How about accepting the
proof of a mathematician?
I mean, if you can accept the proof that there are 180 degrees in a
triangle, why not accept logical truths in metaphysics?
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] (R. Knauer)
Subject: Re: True Randomness
Date: Wed, 24 Feb 1999 13:20:28 GMT
Reply-To: [EMAIL PROTECTED]
On Tue, 23 Feb 1999 16:07:24 -0700, "Tony T. Warnock"
<[EMAIL PROTECTED]> wrote:
>There are more than 2 books on the subject. I'm not denigrating either book, they are
>both good. There are also dozens of journals on statistics and at least 2 on
>cryptography. There are also several on complexity and on computability.
I am surprised that something that is purported to be of such
importance would be left out of a book that has everything and then
some about probability theory.
BTW, can you recommend a book on those two topics.
>Keep on studying. It's a big field.
As long as I have a library card, I fully intend to.
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] (R. Knauer)
Subject: Re: Randomness of coin flips
Date: Wed, 24 Feb 1999 13:23:19 GMT
Reply-To: [EMAIL PROTECTED]
On Wed, 24 Feb 1999 01:49:19 GMT, Darren New <[EMAIL PROTECTED]>
wrote:
>A radical skew in *what* output?
The output that produces the number.
>We're talking about a number that's a
>probability, yes? We're talking about basically a number that tells you
>how many programs of a certain size will halt if run indefinitely. So
>what's the output that skews, and what's the evidence that the
>probability of any particular bit in that probability is 1/2? Am I
>missing something?
I must have misinterpreted what you said, because I did not mean to
imply anything like that. I was merely commenting on one of the quirks
of a uniform Bernoulli process.
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] (R. Knauer)
Subject: Re: Randomness of coin flips
Date: Wed, 24 Feb 1999 13:24:29 GMT
Reply-To: [EMAIL PROTECTED]
On Tue, 23 Feb 1999 23:10:04 -0800, Michael Sierchio <[EMAIL PROTECTED]>
wrote:
>> What on God's Green Earth (tm) is a "quincunx"?
>It's in the heavens and not on the Earth (it is a mildly favorable
>aspect of two planets).
Oh, like the conjunction of Venus and Jupiter last night.
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] (R. Knauer)
Subject: Re: Define Randomness
Date: Wed, 24 Feb 1999 13:27:22 GMT
Reply-To: [EMAIL PROTECTED]
On Tue, 23 Feb 1999 19:06:30 -0500, "D" <[EMAIL PROTECTED]> wrote:
>You know, I was reading this thread and I had an interesting thought. If
>naturally occurring phenomenon are random, and they repeat periodically,
>such as in the adage about history, then shouldn't 'crypto-grade randomness'
>actually be something completely different than randomness?
There are many different kinds of randomness. Crypto-grade randomness
is but one kind.
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] (R. Knauer)
Subject: Re: Define Randomness
Date: Wed, 24 Feb 1999 13:33:47 GMT
Reply-To: [EMAIL PROTECTED]
On Tue, 23 Feb 1999 21:11:50 -0500, "Trevor Jackson, III"
<[EMAIL PROTECTED]> wrote:
>I agree that randomness is a measure of ignorance and that there
>are many examples of imperfect systems that are practically secure without
>being provably secure.
But, how do you know which ones are and which ones are not? What
criteria are you employing to make that determination?
If you apply statistical tests to the actual numbers, you can be
deceived both ways, namely you can be deceived into believing that a
random process is non-random and that a non-random process is random.
The digit expansion of pi appears random from the point of view of
statistical measures, but it is certainly not a random process.
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] (Yikes1010)
Subject: ICS Toolkit
Date: 24 Feb 1999 13:50:04 GMT
There is reference to this program in the book Maximum Security.
The program was written by Richard Spillman.
The program is for cryptanalysis.
Does anyone know where it can be obtained?
If you have it, can you please post it to a binaries group?
Any help is appreciated.
Mike
------------------------------
From: [EMAIL PROTECTED] (Patrick Juola)
Subject: Re: Define Randomness
Date: 24 Feb 1999 08:43:00 -0500
In article <[EMAIL PROTECTED]>,
Anthony Stephen Szopa <[EMAIL PROTECTED]> wrote:
>Define Randomness
>
>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.
>
>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?
Independence of successive outcomes.
-kitten
------------------------------
From: [EMAIL PROTECTED] (Patrick Juola)
Subject: Re: Quantum Cryptography
Date: 24 Feb 1999 08:43:38 -0500
In article <[EMAIL PROTECTED]>,
fungus <[EMAIL PROTECTED]> wrote:
>
>
>"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???
Yes. And also the same government that funded research into communication
via computer networks.
-kitten
------------------------------
From: [EMAIL PROTECTED] (Patrick Juola)
Subject: Re: Testing Algorithms [moving off-topic]
Date: 24 Feb 1999 08:49:41 -0500
In article <7avprg$jvm$[EMAIL PROTECTED]>, <[EMAIL PROTECTED]> wrote:
>In article <x$[EMAIL PROTECTED]>,
> Withheld <[EMAIL PROTECTED]> wrote:
>> 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... :-)
>
>Jokes aside, people STILL can't do arithmetic. Chips have non-zero area
>and consume power. Try computing how much space is needed, how much
>power is needed, and how much cooling is needed to power (say) 10^7
>processors running in parallel.
