Bitcoin address - are there enough for us all?

[HEWRA]

there is no problem with bitcoin addresses, the number is big enough for all of us. There is almost no chance to see the same address generated.

[cryp24x]

there is no problem with bitcoin addresses, the number is big enough for all of us. There is almost no chance to see the same address generated.

I agree, if ever the saturation level of bitcoin address is about to be met, developers will always find another way to add more to the Bitcoin address, adding an extra number or reducing it by a number would greatly increase BTC address capability.  So definitely it is not a problem at all.

[angaper]

there is no problem with bitcoin addresses, the number is big enough for all of us. There is almost no chance to see the same address generated.

I agree, if ever the saturation level of bitcoin address is about to be met, developers will always find another way to add more to the Bitcoin address, adding an extra number or reducing it by a number would greatly increase BTC address capability.  So definitely it is not a problem at all.

Undoubtedly. There are many other crucial problems to be solved in the bitcoin ecosystem, but this one does not seem so urgent, at least for the next ten years.

[BurtW]

So I'm curious, what is the definition of the birthday problem effect in this context? I assume that's the sort of weird mathematical issue where a room of 23 people has something close to a 50% chance of having two people who have the same birthday, so how does it have an impact on the amount of addresses that can be used before there is some kind of overlap? Is it the same thing where approximately only 1 in every 16 usable addresses are actually "useful" since you approach (and pass) a 50% chance of there being a copy of a public key somewhere?
I'm looking at the wikipedia page and the math they use, so is the equation for the pub addresses the same calculation, just modified to p(n)=1*(1-(n-1/2¹⁶⁰))?
I rarely do this kind of math so I'm curious. I wish I got to learn more about it but I only ever do very supplementary math or just read/watch stuff online. Either way it still surprises me that the probability curve moves in the way it does.
I apologize if this is something that I should be going and learning somewhere else.

Please see my related thread here:  https://bitcointalk.org/index.php?topic=1895455.0

(no asshole signature spammers in my thread!)

[Amph]

there is no problem with bitcoin addresses, the number is big enough for all of us. There is almost no chance to see the same address generated.

not sure, a quantum computer with the Grover’s algorithm have better possibility to resolve a collision than normal computer wer have today, they might pose a threat, and they are not so far away in the future like many think

[dinofelis]

There are approximately 2²⁵⁶ public private key pairs.

There are approximately 2¹⁶⁰ Bitcoin addresses.

Due to the birthday problem effect we can only use 2⁸⁰ Bitcoin addresses.

To be safe this should be reduced to at least 2⁷⁰ addresses.

Well, I put the safety much more severe at 2^50 or 2^60, because at 2^70, there's still a chance in a million that a collision will occur.

https://bitcointalk.org/index.php?topic=1891830.msg18795938#msg18795938

That said, the conclusion is that for the moment, there's nothing to worry about, and by the time it becomes a problem, one could always increment it.

BTW, by the time it becomes worrisome, the cryptographic security of the thing becomes problematic too, because if there are 2^70 transactions on the chain (otherwise, 2^70 addresses cannot exist), and a normal spending needs nodes to look quickly through 2^70 transactions, it means that processing power is going to reduce the safety margin of a lot of things.

Most probably, bitcoin will have shut down before reaching that level.  Maybe humanity will have shut down too by then. 

[deisik]

BTW, by the time it becomes worrisome, the cryptographic security of the thing becomes problematic too, because if there are 2^70 transactions on the chain (otherwise, 2^70 addresses cannot exist), and a normal spending needs nodes to look quickly through 2^70 transactions, it means that processing power is going to reduce the safety margin of a lot of things

I wonder what size the blockchain would be then

Apart from that, quickly looking up a transaction should not be an issue even with so many transactions provided the data is organized in a proper way and you don't have substantial delays with accessing this data. As I see it, the main headache would be adding new transactions to a search tree if you want to provide quick lookups. So to find a single transaction in a tree with 2⁷⁰ nodes would require you only around 35 iterations on average, while adding a new transaction to such a tree should get pretty expensive in terms of number of iterations

[eXpl0sive]

https://bitcointalk.org/index.php?topic=24268.msg304195#msg304195

There are exactly 1461501637330902918203684832716283019655932542976 addresses possible. We only have 7 billion people on earth, so I wouldn't call it a problem situation.

On another note you shouldn't worry about the brute-force attacks on private keys either:

[Ayers]

Maybe in 100 years after we are long gone this could become an issue. For now there are plenty of addresses to go around.

Ha... this is not a problem for even another 1000 year... the number is so so so huge...

