Cryptography-Digest Digest #852, Volume #8 Wed, 6 Jan 99 01:13:03 EST
Contents:
Re: On the Generation of Pseudo-OTP (wtshaw)
Re: symmetric vs various asymmetric [was: DH is "stronger" than RSA?] (Bill Unruh)
Re: What is left to invent?
Re: Help: a logical difficulty ("Trevor Jackson, III")
One-time pads not secure ? (NSA's Venona project) (Serge-Antoine Melanson)
Re: coNP=NP Made Easier? (rosi)
----------------------------------------------------------------------------
From: [EMAIL PROTECTED] (wtshaw)
Crossposted-To: talk.politics.crypto
Subject: Re: On the Generation of Pseudo-OTP
Date: Tue, 05 Jan 1999 17:40:16 -0600
In article <[EMAIL PROTECTED]>, [EMAIL PROTECTED] wrote:
>
> >In the above I have made a humble attempt to sketch one possible way
> >of obtaining a pseudo-OTP. I should appreciate your opinions on that
> >and suggestions of other ways of advantageously generating such for
> >applications in the future 56-bit environment.
>
> I suspect that if such systems became widespread, the authorities
> would claim that the pad thus obtained constitute a key of length
> greater than 56 bits, and therefore is restricted.
Let's get it straight, the *authorities* about crypto are not the same
ones that are trying to sell the square wheels. The real fight is not
over what the limit might be designated, but in the reasonable right to
designate things beyond ability to be controlled. The clipboard is like a
copy machine, and copies can be copied themselves. There is no way to
keep ciphertexts from be so handled, so keylengths can combine.
It comes down to whether their is a limit that can be enforced on logic.
Those that pretend that they can arbitarilly make the world dumb-down to
their rules are not too bright, as they just as well might try to
legislate the weather.
Freedom is all about not having to put up with capracious and arbitrary
limitations. It seems that those that most want to do this sort of thing
have a rather poor record when given all the power to superintend the
behavior of their resident populations; can you say depotism and
intolerance?
> After all, the whole purpose for a 56 bit key is that there can only
> be 2^56 possible plaintexts and therefore any intelligible message
> over the unicity length of 8.2 ASCII characters obtained by a brute
> force attack must be the intended message. IOW there is only one
> intelligible message possible of length greater than 8.2 ASCII
> characters with a 56-bit cryptosystem.
It is not as simple as that, numbers have nothing to do with it. Justify
that, as these powermongers do, and keylengths can be set to anything,
including where they would have it, at almost zero, eliminating crypto all
together, at least on paper. Now, those in some spots are so willing to
surrender their privacy and personal options in life, that they rollover
at the least direction. Americans do not respond that way; thinking that
they do is begging for lots of trouble.
Those is some parts of the world tremble when government speaks; most
Americans don't. Many would like Americans to fear the law; we don't
generally. We do obey those things which make sense to us, and thumb our
noses at those that don't.
This is not disrespect for law, but disrespect to those that would use
abuse the law to do things that it should not. There are lots of good
laws, regulations, and common sense practices; we delight in these, and
even some of us, follow lots of uncompelled courtesies; these are the
things that are not crap, juries tend to agree.
Every now and then, groups get a little too big for their britches, and
garner enough power to annouce their intent to reform the world, they
think; it never works here as people don't forever buy that others can
make all jugements for them and restrict their well established and
practiced life choices. We have had just a bit too much of small groups
trying to do this, for their interests are those that they protect first,
the public welfare be damned. So enough of this Boss Hogism.
Politicos like to legislate the truth, to even changing the meanings of
words, 1984-style, to suit their purpose. Cults tend to do the same thing
with meanings. There is no honor in any of this behavior. What they
cannot effectively control, some seek to destroy. Technical truths are
difficult to deal with since nature has its own agenda. America is a
pluralistic society, a proposition that some cannot accept; those that try
seem to always get belted with the pendulum that they tried to kick in the
wrong direction.
Those in other countries, they are generally cannot understand American
dynamics, and many have a history of self-imposed disasters. I wish
Europe well, but their tradition of temporary pax, mixed with their
tradition of loonies getting the most evil things done speaks for itself.
Some see all things as a social contract;America is not built on that as
much a locking in protections that are needed to control the natural
tendencies of government to abuse their power, our contract, if any, is
with logic, reason, and wisdom, things not easily gained, and worth
fighting for to protect.
--
If government can make someone answer a question as they want him to, they can make
him lie, then, punish him for not telling the truth. Such an outrage constitutes
entrapment.
