Bitcoin address - are there enough for us all?

[jonald_fyookball]

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?

Because there's no observable thing.  I believe such wavelengths are always microscopic, let alone "the size of the universe".   And even if there was, that wouldn't refute anything in that image.

[BurtW]

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.

There are on the order of 2³³ people on the planet.

This means each person on the planet gets 2^{70 - 33} = 2³⁷ addresses.

Put another way, the large bitcoin collider system here

https://lbc.cryptoguru.org

is capable of generating over 2⁵⁵ keys per year so they will generate 2⁷⁰ Bitcoin addresses in about

2^{70 - 55} = 2¹⁵ = 33 thousand years

Now you do not need to guess at the number just to post your fucking paid signature.

[deisik]

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?

Because there's no observable thing.  I believe such wavelengths are always microscopic, let alone "the size of the universe".   And even if there was, that wouldn't refute anything in that image

I'm not quite sure what you mean by "observable thing" (or the lack thereof)

If you mean the observable Universe (which is what I myself mean by the size of the Universe), this seems to be a pretty well established concept or notion. Regarding wavelengths, more specifically, you may want to read more about electromagnetic spectrum. Radiowaves (which are the same photons, if you didn't know) have lengths starting from meters and all up to hundreds and thousands of kilometers. That's basically why they can circle around the world. These waves can penetrate seawater as well, which is why they are used for communication with submarines

[Obito]

Yes I think there are enough for us all because we can make accounts using bitcoin. And all are free and is accepted in this program as long as you have an internet connection in able to register on this program. Bitcoin is really enough for us all and it is really useful to be used.

[jonald_fyookball]

^  lol... sorry Burt.  its gonna just keep happening. 

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?

Because there's no observable thing.  I believe such wavelengths are always microscopic, let alone "the size of the universe".   And even if there was, that wouldn't refute anything in that image

I'm not quite sure what you mean by "observable thing" (or the lack thereof)

If you mean the observable Universe (which is what I myself mean by the size of the Universe), this seems to be a pretty well established concept or notion. Regarding wavelengths, more specifically, you may want to read more about electromagnetic spectrum. Radiowaves (which are the same photons, if you didn't know) have lengths starting from meters and all up to hundreds and thousands of kilometers. That's basically why they can circle around the world. These waves can penetrate seawater as well, which is why they are used for communication with submarines

You are right that the waves can be long.  I didn't know that.

However, according to this, the longer the wavelength, the less energy it has
https://en.wikipedia.org/wiki/Photon_energy

[freebutcaged]

So what happens if I alone could generate 100 million addresses and save them all with private keys if I had a powerful computer?
I want to know the CPU power, required computational power to generate 100 trillion addresses each day?
Nothing like bitcoin collision guys are doing since their job requires more computing power than just simply generating addresses.

@Burt, could you give me an estimation on the CPU power to generate at least %80 of all the possible pairs? for example the current hash power of bitcoin network if were to transform into only key generation how many years would it take to do the %80?

[jonald_fyookball]

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.

There are on the order of 2³³ people on the planet.

This means each person on the planet gets 2^{70 - 33} = 2³⁷ addresses.

Put another way, the large bitcoin collider system here

https://lbc.cryptoguru.org

is capable of generating over 2⁵⁵ keys per year so they will generate 2⁷⁰ Bitcoin addresses in about

2^{70 - 55} = 2¹⁵ = 33 thousand years

Now you do not need to guess at the number just to post your fucking paid signature.

I don't think you described the birthday collision accurately.

There are still 2^160 Bitcoin addresses.  All of them are usable.

The Birthday collision only means that if you keep generating addresses,
you will generate the same address about once every 2^80 times. 

A bitcoin address is basically a RIPEMD-160 hash of the public key.
So, if you generated 2^80 public keys and hashed each one,
you would have about a 50/50 chance that you'd end up with
the same Bitcoin address as the output of two different hashes.

This is why there are 2^256 private keys and only 2^160 addresses.

The important thing is that any given Bitcoin address still has 160 bits of security
since you cannot use the birthday attack to crack a private key.

[deisik]

^  lol... sorry Burt.  its gonna just keep happening. 

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?

