[Cryptography] What do we mean by Secure?

[Jonathan Thornburg]

On Wed, Feb 11, 2015 at 06:09:15AM +1100, Dave Horsfall wrote:
> On Tue, 10 Feb 2015, Stephan Neuhaus wrote:
> > Or, to take an example that is probably much closer to what Richard 
> > meant, that there are no integers p and q such that p^2/q^2 = 2. Proving 
> > negatives is definitely possible in maths.
> 
> I've always understood it to mean something like "you cannot prove an 
> absence of anything."

That not true either.

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.

If you want a purely computer-based example, if (on a Unix system) I
execute 'cat /etc/motd' and the output is unexceptional, that proves
the absence of any multi-megabyte-long Secret Plan for World Domination
stored in that file.

This latter example also demonstrates that proofs generally (maybe
always?) assume certain axioms.  In this case, these include that my
shell is finding and executing the right 'cat' program, that 'cat' is
telling the truth about the file contents, and that xterm and the X
server are faithfully rendering those contents into pixels-on-the-screen.
In the face of a sufficiently clever rootkit any/all of these assumptions
might fail.

ciao,

-- 
-- "Jonathan Thornburg [remove -animal to reply]" <jthorn at astro.indiana-zebra.edu>
   Dept of Astronomy & IUCSS, Indiana University, Bloomington, Indiana, USA
   "There was of course no way of knowing whether you were being watched
    at any given moment.  How often, or on what system, the Thought Police
    plugged in on any individual wire was guesswork.  It was even conceivable
    that they watched everybody all the time."  -- George Orwell, "1984"