In Base 81: y\7RBRNBN 6*1O+aDR* QBOMR1OhE \*/XtS4+~ ;g/4,Y=Jn 6)IL;OC;H o93bR?bk\
v+/G(J=lE Ni@8L*x)I L(!\+O6;E Hu~u;Ho;R 9lX=g3x*n :Y(Yce;w~ 3l(9kS;NT YfmnPX=ya
------------------------------
From: [EMAIL PROTECTED] (Bill Unruh)
Crossposted-To:
alt.security.pgp,comp.security.misc,talk.politics.crypto,comp.security.pgp.discuss
Subject: Re: symmetric vs various asymmetric [was: DH is "stronger" than RSA?]
Date: 6 Jan 1999 04:42:11 GMT
In <[EMAIL PROTECTED]> Anne & Lynn Wheeler <[EMAIL PROTECTED]> writes:
>one approximation i've seen is that RSA "strength" is roughly
>10**(sqrt(N))
No!. This was (sort of) the time for the quadratic sieve. However the
Number Field Sieve is more efficient for long keys.
The statement is that it is roughly.
with the coefficient in front and the value of "1.9" are both uncertain.
e^(1.9 (ln(N)^(1/3) (ln(ln(N)))^(2/3)))
On the other hand all such estimates are very rough and probably should
not be believed. (eg the 1.9 I have seen postulated to be as low as 1.5
and high as 1.93. That makes an enormous difference for large keys.)
------------------------------
From: [EMAIL PROTECTED] ()
Subject: Re: What is left to invent?
Date: 6 Jan 99 04:50:45 GMT
Darren New ([EMAIL PROTECTED]) wrote:
: The only thing I can think of is the theory behind making a block
: cypher's S-boxes secure and knowing it (rather than just making it real
: complex and hoping there's no unexpected hole in it).
And that one is probably equivalent to the "halting problem", which means
there's no solution.
Nobody's proved that doing the Shamir three-pass protocol requires the
same kind of math that public-key needs, so one area for progress is
finding out exactly where exponentiation-like steps in a cipher are really
required. That's an "efficiency" issue, but it still has theoretical
meaning, and it isn't an incremental step in efficiency.
Anonymous digital cash requires doing a blind signature of piles of copies
of something. Can we get out of that?
John Savard
------------------------------
Date: Wed, 06 Jan 1999 00:00:47 -0500
From: "Trevor Jackson, III" <[EMAIL PROTECTED]>
Subject: Re: Help: a logical difficulty
Nicol So wrote:
> Of course, because you don't even have enough names for infinite
> sequences. (There are uncountably many infinite strings, but only
> countably many finite strings that can be used as descriptions). The
> infinite binary strings capable of finite representation correspond to the
> decidable languages.
I find this statement confusing. What does "countably many finite" mean as
opposed to "finite". Are there finite numbers that are uncountable???
Also, is there are reason why name or description strings have to be finite?
Consider the string 3.14159265... (in binary or any other radix), with the
name "3.14159265..." (in binary or any other radix). Why is the set of
strings any larger than the set of string names?
------------------------------
From: Serge-Antoine Melanson <[EMAIL PROTECTED]>
Subject: One-time pads not secure ? (NSA's Venona project)
Date: Wed, 06 Jan 1999 00:25:58 -0500
Hi all,
I once read in Bruce Schneier's "Applied Cryptography" that one-time
pads were un-breakable but I saw an article on CNN's web site
about NSA's VENONA project that seems to contradict this:
http://www.cnn.com/SPECIALS/cold.war/experience/spies/spy.gadgets/espionage/one-time.pad.html
So did the russians used pseudo-random number generators to print
those pads or what? If those pads were breakable does it mean their
characters sequence was not truly random or generated using a
reproducible process?
/S.A.M.
------------------------------
From: rosi <[EMAIL PROTECTED]>
Crossposted-To: sci.math,comp.theory
Subject: Re: coNP=NP Made Easier?
Date: Tue, 05 Jan 1999 18:39:45 -0800
Dear Ilias,
You might think that my purpose is to show that your K does
not work in that special manner. Quite the opposite. My purpose is
to show that your K DOES in a special way, if ever possible.
Define function H:
H(S, i', n) // this behaves "as" described in 27
{
// Sorry, used your K
blank out positions (for YES#) on the output tape of K
while [ YES# is not on K's output tape ] do
{
blank out positions (for YES#)
K(S, i', n) // This guy always halts, right? We do not
// have to do it all over again, possibly
// with another K', rihgt?
