Cryptography-Digest Digest #293, Volume #10      Wed, 22 Sep 99 03:13:04 EDT

Contents:
  Re: some information theory (very long plus 72K attchmt) ("Rick Braddam")

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From: "Rick Braddam" <[EMAIL PROTECTED]>
Subject: Re: some information theory (very long plus 72K attchmt)
Date: Wed, 22 Sep 1999 00:32:45 -0500

    Good morning, all. Sorry about the long post, especially with the attachment, but 
if I sent this one paragraph at a time it
would take a week and might generate a lot of noise... and the noise is too high 
already.

   I've been following this thread and I thought I understood what David Scott was 
trying to say. I probably don't understand
entropy correctly, though. I'm hoping that if I write down what I think I know, some 
of you will clarify it for me.

    If I have an 80-character message, the information is encoded in 80 8-bit bytes, 
which uses 640 bits. Only about 1.3 bits per
byte are actually needed to encode the information, though, the rest are redundant. 
This indicates that the message could be encoded
in as little as 10.4 bits. I have had PKZIP 2.04G report 95% compression on large text 
files, so that don't seem too far off.

    That seems to be the objective of compression programs, to sort of squeeze the 
information-carrying bits closer together and
throw away the redundant bits. If entropy is a measure or indication of the amount of 
information represented, it cannot change from
the long string to the shorter one, or you couldn't expand the short string back to 
the longer one. So the short string and the
longer one have to have exactly the same entropy. That would be the entropy of the 
message. However, the shorter string uses fewer
bytes, so the entropy per byte must have increased. I have seen some posters write 
about the entropy of the message, and others
refer to the entropy per byte. Intuitively, entropy per byte makes sense to me, but 
which is correct?

    David Scott promotes using compression before encryption, and several responses 
have agreed with him. If I understand correctly,
compression doesn't increase security, but it increases the work factor needed to 
break the encryption. Why isn't that the same as
increasing security? "Increase the work factor" should be the same as "makes it 
harder" to break the encryption... isn't that what
increasing security means? Maybe it's relative, in that it doesn't make it 
substantially harder like adding one bit to the key
would.

    I couldn't quite figure out how you could uncompress a file which wasn't 
compressed to start with, so I just thought I'd try
what David said to do. Here are the files I generated to run a couple of tests. It 
seems that Adaptive Huffman Compression don't
particularly like pdf files. I couldn't find enough text files to make up 8.4Mb to 
test with DieHardC, especially since they needed
to be that big after compression. ZipMagic with max compression compresses much 
tighter, but if an analyst knows that the first two
letters in my plaintext are PK he/she can throw away wrong keys much quicker. Of 
course, I could do as suggested by one here and
strip off the header and send it as plaintext, and save the analyst some trouble. I 
just want to be a troublemaker for the analyst.

The attachment, outfiles.zip, contains the DieHardC results for each of the tests I 
ran. The first tests use a file of random
numbers generated by the Merseinne Twister.

Filename                        Size
RNDFILE                      8,520,008  The original output from the Merseinne Twister
            the file above passes all DieHardC tests, see rndfile.out for results

TESTUNC  AHC        28,703,076  Original RNDFILE uncompressed to this
            You CAN use h2unc.exe to uncompress a file that has not been compressed

TESTCOMP AHC        8,520,270  Original RNDFILE compressed to this (larger)
            the file above also passes all DieHardC tests
            see testcomp.out for results

TESTUNC  ZIP           10,604,680  Uncompressed file zipped to this (max comp)
            ZipMagic (by Mijenix) used for all zip files... equiv to pkzip 2.04G
            See testuncz.out for results

TESTUNC  CMP          8,520,008  Uncompressed file compressed back to this
            *note* above file is identical to original (see rndfile & rndfile.out)
            if you uncompress a not-compressed file then compress it you DO get the
            original file back.

TEST     PDF              13,231,497  test file built from three pdf files

TESTCOM  AHC        11,745,172  test.pdf file compressed with Adaptive Huffman
            h2com.exe compressor
            this file passes only 37 of 235 tests, see testcom.out.

TEST     ZIP                   7,057,309  test.pdf file zipped (max compression)
            This file too short for DieHardC, exausted input file at OPERM5 test.
            Failed all tests it ran. See testzip.out.

    The last two tests don't show anything, unless it's that zip compresses pdf files 
better. I doubt that passing 37 out of 235
tests is significant. Passing all tests doesn't prove anything, either. It only says 
that the file *looks* random, not that it is.

> [EMAIL PROTECTED]


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