Because there's no observable thing.  I believe such wavelengths are always microscopic, let alone "the size of the universe".   And even if there was, that wouldn't refute anything in that image

I'm not quite sure what you mean by "observable thing" (or the lack thereof)

If you mean the observable Universe (which is what I myself mean by the size of the Universe), this seems to be a pretty well established concept or notion. Regarding wavelengths, more specifically, you may want to read more about electromagnetic spectrum. Radiowaves (which are the same photons, if you didn't know) have lengths starting from meters and all up to hundreds and thousands of kilometers. That's basically why they can circle around the world. These waves can penetrate seawater as well, which is why they are used for communication with submarines

You are right that the waves can be long.  I didn't know that.

However, according to this, the longer the wavelength, the less energy it has
https://en.wikipedia.org/wiki/Photon_energy

Oh, now you come to see my point

And after you take a photon with the longest possible wavelength (which would be equal to the diameter of the whole Universe), you will have a particle with the lowest possible energy as the picture above (or before) suggests. So, if you then accept the basic premise of that picture, i.e. the lowest possible energy level corresponding to logical 1 or 0, and look at the estimated total mass-energy of the Universe, you will see that there is nothing extraordinary in just counting 2²⁵⁶ (and that would have nothing to do with Laundauer's limit, just in case). And this is just one approach which disqualifies the "facts" presented in the "cute picture". There are a few others which involve time quantums (i.e. not linked to energy as such)

[jonald_fyookball]

So what happens if I alone could generate 100 million addresses and save them all with private keys if I had a powerful computer?
I want to know the CPU power, required computational power to generate 100 trillion addresses each day?
Nothing like bitcoin collision guys are doing since their job requires more computing power than just simply generating addresses.

@Burt, could you give me an estimation on the CPU power to generate at least %80 of all the possible pairs? for example the current hash power of bitcoin network if were to transform into only key generation how many years would it take to do the %80?

100 trillion is actually a pretty small number.  The new Antminer S9 does 14 TH/s.  That's 14 trillion hashes a second.   You need I think 4 or 5 different hashes to get an address.  
https://en.bitcoin.it/wiki/Technical_background_of_version_1_Bitcoin_addresses

The entire bitcoin network is almost a million times more powerful.  It  generates 4.5 million TH/s,  (so lets just approximate 1 add/key = 4.5 hashes to get a round number) -- that's 10^18 pairs a second.

This is still very small compared to 2^160, which is more than 10^48... So add another 30 zeroes.  

It would take the entire bitcoin network literally more than 50 million trillion millennia to generate all the addresses....and this is assuming no collisions!, which Burt pointed out.
To actually generate all of them, worst case you need to do 2^256 like the cute picture says

[slaman29]

I read about this many times in this forum, and there was a good explanation about the chance for the person to get even the same address as someone else as to happen AFTER the sun has expired. Meaning to say, even if it is possible, our planet would be destroyed first. In which case, it is not a worry:)

[BurtW]

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.

There are on the order of 2³³ people on the planet.

This means each person on the planet gets 2^{70 - 33} = 2³⁷ addresses.

Put another way, the large bitcoin collider system here

https://lbc.cryptoguru.org

is capable of generating over 2⁵⁵ keys per year so they will generate 2⁷⁰ Bitcoin addresses in about

2^{70 - 55} = 2¹⁵ = 33 thousand years

Now you do not need to guess at the number just to post your fucking paid signature.

I don't think you described the birthday collision accurately.

There are still 2^160 Bitcoin addresses.  All of them are usable.

The Birthday collision only means that if you keep generating addresses,
you will generate the same address about once every 2^80 times.  

A bitcoin address is basically a RIPEMD-160 hash of the public key.
So, if you generated 2^80 public keys and hashed each one,
you would have about a 50/50 chance that you'd end up with
the same Bitcoin address as the output of two different hashes.

This is why there are 2^256 private keys and only 2^160 addresses.

The important thing is that any given Bitcoin address still has 160 bits of security
since you cannot use the birthday attack to crack a private key.

I read a lot of this article:

https://en.wikipedia.org/wiki/Birthday_problem

Specifically this statement:

The birthday problem in this more generic sense applies to hash functions: the expected number of N-bit hashes that can be generated before getting a collision is not 2^N, but rather only 2^N/2. This is exploited by birthday attacks on cryptographic hash functions and is the reason why a small number of collisions in a hash table are, for all practical purposes, inevitable.