}
return YES#
}
I said 'function'. But do not struggle with the Thesis if you
do not see the relevance.
51. Is H poly bound?
Remember, if H does not work, it does not bother us any bit.
Do we have a mechanism for solving SS in poly? If not, there is
noting for us to say and we save our breath. If yes, once we know its
behavior and exactly how it solves SS (positively) in poly, I will
with great confidence construct one for solving coSS (negatively) in
poly.
I made the promise of showing why 26 is NOT acceptable. The above
H shows clearly, and my point is made, I believe.
I believe the reader can see why your adopting of 26 relieves
me of the necessity of the definitions and the assumption. In
particular, if one wants the practice, one can stuck a call to the
function f(n) in H and put y, the clock/counter, in the appropriate
place. Of course, do not forget examining the contents of the output
tape after getting out of the while loop, and you can put i' and i"
to it.
Bryan wondered how a piece of magic rock would work. Just remember
that I only say: if A then B. Give me your magic rock with well-
defined behavior, I show you exactly how coNP=NP. I need no more
details; I do not want to know if the magic rock is D or N.D.
If you magic rock is P bounded, mine for coSS is as well. If yours
if E bounded, so will be mine.
I did not call my mechansim (for poly solving SS embedded in
the NHPSM) an oracle for two considerations:
1. Some define an oracle as a hypothetical 'algorithm' and some
others use real algorithms as oracles. Not calling the embedded NDTM
an oracle is to try to avoid unnecessary confusion.
2. In the majority of the cases where an oracle is used, the oracle
is an indespensible commodity. The M' in which the NDTM is embedded
does not have such dependency. If it (the embedded NDTM) does not work,
it DOES! (i.e. if it fails to work, it actually works for my argument!)
Both you and Bryan have referred to 'acceptor'. I have no desire
of getting into the relationship between an acceptor and a computer;
what is to compute a function and what is to accept an input. Well
over me, already. :)
We have come a very convoluted path. When I used 27, you guys
came up with 26, without showing their equivalence. So what I was
talking about is not shown to be the same thing you guys have been
talking about. I pointed this out at the very start. It is like:
What? Yeah, I see you holding an apple in your
hand, but I am holding an orange in mine. You
say that your apple is red. How could that be?
Look, my orange is ... (orange of course), and
your apple can not be red.
Seeing that kind of stuff, I agreed to take whatever you define and
commit to and construct my argument. But you always seem so reluctant
to give straight answers.
As to the adoption of 27, I need to give some argument. I actually
did. I do not want to 'verbiage'. I just point out that my words
about 'getting even' is a very good heuristic argument, which, in my
opinion, is no less convincing than any formal one.
Some other points are directed at what you said here (in the
following):
ilias kastanas 08-14-90 wrote:
>
> In article <[EMAIL PROTECTED]>, rosi <[EMAIL PROTECTED]> wrote:
> @[EMAIL PROTECTED] wrote:
> @> [snip]
> @
> @ Dear Ilias, I believe you are reknowned and respected. For the
> @people posting in this thread know you are a professor and addressed
> @you by Dr. I nevertheless would never know from your name or e-mail
> @address (which is not a real one). I wonder if I could ask a favor
>
> Hmm, the name "rosi" is not real either... Just kidding. Actually
> the dejanews address above _is_ valid; the "uucp" one, on the other hand,
> (which you may have seen), protects my "real" address admirably -- zero junk
> email.
>
> @of you. Could you get one of the experts involved? Papadimitriou was
> @mentioned more than once. Could you, or any who is following this
> @thread, get one or more of that caliber to say either:
> @ The argument of ROSi is total trash, or
> @ The argument of ROSi deserves a brief look, or
> @ The arguemnt of ROSi (even without looking at it) is not
> @ worth wasting time on?
>
> But what is the argument? I asked for a precise description of the
> proposed machine for coSS, but never saw one.
>
Isn't this a bit ridiculous! My first post of this thread gives
the argument. You are and have been talking about WHAT? I sincerely
doubt your seriousness.
I gave one (machine), you wouldn't take it and kept talking about
your K. Then I started to ask simple questions to get what your NDTM
is and intend to construct the one for coSS with your NDTM. I need
to show that the one you give works iff the one for coSS does.
