Cryptography-Digest Digest #43, Volume #12 Fri, 16 Jun 00 10:13:00 EDT
Contents:
Re: primality tests (Andrew John Walker)
Re: obfuscating the RSA private key (Mark Wooding)
Re: Random sboxes... real info (Tim Tyler)
Re: Application specific SBoxes in Blowfish? ("Sam Simpson")
Re: Cipher design a fading field? (Alan Braggins)
Re: Cipher design a fading field? (Nicol So)
Encryption on missing hard-drives ([EMAIL PROTECTED])
Re: On using compression as proper means of encryption (SCOTT19U.ZIP_GUY)
Re: Encryption on missing hard-drives (S�bastien SAUVAGE)
Re: Random sboxes... real info (SCOTT19U.ZIP_GUY)
Re: Cipher design a fading field? (Mark Wooding)
Re: Cipher design a fading field? ("Trevor L. Jackson, III")
Re: Def of "nonlinear order" (=?iso-8859-1?Q?H=E5vard?= Raddum)
Re: Cipher design a fading field? ("Trevor L. Jackson, III")
Re: Encryption on missing hard-drives (SCOTT19U.ZIP_GUY)
Re: Cipher design a fading field? (Tim Tyler)
Re: Cipher design a fading field? (Alan Braggins)
----------------------------------------------------------------------------
Subject: Re: primality tests
From: [EMAIL PROTECTED] (Andrew John Walker)
Date: 16 Jun 2000 11:30:27 +1000
Bob Silverman <[EMAIL PROTECTED]> writes:
>In article <8ianjq$r15$[EMAIL PROTECTED]>,
> [EMAIL PROTECTED] wrote:
>> hello all,
>>
>> when i implement probabilistic primality tests,
>> i know that
>>
>> with Millrob for one base error possibility 0.25
>False. The probability is bounded above by 1/4, but the actual
>probability depends on the size of p.
An exact fromula is known which requires the factorisation, I posted the
reference just a few days ago in the
"An interesting page on the Rabin-Miller PP test" thread.
Andrew
------------------------------
From: [EMAIL PROTECTED] (Mark Wooding)
Subject: Re: obfuscating the RSA private key
Date: 16 Jun 2000 09:39:25 GMT
Mack <[EMAIL PROTECTED]> wrote:
> The most common form of threshold scheme relies on N-spacial geometry.
Does it? I thought the most usual threshold scheme was Shamir's, which
uses polynomial interpolation in a finite field.
-- [mdw]
------------------------------
From: Tim Tyler <[EMAIL PROTECTED]>
Subject: Re: Random sboxes... real info
Reply-To: [EMAIL PROTECTED]
Date: Fri, 16 Jun 2000 09:59:15 GMT
David A. Wagner <[EMAIL PROTECTED]> wrote:
: Nope, I stand by my statement.
Yes. Drat ;-) It turns out it was me who was dreaming :-|
I should obviously have realised this myself the first time around.
I'll have to mentally mark this area as one where my intuition is
likely to lead me astray unless I am cautious.
My apologies for exposing everyone to what turns out to have been pretty
mindless blathering on the subject.
--
__________ Lotus Artificial Life http://alife.co.uk/ [EMAIL PROTECTED]
|im |yler The Mandala Centre http://mandala.co.uk/ Be good, do good.
------------------------------
From: "Sam Simpson" <[EMAIL PROTECTED]>
Subject: Re: Application specific SBoxes in Blowfish?
Date: Fri, 16 Jun 2000 11:40:25 +0100
That precisely it Tim.
--
Sam Simpson
Comms Analyst
http://www.scramdisk.clara.net/ for ScramDisk hard-drive encryption &
Delphi Crypto Components. PGP Keys available at the same site.
Tim Tyler <[EMAIL PROTECTED]> wrote in message
news:[EMAIL PROTECTED]...
> Andru Luvisi <[EMAIL PROTECTED]> wrote:
> : "Sam Simpson" <[EMAIL PROTECTED]> writes:
> : [snip]
>
> :> My aim is to have a new version of Blowfish totally incompatible
with
> :> existing implementations....
>
> : I wouldn't expect that there would be any problems, but why?
