Cryptography-Digest Digest #453, Volume #14 Sun, 27 May 01 01:13:01 EDT
Contents:
Re: A generic feistel cipher with hash and gf(257) mixers (SCOTT19U.ZIP_GUY)
Re: Mainstream Quasiprobabilities and Memory Theory - Doctorow ("Tom St Denis")
Re: A generic feistel cipher with hash and gf(257) mixers (SCOTT19U.ZIP_GUY)
Re: Small (not fast) RIPEMD-160 (Ian Stirling)
Re: Small (not fast) RIPEMD-160 (Ian Stirling)
Re: A generic feistel cipher with hash and gf(257) mixers (SCOTT19U.ZIP_GUY)
To prove PGP can easily be misused... (Tom St Denis)
Re: Good crypto or just good enough? (SCOTT19U.ZIP_GUY)
Re: Comparison of Diff. Cryptanalysis countermeasures ([EMAIL PROTECTED])
Re: Mainstream Quasiprobabilities and Memory Theory - Doctorow ("Osher Doctorow")
Re: CipherText ("Prichard, Chuck")
Re: To prove PGP can easily be misused... (wtshaw)
----------------------------------------------------------------------------
From: [EMAIL PROTECTED] (SCOTT19U.ZIP_GUY)
Subject: Re: A generic feistel cipher with hash and gf(257) mixers
Date: 26 May 2001 22:48:36 GMT
[EMAIL PROTECTED] (David Wagner) wrote in
<9epagr$p0i$[EMAIL PROTECTED]>:
>
>Don't get the wrong opinion: I'm not saying this out of some kind
>of snobbery. Perhaps it would help if I mentioned that I don't
>really trust myself to design new ciphers, and I've tried to avoid
>it whereever possible. The one time that I did give it a try was
>when I had a team of many other folks experienced at cryptanalysis,
>and we had a great deal of time to thoroughly study our choices,
>*and* we published the design and knew that others would give it
>a great deal of study as well. It is easy to get this stuff wrong,
>no matter how much experience you have in this field.
I think he had to add the snob thing since thats the snobbish
way to attack. Wagner has not intentions of learning from you.
Just as he stated he knows nothing about BICOM. I think he knows
more that he lets on. If course since it was done by one not in
the club and is not one that he can claim litters the road side
as broken. He chooses the common way of never looking at it since
his mind is already made up. Its actaully a quite clever snobbish
way of doing things.
David A. Scott
--
SCOTT19U.ZIP NOW AVAILABLE WORLD WIDE "OLD VERSIOM"
http://www.jim.com/jamesd/Kong/scott19u.zip
My website http://members.nbci.com/ecil/index.htm
My crypto code http://radiusnet.net/crypto/archive/scott/
MY Compression Page http://members.nbci.com/ecil/compress.htm
**NOTE FOR EMAIL drop the roman "five" ***
Disclaimer:I am in no way responsible for any of the statements
made in the above text. For all I know I might be drugged or
something..
No I'm not paranoid. You all think I'm paranoid, don't you!
------------------------------
From: "Tom St Denis" <[EMAIL PROTECTED]>
Subject: Re: Mainstream Quasiprobabilities and Memory Theory - Doctorow
Date: Sun, 27 May 2001 01:27:01 GMT
"Tom St Denis" <[EMAIL PROTECTED]> wrote in message
news:0QXP6.48888$[EMAIL PROTECTED]...
> Why are you posting these messages?
Er, I hope this doesn't seem mean. I just wonder to whom are you addressing
these? What new results are you discussing?
Tom
>
>
> "Osher Doctorow" <[EMAIL PROTECTED]> wrote in message
> news:9epg7u$g05$[EMAIL PROTECTED]...
> > From: Osher Doctorow [EMAIL PROTECTED], Sat. May 26, 2001 4:31PM
> >
> > R. R. Puri (Bhabba Atomic Research Centre, India), in Mathematical
Methods
> > of Quantum Optics, Springer-Verlag: Berlin 2001, presents an excellent
> > introduction to his and others' developments in quasiprobability theory
> > (which relates to entanglement and spherical harmonics among others
> things).
