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Why is it said that AES is unbreakable? Brute force attacks would take years to crack it, so is it possible to crack it if the computational speed of machines increase in the following decade?

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First, it's not said that AES is unbreakable, merely that none of the currently known attacks reduce the computational cost to a point where it's feasible. The current best attack on AES-128 takes 2^126.1 operations, if we had a computer (or cluster) several million times more efficient than any current computer and could operate at the thermodynamic Landauer limit, it would take 234 petajoules just to increment a counter through every key value. That's about half of the annual electricity consumption of Norway. Actually computing an AES round takes several times that much energy.

Now consider a round. A round in an optimized implementation takes 16 table lookups and 16 exclusive-or operations. Let's just say each operation is fundamental and takes the same energy as incrementing a bit in a counter, so 32 operations per round, times 10 rounds means you're at the annual electricity production of the USA.

Remember that that was with a computer operating at the minimum possible thermodynamic energy requirements. So you probably want to multiply that by a few million, at which point you're reaching the total energy from the sun which hits the earth each year.

Thus, for any practical computer the energy costs are too high, and even for a theoretical computer the costs would be large enough that it would take several years to brute force a single key, even for a very large nation.

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    $\begingroup$ The answer started with an optimistic note in the first sentence and then blasted me back into reality by the end of the second sentence . Thanks ! $\endgroup$ – eatq Mar 8 '15 at 17:10
  • $\begingroup$ But it will still be faster than computing the answer to the ultimate question of life, the universe and everything! ;-) $\endgroup$ – Matt Mar 9 '15 at 18:19

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