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Unformatted text preview: hese numbers significantly. Don’t even ask me about nanotechnology. Thermodynamic Limitations
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*1056 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 2192. 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 1051 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. 7.2 Public-Key Key Length
One-way functions were discussed in Section 2.3. Multiplying two large...
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This note was uploaded on 10/18/2010 for the course MATH CS 301 taught by Professor Aliulger during the Fall '10 term at Koç University.
- Fall '10