Total number of bitcoins will DECREASE

[tspacepilot]

Uh, 256 bit will be secure while you live.. Maybe. But we're all betting that it is secure for a very long time. Maybe not billions or millions of years, but if it actually survives a few hundred years, that's good enough for now.

Practially, I agree with this statement ^^^.  Nonetheless, the discussion of how quantum computers relate to breaking sha 256 is pretty interesting. 

The image above with the solar system sized "perfect-computer" is cute, but it lacks detail.  What's the valuation of "least engery possible to record a change of state"?

Sorry I'm so dumb.

[jonald_fyookball]

A quick google search turned this up.

http://en.wikipedia.org/wiki/Landauer's_principle

Landauer's principle asserts that there is a minimum possible amount of energy required to change one bit of information, known as the Landauer limit:

    kT ln 2,

where k is the Boltzmann constant (approximately 1.38×10−23 J/K), T is the temperature of the circuit in kelvins, and ln 2 is the natural logarithm of 2 (approximately 0.69315).

Way off the original topic of the thread, but fascinating stuff.
What is unclear to me about Boltzmann's prinicple, (from
which Landauer's principle is derived) is how there are only a certain number of micro states,
because couldn't temperature be anything?
Or is it a discrete measurement?

In otherwords, is temperature a discrete thermondynamic
value?

Maybe our phd in physics friend can explain further.

[ranlo]

One thing that most people don't seem to understand is that after 21 million Bitcoins have been produced, the TOTAL number of Bitcoins in circulation will decrease in a LINEAR fashion each year.

While I do agree that the total number of spendable Bitcoins would decrease, I disagree that it would be in a linear fashion. Those who made the mistake in the past are unlikely to do so again and the experienced veterans are unlikely to lose their keys so to me it seems more like an exponential decay curve as the rate of change of total spendable coins. Nonetheless, as long as other market factors are unaffected price should logically rise as supply decreases.

I'm going to agree with this, and I would venture out to say that at some point we may hit negligible losses. As the value goes up people are being more careful with their coins. Most of them as of lately are lost due to hacks, rather than true losses, so they are still floating out there on the market.

The issue is we don't even know how many coins are actually lost. Tons of people have guesses, but there is no way to know for sure.

[DeathAndTaxes]

Nonetheless, the discussion of how quantum computers relate to breaking sha 256 is pretty interesting.

Quantum computers will be very boring when it comes to SHA and all other hashing algorithms.

The image above with the solar system sized "perfect-computer" is cute, but it lacks detail.  What's the valuation of "least engery possible to record a change of state"?

The second law of thermodynamics and Boltzman constant.  If it isn't clear the required energy only applies to "classical computing" and a brute force attack.  It is possible that someday ECDSA will be weakened such that it doesn't provide 256 bits of security, or quantum computing would allow breaking keys with a significant reduction in required energy, or that reversible computing allows for computers which use less or potentially no energy.  Of course we have no idea if those methods will ever become practical in our lifetime or even in the next milenium.   We do know that keys can be brute forced using classical computing however the number of possible values in a key with 256 bit security and the limits of the laws of thermodynamics mean that while it is "possible" it has energy requirements which make it infeasible.

Here is a quote from Applied Cryptography (a dated but very good book for those interesting in understanding 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°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 2.7×10^56 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 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.

[jonald_fyookball]

 thanks for the book reference  

yes, Boltzmann constant multiplied by
circuit temperature, which is why
the graphic says "cooled to absolute zero".

Perhaps the image should be a frozen sun,
nes pa?


 
P.S. why would quantum computers be "boring" ?

[DeathAndTaxes]

P.S. why would quantum computers be "boring" ?

They are boring for hashing algorithms as Shor's algorithm is not applicable against cryptographic hashes.

[jonald_fyookball]

P.S. why would quantum computers be "boring" ?

They are boring for hashing algorithms as Shor's algorithm is not applicable against cryptographic hashes.

But... Shor's algo can be applied to ECDSA right?  Which uses a hash function within it...

