Skip to main content
1 of 7
ir01
  • 4k
  • 3
  • 22
  • 31

There is some Thermodynamic Limitations. A good explanation about Thermodynamic Limitations is by Bruce Schneier in Applied Cryptography:

One of the consequences of the second law of thermodynamics is that a certain amount of energy is necessary to represent information. 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. (Stick with me; the physics lesson is almost over.)

Given that $k =1.38*10^{-16} erg/°Kelvin$, and that the ambient temperature of the universe is $3.2°K$, an ideal computer running at $3.2°K$ would consume $4.4*10^{-16}$ ergs every time it set or cleared a bit. To run a computer any colder than the cosmic background radiation would require extra energy to run a heat pump.

Now, the annual energy output of our sun is about $1.21*1041 ergs$. 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. If we built a Dyson sphere around the sun and captured all of its energy for 32 years, without any loss, we could power a computer to count up to $2^{192}$. Of course, it wouldn’t have the energy left over to perform any useful calculations with this counter.

But that’s just one star, and a measly one at that. A typical supernova releases something like $10^{51} > ergs$. (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.

These numbers have nothing to do with the technology of the devices; they are the maximums that thermodynamics will allow. And they strongly imply that brute-force attacks against 256-bit keys will be infeasible until computers are built from something other than matter and occupy something other than space.

ir01
  • 4k
  • 3
  • 22
  • 31