
The Physics of Brute Force (2016) - tiord
https://pthree.org/2016/06/19/the-physics-of-brute-force/
======
Qision
>where 0 Kelvin is defined as a system devoid of energy

This is not true, in quantum mechanics at zero kelvin (so in its fundamental
state) a system has a non zero energy. See this:
[https://en.wikipedia.org/wiki/Quantum_harmonic_oscillator#Ha...](https://en.wikipedia.org/wiki/Quantum_harmonic_oscillator#Hamiltonian_and_energy_eigenstates)

~~~
pif
You're right. Zero Kelvin means no _entropy_.

~~~
dmarchand90
Is that true either? E.g a metastable glass structure sent to 0k probably
still has an entropy?

~~~
ExThermoGuy
[edit:] Third law states 0K is impossible. That's the obvious and simplest
answer. So everything bellow assumes the limit as you approach 0K.

I think in that case you reach a paradox because temperature is a quantity
(typically) defined in thermodynamics, i.e. systems in equilibrium. A
metastable glass is not in its ground state, therefore not in equilibrium,
therefore not technically within the purview of thermo. This might seem like a
cop out, but a similar question was asked in my qualifier. The answer, glass
is not technically described my thermo and at 0K the whole thing breaks down
[1]

Sure we still talk about entropy and temperature of glass, but it's stretching
the definitions.

Another way to look at it, though, is that at 0K there is only one state
available to the system (even though it is a glassy one). Therefore call the
glass a new state of matter, and set S=0. If that feels weird because it's not
the ground state, consider that glass' constituents, Si and O, are not in a
ground state either, that'd be Fe. You don't have any problems dealing with
metastable Si and O, do you? Either way, 0K makes no sense!

Also, it's weird (actually wrong) to even think about materials at 0K. In
classical thermo your heat capacity is zero. In modern physics your atoms'
"positions'" are fully determined, therefore their "momentum" is fully
undetermined. So 0K is a state that makes zero sense.

[1] I forget the question. I think it was like this: the entropy of glass has
a greater slope than the crystal, therefore, if you cool the glass low enough
it will achieve a lower entropy than the crystal. How can a glass have lower S
than its crystal state?

------
effie
Of course, current computers are nowhere near capable to try out substantial
portion of all 256 bit keys. It requires massive amount of energy and time to
perform single bit operation, much larger than kT for room temperature T
(several orders of magnitude). Not mentioning costs of trying out the
resulting bit sequence for validity as a key. That should be the argument for
"256 bit keys are enough".

There isn't any fundamental energy cost imposed by physics here, however. Both
because 1) bit flipping can be done in a logically reversible way, just go
systematically from 0 to 2^256 - 1 so Landauer's assumptions do not even apply
2) Landauer's idea has been criticized for being vague/badly reasoned. Most
weirdly, Landauer assumes that erasure of a bit register in general requires
that thermodynamic entropy _k_ ln 2 per bit is acquired by the environment. It
seems people are confused and can't distinguish information entropy and
thermodynamic entropy here. In real computers, erasure of bit register
decreases information entropy by _k_ ln 2 and increases thermodynamic entropy
(by HW-specific amount) associated with the register. These are two different
kinds of entropies.

In short, real world energy costs are far higher than Landauer's limit due to
current tech limitations, and possible energy cost savings in the future
aren't hard limited by Landauer's limit at all. Landauer's idea is simply too
problematic. Don't rely on it for any argument about real world.

Finally, don't learn physics from computer science guys, even if their name is
Bruce Schneier. Just as you wouldn't learn computer science from physics
experts.

------
effie
> _" One of the consequences of the second law of thermodynamics, is that it
> requires energy to do a certain amount of work."_

No, that is a restatement of the First law of thermodynamics. Second law
states that it is impossible to systematically (cyclically) extract heat and
turn it completely into equivalent amount of work.

------
effie
> So, we'll run this ideal computer at 2.72548 Kelvin.

The record for lowest temperature is 1e-10 Kelvin and there is no theoretical
limit as to how many zeroes can be added. So there is no hard limit, given
good enough cooling/thermal isolation, the energy cost can be brought down. In
theory, it can be brought down to zero.

~~~
SolarNet
This is addressed:

> To run a computer cooler than that would require a heat pump, which means
> adding additional energy to the system than what is needed for our
> computation.

~~~
effie
That does not address it. It is true that heat has to be removed to maintain
the lower temperature. But the rate at which this has to be done depends on
heat generation and quality of isolation. If temperature inside is 1e-100 K,
energy cost of only bit flipping becomes negligible. Energy cost of
refrigeration depends then on how good the isolation is. With better and
better isolation, the cost goes down, the only limit is zero.

------
murgindrag
The problem is I don't need to search the whole key space. Even with very
goods encryption algorithms, there are faster attacks. They're not FAST
attacks, mind you, so the keys are safe, but they are FASTer.

~~~
PaulHoule
I think most of the time there is some attack on a cipher which is faster than
the most obvious brute force attack.

Sometimes the speed-up is a little, sometimes it is a lot.

