Re: Newbie question(s)...

From: Mok-Kong Shen (mok-kong.shen_at_t-online.de)
Date: 09/19/03 

Date: Fri, 19 Sep 2003 15:59:52 +0200

Jonathan Baker wrote:
>
[snip]
> Suppose my key "source" (if that term is appropriate) is the square
> root of 2 in base 2...
> Suppose my key "bit-selector" (loose terminology here, please
> correct/criticize me!) is the square root of 3 in base 2...
>
> So I generate roughly twice as many bits of the key "source" as I
> would want for my actual key... Same goes for the key
> "bit-selector"...
>
> If the "bit-selector" is a 1, then add the current bit of the "source"
> to our key. If the "bit-selector" is a 0, then skip the current bit of
> the "source"...
>
> This is a REALLY simple idea (could go anywhere with this idea... But
> how would an attacker go about analyzing this?
>
> Say Alice and Bob secretly exchange their key "source" and
> "bit-selector" as square roots of 2 and 3 respectively... (obviously,
> we would really use a hard to guess irrational number)... Charlie,
> that scheming ***... does he stand a chance of figuring this out?
>
> Suppose there are two more key sources... another irrational number,
> say the square root of 5... if a bit is a zero, skip the current key
> bit... if it is a one, then exchange the current bit with the bit in
> front of it... (unencode in reverse)...
>
> And the fourth irrational number, say Pi, or something... You could
> have zero mean XOR the plaintext and key, and one mean IFF the
> plaintext and key...

Some comments based on my poor knowledge: It would be
advantageous that you also have (secret) offsets, i.e.
starting to use bits from certain locations of the bit
sequences. The idea of selection of bits of one sequence
depending on another sequence is not new. (cf. shrinking
generators. I had a humble stream cipher design utilizing
similar idea.) You could also further process a number
of such resulting bit sequences in some ways, e.g. xor-ing
them together or doing sort of von-Neumann unbiasing, etc.
etc. Heuristically, it is reasonable to expect that you
would obtain results that are quite satisfactory, though
it's hard (I would think impossible) to have rigorous
evaluations of them (through formal mathematical means).

M. K. Shen