bitcoin addresses question

[albert11]

- more an more users
- more and more services that generate a new address for every transaction ( localbitcoins for instance) for more privacy


I know there is a huge amount of different key pair but as time goes by this amount will decrease which means people might generate a key pair that belongs or has been used by someone else? wouldn't this be problematic in the future? anyone heard of someone having generated a key pair that was used already? maybe i'm missing something...

[numanoid]

- more an more users
- more and more services that generate a new address for every transaction ( localbitcoins for instance) for more privacy


I know there is a huge amount of different key pair but as time goes by this amount will decrease which means people might generate a key pair that belongs or has been used by someone else? wouldn't this be problematic in the future? anyone heard of someone having generated a key pair that was used already? maybe i'm missing something...

No! I do understand that amount will increase , but seeing the length of the key , it has trillions of probabilities and it will never produce same key or address twice

[tonygal]

Although it is not exactly aimed at this question, I still think that the following image is
helpful in order to grasp the numbers involved:

[albert11]

- more an more users
- more and more services that generate a new address for every transaction ( localbitcoins for instance) for more privacy


I know there is a huge amount of different key pair but as time goes by this amount will decrease which means people might generate a key pair that belongs or has been used by someone else? wouldn't this be problematic in the future? anyone heard of someone having generated a key pair that was used already? maybe i'm missing something...

No! I do understand that amount will increase , but seeing the length of the key , it has trillions of probabilities and it will never produce same key or address twice

do you know the exact number of possibilities?

Imagine if half the population uses bitcoin, that's 3.5 billion.

Say each person generate 1 new key pair per day on average, that's 365 new key pair multiply that by 3.5 billions  that's more than 1 trillion per year.

Now considering the average is likely more than 1 new key pair/day since many people uses a different address for every transaction so that would tens of trillions per year multiply that by 100 years and thats thousands of trillions so surely some people will use a key that has been used already wouldn't they?

[RodeoX]

Your right that it is a finite number. But there are just under 2^256 public keys, and that is a huge number. A trillion is nothing.

[albert11]

Your right that it is a finite number. But there are just under 2^256 public keys, and that is a huge number. A trillion is nothing.

how many is 2^256?  how many zeros is that?

[DeathAndTaxes]

2^256 is roughly 1 followed by 77 zeroes.   

[RodeoX]

Your right that it is a finite number. But there are just under 2^256 public keys, and that is a huge number. A trillion is nothing.

how many is 2^256?  how many zeros is that?

2^256 is roughly 1 followed by 77 zeroes.   

So like this: 100,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000

For comparison here is a measly trillion: 1,000,000,000,000
And remember that every additional zero makes the number 10 times larger. It's a staggering number really.

[tonygal]

It should be easy to determine the probability that in 100 years of this
trillion-assumption there occurs a clash (along the lines of
http://en.wikipedia.org/wiki/Birthday_problem), and I guess
it will look like 0.0000....1 %

[albert11]

omg that's a lot of possibilities indeed, no need to worry then!


we could do a lottery actually, the first person who generate an already used key pair wins all of N.satoshi's bitcoin

[Mikestang]

Here are a couple graphics that help drive home the number of potential btc addresses.

[albert11]

nice graph,

[odolvlobo]

Your right that it is a finite number. But there are just under 2^256 public keys, and that is a huge number. A trillion is nothing.

how many is 2^256?  how many zeros is that?

2²⁵⁶ is not the right number because every bitcoin address has 2⁹⁶ private/public keys on average.

There are 2¹⁶⁰ bitcoin addresses. 2¹⁶⁰ = 1,461,501,637,330,902,918,203,684,832,716,283,019,655,932,542,976 or about 1.46x10⁴⁸. 2¹⁶⁰ is a much much much smaller number than 2²⁵⁶, but it is still an incredibly huge number.

For perspective, 2¹⁶⁰ is approximately 3 times the number of water molecules on the earth. You are three times more likely to pick a specific molecule of water somewhere on the earth than you are to duplicate a specific bitcoin address (assuming that bitcoin address generation is completely random).