>
> Possibility of existence of off-the-shelf Blowfish cracking
machine?
> --
> __________ Lotus Artificial Life http://alife.co.uk/
[EMAIL PROTECTED]
> |im |yler The Mandala Centre http://mandala.co.uk/ Goodbye
cool world.
------------------------------
From: Alan Braggins <[EMAIL PROTECTED]>
Subject: Re: Cipher design a fading field?
Date: 16 Jun 2000 13:04:46 +0100
"Douglas A. Gwyn" <[EMAIL PROTECTED]> writes:
> for any given example program P there is a deterministic method M
> that creates a program H = M(P) that will determine in finite time
> whether or not P halts. Thus, M itself is a component of a fixed
> procedure T that applied to *arbitary* P will determine in finite
> time whether or not P halts.
Consider all possible 1 bit programs and "Halts" outputs, and
construct the tables
( ( ( 1 ), 1 ), ( ( 0 ), 1 ) )
( ( ( 1 ), 1 ), ( ( 0 ), 0 ) )
( ( ( 1 ), 0 ), ( ( 0 ), 1 ) )
( ( ( 1 ), 0 ), ( ( 0 ), 0 ) )
We lookup the program in the first element of a pair, and output the
second element. This is four programs. One of them will give the right
answer for both cases.
So we have deterministically created a suitable program (and 3 junk
ones). We don't know which is which, so we can't use this as a
building block to the general case, but the correct program _exists_).
Now consider all possible 2 bit programs, and construct the tables
( ( ( 11 ), 1 ), ( ( 10 ), 1 ), ( ( 01 ), 1 ), ( ( 00 ), 1 ) )
( ( ( 11 ), 1 ), ( ( 10 ), 1 ), ( ( 01 ), 1 ), ( ( 00 ), 0 ) )
( ( ( 11 ), 1 ), ( ( 10 ), 1 ), ( ( 01 ), 0 ), ( ( 00 ), 1 ) )
( ( ( 11 ), 1 ), ( ( 10 ), 1 ), ( ( 01 ), 0 ), ( ( 00 ), 0 ) )
( ( ( 11 ), 1 ), ( ( 10 ), 0 ), ( ( 01 ), 1 ), ( ( 00 ), 1 ) )
( ( ( 11 ), 1 ), ( ( 10 ), 0 ), ( ( 01 ), 1 ), ( ( 00 ), 0 ) )
( ( ( 11 ), 1 ), ( ( 10 ), 0 ), ( ( 01 ), 0 ), ( ( 00 ), 1 ) )
( ( ( 11 ), 1 ), ( ( 10 ), 0 ), ( ( 01 ), 0 ), ( ( 00 ), 0 ) )
( ( ( 11 ), 0 ), ( ( 10 ), 1 ), ( ( 01 ), 1 ), ( ( 00 ), 1 ) )
( ( ( 11 ), 0 ), ( ( 10 ), 1 ), ( ( 01 ), 1 ), ( ( 00 ), 0 ) )
( ( ( 11 ), 0 ), ( ( 10 ), 1 ), ( ( 01 ), 0 ), ( ( 00 ), 1 ) )
( ( ( 11 ), 0 ), ( ( 10 ), 1 ), ( ( 01 ), 0 ), ( ( 00 ), 0 ) )
( ( ( 11 ), 0 ), ( ( 10 ), 0 ), ( ( 01 ), 1 ), ( ( 00 ), 1 ) )
( ( ( 11 ), 0 ), ( ( 10 ), 0 ), ( ( 01 ), 1 ), ( ( 00 ), 0 ) )
( ( ( 11 ), 0 ), ( ( 10 ), 0 ), ( ( 01 ), 0 ), ( ( 00 ), 1 ) )
( ( ( 11 ), 0 ), ( ( 10 ), 0 ), ( ( 01 ), 0 ), ( ( 00 ), 0 ) )
Again, one of these will give the right answers for all four possible
programs, so we have deterministically created a suitable program (and
15 junk ones - we don't know which is which, so we can't use this as a
building block to the general case, but the correct program _exists_).
We can extend this to any given finite size example program P.
------------------------------
From: Nicol So <[EMAIL PROTECTED]>
Subject: Re: Cipher design a fading field?
