Last week I discussed Landauer's principle and attempted to determine how long an encryption key would need to be before the necessary energy exceeded the global energy consumption rate.

I made a mistake.

My algebra was correct, but I tripped at the finish line. I made a mistake entering the formula into WolframAlpha and came up with a lower answer than I should have. Essentially I botched my parenthesis, one of the perennial annoyances of software development.

Here's the formula I mistakenly wound up entering:

Note how the natural log (with its parenthesis) encloses the entire left-hand side. The formula I intended to enter has the natural log of the overall numerator:

And what a difference that makes: from 96 bits to 137. This actually somewhat exceeds the default key length for AES (128 bits) although AES can also support longer key sizes. Enumerating all possible 128-bit keys would require a little less than 0.2% of the global energy consumption in 2013.

This comes out to 211 billion kilowatt-hours. WolframAlpha helpfully informs me that this is 23 days' worth of combined energy production from all the nuclear power plants on the globe.

While this is a generous upper limit of search capabilities, it suggests that a sufficiently powerful and determined organization could brute-force a 128-bit key. It would require a great deal of energy, a near-optimum computing facility, and weeks or months to do, but it could be done. And with growing energy production and computing efficiency, it may be possible in the not-too-distant future.

Luckily, each additional bit of key material doubles the search space. All it takes to avoid brute force is to make encryption keys that are just that much longer.