You never saw one is because you never gave one (that works for
solving SS poly, and I only say: if A then B). If you give, say in a
semi-formal manner, how your NDTM can solve SS poly and show us
something complete that solves the SS (positively) in poly. I
promise you and the world, once you give me one with well-defined
halting and output patterns for SS (the positive part), I will
immediately give you one for coSS. But if you do not give me one,
I will never blame you. NEVER! I only challenge you, when you say
there exists an NDTM, to showing one (hypothetical fine) with
good-behavior that solves SS (positively) in poly.
Let me remind you that your K is never shown to have solved the
SS in poly. It was only shown to fail (in perhaps some 'incomplete'
execution). If you can show an algorithm in which your K is invoked
that solves SS (positively) in poly, without such vague stuff like:
one of the computations will get it, you will get one concrete for
coSS.
> In article <[EMAIL PROTECTED]>, rosi <[EMAIL PROTECTED]> wrote:
> @Dear Ilias,
> @
> @ I see that you see that M behaving as described in 26 is NOT
> @fine.
> @
> @ But you said there exists such a mechanism, NDTM to be exact,
> @that behaves as described in 26 (and you do not need to show its
> @construction and it simply exists). I seem to have the impression
>
> I've _shown_ the construction of K. Behavior: for any S,i, if i is
> a subset-sum, THERE EXISTS some computation of K (among the many possible for
> that S and that i) printing YES#. And there exists none if i isn't.
> _This_ behavior is called "accepting SS in ND pol. time".
No desire of getting into the relationship between an acceptor
and a computer. I think we already committed to 'computer' with
agreement on 'halting' and 'outputing YES#'.
Many? We are never interested in how many. We are interested in how
to get this computation (or acceptation?) and whether getting it would
be in polynomial bound.
If you adopt that this ND pol. time thing, in the worst case, gets
to this computation (or acceptation) in polynomial time, we would like
to know how it does it. Showing one failure is no good. Saying it is
possible to get it is no good either, for it may reach it in exp time
(in the worst case).
If you adopt the opposite, you know the case is firmly closed.
>
> You want to think about other behaviors? Good. But they don't
> affect the definition of NP.
>
> @from your that the only valid type of NDTM are those behaving as
> @described in 26 (as you would not take anything but your K).
>
> @ Now things are simpler. As there can only be NDTM behaving as
> @described in 26, the answer to my FIRST crucial question should be
> @NO. Because obviously, your K (a representative of those NDTM's
> @behaving as described in 26) can halt with things other than YES#
> @on its output tape, your K is not the mechanism I am asking for.
>
> You are asking for "FOR ALL" instead of "THERE EXISTS" above.
> A different behavior. Of course K doesn't have it.
>^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
"K does not have it" does not mean (and you certainly CAN NOT assert)
that there is none that has it. When someone gives one, you need to
evaluate that one according to its attributes, properties and behavior
and NOT repeating your K to say: since K does not work, neither does
that one of yours.
>
> @And according to you, unless I am wrong, that the only halting and
> @output behaviour of an NDTM is as described in 26, so no NDTM can
> @be the one I am asking for. So the answer should be simply NO. I
>
> I believe the correct answer will turn out to be NO... but that
>^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
But unfortunately, you have contradicted yourself. Based on your
commitment, the correct answer will turn out to be YES (if NDTM is
defined to be a mechanism that solves NP in poly).
> is belief, not proof. ^^^^^^^^^^^^^^^^^^^^
The confidence you showed in rebutting my argument sounds like you
have it as a proof. Sorry, I am wrong! :)
>
>
> @do not understand why always such fuss. Just as for the simple
> @answer to the simple question about a mechanism that solves SS
> @in finite time, I can not understand why the fuss about NDTM and
> @DTM. If there exists one (DTM or NDTM), just say YES. A primary
> @school kid would do so.
>
> And then, in junior high, the kid would be shocked to realize it's
> presently _unknown_ what the answer is... YES?... or NO?
>
> Why so? Imagine a ND TM such that, given S,i as above (i subset sum)
> ALL computations print YES#, and given i non-subset-sum no computation prints
> YES#. If such exists, you can cut it down to deterministic by eliminating
> alternative transitions... and thus get a D TM that accepts SS! So your
> question is equivalent to: is P = NP ? Sorry, Yes or No to _that_ is a bit
^^^^^^
Sorry, I never asked such a question. The piece of homework I offer
here
will _evaluate_ (I did not use the word 'answer') such a question
properly.
Sorry again. Notice the word 'finite'. My that question did not ask
for a poly bound, and therefore P?=NP was never brushed upon there.
> of a fuss... not exactly "simple"... for kids, and even for grownups.