Date: Fri, 16 Jun 2000 08:41:49 -0400
Reply-To: see.signature
"Douglas A. Gwyn" wrote:
>
> "Trevor L. Jackson, III" wrote:
> > The issue isn't how difficult it is to write the program, but that
> > with sufficient ingenuity it is possible to write the program. The
> > halting problem states that such a program is impossible to write,
> > even for Karnak, if the set of programs is infinite.
>
> There is nothing about an infinite set of programs in the actual
> theorem.
As I pointed out in an earlier message, any problem with only a finite
number of instances is trivially decidable. (The question of
decidability is interesting only because we're trying to capture an
infinite number of answers with a finite representation (an algorithm).
Any finite language can be recognized by table lookup, using an
appropriate table.)
The usual proof of undecidability for the halting problem fails when a
"size restricted" version of the halting problem is substituted for the
general one.
The usual proof goes like this:
(1) Assume that the halting problem is decidable by a Turing Machine H.
(2) From H, we can construct a derived TM G with the property that: G
halts on exactly the descriptions of those TM's which don't halt on
their own descriptions.
(3) Does G halt on its own description?
(4) The answer can be neither affirmative nor negative, because either
would violate the property established in (2).
(5) Therefore the (only) assumption in the argument must be false.
If we replace the halting problem with a size restricted version, the
property of G would become:
G halts on exactly the descriptions of those TM's which don't halt on
their own descriptions, which are short than size limit L.
"No" would be a possible answer to (3) because the description of G
could be longer than L. You cannot force a dilemma as before.
--
Nicol So, CISSP // paranoid 'at' engineer 'dot' com
Disclaimer: Views expressed here are casual comments and should
not be relied upon as the basis for decisions of consequence.
------------------------------
From: [EMAIL PROTECTED]
Subject: Encryption on missing hard-drives
Date: Fri, 16 Jun 2000 12:43:16 GMT
I'm sure we've all read or heard the news lately about the
security "lapses" at some government facilites with respect to computer
equipment (first laptops at the State Dept, now hard drives from Los
Alamos). In both cases, officials have responded that no secrets are in
jepardy because the equipment uses encryption.
So, I'm thinking, yeah, with PGP or some other stong encryption, that
data is probably secure. Then I realize, hey wait a minute, we're
talking the Fed Gov't here! They don't use PGP! The Feds are generally
the ones who pooh-pooh breaks, cracks and glitches turned up by
the "amateur" hacker community.
So, now I'm curious.
What *do* they use? What is the current "state-of-the-art" GAO approved
encryption system. Please don't tell me they still you single round
DES! Kiss that data good-bye!
Anyone know?
Sent via Deja.com http://www.deja.com/
Before you buy.
------------------------------
From: [EMAIL PROTECTED] (SCOTT19U.ZIP_GUY)
Subject: Re: On using compression as proper means of encryption
Date: 16 Jun 2000 12:52:06 GMT
[EMAIL PROTECTED] (David Hopwood) wrote in
<[EMAIL PROTECTED]>:
>-----BEGIN PGP SIGNED MESSAGE-----
>
>"SCOTT19U.ZIP_GUY" wrote:
>> [EMAIL PROTECTED] (David Hopwood) wrote in
>> <[EMAIL PROTECTED]>:
>> >Mok-Kong Shen wrote:
>> >[snip]
>> >> Use a PRNG (crypto strength unessential) with a key as
>> >> seed to generate a sequence of symbols (length of sequence
>> >> determined by PRNG) to initialize an adaptive Huffman
>> >> compression algorithm, taking care that all symbols of the
>> >> plaintext alphabet are input at least once. The output in
>> >> this initialization phase is discarded. Then start feeding
>> >> symbols of the plaintext into the algorithm. Use the result
>> >> as ciphertext. Decryption amounts to a corresponding
>> >> decompression after doing the same initialization.
>> >
>> >This is very weak. It amounts to no more than a simple
>> >substitution on variable-length symbols. Frequency analysis
>> >can be applied almost as easily to variable-length symbols as
>> >it can to fixed-length symbols.
