Hey there,
>> ~= 5.1E-57
>
> Bah. My math is wrong. I was never very good at P&S. I'll ask someone at
> work tomorrow to look at it and show me the folly. Wikipedia has it right,
> but I can't evaluate numbers to the few-hundredth power in any calculator
> that I have handy.
bc -l <<EOF
scale=150
define bday(n, h) { return 1 - e(-(n^2)/(2*h)); }
bday(2^35, 2^256)
bday(2^35, 2^256) * 10^57
EOF
Basically, ~5.1 * 10^-57.
Seems your number was correct, although I am not sure how you arrived at it.
It appears that number is ~ consistent with the tables on Wikipedia article
on birthday attack (http://en.wikipedia.org/wiki/Birthday_attack): p=10^−15
for 256-bit hash collision requires 1.5*10^31 (O(2^103)) hashes, assuming
the hashes are randomly distributed.
That's definitely improbable.
For anecdotal evidence to the contrary, we once had apps using GUIDs. We did
believe collisions would be extremely improbable. Yet GUID conflicts turned
into recurring events, at worst several collisions a week. It may or may not
be related - in our case it turned out the GUIDs weren't anywhere near as
random as people thought they would or should be. In retrospect we clearly
used a flawed GUID generator which rendered our assumptions about randomness
invalid. SHA256 on (even non-random) data is different, but do be careful
about what you assume.
Regards,
Lassi
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