No, you are confusing things. A question may be very complex. But the
answer can be simple and straightforward: YES or NO or I HONESTLY do not
know. It is in that sense I used the word 'fuss'.
Please do not think that to show that coNP=NP (derived from some
assumptions) is too difficult. You really can do it. A lot of people
can do it as well. I do not doubt. It is just that you have to be
critical in thinking and get rid of the stereotypes. If you think
closely, we only need to show a very 'narrow' case and other cases
are well taken care of (by the definitions themselves).
>
> @ We are slowing down. Let me speed up by asking the crucial
> @question once more (and this time in full to save us one round of
> @posts):
> @ 41. Does there exist a mechanism MM (ANY mechanism) that,
> @ when S, a finite set of integers, i', a subset sum of S,
> @ and n the size of the input/problem) are given as input,
> @ _ALWAYS_ HALTS within a polynomial bound (or in other
> @ words: whose complexity is bounded by some polynomial
> @ function f(n) where n is the input/problem size) and
> @ _ALWAYS_ ANSWERS POSITIVELY (or our version to be specific:
> @ prints YES# on its output tape on halt); AND that, when S,
> @ a finite set of integers, i", an integer that is NOT a
> @ subset sum of S, (and n the size of the input/problem) are
> @ given as input, _NEVER_ prints YES# on its output tape?
>
> To be sure, it is a crucial question: is P=NP?. Not exactly a new one,
> but... hey.
>
Again, the question P?=NP is and was not asked of you or of anybody.
> @ Repetition and details do not bore everybody every time. So
> @here we go again:
> @ If MM(S, i', n) EVER prints anything other than YES# at halt,
> @it is NOT the mechanism I am asking for.
> @ *** IMPORTANT: it seems that your K is obviously ruled out,
> @ *** and you should have realized this long, long ago. A high-
> @ *** school kid would. So please do not bring it back to create
>
> Ah!... The light dawns.
>
> @ *** further headache. I am asking for one that ALWAYS prints
> @ *** YES# at halt AND halts within polynomial bound. If you can
> @ *** not think of one or can prove that in this whole wide
> @ *** world there is none, you can simply say "NO" to the question.
> @ *** If you are right, you will be right. The world is watching us).
>
> Why ask me?!... Ask the high-school kid. ^^^^^^^^^^
You did not post anything to show your knowledge in complexity
theory by disproving things that you do not even seem to have read
carefully, right? A high-school kid will provide straight and clear
answers. He can say: I assume YES, or I assume NO, or honestly
I do not know (in that case, he will never say the argument of mine
is problematic, for he is honest enough to realize that he does not
have the ability to do so. He may doubt and ask questions, but that
is definitely different from concluding that my argument does not
work). I see no reason for bluffing.
>
> @ If MM(S, i', n) EVER prints YES# only after exp time, it is
> @NOT the mechanism I am asking for. (This means if there is ever an
> @instance with the tuple <S, i', n> that results in MM printing YES#
> @only after exp time, it is NOT the mechanism I am asking for.)
> @ If ALWAYS MM(S, i', n) < f(n) and prints YES# at halt, and
> @ALWAYS MM(S, i", n) < g(n) for some polynomial g and NEVER prints
> @YES#, it _IS_ the mechanism I am asking for (am not implying in
> @any way that it exists).
> @ If ALWAYS MM(S, i', n) < f(n) and prints YES# at halt, and
> @MM(S, i", n) NEVER halts and NEVER prints YES#, it _IS_ the
> @mechanism I am asking for.
> @ If MM(S, i", n) EVER prints YES#, it is NOT the mechanism I
> @am asking for.
> @ I repeat, there is no multiple run issue. This mechanism should,
> @if one exists at all, _ALWAYS_ halt within polynomial bound and
> @print YES# at halt after it is started (or the "START" button is
> @pushed).
>
> The mechanism's existence (i.e. P=NP) trivially implies NP=coNP.
^^^^^^^^^
I love this word! So the belief that NP!=coNP indicates the belief
that such mechanism does not exist? How wonderful! But then doing it
once more:
"NP!=coNP" implies "there is no NDTM (NDTM is a fake)"
Isn't it ridiculous that we worry about NP?=coNP at all?
Do we see the deep contradiction of the two:
1. belief: P!=NP
2. belief: coNP!=NP
???
As to the other: P?=(coNP int NP), I don't know what to say
is best.
