Cryptography and the Landauer Limit

Sunday, July 5, 2009

In Hollywood, decrypting encrypted data is a simple matter of handing it off to a government lab or wunderkind and coming back in a few hours.

However, even if we were lenient toward Hollywood's fanciful views on computing power, there is another limitation which hackers are unlikely to get the better of: energy.

To bruteforce the decryption to AES-256 encrypted harddrive (commonly available for purchase) would require more energy than exists in the entire solar system. Even if you converted the sun and all the planets into pure energy, you would still come up short.

This is due to Landauer's principle. For a computational operation in which 1 bit of logical information is lost, the amount of entropy generated is at least k ln 2, and so the energy that must eventually be emitted to the environment is E ≥ kT ln 2. (k is the Boltzman constant and T is the temperature of the computer). For AES-256, 2^256 bits must be computed, which is quite a lot!

Possible remedy to this limitation may lie in the future development of reversible computing. If no information is erased, computation may be achieved which is thermodynamically reversible, and require no release of heat. The caveat is that this requires remembering previous states of the system, and must have available the memory necessary to do so.