Cold storage questions

[jonald_fyookball]

Moore's law has been more of a general observation (a trend) rather than any kind of
fundamental property.

It can't continue forever.  In fact, it is already running into its inherent limitations.

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[DeathAndTaxes]

Wow, Light! Mind blown, and satisfied, at the same time. Guess I'll stop worrying about collisions and leave it to those that have a greater understanding of how the system works.

The idea that security rests of an unlikely event is often a hard concept to accept.  This is because outside of cryptography we often (incorrectly) accept highly unlikely events as "impossible".  That sets mentally sets up a false "it should be in impossible to be secure" requirement.  Even in the material world there is no such thing as an impossible event.  You could right now stand up and walk right through the nearest wall on your first attempt due to Quantum tunneling.  The odds are so remote we just say it is impossible, to avoid explaining that while it is possible it is so improbable that it might as well be impossible.  Still for the sake of the argument, Just because it is "possible" to pass through a wall due to quantum tunneling, would you buy a safe to put inside another larger safe just to protect your gold from the possibility that the burglar will get "lucky" and be able to reach through the outer safe wall by quantum tunneling?  Of course not.  Even the idea seems silly but we somehow with math it seems more of a risk because the exact probability can be computed and we can show that collisions are possible with smaller numbers.

To get technical, even a collision isn't even sufficient to steal coins.  A collision involves any two random values from the set of possible values.  For Bitcoin, the overwhelming majority of the keyspace will never be used, so even in the (so unlikely as to be considered impossible) event that there is a collision, it is most likely to involve a pair of keys that have never been nor ever will be funded.  For your coins to be compromised would require a preimage attack which is even less likely.  Unless the divisibility is increased there can never be more than 2.1 quadrillion funded addresses (21M * 1E8).  2.1 quadrillion funded addresses gives the highest probability but it also means the smallest payoff, as under that scenario all addresses would contain only a single satoshi.

None of this is Bitcoin specific.  You could in theory bang on your keyboard and by random chance produce a private key which corresponds to the public key in use right now for google's SSL cert.  You could also arm and launch a nuclear warhead, or spoof a bank atm's authentication by the same near but not zero probability.   If you say "impossible" I have learned you get thirty responses saying it can be done so the word is "infeasible".  It is infeasible to brute force a random key using classical computing which has 128 bit security/strength.

[jonald_fyookball]

A hash collision is much more likely to happen than a monkey randomly typing the complete
text of Hamlet on a typewriter on the first try, which is a probability of 1 to 3.4 × 10^183,946 against.

http://en.wikipedia.org/wiki/Infinite_monkey_theorem

[Peter R]

Is there anything that is actually impossible (P=0)?

If you don't count abstract math and logic (e.g., 1+1 != 2) then I think everything is possible.  Physics would say that moving through time in a way that violates causality is impossible, but I think you could argue that that breaks abstract logic at the same time so it doesn't count.  Some physicists would say that it is impossible to get from Point A to Point B faster than the speed of light, but even this is debatable with convincing evidence of quantum non-locality.  

I think it would make sense for anything to be possible because I think it makes sense that the universe itself is universal (i.e., Turing complete).

[jonald_fyookball]

yep, everything is possible (unless its impossible). lol.

[cp1]

Is there anything that is actually impossible (P=0)?

If you don't count abstract math and logic (e.g., 1+1 != 2) then I think everything is possible.  Physics would say that moving through time in a way that violates causality is impossible, but I think you could argue that that breaks abstract logic at the same time so it doesn't count.  Some physicists would say that it is impossible to get from Point A to Point B faster than the speed of light, but even this is debatable with convincing evidence of quantum non-locality.  

I think it would make sense for anything to be possible because I think it makes sense that the universe itself is universal (i.e., Turing complete).

It's impossible to violate the laws of thermodynamics.

[Peter R]

Is there anything that is actually impossible (P=0)?

If you don't count abstract math and logic (e.g., 1+1 != 2) then I think everything is possible.  Physics would say that moving through time in a way that violates causality is impossible, but I think you could argue that that breaks abstract logic at the same time so it doesn't count.  Some physicists would say that it is impossible to get from Point A to Point B faster than the speed of light, but even this is debatable with convincing evidence of quantum non-locality.  

I think it would make sense for anything to be possible because I think it makes sense that the universe itself is universal (i.e., Turing complete).

It's impossible to violate the laws of thermodynamics.

