Randomness of a bit string

Ray rjc at gnu.ai.mit.edu
Tue Jan 25 11:36:52 PST 1994

Tim writes:
>But can he ever say "I can prove the number is random"? No. There's
>always some chance an even-cleverer puzzle solver will find the
>pattern, the key that unlocks the randomness. For example, most
>ciphertexts pass nearly all statistical tests for randomness, "look"
>random, and even _act_ like random numbers (recall the Blum-Blum-Shub
>pseudorandom number generator and how good it is). But simple
>application of the key turns the seemingly random
>"100010001010110010101" into "ATTACK."

   But can we say that "100010001010110010101" has been ``compressed''
into "ATTACK"? How do we know? Let IC(x) stand for the amount of information
storage used by x. Is 

     IC(100010001010110010101) > IC(ATTACK) + IC(key) + IC(algorithm)?

   It is not at all clear that this relationship would hold. (in fact,
I don't think it will even begin to work out unless the cyphertext
is much longer than the plaintext) So in fact, cryptorandom numbers
can be considered incompressible if you take into account the algorithm
required to perform the operation -- just as if I had used a 100 terabyte 
dictionary to compress via lookup, or better yet, a one time pad.

All of this is meaningless anyway. Information theory was proven wrong
by WEB technologies when they invented a compression program that can
recursively compress any input data down to 64k. Harddrives are now

-- Ray Cromwell        |    Engineering is the implementation of science;    --
-- rjc at gnu.ai.mit.edu  |       politics is the implementation of faith.      --

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