[Cryptography] Any Electrical Engineers here who know about noise filtering?

[dj at deadhat.com]

> Here's my problem:
>
> I'm trying to characterize a 1x pad.
>
> A 1x pad *adds* (modulo, but that shouldn't matter)
> uniformly distributed "noise" (the "key") to the
> "message" signal.
>
> Classical filtering theory says that given a
> noise spectrum, one can compute an optimal
> filter to remove as much noise from the signal
> as possible.
>
> I'd like to go through this mathematical
> exercise with modular addition and the
> noise spectrum one might want for a key
> distribution to show that such an
> optimal filter *for this case* is the
> identity -- i.e., even the optimal
> filter can do *nothing* to remove any
> "noise" -- i.e., the 1x pad random
> signal.
>
> I seem to recall ideas such as "Weiner
> filters", and the like.
>

The noise spectrum of any bitstream XORed with a fully random (for your
preferred definition of fully random) bitstream will be uniform as the
quantity of data tends to infinity.

Compared to classical EE filtering theory, it isn't a case of
filter(signal+noise). It's signal convoluted with noise. So a frequency
selective filter would not be able to recover the signal from the noise. A
deconvolution process would require that you can regenerate the
pre-convolution random noise, which is where the need for the uniqueness
and unpredictability properties of the random sequence become important.