.... making assumptions based on current technology.
The fundamental limit of powering a computer processor is *ZERO*.
Power provides *NO* limitation on how big you can make a computer.
-kitten
------------------------------
From: [EMAIL PROTECTED] (Patrick Juola)
Subject: Re: What do you all think about the new cipher devised by a 16 year old?
Date: 24 Feb 1999 08:47:56 -0500
In article <[EMAIL PROTECTED]>,
Anthony Naggs <[EMAIL PROTECTED]> wrote:
>After much consideration fungus decided to share these wise words:
>>
>>It's still a secret, until the "patents go through".
>
>Indeed.
>
>>This sounds like twaddle to me. Once a patent is filed, you can publish
>>the algorithm, whether it finally gets granted or not.
>
>Only in the USA.
I believe post-application publication is legitimate anywhere in the
world.
-kitten
------------------------------
From: [EMAIL PROTECTED] (Patrick Juola)
Subject: Re: Testing Algorithms
Date: 24 Feb 1999 08:52:48 -0500
In article <[EMAIL PROTECTED]>,
Tim Woodall <No Spam [EMAIL PROTECTED]> wrote:
>
>Steven Runyeard wrote in message <[EMAIL PROTECTED]>...
>>Someone wrote:
>>>There's no garantee that this growth rate will continue. In fact
>>>everything points to the opposite.
>>
>>No, there is no quarantee of this. There is also no quarantee that the
>>speed of light will be a barrier.
>
>You really don't understand how big 2^256 is.
>
>Consider a computer consisting of a single water molecule.
>Consider that this computer can test 10^9 keys per second.
Why 10^9? As long as we're making silly assumptions, I'm going
to assume that it can test 10^80 keys per second.
Why is your assumption less silly than mine?
-kitten
------------------------------
From: [EMAIL PROTECTED] (R. Knauer)
Subject: Re: Define Randomness
Date: Wed, 24 Feb 1999 13:58:37 GMT
Reply-To: [EMAIL PROTECTED]
On Tue, 23 Feb 1999 20:40:53 -0800, Anthony Stephen Szopa
<[EMAIL PROTECTED]> wrote:
>( A TRNG that is not perfect is not a TRNG?? Might it be a PRNG??)
No, it is not a PRNG. A PRNG is a process that calculates
pseudo-random numbers algorithmically from some initial state.
A TRNG is a process that is capable of generating all possible finite
sequences equiprobably. It is known that algorithms cannot be TRNGs
(von Neumann).
Notice the key work "capable". A TRNG is not required to actually
produce all such numbers, just be capable of doing so. A
less-than-perfect TRNG is still a TRNG - it is just less than perfect.
Look at it in terms of circularity and a wheel that is machined to a
very high degree of circularity. Strictly speaking the wheel is not
perfectly circular but it is so close that for all effects and
purposes it is circular. IOW, it was designed to be circular but fell
slightly short of the mark. That does not make it a square.
The same holds for the TRNG. We realize that the implementation of the
TRNG specification in the real world will not be perfect - nothing in
the real world is ever effectively perfect. But that does not mean
that the slightest imperfection makes the TRNG something fundamentally
different.
Just as the crucial test of the wheel for circularity is whether it
rolls properly or not, the crucial test for a real-world TRNG is
whether it makes unbreakable ciphers or not. As some people have
proposed, there are candidates for TRNG simulators which, it is
alleged, have the ability to generate numbers that, for all practical
purposes, are crypto-grade random (i.e., unbreakable).
But conducting statistical tests on their output does not certify that
they are crypto-grade. You have to use them to make test ciphers and
then try to break those test ciphers. If the test ciphers withstand
such attacks, you might have some confidence that they cannot be
broken. But that depends on your intended usage of the system. If you
use it too much, you need to test it some more.
And so you start chasing your tail unless you can come up with some
test method that converges on a result - like Bayesian inference,
where each turn of the inferential data-hypothesis crank leads to a
more "probably approximately correct" (pac) result. I have not seen
such a method discussed here.
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] (Patrick Juola)
Subject: Re: True Randomness
Date: 24 Feb 1999 08:58:37 -0500
In article <[EMAIL PROTECTED]>,
R. Knauer <[EMAIL PROTECTED]> wrote:
>On Tue, 23 Feb 1999 16:07:24 -0700, "Tony T. Warnock"
><[EMAIL PROTECTED]> wrote:
>
>>There are more than 2 books on the subject. I'm not denigrating either book, they are
>>both good. There are also dozens of journals on statistics and at least 2 on
>>cryptography. There are also several on complexity and on computability.
>
>I am surprised that something that is purported to be of such
>importance would be left out of a book that has everything and then
>some about probability theory.
Um, Li and Vitanyi doesn't have everything about probability theory;
it's a specialized book on a niche area. It has a hell of a lot
of stuff specifically about the theory of Kolmogorov complexity;
but even in the area of complexity theory, there are several dozen
competing definitions that don't get a look-see; for example, the
topic "linear complexity" doesn't appear in the index.
-kitten
------------------------------
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