And the table in the article titled "Probability table" which shows that at 2^N/2 the probability of a collision is about 75%, which is totally unacceptable.  Therefore, I concluded that about 2⁷⁰ addresses is all we should use before we start getting too many collisions.

2⁷⁰ is just an estimate.  If we can agree on what is an acceptable probability of a collision 10^-15? 10^-18? etc. then we could calculate a more exact acceptable number of Bitcoin addresses to be used (before we switch algorithms).

[jonald_fyookball]

And the table in the article titled "Probability table" which shows that at 2^N/2 the probability of a collision is about 75%, which is totally unacceptable.  Therefore, I concluded that about 2⁷⁰ addresses is all we should use before we start getting too many collisions.
 

Right.  If we had 2^80 addresses in use , we would have a good chance to see a single collision.

I just didn't want people to get the wrong idea like you could crack keys by generating 2^80 addresses.

[Meowth05]

So much letter and number in the bitcoin address i guess it almost impossible to hack and with that combination i think that's enough for us but as many bitcoin user's creating wallet even one bitcoin user's almost have a 5-10 wallets.

[BurtW]

So much letter and number in the bitcoin address i guess it almost impossible to hack and with that combination i think that's enough for us but as many bitcoin user's creating wallet even one bitcoin user's almost have a 5-10 wallets.

Go to hell sig spammer.  Reported.

In fact I am going to go back and report every one of you assholes in this thread.  I hope you all get perm bans.

[YuginKadoya]

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?

Considering if all of the people in the world would use bitcoin but in my opinion will not anytime soon, and your need to picture this out there are trillions and trillions of combination that the wallets have been making and it is not consist by only numbers alone but a combination of capital and small letters and numbers that is why there are so many combination a wallet can give to all users I think they can accommodate all users of bitcoin regarding there are many people using a multiple accounts on wallet!

[BurtW]

^^ POS sig spammer reported

[dothebeats]

The amount of bitcoin addresses that can be generated is 2^160, and that, alone is incomprehensible and wouldn't be exhausted for the next 100 (or even a millenia) or so years should a billion of bitcoin users change their addresses 10 times a day. You need not to worry about losing an address, what you need to worry more is the security of your wallet and coins above anything else.

[sikke]

Yes, there is no doubt that we are not going to have any issues with the amount of bitcoin addresses available for particular persons.
There is no problem for every single person on earth to have even 10,000 wallets, there are still so many possibilities that there is enough of combinations to allow 9 billion people to use blockchain network with their own addresses.

Take a look what option do blockchain.info wallet services provides: obviosuly, many other wallet softwares are providing the exactly same thing, but it is just an example.
Every time you want to transfer any bitcoins on your wallet, or give an address to someone to transfer them: the programme changes the address on which you send.

That still does not make any difference, still that is enough of combinations for whole human kind.

[MingLee]

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.

There are on the order of 2³³ people on the planet.

This means each person on the planet gets 2^{70 - 33} = 2³⁷ addresses.

Put another way, the large bitcoin collider system here

https://lbc.cryptoguru.org

is capable of generating over 2⁵⁵ keys per year so they will generate 2⁷⁰ Bitcoin addresses in about

2^{70 - 55} = 2¹⁵ = 33 thousand years

Now you do not need to guess at the number just to post your fucking paid signature.

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.

[jonald_fyookball]

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.

There are on the order of 2³³ people on the planet.

This means each person on the planet gets 2^{70 - 33} = 2³⁷ addresses.

Put another way, the large bitcoin collider system here

https://lbc.cryptoguru.org

is capable of generating over 2⁵⁵ keys per year so they will generate 2⁷⁰ Bitcoin addresses in about

2^{70 - 55} = 2¹⁵ = 33 thousand years

Now you do not need to guess at the number just to post your fucking paid signature.

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.

Not sure what you are confused about.  The "room of 23 people having 50% chance to have a birthday collision" is the same exact principle, except that instead of 365 days, there's 2^160 bitcoin addresses...and instead of 23 people, its 2^80.

If the total bitcoin addresses in use worldwide reaches 2^80, there's a 50/50 chance you'd see one collision.  2^80 doesn't seem like that much (its about a trillion trillion)...this could be generated in about 2 weeks using the entire bitcoin network.  But we wouldn't grow much beyond that without taking a very large amount of time, so practically speaking, collisions aren't a problem.