Bitcoin Forum

- 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

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:
http://img5.picload.org/image/cwgrdap/btc.jpg

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?

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.

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 (http://en.wikipedia.org/wiki/Birthday_problem)), and I guess
it will look like 0.0000....1 %

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 :)

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

https://i.imgur.com/ag3KQ0L.png

https://dealingwithdisruption.files.wordpress.com/2014/04/addresses.jpg

nice graph,

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).