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Author Topic: How many possibly bitcoin addresses are there exactly? And how long does it...  (Read 29123 times)
gigabytecoin
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June 29, 2011, 10:00:18 AM
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How many possibly bitcoin addresses are there exactly?

How long does it take to generate one?
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June 29, 2011, 10:05:03 AM
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I heard 2^160.

A fast setup could do thousands each second.

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June 29, 2011, 03:21:07 PM
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And if you're thinking what I think you're thinking, remember that you don't actually have to find their private key to claim someone else's bitcoins. All you have to do is find any one of the roughly 2^96 private keys whose corresponding public key hashes to that address.

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June 29, 2011, 11:06:30 PM
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There are exactly 2^160 possible addresses as long as we keep using RIPE-MD160.

2^160 is 1,461,501,637,330,902,918,203,684,832,716,283,019,655,932,542,976.

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June 29, 2011, 11:12:01 PM
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The total address space is 2^160

To put that in perspective, there are only 2^63 grains of sand on all of the beaches of the Earth (http://www.hawaii.edu/suremath/jsand.html)

Before you run out and build an RPC program to generate addresses, do some math first.

Or read this:  http://forum.bitcoin.org/index.php?topic=1387.0

The total pool of Bitcoin addresses in use is so minuscule compared to the total population of addresses you *could* create, that the odds of you creating a private key for an address that is already in use is so small (near zero), that you'd be better off just writing malware to infect computers and just steal them.

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June 30, 2011, 05:48:01 AM
 #6

A more profitable way to make money from generating random numbers would be the state lottery.

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June 30, 2011, 08:53:43 PM
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And if you're thinking what I think you're thinking, remember that you don't actually have to find their private key to claim someone else's bitcoins. All you have to do is find any one of the roughly 2^96 private keys whose corresponding public key hashes to that address.

Ok so for somebody to be lucky enough to steal the bitcoins out of my main backup address...

They first need to generate my address which could be any one of 2^160 possibilities. And then they must generate the corresponding public key that gives them access to the bitcoins in my address? Of where there at 2^96 possibilities?

Or must they simple generate 2^96 bitcoin keys... at which point they would control every single bitcoin address in the world?
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July 01, 2011, 12:35:02 AM
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And if you're thinking what I think you're thinking, remember that you don't actually have to find their private key to claim someone else's bitcoins. All you have to do is find any one of the roughly 2^96 private keys whose corresponding public key hashes to that address.

Ok so for somebody to be lucky enough to steal the bitcoins out of my main backup address...

They first need to generate my address which could be any one of 2^160 possibilities. And then they must generate the corresponding public key that gives them access to the bitcoins in my address? Of where there at 2^96 possibilities?
Generating the public key is trivial.

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Or must they simple generate 2^96 bitcoin keys... at which point they would control every single bitcoin address in the world?
The most sensible way to attempt the attack (which is still insane) is to generate random private keys, calculate the corresponding addresses, and then see if that address has a non-zero balance. I believe there are 2^160 possible addresses. So even if there are 1,000,000,000 addresses with non-zero balances, your odds of getting a non-zero balance on a single key are 1 in 2^128.

So brute-forcing a single bitcoin address with a non-zero balance (assuming there are a billion of them, which is generous), is as hard as, say, brute-forcing a given 128-bit AES key.

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July 01, 2011, 01:27:31 AM
 #9

Bitcoin already supports OP_HASH256 in script, so it would be trivial to increase the number of addresses if it ever became a problem.

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December 21, 2013, 11:13:14 PM
 #10

So there are 2^160 public keys but only 2^96 private keys? Ho does that add up?
Are there private keys than unlock more than one public key?
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December 22, 2013, 01:11:42 AM
 #11

So there are 2^160 public keys but only 2^96 private keys? Ho does that add up?
Are there private keys than unlock more than one public key?

This discussion might help:   :-)

https://bitcointalk.org/index.php?topic=199212.0
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December 22, 2013, 07:50:30 AM
 #12

So there are 2^160 public keys but only 2^96 private keys? Ho does that add up?
Are there private keys than unlock more than one public key?
There are just under 2^256 private keys, just under 2^256 public keys, and 2^160 addresses. There are some addresses that have more than one corresponding public key and thus more than one corresponding private key.

I am an employee of Ripple.
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December 22, 2013, 04:36:31 PM
 #13

Ok so the quote that there are 2^96 private keys is wrong then
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December 22, 2013, 09:29:46 PM
 #14

More than atoms in the universe

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May 07, 2014, 08:48:45 AM
 #15

More than atoms in the universe
That is not correct, not even close.
The estimated number of atoms in the observable universe (10^80) is 71 million trillion trillion times greater than 2^160.
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