[Beliathon]

Losing private keys must really suck, but I see your point. Isn't there someway to protect it?

Yes.

Create backups.

This. Noobs.

[DeathAndTaxes]

P.S. why would quantum computers be "boring" ?

They are boring for hashing algorithms as Shor's algorithm is not applicable against cryptographic hashes.

But... Shor's algo can be applied to ECDSA right?

Yes

Which uses a hash function within it...

No although you are signing a digest (hash of the message).   Attacking a private ECDSA key using quantum computing would require a general purpose QC capable of implementing  Shor's algorithm on 512 bit keys (tens of thousands of qubits) AND the PubKey must be known.   

[DeathAndTaxes]

thanks for the book reference 

yes, Boltzmann constant multiplied by
circuit temperature, which is why
the graphic says "cooled to absolute zero".

Perhaps the image should be a frozen sun,
nes pa?

Well the power source wouldn't be near absolute zero, the computer would be.  The higher the temp the higher the min energy requirement.  The background temp of space is pretty close to 0 K, at room temp it would need a lot more energy.

[jonald_fyookball]

Isn't the first step, hashing the message...so then that's part of the signature generation algorithm.

Btw, It seems the sun would be both the power source and the computer (dyson sphere) in this made up scenario that the graphic talks about.  Do we really have to debate minutiae ?   

[jonald_fyookball]

A quick google search turned this up.

http://en.wikipedia.org/wiki/Landauer's_principle

Landauer's principle asserts that there is a minimum possible amount of energy required to change one bit of information, known as the Landauer limit:

    kT ln 2,

where k is the Boltzmann constant (approximately 1.38×10−23 J/K), T is the temperature of the circuit in kelvins, and ln 2 is the natural logarithm of 2 (approximately 0.69315).

Way off the original topic of the thread, but fascinating stuff.
What is unclear to me about Boltzmann's prinicple, (from
which Landauer's principle is derived) is how there are only a certain number of micro states,
because couldn't temperature be anything?
Or is it a discrete measurement?

In otherwords, is temperature a discrete thermondynamic
value?

Maybe our phd in physics friend can explain further.

A little more digging reveals that temperature, while
normally continuous, may theoretically become
discrete at the quantum/particle level.

What is then, the smallest theoretical unit by
which to measure temperature?  

[DeathAndTaxes]

What is then, the smallest theoretical unit by
which to measure temperature?  

There is no such smallest unit (precision) for temperature*.   However it does not matter as the only form of cooling which would not require the expenditure of energy would be to passively radiate it to the outside environment.  In this case that would be open space and the background temperature is ~3K.   To cool the device below the ambient temp would require the expenditure of energy.  As the textbook example indicates you could use a heat pump but that would negate the benefits of the improved efficiency.

The quote should probably have said "near absolute zero" indicating a high conductivity passive radiator which keeps the computer within fraction of a degree of the background temperature of space and use a K value of ~3K for the energy requirements.


* On edit: It looks like Planks Temperature would indicate the smallest unit of temperature is ~7x10^-33 K although this doesn't materially change the facts.

[Dabs]

Who wants to try cracking a bitcoin address? I'll put some coin into it. ... actually, you can do that now, there are a bunch of addresses out there that have hundreds or thousands of bitcoins.

[Dabs]

I believe nothing can reach absolute zero. Everything in outer space is very close to it, but nothing is going to hit zero, and we have no way to measure that (or maybe it can be measured.)

[jonald_fyookball]

What is then, the smallest theoretical unit by
which to measure temperature?  

There is no such smallest unit (precision) for temperature*.   However it does not matter as the only form of cooling which would not require the expenditure of energy would be to passively radiate it to the outside environment.  In this case that would be open space and the background temperature is ~3K.   To cool the device below the ambient temp would require the expenditure of energy.  As the textbook example indicates you could use a heat pump but that would negate the benefits of the improved efficiency.