>>
>> I am not saying it is as strong as scott19u.zip but
>> it is very hard to try to do frequency analysis on variable
>> length symbols.
>
>I don't see why, but maybe we have different ideas of what is
>"very hard". It would be extremely tedious to do by hand, but
>shouldn't be too difficult on a PC.
>
>> Becasue with out a tree you do not know where one symbol starts
>> and one symbol ends.
>
>You don't need to know that in advance. One possible approach is
>to assume that any bit position could be the start of a symbol,
>and tabulate the frequencies of all bit sequences (of lengths up
>to some reasonably small bound) starting from each position.
>Some of the actual symbols should stand out despite the noise
>caused by incorrect symbol boundaries; at that point you can
>guess most of the boundaries and repeat to give a more accurate
>frequency analysis.
>
>> Obviously you haven't given this much thought.
>
>Obviously you think that just because *you* don't know how to do
>something, it must be difficult.
Even Mr Rivest who seems to have some understanding of the usefulness
of all or mothing encryption seems to realize this is not a trival
problem and even with small alphabets can lead to ambiguities that
do not lead to a solution. This is not to say that repeated plain text
attacks would not work but does say that in many cases that a single
compressed file can be such that no one solution can be found.
I would expect this reply from Tommy but at least I thought you
would read the following
"On the Cryptanalysis of Huffman Codes
by
Mojdeh Mohtashemi
Submitted to the Department of Electrical Engineering and Computer Science
in partial fulfillment of the requirements for the degree of
Master of Science in Electrical Engineering and Computer Science
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
May 1992
c
fl Massachusetts Institute of Technology 1992
Signature of Author
Department of Electrical Engineering and Computer Science
May 18, 1992
Certified by
Ronald L. Rivest
Professor of Computer Science
Thesis Supervisor"
The above paper looks at the problem from the point of view
of static huffman coding. But even though it fails to treat the
end of the compression stream or consider the addtioanal complexites
of "adaptive huffman compression" I am sure that a man of your
intelligence would fing it enlightening.
http://members.xoom.com/ecil/compress.htm
------------------------------
Subject: Re: Encryption on missing hard-drives
From: [EMAIL PROTECTED] (S�bastien SAUVAGE)
Date: Fri, 16 Jun 2000 13:09:14 GMT
[EMAIL PROTECTED] wrote in <8id7d0$j55$[EMAIL PROTECTED]>:
<snip>
>Anyone know?
I don't know what they use, but I use ScramDisk and E4M.
That's on-the-fly disk encryption.
Every single sector of the disk is encrypted (boot sector, FATs,
directories, files, empty sectors).
Free, transparent, source code included, fast, easy to use, reliable.
Give them a try !
http://www.scramdisk.clara.net/
http://www.e4m.net/
I truly doubt any Fed would be able to decipher easily 256 bits Blowfish,
IDEA or TripleDES :-)
--
==================================
S�bastien SAUVAGE
[EMAIL PROTECTED]
http://www.bigfoot.com/~sebsauvage
==================================
------------------------------
From: [EMAIL PROTECTED] (SCOTT19U.ZIP_GUY)
Subject: Re: Random sboxes... real info
Date: 16 Jun 2000 13:06:43 GMT
[EMAIL PROTECTED] (Tim Tyler) wrote in <[EMAIL PROTECTED]>:
>David A. Wagner <[EMAIL PROTECTED]> wrote:
>
>: Nope, I stand by my statement.
>
>Yes. Drat ;-) It turns out it was me who was dreaming :-|
>
>I should obviously have realised this myself the first time around.
>
>I'll have to mentally mark this area as one where my intuition is
>likely to lead me astray unless I am cautious.
>
>My apologies for exposing everyone to what turns out to have been pretty
>mindless blathering on the subject.
Tim that shows your more of a man than "David A. Wagner" who falsely
stated his "Slide Attack" has destroyed scott16u.zip and later only
vagley admitted that he could not be really bothered to look at the
C code when people tried to find a weakness in my method amd it was not
there when they tried to use his weak methods.