> > His theory and others like it are examples of what I refer to as the
> > *Enlightened Mainstream* of quantum theory, which instead of deserting
> > probability or treating it in a cavalier fashion, analyzes it and uses
> some
> > of its best characteristics to either apply it to quantum theory or to
> apply
> > somewhat analogous methods to quantum theory. Because of its special
> value
> > in entanglement, I would urge sci.crypt members to read especially
chapter
> 4
> > of his book, Quasiprobabilities and Non-classical States, 81-97, and
also
> > some of the references on which the chapter is based, including R. R.
Puri
> > J. Phys. A29, 5719 (1996). Quantum statistics as used by some
researchers
> > recently is also contributing heavily to the Enlightened Mainstream, but
> > especially in statistics they have far to go to overcome what was a
> general
> > trend of even eminent theoretical physicists to use probability and
> > statistics without exceptionally profound understanding of them - from
the
> > 1920s onward. Expertise and even genius in non-probability/statistics
> > fields does not, in my opinion, transfer over to probability/statistics,
> and
> > even beyond that probability or statistics specialists (including
myself)
> > are only presently at the tip of the iceberg and need to be very careful
> to
> > allow and even search out competing ideas.
> >
> > I will only give a few general comments here on quasiprobabilities.
They
> > are analogs of classical phase space distribution functions which are
> > constructed by rules of replacement somewhat similar to the way in which
> > quantum field theory was constructed from quantum mechanics (although
the
> > rules are very different ones). It turns out that when this is done,
the
> > resulting quasiprobabilities depend strongly on spherical harmonics
among
> > other things, especially in reference to spin. Puri proved in his 1996
> > paper that classical versus non-classical quantum states of a system of
N
> > spin-1/2 s components are distinguished by whether the joint
> > quasiprobabilities for the eigenvalues of the components for each spin
in
> > three perpendicular directions (one of which is the average direction of
> the
> > spin) are all nonnegative or not (in the not case at least one is
> negative)
> > respectively. Uncorrelated states are regarded as classical. Puri's
> proof
> > identifies the coherent states as classical and also the single
spin-1/2,
> > but any pure entangled state of two spin-1/2s as non-classical, and
> squeezed
> > spin states are non-classical.
> >
> > I will hopefully have time in the near future to make some more
comments.
> >
> > Osher Doctorow Ph.D.
> > Doctorow Consultants
> >
> >
> >
> >
> >
> >
>
>
------------------------------
From: [EMAIL PROTECTED] (SCOTT19U.ZIP_GUY)
Subject: Re: A generic feistel cipher with hash and gf(257) mixers
Date: 26 May 2001 20:17:53 GMT
[EMAIL PROTECTED] (Roger Schlafly) wrote in
<y7SP6.66$[EMAIL PROTECTED]>:
>"David Wagner" <[EMAIL PROTECTED]> wrote
>> If the goal is `slow but secure', how does it compare to the GGR
>> tree-based scheme that I posted earlier? (I've posted the citation to
>> GGR several times before on this newsgroup, so I won't do it again.)
>
>Sounds intriguing, but could you give us a clue? I missed your previous
>cites. A search turned up references to GGM and CTR, but I don't
>know if these are the same or not.
>
Its quite possible he meant GGM but a search of sci.crypt does
find 2 references to GGR. Wagner is known to confuse facts quite
a bit both of these talk about previous references that don't seem
to be in the Google sci.crypt data base for him.
And he likes to quote references that may require a suscription
to actually get anything. However GGM did get a few hits with his name
in Google usenet seach of sci.crypt Don't be to hard on him for this
he can't think to well when talking to me his hate shows through.