It is definitely possible for events in nature to violate the the 2nd law of thermodynamics.  In fact, it's not even a law, it's just a bold statement about probability.  The vast majority of physicists would agree.  

The idea that entropy never decreases is just another way of saying that things that are infeasible don't actually happen.  If you video record someone playing pool and breaking the racked balls with the cue ball, and then if you play the video backwards and apply Newton's laws to each collision, you'll see that the physics was valid both moving forward in time and moving backwards in time.  The backwards event never happens (all the balls converging to a perfect triangle), however, because it is is statistically extremely unlikely.  

Everything that can happen moving forward in time can happen in reverse too (uncracking an egg for instance), but it never does because the probability of all the atoms moving in exactly the right way is like 10^-892709498239489023849028309482904820384920.

[DeathAndTaxes]

It's impossible to violate the laws of thermodynamics.

Unless the "law" is incorrect and our understanding of the universe is incomplete.   At one time we believed it was impossible to sail around the world because it was flat.

[jonald_fyookball]

What's interesting about the infinite monkey theorum is the "almost surely" probability.

Given infinite time, a monkey will almost surely type out hamlet, but
there is no absolute guarantee of it ever happening.

Same thing with cracking an egg in reverse.

However the small the chances of it happening, it is almost surely
going to happen with enough eons of time, but there's nothing
compelling it to necessarily do so.

These concepts can become a brain-twister.

[cp1]

As long as the total entropy of the universe doesn't decrease, an egg can re-assemble itself all it wants and the 2nd law won't be violated.

[Peter R]

As long as the total entropy of the universe doesn't decrease, an egg can re-assemble itself all it wants and the 2nd law won't be violated.

Right, so the probability of the egg-uncracking event is non-zero.  So what is an event that you could describe and that we can imagine playing out in physical reality but that has identically zero probability of occurring?  

The answer can't something like "the sum of the force acting on a particle doesn't equal it's mass times acceleration" because all the laws of physics are abstract models that describes nature--they aren't nature itself.  Newton's second law is always true for the same reason that 1+1 = 2 is always true.  

[jonald_fyookball]

As long as the total entropy of the universe doesn't decrease, an egg can re-assemble itself all it wants and the 2nd law won't be violated.

Right, so the probability of the egg-uncracking event is non-zero.  So what is an event that you could describe and that we can imagine playing out in physical reality but that has identically zero probability of occurring?  

Perhaps time travel.

[cp1]

Me living to be one billion years old?

[jonald_fyookball]

Me living to be one billion years old?

No, I think my answer is more what Peter is looking for.

You could theoretically live to be a billion years old because
some cell generation technology (biological immortality)
could be invented without contradicting
the laws of physics and perhaps you won't have
any fatal accidents in the next billion years.  

However unlikely this may be, it
doesn't fit Peter's request of

actually impossible (P=0)?

But, we can imagine time travel, yet it may be
actually impossible outside of our imagination.

[Peter R]

Me living to be one billion years old?

No, I think my answer is more what Peter is looking for.

You could theoretically live to be a billion years old because
some cell generation technology (biological immortality)
could be invented without contradicting
the laws of physics and perhaps you won't have
any fatal accidents in the next billion years.  

However unlikely this may be, it
doesn't fit Peter's request of

actually impossible (P=0)?

But, we can imagine time travel, yet it may be
actually impossible outside of our imagination.

I think time travel is probably the best answer, but I still don't think it works.  The reason I don't think it works is because we can only imagine time travel if we abandon logic (we abandon causality, or sequence).  So I think my argument holds: If you don't count abstract math and logic (e.g., 1+1 != 2) then I think any event has non-zero probability.  

Will everything that has non-zero probability eventually happen?  I think it depends on how many bits of resolution time has.  We know time exists on scales as large as the age of the universe (~14 billion years = 4.4 x 10¹⁷ s) to as small as the the Planck time (5.4 × 10⁻⁴⁴ s).  So we know time has at least log₂(4.4 x 10¹⁷ / 5.4 × 10⁻⁴⁴) = 202 bits of resolution (less than a bitcoin private key).  For a monkey to type out Hamlet at P = 10^-183,946 means we need at least log₂(10^183,946) = 611000 bits.  Which means that for this to actuallly happen, we need to be enormously closer to the beginning of time than we are to the end.  I'm not sure that's reasonable.  


So time has perhaps 202 bits.  We can do the same calculation for space:

   log₂(radius_of_universe / Planck_length) = log₂(5.7x10^25 m / 1.6x10^-35 m) = 204 bits

Since we have 3 spatial dimensions, I think it would be reasonable to say that the universe has at least 202 + 3 x 204 ~= 800 bits of resolution.  

