Re: Is MD5 outdated ?

From: Phil Carmody (thefatphil_demunged_at_yahoo.co.uk)
Date: 10/06/03 

Date: 06 Oct 2003 14:35:26 +0300

Pilou <pilou@kma.eu.org> writes:

> > 2**64.5 is 26087635650665564424.6991..., but if n is only
> > 26087635650665564425, the probability is still less than 1/2, namely
> > 0.49999999999999999999236.... Only when n is at least
> > 26087635650665564426 is the probability greater than 1/2, namely
> > 0.50000000000000000003069....
> > Any number from +0.3009 to +1.3008 would have worked as well as
> > +0.5, but 0.5 was a correct value that I could find without using a
> > calculator.
>
> Actually, as far as I can tell, your numbers are wrong.

Wrong? They're complete bull***! I can only surmise that whoever
wrote them is in my killfile, as you chopped their name off the top.
I can only thence surmise that they deserve to be there!

> Let f(k) = P(no collision with k people and 2^128 birthdays)
>
> f(26087635650665564425) =approx 0.367878
>
>
> Let kk be the unique integer such that f(kk+1) < 0.5 < f(kk)
>
> Let i = int(sqrt(2*ln(2)*n))
>
> I can assure you that i-50 < kk < i+50
>
> i = 21719381355163562491 (approx 2^64.2356)

However, I think (hope) what was meant a few posts back may have been
  2**(64.5 +/- 0.5)
and 2**64.2356 certainly meets that bound.

Phil

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