David A. Scott
--
SCOTT19U.ZIP NOW AVAILABLE WORLD WIDE "OLD VERSIOM"
http://www.jim.com/jamesd/Kong/scott19u.zip
My website http://members.nbci.com/ecil/index.htm
My crypto code http://radiusnet.net/crypto/archive/scott/
MY Compression Page http://members.nbci.com/ecil/compress.htm
**NOTE FOR EMAIL drop the roman "five" ***
Disclaimer:I am in no way responsible for any of the statements
made in the above text. For all I know I might be drugged or
something..
No I'm not paranoid. You all think I'm paranoid, don't you!
------------------------------
From: Ian Stirling <[EMAIL PROTECTED]>
Subject: Re: Small (not fast) RIPEMD-160
Date: Sun, 27 May 2001 01:39:31 GMT
Tom St Denis <[EMAIL PROTECTED]> wrote:
>Ian Stirling wrote:
>>
>> Mark Wooding <[EMAIL PROTECTED]> wrote:
>> >Ian Stirling <[EMAIL PROTECTED]> wrote:
>> >> jlcooke <[EMAIL PROTECTED]> wrote:
>> >> >I've got RIPEMD160 to 1990bytes. SHA-1 to 1360bytes.
>> >>
>> >> Thanks. I've got RIPEMD160 down to 3040 bytes, (with gcc) from around 7K.
>> >>
>> >> I know how to get down to around 2540 or so, perhaps 2200, but there
>> >> I think it's going to stick.
>>
>> >I got it to 1570 bytes in C. (Implementation mailed to poster.)
>>
>> Impressive, though the stripped .o file is >2K, with all the compilers
>> I have. (egcs and gcc).
>>
>> What's the proper tool to show me bytes per function, or better, bytes
>> per line of code?
>>
>> I'm pretty sure I can get it a little smaller than this, as I have a
>> cunning plan...
>>
>> Anyway, I'll post an update in a week or so, as to how I've done.
>Bah it's not hard to make small code. It's making small human readable
>code that's the trick.
I know :)
Trying to keep it legible is fun.
--
http://inquisitor.i.am/ | mailto:[EMAIL PROTECTED] | Ian Stirling.
===========================+=========================+==========================
"I am the Emperor, and I want dumplings." - Austrian Emperor, Ferdinand I.
------------------------------
From: Ian Stirling <[EMAIL PROTECTED]>
Subject: Re: Small (not fast) RIPEMD-160
Date: Sun, 27 May 2001 01:48:35 GMT
Roger Schlafly <[EMAIL PROTECTED]> wrote:
>If SHA-1 is smaller and something small is needed, then why not use SHA-1?
>Does RIPEMD-160 have any advantage over SHA-1?
The original program that took a password, and hashed it, used
RIPEMD-160.
So, if SHA-1 is used, it would either be incompatible with the earlier
one, or need a magic constant computed with another tool.
If size was the only goal, then the block device that is being used
could be made to do the encryption.
--
http://inquisitor.i.am/ | mailto:[EMAIL PROTECTED] | Ian Stirling.
===========================+=========================+==========================
He had been eight years upon a project for extracting sunbeams out of cucumbers,
which were to be put in vials hermetically sealed, and let out to warm the air
in raw inclement summers. -- Jonathan Swift, "Gulliver's Travels" (1726)
------------------------------
From: [EMAIL PROTECTED] (SCOTT19U.ZIP_GUY)
Subject: Re: A generic feistel cipher with hash and gf(257) mixers
Date: 27 May 2001 00:02:25 GMT
[EMAIL PROTECTED] (David Wagner) wrote in
<9epend$pbf$[EMAIL PROTECTED]>:
>SCOTT19U.ZIP_GUY wrote:
>>Do you have a place where the source code can be down loaded.
>
>No, not that I know of. I guess you'll have to implement it yourself.
>See my other post for a description of the construction, if you'd like to
>try it out.
>
Well if its not coded what good is it. Since I can't
test if its bijective it would be hard to compare it with
BICOM. Anyway I doubt you would trust my implementation.
Funny you compare BICOM to a model you haven't even coded
even you should know the devil is in the details.
