[Cryptography] What do we mean by Secure?

[Jerry Leichter]

On Feb 11, 2015, at 12:01 AM, Dave Horsfall <dave at horsfall.org> wrote:
>> For example, by looking around the (farily small) room in which I'm 
>> sitting right now, I can prove the absence of adult elephants in this 
>> room.
> 
> OK, for the sake of the argument (moderator(s) willing and the creek don't 
> rise), prove to me the absence of an adult elephant in your room.  Please 
> note that I am unable to physically verify same for myself, as I'm in 
> Australia and you aren't.
Prove to me the *presence* of a desk in the room in which you are working (or of any other specific fact).

The problem here isn't with the kind of fact, it's with the whole notion of "proof".  Mathematics has "proofs" that are alleged to be eternal and independent of the prover and of any specific background.  No such things *ever* exist about facts in the real world, where facts are inherently contingent, reliant on particular observations, dependent on interpretation.

And you know what:  Even the mathematical proofs aren't quite what they seem.  While they may appear to exist in some Platonic elsewhere, independent of human beings, it's ultimately created and checked by humans (or perhaps these days by programs created and checked by humans).  Proofs have stood for years, only to be found erroneous later.  Their meaning is embedded in a huge matrix of definitions and complexities; later reinterpretations have rendered them, not false, but not as all-powerful as they seemed.  It's trivial to prove that there are no infinitesimal values in the real numbers.  But ... it's also possible to define "non-standard" models of the reals that share all the properties you thought defined the reals ... but which have infinitesimals.  Logic itself isn't as black and white as we like to think.  The the ancient Greeks, the parallel postulate was either true or false - we just hadn't found a proof one way or the other.  Well ... no.
                                                        -- Jerry