Quote from: Syke on March 12, 2014, 11:56:14 PM

I'll let Bruce educate you.

Quote

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°Kelvin, 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 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.

Thanks refresh on the basics thermodynamics, The calculation is a bit off and pretty simplistic and in fact the amount of energy needed is more than that, but again that calculation is only taking into consideration TODAYS computing power and we are just repeating our selfs here,And I don't understand what you don't get here, there is no point on starting a computation today to do such a thing and this what the argument above is presenting no more no less. the minimum amount of time needs is in the order of 10^55 years, in by the second law of themodynamics by that time there will be nothing left in the universe not a single star the only things left would be blackholes and even those will eventually start evaporating (degenerescence or blackhole era)

Anyway let me simplify things since a lot of people seems to be confused here:

Just to put things in a human scale, let's assume that there are no oceans and you can "walk" all the way between continents, a few centuries ago, it would be impossible to go around the world (objective here to go around the world at the equator 10 times) and at the period the best you can do on ground is walking/running using horses and as we can it was impossible to come even close to a faction of the necessary distance to achieve the objective (the circumference of earth at the equator is 40 075,017, and your speed won't exceed an average of 5km an hour it's easy to see the issue here we are talking easily millennias ). Today, it take the International space station around 90min to orbit the earth so 10 orbits should take around 15hrs.

Quote

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.

This is totally wrong, and it is your own misinterpretation, and you are welcome to quote the exact word they used. I'm pretty sure what they mean is that with todays technology to be able to brute force against 256bit you'll need a computer of a size bigger than the universe (which is to say yet again Impossible!)

I'll also invite you just for the sake of reference, to check the 80s tech and security magazines if you have access to those in your city library and check what they were saying about 56bit encryption at the time, you'll be really surprised on how the argument you are advancing are similar if not the same of what was said at the time.