Let me put it another way. You gloated how GGR is the
hot one to beat. Yet it does not exist. BICOM does exist
and many have tested it. Sure there may be bugs in it I don't
know but it better for one to use it than one that does not exist.
Hell even RIJNDEAL is bijective till one tries to write
code for it. That is where most people screw up. Instead of
taking the time to do the implementation a correct they do
it in a weak nobijective way. As in the way PGP does its
compression encryption its very bad.
David A. Scott
--
SCOTT19U.ZIP NOW AVAILABLE WORLD WIDE "OLD VERSIOM"
http://www.jim.com/jamesd/Kong/scott19u.zip
My website http://members.nbci.com/ecil/index.htm
My crypto code http://radiusnet.net/crypto/archive/scott/
MY Compression Page http://members.nbci.com/ecil/compress.htm
**NOTE FOR EMAIL drop the roman "five" ***
Disclaimer:I am in no way responsible for any of the statements
made in the above text. For all I know I might be drugged or
something..
No I'm not paranoid. You all think I'm paranoid, don't you!
------------------------------
From: Tom St Denis <[EMAIL PROTECTED]>
Subject: To prove PGP can easily be misused...
Date: Sun, 27 May 2001 02:39:44 GMT
Hmm might not be news to you, but think about this. What if some
politician happened about this and decided to trust it without
confirmation? Ouch... bad news...
=====BEGIN PGP PUBLIC KEY BLOCK=====
Version: GnuPG v1.0.4 (GNU/Linux)
Comment: For info see http://www.gnupg.org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=pmDj
=====END PGP PUBLIC KEY BLOCK=====
------------------------------
From: [EMAIL PROTECTED] (SCOTT19U.ZIP_GUY)
Subject: Re: Good crypto or just good enough?
Date: 27 May 2001 00:55:07 GMT
[EMAIL PROTECTED] (John Savard) wrote in
<[EMAIL PROTECTED]>:
>On 26 May 2001 01:07:16 GMT, [EMAIL PROTECTED]
>(SCOTT19U.ZIP_GUY) wrote, in part:
>
>>If I was working on a break and found one
>>I would fear for my life.
>
>Just splash it all over the Internet before anyone knows what you were
>working on. That _should_ work.
>
I don't think so. Fist of all the proof would be so complex
and written in such a nonstandard why few would understand it
except for those that you don't wish to know. As an example
look at bijective compression encryption. Its obviously a
better why to go for most encryption in the days of coming
quatum computers but look at how few seem to understand the
concepts.
David A. Scott
--
SCOTT19U.ZIP NOW AVAILABLE WORLD WIDE "OLD VERSIOM"
http://www.jim.com/jamesd/Kong/scott19u.zip
My website http://members.nbci.com/ecil/index.htm
My crypto code http://radiusnet.net/crypto/archive/scott/
MY Compression Page http://members.nbci.com/ecil/compress.htm
**NOTE FOR EMAIL drop the roman "five" ***
Disclaimer:I am in no way responsible for any of the statements
made in the above text. For all I know I might be drugged or
something..
No I'm not paranoid. You all think I'm paranoid, don't you!
------------------------------
From: [EMAIL PROTECTED]
Subject: Re: Comparison of Diff. Cryptanalysis countermeasures
Date: Sat, 26 May 2001 19:23:53 -0800
David Wagner wrote:
>
>
[snip]
> In any case, from my point of view, the main attraction of key-dependent
> S-boxes is *not* that they stop differential cryptanalysis. We already
> know how to build ciphers that stop differential cryptanalysis cold.
[snip]
Would you be willing to expound on this if you're thinking of a method
of thwarting D.C. that hasn't already been discussed in this thread?