I assime you would also state that you are wrong about 1-1 compression
if you ever saw that it was bad. But Mr wagner is so full of it, That
he falsely assumes that there is no advantage to 1-1 compression since
I seem to be the first one to right about it and he like so many people
with an over inflated ego think they no everything. So don't worry about
this one point learn from it and go on. But it least no that Wagner lacks
a lot of what you know about compression.
http://members.xoom.com/ecil
------------------------------
From: [EMAIL PROTECTED] (Mark Wooding)
Subject: Re: Cipher design a fading field?
Date: 16 Jun 2000 13:12:05 GMT
Alan Braggins <[EMAIL PROTECTED]> wrote:
> Consider all possible 1 bit programs and "Halts" outputs, and
> construct the tables
[etc.]
> We can extend this to any given finite size example program P.
Aha. I see the problem. Your two programs are different sorts of
things. Your program to decide the haltingness of something accepts a
program as input and reports an answer; the programs which are its
arguments don't accept input.
The argument can be described formally like this:
Let P be a finite set of programs which accept input from a finite set
I. For any subset Q of P x I, define H_Q : P x I -> { 0, 1 } to have
the value 1 if its input is a member of Q and 0 otherwise. We can
clearly implement programs to compute H_Q for all Q: there are 2^{|P x
I|} of them to write, and they're not very interesting.
There is some subset Z of P x I with the property that (p, i) <- Q iff
program p halts when given input i. And therefore there is a program
H_Z which computes the halting function.
This is fine. However, this isn't like the general halting problem. In
particular, our `halting program' is *not* part of the set we're
considering. In particular, since I is finite, there is no injection
which maps pairs from P x I to I, so H_Z's input space doesn't match.
-- [mdw]
------------------------------
Date: Fri, 16 Jun 2000 09:26:56 -0400
From: "Trevor L. Jackson, III" <[EMAIL PROTECTED]>
Subject: Re: Cipher design a fading field?
"Douglas A. Gwyn" wrote:
> "Trevor L. Jackson, III" wrote:
> > The issue isn't how difficult it is to write the program, but that
> > with sufficient ingenuity it is possible to write the program. The
> > halting problem states that such a program is impossible to write,
> > even for Karnak, if the set of programs is infinite.
>
> There is nothing about an infinite set of programs in the actual
> theorem. If it required such a condition, that would imply that
> for any given example program P there is a deterministic method M
> that creates a program H = M(P) that will determine in finite time
> whether or not P halts. Thus, M itself is a component of a fixed
> procedure T that applied to *arbitary* P will determine in finite
> time whether or not P halts.
> proc T(prog P):bool def={ import M(prog):bool; return eval M(P) }
> That means that T solves the general halting problem, but we know
> that has been shown to be impossible. One concludes that the
> starting assumption was false (so such a condition isn't required).
The construct you describe is a generalization from a specific, always a
slippery process. The non-existence of T tells us nothing about the existence
of M.
------------------------------
From: =?iso-8859-1?Q?H=E5vard?= Raddum <[EMAIL PROTECTED]>
Subject: Re: Def of "nonlinear order"
Date: Fri, 16 Jun 2000 15:17:03 +0100
Mike Rosing wrote:
> tomstd wrote:
> >
> > I am confused now (uh-oh) I thought the nonlinear order of a
> > function can be computed using a modification of the Bit
> > Independence Criterion (BIC). For example a function is
> > nonlinear to the order r if for all masks with a hamming weight
> > of 2..r you can perform a BIC test and pass.
> >
> > For example the mask '3' would be 11 in binary and mean to test
> > the first and second nx1 sboxes. 7 would be 111 and mean to
> > test the first three.
> >
> > In otherwords no r-tuple of nx1 sboxes are linearly dependent.
> >
> > If this is the case then the findings of Knudsen and Jakobsen
> > are wrong when they discuss the nonlinear order of cubics and
> > quadratics (etc) in GF(2^n). For my 20 sboxes I posted earlier
> > they were found to be perfectly nonlinear upto 7-tuples of 8x1
> > sboxes...
>
> I have no idea what you're talking about, so I expect that by the
> time you explain it to me you'll have figured out the problem :-)
>
> Linearly dependent means we can build a function from the sboxes
> with constant coefficients. I don't understand what you mean by
> "nonlinear order". If you build a function with powers of sboxes
> (is that what qudratics and cubics mean?) then it's automaticly
> nonlinear.
