Useful factoid

Aaron Toponce aaron.toponce at
Wed Oct 12 04:51:18 CEST 2011

On Tue, Oct 11, 2011 at 04:32:18PM -0400, Robert J. Hansen wrote:
> Accurate to 6%, there are 2**25 seconds in a year.  Worth remembering:
> it makes certain kinds of computations much easier.  (It follows there
> would be about 2**35 seconds in a thousand years, or 2**45 seconds in a
> million.)
> E.g., let's say you want to brute-force an 64-bit key on a CPU that can
> do a million (2**20) attempts per second.  This requires, on average,
> 2**63 attempts.  2**63 / 2**20 = 2**43 seconds: 2**43 / 2**45 = 2**-2 =
> a quarter of a million years.
> I don't know why it took me so long to notice that: seems like the sort
> of thing I should've noticed a decade ago.  It makes certain kinds of
> computations so much easier.
> Anyway, figured I'd throw it out on the off chance there were others who
> hadn't noticed it.

This is actually pretty cool. Puts things in perspective. I usually show
people The
distributed computing project is working on brute forcing the key that will
break the RSA 72-bit crypto challenge. Currently, they're moving at a pace
of 324 billion keys per second (substantially faster than Robert's
example), and even at that rate, it would take them ~450 years to exhaust
the entire keyspace.

Of course, I realize that the probability of them finding the key tomorrow
is the same as finding the key in 450 years, but the point remains-
breaking a 72-bit key is substantially more difficult, and requires a
serious amount of computing power.

For all intents and purposes, I am fine with 72-bits worth of entropy on my
passwords, and building systems relying on 72-bit keys for my personal

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