------------------------------
From: "Osher Doctorow" <[EMAIL PROTECTED]>
Subject: Re: Mainstream Quasiprobabilities and Memory Theory - Doctorow
Date: Sat, 26 May 2001 22:26:13 -0700
From: Osher Doctorow [EMAIL PROTECTED], Sat. May 26, 2001 9:08PM
It doesn't necessarily seem mean, especially if you could explain to me what
you mean by *to whom are you addressing these? What new results are you
discussing?* I will take a guess and suppose that you either (a) have not
been following my previous posts, or (b) cannot see how this post ties in
with previous posts, or both. In that case, the easiest way is to look up
my previous posts, including ones on sci.physics, sci.physics.relativity,
sci.optics, sci.polymers, sci.energy, sci.engr.control, sci.math,
sci.math.stat, etc. Or look up abstracts of 54 of my papers at
http://www.logic.univie.ac.at, Institute for Logic of the University of
Vienna (select ABSTRACTS, then BY AUTHOR, then my name). Or read my paper
in B. N. Kursunuglu (Ph.D. Cambridge University under Paul Dirac), S. L.
Mintz, and A. Perlmutter (Eds.) Quantum Gravity, Generalized Theory of
Gravitation, and Superstring Theory-Based Unification, Kluwer
Academic/Plenum: N.Y. 2000.
Several possibilities also occur to me. If you do not see why you should go
to the trouble of looking up those papers and wish me to summarize things so
that you can decide, well, perhaps all is fair in love and war. I am
talking about the entanglement aspect of quantum cryptography and quantum
computers. Memory (M) Theory, which I have been developing in the past
year as a generalization of the paper in Kursunuglu et al, uses spherical
harmonics, spherical expansion/contraction, radiation, among its main tools
and objects, and I am showing how quasiprobability - a very deep approach -
is coming up with some similar results and methods. I said that in my
contribution.
The brevity of your message, *Why are you doing this?* also leads me to
ask: *How are you doing anything with messages of such cryptic brevity?*
But then, I suppose you have different standards when addressing one of the
Patriarchs of Science or of the Computer World. As long as you are asking
yourself the same questions (how often, by the way?), perhaps it is all a
good learning experience and for the better.
Osher Doctorow Ph.D.
Doctorow Consultants
Formerly California State Universities and Community Colleges (still
intermittently teaching)
"Tom St Denis" <[EMAIL PROTECTED]> wrote in message
news:FJYP6.49202$[EMAIL PROTECTED]...
>
> "Tom St Denis" <[EMAIL PROTECTED]> wrote in message
> news:0QXP6.48888$[EMAIL PROTECTED]...
> > Why are you posting these messages?
>
> Er, I hope this doesn't seem mean. I just wonder to whom are you
addressing
> these? What new results are you discussing?
>
> Tom
>
> >
> >
> > "Osher Doctorow" <[EMAIL PROTECTED]> wrote in message
> > news:9epg7u$g05$[EMAIL PROTECTED]...
> > > From: Osher Doctorow [EMAIL PROTECTED], Sat. May 26, 2001 4:31PM
> > >
> > > R. R. Puri (Bhabba Atomic Research Centre, India), in Mathematical
> Methods
> > > of Quantum Optics, Springer-Verlag: Berlin 2001, presents an excellent
> > > introduction to his and others' developments in quasiprobability
theory
> > > (which relates to entanglement and spherical harmonics among others
> > things).
> > > His theory and others like it are examples of what I refer to as the
> > > *Enlightened Mainstream* of quantum theory, which instead of deserting
> > > probability or treating it in a cavalier fashion, analyzes it and uses
> > some
> > > of its best characteristics to either apply it to quantum theory or to
> > apply
> > > somewhat analogous methods to quantum theory. Because of its special
> > value
> > > in entanglement, I would urge sci.crypt members to read especially
> chapter
> > 4
> > > of his book, Quasiprobabilities and Non-classical States, 81-97, and
> also
> > > some of the references on which the chapter is based, including R. R.