>
> For example, if S(x) = x1 + x2 + x3 is the sum of 3 sboxes, it's
> linear. If S(x) = x1^2 + x2^3 + x3^5 it's nonlinear. The order
> of S is 5 in this case. Is that what you mean?
>
> Patience, persistence, truth,
> Dr. mike
A definition of non-linear order :
Consider an mxn sbox (m bits of input and n bits of output) Each of the
n outputbits can be
expressed as a polynomial in the m inputbits x_0,....,x_{m-1}. Let
these polynomials be
f_1,...f_n. If we xor some of these f_i's together, it might happen
that some high-degree terms
cancel out, so that the sum of these f_i's has lower degree than any of
the individual f_i's. The
lowest degree polynomial one can create by summing a non-empty subset of
{f_1,...,f_n}
together is the non-linear order of the sbox.
------------------------------
Date: Fri, 16 Jun 2000 09:44:49 -0400
From: "Trevor L. Jackson, III" <[EMAIL PROTECTED]>
Subject: Re: Cipher design a fading field?
"John A. Malley" wrote:
> "Douglas A. Gwyn" wrote:
> >
> > The original question was whether cryptanalysis was equivalent to
> > solving
> > the halting problem.
>
> And what a marvelous question. Here's a thought experiment. Consider
> this "cryptanalysis" of a substitution cipher.
>
> String P of the set of strings of the English language E gets encrypted
> with a uniliteral substitution. Let's model the uniliteral substitution
> as a finite state transducer (FST), a deterministic finite automaton.
> Each state transition of an FST is labeled with two symbols, one for the
> input symbol for that transition and the other for the output symbol for
> that transition. The FST takes an input plaintext string P and makes an
> output cipher text string C.
>
> Here's the proposed cryptanalysis:
>
> Make an FST corresponding to all possible uniliteral substitutions. We
> get a finite set of k FSTs. Run the cipher text C through each FST. We
> get k candidate plain text strings in a set S.
>
> Now we must decide which element s of S is a member of the set of
> English language strings E. We (assume) only one element of S should be
> "sensible English." The FST for the s in E is the "key" to the
> uniliteral substitution cipher mapping cipher text to plain text.
>
> Is the question, "Is s an element of E?" , decidable (by an algorithm) ?
>
> Decidability depends on the language E.
>
> Every context-free language is decidable.
> Regular languages are a subset of context free languages, so every
> regular language is decidable.
> BUT, there are Turing-recognizable languages that are not decidable and
> even some languages that are NOT Turing-recognizable. (Please please
> post it if you ever find it. Would love to see one.)
>
> So, if E is a regular or context-free language, a Turing machine could
> decide that s is an element of E.
> If E is Turing-recognizable and not regular or context free, it may or
> may not be decidable.
>
> So what kind of language is English? Is there an algorithm that can
> decide is a string belongs to the English language? (As well as other
> human languages.)
English and other human languages aren't formally defined, so categorizing
them precisely is not possible.
Consider that excluding a particular class of strings from formal English
would almost guarantee that poets, punsters, and comics would work the
excluded area and find ways to incorporate the forbidden fruit into their
material. If the writers managed to use the forbidden area to communicate
with an audience it would be very difficult to defend the idea that the
excluded area was not part of the language.
We'd need to timestamp the language definition the way programming languages
are time stamped by the date of their standards and fiat currency is time
stamped by the date of its issuance (1970 USD versus 1999 USD and F66 versus
F77).
------------------------------
From: [EMAIL PROTECTED] (SCOTT19U.ZIP_GUY)
Subject: Re: Encryption on missing hard-drives
Date: 16 Jun 2000 13:33:04 GMT
[EMAIL PROTECTED] wrote in <8id7d0$j55$[EMAIL PROTECTED]>:
>I'm sure we've all read or heard the news lately about the
>security "lapses" at some government facilites with respect to computer
>equipment (first laptops at the State Dept, now hard drives from Los
>Alamos). In both cases, officials have responded that no secrets are in
>jepardy because the equipment uses encryption.