I mentioned at least once about the visualization of the relationship
of P, NP, etc. There is that Halloweeny picture of ghostly circles of all
shapes and sizes. There is also the one in Bruce Schneier's book. I do
have a preference. I go to the latter every single time. I am not saying
that the one in Bruce's is perfect (I do not believe in Drawing
McArthyism). I am not even saying that the latter is better than the
former. THEY SIMPLY CAN NOT BE COMPARED!
I do not care who writes what. I am only concerned about consistency
and truth. Whoever is right is. I do not care if one's Advisor^n, for
some natural number n for which Advisor^n is defined, is Church. I am
not afraid of confronting anybody. If God creates something stupid,
I will confront himself. NO DOUBT!
> A clean sweep, what.
>
I did not ask the question P?=NP! I simply did not! Do not distort
things. What I meant was that it is difficult to look at coNP?=NP
without wondering about the bigger picture. I said I would not say too
much about the issue P?=NP and I certainly did not ask you to answer
such a question. If I conveyed such an impression, I apologize and
make it explicit that I did not mean it.
Maybe a clean sweep, maybe not. I am not so sure.
I truly have no appetite to go to details. But ....
I first commit to what I adopt as the definition for the complexity
class of P (which is quoted from "Handbook of Applied Cryptography" by
Menezes et al):
The complexity class P is the set of all decision problems
that are solvable in polynomial time.
I here also commit my understanding of the definition. As long as
the problem is solvable in polynomial time, be via DTM or NDTM, it is
in P.
Now, there is an interesting question assuming the existence of
NDTM. That is: does DTM's solve the same set of problems as NDTM's?
The reader will not fail to see why I say I am not so sure that it is
a clean sweep.
It is awkward, but some may believe, that the two have the same
computing power. I do not want to confuse people here, for this is
well above and beyond me. However, in this case it IS trivial that
coNP=NP as coP=P and P=NP. Ilias, you are right here.
But, if DTM only solves a proper subset of problems that NDTM
solves (in poly of course), then we are still face with the question:
coNP?=NP. Now the problem comes in. I showed exactly with my argument
that coNP=NP including this case. You guys tried to disagree. But
coP=P and P=NP, then where do we put coNP? We refute P=coP?
On the other hand, if we say coP=P and if we ever assume that
NDTM can be real, where do we put coNP? I think it is clear that
such arguments are not above high-school level. You can disagree.
There is one more (trivial) case in which to talk about coNP?=NP,
which is left for the homework I give here at the end.
(I believe there are many, many ways of looking at such issues)
> @ As far as I can see, there are only three meaningful answers to
> @41 (or 42):
> @ YES, THERE IS (or I ASSUME THE EXISTENCE)
> @ NO, THERE IS NONE (or I ASSUME THE NON-EXISTENCE)
> @ I DO NOT KNOW
> @
> @ Please provide straight and clear answers. Please do not evade.
>
> Oh. Anything else?
What else do I need to ask for (than a straight clear answer)?
>
> @ When answer other than "I DO NOT KNOW" to 41 (or 42) is provided,
> @I will evaluate the answer and bring this boring topic to an end
> @(hopefully).
>
> It's good to end on a hilarious note.
>
> @ As to "I DO NOT KNOW", I can close the chapter right here.
> @ You do not know what you have been talking about. You have
> @wasted people's time and bandwidth.
>
> Don't worry, the chapter is closed already.
You close a chapter for me? Thanks. Actually you kind of DID!
>
> Look, Rosi, it's nice you've just re-discovered P=NP? is an open
What else can you assert for other people? See your problem?
> question. My postings are out there for everyone to see and judge. Your
> new tone and attitude you can practice with somebody else.
>
> Ilias
I am aware of other issues raised along this thread. Most of them by
now should need no further waste of time.
Finally, all we have talked about can become crystal clear, I think,
when the following piece of homework is completed:
Is it ridiculous (certainly not stupid) to believe or even
expect that P!=NP? (EXTREMELY IMPORTANT: I never mean that
P=NP, and I certainly do not ask if P=NP.)
An alternative question in sharper focus is: If P!=NP (which
can certainly be said in a more sensible way), where do we
put the SS (I mean the 'complete' question)?
Thank you all who have followed this.
--- (My Signature)
P.S.
Dear Ilias, I keep my promise. If there is no major thing for the
questions I asked, you can ask me any questions you would like. I
will try my best to answer them in a straight and clear manner. I
would appreciate that you first ask questions to get us in sync with
all the concepts and notions we depend on for other further questions.
If you also would like me to comment on your other posts, I can do.
But just do not feel offended for I will use free style and be
candid.
Thank you very much.
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