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For how long will whatever encryption they use be secure? Computers get ever more powerful, and with today's computers, we can brute-force stuff that was pretty much inconceivable a decade or two ago.

A 2048 bit key is not twice as hard to brute force as a 1024 bit key.

It's 2^1024 times as hard.

If every atom in the universe was a super-computer capabale of checking one Trillion (10^12) keys per second, and all those atoms had been working in parralel since the Big Bang, they wouldn't even have made a small dent in the actual keyspace.

Number of atoms (supercomputers) in the Universe: ~10*10^80 (generous by an order of magnitude)
Number of seconds since the Big Bang: ~6*10^23

Actually that's kind of boring, let's get ridiculous!

Let's assume one of those supercomputers per Planck Length (cubed) doing one Trillion key checks per Planck Time (iteration)

Planck Time = ~5.4*10-44 seconds
Planck Times since the Big Bang: ~2*10^62 (~15 Billion years)

Planck Length = ~10^-35 meters
One cubic meter: ~10^105 Planck cubes

Hubble limit = ~10^26 meters
Hubble sphere: ~10^183 Planck cubes

Planck iterations since the Big Bang: ~2*10^245
Keys brute forced since the Big Bang: ~2*10^257 or ~2*2^854

That represents about one 2^1194th of the keyspace (~ 3*10^-357 %).

Projecting out to the heat death of the universe won't help either. Those keyspaces are simply not brute forceable.

It is infinitely more likely that weaknesses will be found in the encryption algorithms themselves (or key generation algorithms), then for any brute forcing attempt to be viable using currently known technology.

Moore's Law won't help (I kind of took it part way to it's logical conclusion above).

2012-05-10 12:40:37


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