Re: [OT] The PGP Signed Posts Farce
From: Bill Unruh (unruh_at_string.physics.ubc.ca)
Date: 10/27/03
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Date: Mon, 27 Oct 2003 11:47:20 +0000 (UTC)
ptb@oboe.it.uc3m.es (P.T. Breuer) writes:
]Ed Murphy <emurphy42@socal.rr.com> wrote:
]> On Mon, 27 Oct 2003 05:20:03 +0000, Peter T. Breuer wrote:
]> > Alan Connor <zzzzzz@xxx.yyy> wrote:
]> >> I think even that is illusory. There's just no way to know what the NSA
]> >> is capable of.
]> > They have to obey mathematics, and yes, there is every way to know. Do
]> > you really have to parade your obvious mathematical handicap again?
]> Theoretically, it's *possible* that the NSA has discovered an efficient
]It's not possible in any sense that I understand the word! They would
]have to have an algorithm for solving p-complete problems in polynomial
]time, and an implementation of it that took less than the time of the
]universe to run on a 1K bit key. It's about as likely as a leaf of
]grass reforming its atoms into a passable facsimile of a silver-plated
]teacup, which is also "*possible*".
No.
This is not true. Even if say factoring were an NP and not P problem and
P!NP, it is possible that there exists an extremely fast algorithm for
factoring numbers less than say 10^99. P, NP, etc, all refer to the
assymptotic behaviour of the algorithms to solve the problem, and say
nothing about the speed of the algorithms for any finite length of the
problem. Furthermore, if it could be proven that factoring say is in P,
it could be that the assymptotic polynomial has degree 10^(10^10)
which would be completely useless for breaking a cypher based on
factoring. Ie, there is not relation between the mathematical
assymptotic class of a problem and its usefulness or otherwise as a
cryptosystem.
]> way to factor huge numbers, and is sitting on it. Practically, how
]> likely do you think that really is?
]Zilch. Zero. Nada. If they could do that they could do all sorts of
]things that they aren't doing, like lay out chip masks with maximum
]efficiency, reverse engineer logic diagrams from output measurements,
]etc. etc.
no, there is no necessity. Being able to solve one finite problem
efficiently need have no bearing on other finite problems.
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