Kevin Wampler <wam### [at] uwashingtonedu> wrote:
> Warp wrote:
> > 
> >   If the proof results to be correct, I think a *lot* of people out there
> > are going to sigh in relief (because an enormous amount of math and
> > practical computer code out there rely on the assumption that P != NP).
> > 

> This is not to argue with your point, which I imagine is correct, but 
> were you thinking of any particular example of useful code which P!=NP 
> would ensure the applicability/correctness of?  I can certainly think of 
> many things that P=NP would mess up, but nothing comes to mind which 
> couldn't still be messed up despite P!=NP holding.  Or were you more 
> just saying that P!=NP at least removes one possible way that, for 
> instance, modern cryptography could be broken?

  The vast majority of modern cryptography uses algorithms which have been
proven to be NP, and their security relies on the assumption that P != NP.

  If P != NP indeed is correct, then it's certain that no algorithm can
exist that cracks an NP encryption in polynomial time. Not now, nor any
time in the future.

  Thus future-proofing an encryption algorithm becomes (relatively) simple:

1) Prove mathematically that your encryption algorithm is NP.
2) Add enough bits to the keys to last forever.

  (Of course there's still the possibility that a new discovered physical
phenomenon can be used to solve NP problems fast with enormously massive
parallelism or other weirdness.)

-- 
                                                          - Warp

Post a reply to this message