That claim has been refuted many times

And exactly according to the laws of physics (or of this Universe if you want me to put it this way). In short, the lowest theoretically possible amount of energy equals the energy of a single photon whose wavelength is approximately the size of the observable universe. You see that would be small enough to theoretically build a device that would count to 2^256 in less than half a jiffy, so "nothing more efficient possible" is a false assumption. And that has nothing to do with thermodynamics as such (as this picture suggests)

What the heck are you babbling about?

Laundauer's limit defines the amount of energy needed here.  
https://en.wikipedia.org/wiki/Landauer%27s_principle

Did you read my posts above and before?

I think you may really want to read them again to understand that you have chosen the wrong person to jump at. If you still fail to understand what my "babbling" is about (which I'm not surprised, anyway), I can tell you that the question is certainly not about building a real computer (as the legend makes it unambiguously clear). Nevertheless, I can point you to the relevant part which you seem to have missed entirely:

Since the text in the picture above talks about the lowest possible energy for storing a single bit (it is not my idea after all, so ask the dude who drew that image), a photon with a wavelength equal to the size of the Universe will have such energy

So wtf are you attacking me here? And what exactly do you disagree with?

but what you refer is another thing in that image they are talking about brute forcing, not the lowest possible energy, and brute forcing isn't possible no matter how much energy you get, this was the point of that image, nitpicking and playing with semantic just to say that something is wrong is stupid

How is it stupid to say and prove that something is wrong?

Are you serious or what? The creator of that image bases his point on the premise that it is not even hypothetically possible to count to 2²⁵⁶ given the resources available in the Universe. So, according to you, proving that this premise as absolutely wrong is nitpicking and playing with semantics? May I ask you what semantics do you refer to here? Maybe, it is in fact you who is "playing with semantics" in this case?

but it's not wrong, the statement say that you can't bruteforce a private key of 256 bit which is true, what is wrong about this exactly? you are nitpicking a portion of the phrase and take it out of whole context just to prove something else that has nothing to do with the final principe on which that image is based

[deisik]

How is it stupid to say and prove that something is wrong?

Are you serious or what? The creator of that image bases his point on the premise that it is not even hypothetically possible to count to 2²⁵⁶ given the resources available in the Universe. So, according to you, proving that this premise as absolutely wrong is nitpicking and playing with semantics? May I ask you what semantics do you refer to here? Maybe, it is in fact you who is "playing with semantics" in this case?

but it's not wrong, the statement say that you can't bruteforce a private key of 256 bit which is true, what is wrong about this exactly? you are nitpicking a portion of the phrase and take it out of whole context just to prove something else that has nothing to do with the final principe on which that image is based

You seem to have apparent issues with logic and reasoning

If we follow the assumptions in that "cute image", it will be a wrong statement flat-out. The point of this image is that with all resources existing in the Universe (well, in the Solar system), it won't be possible to even hypothetically find all the keys. If you didn't notice, cracking all the keys is considered equal to counting to 2²⁵⁶. If you disagree with that, don't "bruteforce" me since it is not my assumption, after all. I didn't think up anything myself, I just followed the assumptions taken by the author of that image which as he thinks prove his point. In fact, you don't even need the whole Solar system to do that or energy as such

[BurtW]

This thread has been totally trashed by signature spammers.

I have started a thread for serious discussion about the application of the birthday problem to the 160 bit hash space of Bitcoin.

Please join the signature spam free discussion here:  https://bitcointalk.org/index.php?topic=1895455.0

I may copy a few of the interesting posts from this thread over there.

[stomachgrowls]

Considering that bitcoin addresses get wasted and discarded like plastic bottles of water, is there ever a risk that we'd use up all the bitcoin addresses?

I realize the possible combinations is 36 to the power of 32, but I don't have a way to make sense of the resulting number. How many address are used in a day? How quickly are we going through these possible combinations?

Even global population wont able to accumulate all bitcoin addresses and i cant think of that we would ran out of possible combinations considering there are long combinations even having a capitalization of a certain letter would already give the difference which theres no sense to be worried about even all people would really use bitcoin and having their own wallet addresses, Dont make to stress into yourself.

[jonald_fyookball]

How is it stupid to say and prove that something is wrong?