The quote should probably have said "near absolute zero" indicating a high conductivity passive radiator which keeps the computer within fraction of a degree of the background temperature of space and use a K value of ~3K for the energy requirements.


* On edit: It looks like Planks Temperature would indicate the smallest unit of temperature is ~7x10^-33 K although this doesn't materially change the facts.

right, there we go ... plancks unit... i saw that earlier but was confused for
a second about that being absolute hot (planck temperature of 1)
it would have to be something (even if unnamed) or else it doesn't
make sense that we could define a Boltzmann constant I think.

One thing is for sure... there is a very deep rabbit hole to go
down if one wishes to explore all the theory behind the
energy claim in that sun pic.  even Landauer's principle
is not without its challenges.

One interesting thing though is this:

In a 2012 article published in Nature, a team of physicists from the Ecole Normale Supérieure de Lyon, University of Augsburg and the University of Kaiserslautern described that for the first time they have measured the tiny amount of heat released when an individual bit of data is erased.

----

Who wants to try cracking a bitcoin address?

Not me.  If I thought it could be done, I wouldn't be a bitcoin investor.

[Dabs]

I'm a bitcoin investor. But I know it can be done. In about a few hundred years, at least, up to a few billion years.

[adaseb]

I think a lot of bitcoins where lost in 2009-2010 when people formatted their drives because they didn't care about having a coin worth literally nothing.

[Peter R]

What is then, the smallest theoretical unit by
which to measure temperature?  

Does that question even make sense?

The concept of temperature is a human abstraction.  A useful definition for temperature is:

   "Temperature is the thing that's the same for two objects, after they've been in contact long enough."  [1]

Physicists then build up mathematical models on top of this definition (and other definitions) that explain what we observe in nature--models such as Boltzmann Factors, the Equipartition Theorem, and even things like the Bose-Einstein and Fermi-Dirac distributions.  But the crazy thing is that none of the parameters of physics (temperature, force, energy, etc) are real in the sense that the computer I am typing on is real.  They are all just useful abstractions that help us explain what we see in nature.  


Jonald: purchase the book "Feynman Lectures on Computation" by R.P. Feynman.  It is fantastic, it will answer a lot of your questions, and it will give you a bunch of new ideas!


[1] DV Schroeder, "Introduction to Thermal Physics," Addison-Wesley Longman, 2000.  

[Aswan]

One thing that most people don't seem to understand is that after 21 million Bitcoins have been produced, the TOTAL number of Bitcoins in circulation will decrease in a LINEAR fashion each year.  Why? Because a consistent number of people (maybe 0.05%) will always - ALWAYS - lose their private keys.  This is inevitable.

So with the number of Bitcoins DECLINING (after 21 million) and the demand RISING, classical economics tells us that the price will SURGE.

When bitcoin becomes more and more mainstream, the demand for banks securely storing bitcoin will rise. Most people will have their BTC with a bank because they don't care about privacy and are scared of not being able to secure their coins. Additionally, most people are susceptible to those ads big banks are gonna eventually use make more people deposit money with them.
As a result, most BTC transactions will not be person to person (or address to address) but bank to bank just like today. Because of this, it will be easy for banks to increase the supply of BTC by using fractional reserve banking and only issuing IOU which are only backed by 10% (or less) resulting in a huge spike of BTC supply (similar to gold today).
Because of said banks having to much money (today and during the transition and thanks to the BTC fractional reserve banking, also after the transition), they will be able to monopolize this sector and become bigger and bigger inflating the BTC supply even more - because they can and because that way they get something for nothing while everyone else loses.

As a result, while the actual number of BTC are declining, the number of BTC that are used for payment etc are going to increase a lot faster than they are meant to increase by the protokoll.

The only difference might be that you can be your own bank - and that once a bank fails to pay out, they can't magically conjure new BTC. Again this might be the case - they could as well pay some politicians to only allow whitelisted addresses to make payments to merchants (which are audited) and force you to accept their inflated BTC for settlement of debt by paying men with guns to enforce their made up rules.


just my 2 satoshis..