[Cryptography] GHCQ Penetration of Belgacom

[John Levine]

>I still remain astonished, that, since Babbage/Lovelace/Turing/etc, that 
>many alleged programmers still do not know that 0.0 != 0.

To pile on a little, on every reasonably modern* architecture I know,
0.0 == 0, both semantically and the bit representation.

On the other hand, floating point numbers are an approximation to
reals, and due to accumulated quantization and rounding errors, a
calculation for which the real result would be zero will often produce
something else in floating point.  It's been about 40 years since I've
had a numerical analysis course, but I recall that a lot of it was
about estimating error bounds so I could decide how different from
zero an answer could be and still be close enough to be semantic zero
for the problem under discussion.

It seems to me there are a lot of places in crypto that have similar
issues, the code we have is only an approximation to the Platonic
ideal, e.g., a Platonic CA would reliably check that alleged identity
exactly equals the real identity, but actual CAs tell us that alleged
identity equals real identity +/- 0.0004715 and we don't have a
very good understanding of how to deal with that.

R's,
John

* - no older than the PDP-6 or IBM S/360, which were designed 50 years ago