Are you serious or what? The creator of that image bases his point on the premise that it is not even hypothetically possible to count to 2²⁵⁶ given the resources available in the Universe. So, according to you, proving that this premise as absolutely wrong is nitpicking and playing with semantics? May I ask you what semantics do you refer to here? Maybe, it is in fact you who is "playing with semantics" in this case?

but it's not wrong, the statement say that you can't bruteforce a private key of 256 bit which is true, what is wrong about this exactly? you are nitpicking a portion of the phrase and take it out of whole context just to prove something else that has nothing to do with the final principe on which that image is based

You seem to have apparent issues with logic and reasoning

If we follow the assumptions in that "cute image", it will be a wrong statement flat-out. The point of this image is that with all resources existing in the Universe (well, in the Solar system), it won't be possible to even hypothetically find all the keys. If you didn't notice, cracking all the keys is considered equal to counting to 2²⁵⁶. If you disagree with that, don't "bruteforce" me since it is not my assumption, after all. I didn't think up anything myself, I just followed the assumptions taken by the author of that image which as he thinks prove his point. In fact, you don't even need the whole Solar system to do that or energy as such

Maybe you can re-summarize your point in a sentence...it seems to have gotten lost.

[deisik]

How is it stupid to say and prove that something is wrong?

Are you serious or what? The creator of that image bases his point on the premise that it is not even hypothetically possible to count to 2²⁵⁶ given the resources available in the Universe. So, according to you, proving that this premise as absolutely wrong is nitpicking and playing with semantics? May I ask you what semantics do you refer to here? Maybe, it is in fact you who is "playing with semantics" in this case?

but it's not wrong, the statement say that you can't bruteforce a private key of 256 bit which is true, what is wrong about this exactly? you are nitpicking a portion of the phrase and take it out of whole context just to prove something else that has nothing to do with the final principe on which that image is based

You seem to have apparent issues with logic and reasoning

If we follow the assumptions in that "cute image", it will be a wrong statement flat-out. The point of this image is that with all resources existing in the Universe (well, in the Solar system), it won't be possible to even hypothetically find all the keys. If you didn't notice, cracking all the keys is considered equal to counting to 2²⁵⁶. If you disagree with that, don't "bruteforce" me since it is not my assumption, after all. I didn't think up anything myself, I just followed the assumptions taken by the author of that image which as he thinks prove his point. In fact, you don't even need the whole Solar system to do that or energy as such

Maybe you can re-summarize your point in a sentence...it seems to have gotten lost

I don't have issues with summarizing

Here's just one sentence. Computing is an illusion. If you want a more detailed answer I can explain it to you in a greater detail (no problem with that either). What we think as computing (in practice) are no more than some physical processes going on at the lower level. It is the way we interpret them that turn them into "computing". Thereby, any claims that something cannot be "computed" with reference to some physical parameters, constants or qualities (e.g. lowest possible energy) are conceptually false, since at the lowest, physical level "computing" as such doesn't even exist. These claims are just meaningless

[dinofelis]

Thereby, any claims that something cannot be "computed" with reference to some physical parameters, constants or qualities (e.g. lowest possible energy) are conceptually false, since at the lowest, physical level "computing" as such doesn't even exist

That is true.  However, one may very well define mathematical problems of which the computation cannot be performed in the observable universe, at least, with a given algorithm.

I would think that we start to reach some reasonable upper limit of "number of steps in a computation that the observable universe can perform" if we consider the number of Planck "volumes" in the estimated state space of the observable universe.

[jonald_fyookball]

  These claims are just meaningless

But they take time and energy.

[deisik]

Thereby, any claims that something cannot be "computed" with reference to some physical parameters, constants or qualities (e.g. lowest possible energy) are conceptually false, since at the lowest, physical level "computing" as such doesn't even exist

That is true.  However, one may very well define mathematical problems of which the computation cannot be performed in the observable universe, at least, with a given algorithm.

I would think that we start to reach some reasonable upper limit of "number of steps in a computation that the observable universe can perform" if we consider the number of Planck "volumes" in the estimated state space of the observable universe

I think this is not so

I see where you are getting at but I still think this is not the real limit. You basically make the same mistake as the ones who are trying to challenge my point, though at another, higher level (if that comforts you somehow). Now see how I can explain that in just one sentence again (you know why I say that). In short, in real world you may not need to take or make all the steps which your algo requires to get the result of your computation. As I understand it, this is what quantum computing is essentially about. You don't need huge amount of time, energy and effort if you can just obtain the result directly without actually having to "compute" anything (computing as a sequence of steps leading to a certain result according to the rules of some algo)

  These claims are just meaningless

But they take time and energy.

Claims require time and energy? Meaningless claims certainly do, that's why disproving meaningless claims is as meaningless. If someone starts claiming that Earth is flat and Elvis Presley still alive, are you going to prove him wrong?

[jonald_fyookball]

computations take time and energy

[BurtW]

But they take time and energy.

Claims require time and energy?

Yes, your meaningless claim took time and energy.

Counting also takes time and energy.

Prove me wrong.

Proving me wrong will also take time and energy.