Therefore, I think any event that has a probability significantly less than 2^-800 = 10^-240 is most certainly impossible.  

In other words, even if every particle in the universe was a monkey and ever increment of time was a keyboard press, those monkeys never type out Hamlet!

[sgk]

Hi there. First post/topic.

I'm about to put coins away in cold storage on a long term, to be forgotten about, basis and have some newbie questions:

1. I understand I can use the bitaddress.org HTML document, copied on a clean USB stick to a live USB version of Linux (Tails) which has never been connected to the web to generate a public address and private key. How do I know that the pair that's generated is unique and hasn't already been generated? What are the mathematical odds of someone coincidentally having the same private key?

2. Is there a "scene" for people using powerful computing technology (high-end GPU's etc.) to generate and test thousands of private keys in the hope that they'll stumble upon some coins?

In short, am I OK to store a couple of coins in a paper document and forget about them for a year or two?

Thanks muchly. I find this site very interesting, even though some of the more mathematical explanations can go over my head.

These are the mathematical odds:
https://bitcointalk.org/index.php?topic=587371.msg6434251#msg6434251

[jonald_fyookball]

Since we have 3 spatial dimensions, I think it would be reasonable to say that the universe has 202 + 3 x 204 ~= 800 bits of resolution.  

Therefore, I think any event that has a probability significantly less than 2^-800 = 10^-240 is most certainly impossible.  
 

i think the universe (or multiverse) has to be infinite in space and time.

[Peter R]

Since we have 3 spatial dimensions, I think it would be reasonable to say that the universe has 202 + 3 x 204 ~= 800 bits of resolution.  

Therefore, I think any event that has a probability significantly less than 2^-800 = 10^-240 is most certainly impossible.  

i think the universe (or multiverse) has to be infinite in space and time.

It is an open question in physics so either opinion is valid; perhaps one day we will know.  All we know now is that the concept of time makes sense from a scale as small as the Planck time to a scale as large as the estimated age of the universe (~200 bits of resolution). 

Personally, I think "infinity" is an abstraction and cannot exist in physical reality.  I think this would also mean that all the physical constants are actually rational numbers.

[jonald_fyookball]

Since we have 3 spatial dimensions, I think it would be reasonable to say that the universe has 202 + 3 x 204 ~= 800 bits of resolution.  

Therefore, I think any event that has a probability significantly less than 2^-800 = 10^-240 is most certainly impossible.  

i think the universe (or multiverse) has to be infinite in space and time.

It is an open question in physics so either opinion is valid; perhaps one day we will know.  All we know now is that the concept of time makes sense from a scale as small as the Planck time to a scale as large as the estimated age of the universe (~200 bits of resolution). 

Personally, I think "infinity" is an abstraction and cannot exist in physical reality.  I think this would also mean that all the physical constants are actually rational numbers.

Agree that either opinion is valid. 

For me, I just cannot imagine some arbitrary border of which there is nothing beyond, nor can I imagine time can "stop" one day, or that there was a starting point where nothing existed before and suddenly existence was born one day. 

[Peter R]

Since we have 3 spatial dimensions, I think it would be reasonable to say that the universe has 202 + 3 x 204 ~= 800 bits of resolution.  

Therefore, I think any event that has a probability significantly less than 2^-800 = 10^-240 is most certainly impossible.  

i think the universe (or multiverse) has to be infinite in space and time.

It is an open question in physics so either opinion is valid; perhaps one day we will know.  All we know now is that the concept of time makes sense from a scale as small as the Planck time to a scale as large as the estimated age of the universe (~200 bits of resolution). 

Personally, I think "infinity" is an abstraction and cannot exist in physical reality.  I think this would also mean that all the physical constants are actually rational numbers.

Agree that either opinion is valid. 

For me, I just cannot imagine some arbitrary border of which there is nothing beyond, nor can I imagine time can "stop" one day, or that there was a starting point where nothing existed before and suddenly existence was born one day. 

Neither can I.  I don't think it is possible from inside the system where our rules of logic apply (1+1=2, causality, sequence).  But if you truly have nothing then perhaps you don't have logic either.  And if you don't have logic then nothing can be something….and then my brain starts to hurt...


Anyways, this thread has diverged far away from its original scope!  I think we've confirmed once again that bitcoin addresses are definitely safe against brute force attacks LOL.