>
>So, I'm thinking, yeah, with PGP or some other stong encryption, that
>data is probably secure. Then I realize, hey wait a minute, we're
>talking the Fed Gov't here! They don't use PGP! The Feds are generally
>the ones who pooh-pooh breaks, cracks and glitches turned up by
>the "amateur" hacker community.
>
>So, now I'm curious.
>
>What *do* they use? What is the current "state-of-the-art" GAO approved
>encryption system. Please don't tell me they still you single round
>DES! Kiss that data good-bye!
>
>Anyone know?
>
>
>Sent via Deja.com http://www.deja.com/
>Before you buy.
>
Well as an X governemnt worker I would bet that the story that the
data was encrypted is false. Also condsidering the locked bag had the
keys to unlock it on the wall, IF it was encrypted which I doubt. The
one who stole it either already new the password to decrypt it or got
the password from some notes lying around in the valut.
But why does any one really care. Is there really any useful nuclear
info laying around that the chinese have not already stolen or bought
or got through government contractors.
My question to you is. Why on earth would you belive anything
that this administration has said about security? Only congress
seems to belive the repeated lies over and over again or at least
they pretend they belive the lies or they would have removed Clintin
and his assocates long ago. Surely our congressman could have checked
on the lies that our nuclear secrets are safe or maybe there so busy
the security of this country is of no concern to them.
We don't need to worry until at least 5 yers down the road when
the chinese decide to take us on and start testing the nuclear
devices on our crime ridden cites. But then again I guess we reap
what we sow.
What the news media in its zeal to protect their Saint Clinton
his forgotten to mention is that sine there is no real accounting
system in place for the vault. Is that anyone could have taken not
only the missing disks but others and coped them and replaced the
originals. If it were not for the fire. No one would have even known
that the disks were taken. They would have been coped and returned.
then Clinton and his sidekicks could honestly say that the security
improvements at Los Alamos that they bragged about have shown that
no more data was stolen. It is hard to prove data is missing if you
close your eyes to it. Something politicans seems to know very well.
Maybe the clown who started the fire should get a reward. If is was
not for his great fore sight. We would never have known that Los
Alamos has less security than your local library.
------------------------------
From: Tim Tyler <[EMAIL PROTECTED]>
Subject: Re: Cipher design a fading field?
Reply-To: [EMAIL PROTECTED]
Date: Fri, 16 Jun 2000 13:48:57 GMT
Douglas A. Gwyn <[EMAIL PROTECTED]> wrote:
: There is nothing about an infinite set of programs in the actual
: theorem. If it required such a condition, that would imply that
: for any given example program P there is a deterministic method M
: that creates a program H = M(P) that will determine in finite time
: whether or not P halts. [...]
I don't think so. It would imply that for any given example program
P there *exists* a program which would determine whether that program
halts. This is true - many such programs exist.
An example would include one of:
10 PRINT "This program halts."
...or...
10 PRINT "This program never terminates."
The halting problem as normally understood relates to the *existence*
(or otherwise) of the halting-determination program. Finding the
halting-determination program another issue.
--
__________ Lotus Artificial Life http://alife.co.uk/ [EMAIL PROTECTED]
|im |yler The Mandala Centre http://mandala.co.uk/ Niagra falls.
------------------------------
From: Alan Braggins <[EMAIL PROTECTED]>
Subject: Re: Cipher design a fading field?
Date: 16 Jun 2000 15:07:24 +0100
[EMAIL PROTECTED] (Mark Wooding) writes:
> Alan Braggins <[EMAIL PROTECTED]> wrote:
> > We can extend this to any given finite size example program P.
>
> Aha. I see the problem. Your two programs are different sorts of
> things. Your program to decide the haltingness of something accepts a
> program as input and reports an answer; the programs which are its
> arguments don't accept input.
Or at least they only accept a finite amount of input, since then we can
just encode the possible inputs along with the program (e.g. stick the
program encoding and its input on a finite length input to a Universal
Turing machine).
Which I think means my post was a valid illustration of the argument
someone else was making earlier, but that that argument (and my post)
was wrong if we include finite programs taking a potentially infinite
input, which we should. Rats. This is what comes of not thinking
carefully enough before making sci.crypt postings when bored waiting
for a long compile to halt....
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