I meant actually, as statistically speaking, the probability of
picking any one point from any continuous interval on the real number
line is exactly 0, which is why we deal with probability density
functions over intervals instead of probability mass function at
points. But I think I just got way off topic :)
--Avi
On 1/20/11, Peter Pentchev <roam(_at_)ringlet(_dot_)net> wrote:
On Thu, Jan 20, 2011 at 11:36:32AM -0500, Avi wrote:
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Hash: SHA512
Even more strongly, there is the difference between "almost
never" and "never". Even if there were an infinite number of key
id's along the real number continuum, the possibility of a
collision is mathematically 0%,
...I believe you mean "practically 0%", since mathematically,
it is definitely not 0% :)
but it is still possible. Heck,
the possibility of ANY id would be mathematically 0, but each
key would still have an ID.
Same here, ITYM "practically" or "virtually" 0 :)
Here, we are dealing with a discrete distribution, so there
/are/ mass points (be they VERY very small) at each ID, so yes,
it is 100% certain that eventually, not only will there be a
collision, but every key will have a collision.
Theoretically, this is not necessarily true. It depends a lot on the
hashing algorithm used - it is completely possible to design a hashing
algorithm that would produce a certain digest for one input value and
one input value only - hell, it's trivial to design one based on another
hashing algorithm: "If the input is 'abcd', produce SHA1('abcd'); else,
if SHA1(input) == SHA1('abcd'), produce SHA1('abcde'); else, produce the
same result as SHA1(input)."
I'm pretty much certain that for SHA1 your statement would be true, but
I'm not certain if it has been proved - greater minds here would
probably know: has anyone looked into that, and has it been proven that
there does not exist any sequence of bytes which would have an unique
SHA1 hash, that is, against which it is impossible to do a preimage
attack?
It may be
though, that the waiting time may be longer than the heat death
of the universe for the latter, so we don't have to worry about
that too much :).
G'luck,
Peter
--
Peter Pentchev roam(_at_)ringlet(_dot_)net roam(_at_)FreeBSD(_dot_)org
peter(_at_)packetscale(_dot_)com
PGP key: http://people.FreeBSD.org/~roam/roam.key.asc
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Hey, out there - is it *you* reading me, or is it someone else?
--
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