Redundancy in XOR encryption

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I have a question I hope someone here might be able to answer:

As the method of cryptanalysis of XOR (Ie. index of coincidence) 
relies on redundancy in the plaintext, would the following be strong:

Compress P to get perfect compression (ie. 0 redundancy)
Encrypt F (the compressed text) using a repeated key XOR

of course this is all rather theoretical as there is no such thing as 
perfect compression, but I just thought it might be interesting to 
see if this is indeed strong, superficially it appears so to me...


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  Datacomms Technologies web authoring and data security
     Paul Bradley, Paul@fatmans.demon.co.uk
       Http://www.fatmans.demon.co.uk/crypt/
         "Don`t forget to mount a scratch monkey"

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paul@fatmans.demon.co.uk wrote:
> 
> -----BEGIN PGP SIGNED MESSAGE-----
> 
> I have a question I hope someone here might be able to answer:
> 
> As the method of cryptanalysis of XOR (Ie. index of coincidence)
> relies on redundancy in the plaintext, would the following be strong:
> 
> Compress P to get perfect compression (ie. 0 redundancy)
> Encrypt F (the compressed text) using a repeated key XOR
> 
> of course this is all rather theoretical as there is no such thing as
> perfect compression, but I just thought it might be interesting to
> see if this is indeed strong, superficially it appears so to me...
> 

Paul:
   I think that if the cryptanalyst knows that F has zero redundancy
that he can run searches from 0 to n bits for the key and have
the computer flag solutions that have zero redundancy.  

   I also think that a perfectly compressed file would have a relative
entropy value close to one also, hence the computer could flag possibles 
that have both characteristics.

   Hence, instead of searching for plaintext by counting coincidences,
we are searching the decrypts for solutions that have zero redundancy
and a relative entropy value close to one.  How many solutions will
have both these qualities?  I don't know.  But if the compression method 
is known, brute force will be tried, and only having to try to 
decompress (read) data that has the resultant characteristics
of compressed information will speed things up by quite a bit.

   Others may disagree with my thought-experiment and my approach,
but I think this is quite possible ... even to persons with limited
computing resources.

   Brian Durham
   bdurham@metronet.com