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

Henry Baker hbaker1 at pipeline.com
Sat Jan 2 21:16:33 EST 2016


At 04:47 PM 1/2/2016, Ron Garret wrote:
>On Jan 2, 2016, at 6:50 AM, Henry Baker <hbaker1 at pipeline.com> wrote:
>> Here's my problem:
>>
>> I'm trying to characterize a 1x pad.
>>
>> A 1x pad *adds* (modulo, but that shouldn't matter)
>
>But it does matter.
>
>That's what makes it secure.
>
>> 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.
>
>Yes.
>
>In a linear system.
>
>XOR is non-linear.

Actually XOR *is* linear.  The problem isn't linearity, but the "folding" that happens with modulo.

Consider a modular system [0..N), and a single message 0<=m<N and a single key 0<=k<N.

So long as p(K=k) is precisely uniform, i.e., p(K=k)=(1/N) for all k, then p(M+K=e)=(1/N), for all Eve's received messages e.

But without the folding from modulo, we no longer get uniformity from p(M+K=e).

I'm trying to see whether there is an analogy between this folding and *aliasing* (the really old fashioned kind prior to sampled digital signal processing).



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