Re: Computerized OTP (was 5th AMENDMENT & DECRYPTION)

[nobody@alumni.cco.caltech.edu]

Murdering Thug wrote:

> Yes I do think the idea of making a "more random than random" stream
> by filtering out long runs of 0's or 1's weakens the the key stream
> in theory, but in practical use it strengthens it, because if the stream
> is left alone, runs of 500 bits of 0's or 1's can come through, and any
> fool can then extract plain text using XOR in this area of the cyphertext.

Thug is wrong about this, but it's a common mistake.  It does seem like
those runs of 0's (and, to a lesser extent, 1's) are dangerous - there's
your plaintext, totally exposed to the prying eyes of strangers!

But, what is forgotten is this: for every run of 0's which would reveal
your plaintext, there is an equally likely pattern of 1's and 0's which
transforms your plaintext into one of Shakespeare's plays.  Or into the
Declaration of Independence.  Or into anything else you like.

You see, xor'ing your message with a random stream means that the
resulting output is equally likely to be _any_ original message.
There is no way in theory or in practice to determine what the message
originally was; that is, all bit patterns are equally likely to be
the original message.

To see an example of this, suppose you had one of the simplest possible
original messages: all 1's.  Now you xor this with a random pattern.
To your dismay, your random stream happens to come up with a large block
of 0's.  This is what would happen:

Original message:   1111111111111111111111111111111111
Random stream:      0011010010000000110111010111001010
Resulting output:   1100101101111111001000101000110101

Look at that big block of 1's in there.  Won't that give it away?  No.
Such a block of 1's is expected to occur occasionally no matter what
the original message.  It's just as likely that the original message
and random stream looked like:

Original message:   1010101010101010101010101010101010
Random stream:      0110000111010101100010000010011111
Resulting output:   1100101101111111001000101000110101

There is no way to tell what the original message was, even when you see
a block of output which seems to match some pattern.  It doesn't tell
you anything.

Hal
74076.1041@compuserve.com