Re: The Mathematics of Relative Security

[Crispin Cowan <crispin () immunix com>]

Chris Pugrud wrote:

> --- Crispin Cowan <crispin () immunix com> wrote:
>  
>
> > More succinctly, if you ask the question "am I secure?" in a highly 
> > rigorous fashion, the likely answer is "Hell no" :)
> >    
> This is distinctly the intuitively obvious answer.  The more rigourous answer
> is that only insecurity can be proven, testing security reduces to the halting
> problem.
>  
That is not quite correct: security *can* be proven. Turing's Halting 
Problem says that you cannot build a general-case security proving 
program, because the proof is based on diagonalization, i.e. apply the 
prover to itself.

However, in the cases where you can prove security, the costs of proving 
it are astronomical, and the costs of achieving that security are pretty 
high too.

> TCP also introduces a wrinkle that is not easily covered by the set theory I
> have learned, or I'm missing something - the concept of one-way membership.
Consider using graph theory instead of set theory, as it at least has a 
built-in notation for directionality on edges.

Crispin

--
Crispin Cowan, Ph.D.  http://immunix.com/~crispin/
CTO, Immunix          http://immunix.com

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