> Puri
> > > J. Phys. A29, 5719 (1996). Quantum statistics as used by some
> researchers
> > > recently is also contributing heavily to the Enlightened Mainstream,
but
> > > especially in statistics they have far to go to overcome what was a
> > general
> > > trend of even eminent theoretical physicists to use probability and
> > > statistics without exceptionally profound understanding of them - from
> the
> > > 1920s onward. Expertise and even genius in
non-probability/statistics
> > > fields does not, in my opinion, transfer over to
probability/statistics,
> > and
> > > even beyond that probability or statistics specialists (including
> myself)
> > > are only presently at the tip of the iceberg and need to be very
careful
> > to
> > > allow and even search out competing ideas.
> > >
> > > I will only give a few general comments here on quasiprobabilities.
> They
> > > are analogs of classical phase space distribution functions which are
> > > constructed by rules of replacement somewhat similar to the way in
which
> > > quantum field theory was constructed from quantum mechanics (although
> the
> > > rules are very different ones). It turns out that when this is done,
> the
> > > resulting quasiprobabilities depend strongly on spherical harmonics
> among
> > > other things, especially in reference to spin. Puri proved in his
1996
> > > paper that classical versus non-classical quantum states of a system
of
> N
> > > spin-1/2 s components are distinguished by whether the joint
> > > quasiprobabilities for the eigenvalues of the components for each spin
> in
> > > three perpendicular directions (one of which is the average direction
of
> > the
> > > spin) are all nonnegative or not (in the not case at least one is
> > negative)
> > > respectively. Uncorrelated states are regarded as classical. Puri's
> > proof
> > > identifies the coherent states as classical and also the single
> spin-1/2,
> > > but any pure entangled state of two spin-1/2s as non-classical, and
> > squeezed
> > > spin states are non-classical.
> > >
> > > I will hopefully have time in the near future to make some more
> comments.
> > >
> > > Osher Doctorow Ph.D.
> > > Doctorow Consultants
> > >
> > >
> > >
> > >
> > >
> > >
> >
> >
>
>
------------------------------
From: "Prichard, Chuck" <[EMAIL PROTECTED]>
Subject: Re: CipherText
Date: Sun, 27 May 2001 04:50:27 GMT
"Tom St Denis" <[EMAIL PROTECTED]> wrote in message
news:[EMAIL PROTECTED]...
>
> If you're program is not free, open source or "a good learning tool"
you
> are spamming this group. I ask that you stop.
>
> Tom
Its a demonstration of encryption that uses an unusual delivery
mechanism.
The program boasts the unusual capabillity of delivering an encrypted
message to both Microsoft Outlook Express and Netscape Communicator
without requiring additional software.
Its partly my duty to inform the NSA of my progress on such a development
Tom.
If they are concerned, I trust I will hear about it.
I thing I have proven concept. A few fixups and the application will be
marketable. Hard to say what restrictions there will be on an
old-fashioned ASCII algorithm that has a couple of innovations in it. No
cryptologists want much to do with it.
You must understand that only 7-bit ASCII characters are permitted in
HTML textareas. Also to be cut and pasteable in Windows, the text must be
7-bit. CipherText maintains this measure of compliance to take advantage,
and voila! a delivery mechanism to all email users is possible.
Message length is restricted to 2,000 characters however.
Now that I have created an actual demonstration application, its possible
the algorithm will get a little more attention. Its not the sort of
encryption for goverment use, but its good enough for my credit card and
personal email any day.
---C. Prichard
------------------------------
From: [EMAIL PROTECTED] (wtshaw)
Subject: Re: To prove PGP can easily be misused...
Date: Sat, 26 May 2001 22:27:51 -0600
In article <[EMAIL PROTECTED]>, Tom St Denis
<[EMAIL PROTECTED]> wrote:
> Hmm might not be news to you, but think about this. What if some
> politician happened about this and decided to trust it without
> confirmation? Ouch... bad news...
>
Obviously, intelligence and good judgement are not prerequisites to be a
politician. All to often, politics is based on the hype of catch phrases
and spirit of blind trust. A typical muckraking politician is a PKA
abuser's likely customer.
--
Suppose California quit sending food back East.
Would Gerorge be ready to barter with energy?
------------------------------
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