These numbers have nothing to do with the technology of the devices they are the maximums that thermodynamics will allow. (About a hundred times as much energy would be released in the form of neutrinos, but let them go for now.) If all of this energy could be channeled into a single orgy of computation, a 219-bit counter could be cycled through all of its states. A typical supernova releases something like 10 51 ergs. Of course, it wouldn’t have the energy left over to perform any useful calculations with this counter.īut that’s just one star, and a measly one at that. If we built a Dyson sphere around the sun and captured all its energy for 32 years, without any loss, we could power a computer to count up to 2 192. This is enough to power about 2.7×10 56 single bit changes on our ideal computer enough state changes to put a 187-bit counter through all its values.
Now, the annual energy output of our sun is about 1.21×10 41 ergs. To run a computer any colder than the cosmic background radiation would require extra energy to run a heat pump. Given that k = 1.38×10 -16 erg/°Kelvin, and that the ambient temperature of the universe is 3.2°Kelvin, an ideal computer running at 3.2°K would consume 4.4×10 -16 ergs every time it set or cleared a bit. (Stick with me the physics lesson is almost over.) To record a single bit by changing the state of a system requires an amount of energy no less than kT, where T is the absolute temperature of the system and k is the Boltzman constant. One of the consequences of the second law of thermodynamics is that a certain amount of energy is necessary to represent information. Obviously this is different than a password, but interesting nevertheless.įrom Bruce Schneier's book Applied Cryptography (1996): This was used as reasoning why you probably don't need more than 256-bit encryption.
You can actually use physics and thermodynamics to pretty well prove symmetric keys cannot be brute forced reasonably.
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