<p><a href="https://bitcoin.stackexchange.com/q/22/659">Is it possible to brute force bitcoin address creation in order to steal money?</a> is the same question, and has an argument about what "possible" means in which a majority of people seem to think that something can have a greater than zero probability and also be impossible at the same time.  Check it out!</p>

CC BY-SA 3.0
2012-05-15T20:27:28.023Z
I was aware of that question, thanks :) Here I was asking specifically if its profitability could change due to some addresses containing a substantial amount of money.
o0'.
CC BY-SA 3.0
2012-05-15T23:55:02.297Z
Oh, I see.  So are you happy with your answer?  It's "not really, no", because the substantial reward is offset by the much-more-than-substantial difficulty in stealing money the way you describe.
Chris Moore
CC BY-SA 3.0
2012-05-16T06:39:10.253Z
Incidentally, you can also have something with zero probability that is possible. See http://en.wikipedia.org/wiki/Almost_surely.
Meni Rosenfeld
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2012-05-16T07:17:03.350Z
@ChrisMoore yes I'm totally satisfied, in fact I accepted it.
o0'.
CC BY-SA 3.0
2012-05-15T20:25:32.573Z
2012-05-15T20:25:32.573Z
2017-04-13T12:47:33.610Z
Chris Moore
<p>The chance of generating the key of a very rich address is effectively zero. That is, in the entire history of humanity, nobody has come anywhere close to accomplishing such a feat. </p>

<p>Let's consider 1 Bitcoin a score. Since there can never be more than 21 million bitcoins or so, you need to hit on one of at most 21 million accounts. Let's say you could try 2 trillion accounts per second. Your odds of matching an account in a hundred years are approximately one in 11 billion billion.</p>

<p>Good luck.</p>

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2012-05-15T20:30:08.260Z
You're thinking that you need to find the same private key to steal funds, but you don't.  You only need to find a private key that hashes to the same (160 bit) bitcoin address.  So it's 2^(256-160) times easier than you thought, and so your odds are really approximately one in 11 billion billion - a much safer bet!
Chris Moore
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2012-05-15T20:31:09.930Z
To get David's number, "pow(2,256) / (21*pow(10,6) * 2*pow(10,12) * 60 * 60 * 24 * 365.25 * 100 * pow(pow(10,9), 5))".  To get mine: "pow(2,160) / (21*pow(10,6) * 2*pow(10,12) * 60 * 60 * 24 * 365.25 * 100 * pow(pow(10,9), 2))".  Both typed at a Python prompt.
Chris Moore
CC BY-SA 3.0
2012-06-18T03:57:45.803Z
@Chris We can currently have up to 2100 trillion accounts since there's 2100 trillion units. So instead of 1 in 11 billion billion, we now have 1 in 110k.
Pacerier
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2012-06-18T05:09:44.477Z
@Pacerier if you could test all 2100 trillion accounts in the time it took David to test one account (ie. one 2 trillionth of a second) then OK.  If your computer gets 2100 trillion times faster, your odds get about 2100 trillion times better.
Chris Moore
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2012-06-18T05:12:39.303Z
@Chris Right, I'm just pointing out the cap of 21 million accounts is wrong.
Pacerier
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2012-06-18T07:51:10.890Z
@Pacerier Fair enough, but I think the original point was that it's not worth spending so many billions of years if you're not going to be able to steal at least one bitcoin.
Chris Moore
CC BY-SA 3.0
2012-05-15T09:56:54.660Z
2017-10-01T15:12:16.877Z
2017-10-01T15:12:16.877Z
David Schwartz
<p>It is known that the type of computing power required for mining is the same used to generate addresses, and it is known that "in general" it is much more profitable to simply mine, rather than try to generate addresses hoping to stole their content.</p>

<p>But AFAIK there are some addresses out there which contain a huge amount of bitcoins: successfully generating their private key would award you <em>a lot</em> more bitcoins than those you would get generating a new block.</p>

<p>Has someone actually made some figures comparing the average revenue of mining vs. the chance of generating the key of a very rich address?</p>

CC BY-SA 3.0
2012-05-15T20:24:02.497Z
possible duplicate of [Is it possible to brute force bitcoin address creation in order to steal money?](http://bitcoin.stackexchange.com/questions/22/is-it-possible-to-brute-force-bitcoin-address-creation-in-order-to-steal-money)
Chris Moore
CC BY-SA 3.0
2012-05-16T07:17:46.030Z
Not a duplicate, as I explained in my comments to @ChrisMoore's answer.
o0'.
<security><mining-profitability>
Has someone compared the cost of mining vs. that of brute-forcing addresses?
o0'.
# Has someone compared the cost of mining vs. that of brute-forcing addresses?

(Asked by: username_0 on 2012-05-15)

It is known that the type of computing power required for mining is the same used to generate addresses, and it is known that "in general" it is much more profitable to simply mine, rather than try to generate addresses hoping to stole their content.

But AFAIK there are some addresses out there which contain a huge amount of bitcoins: successfully generating their private key would award you *a lot* more bitcoins than those you would get generating a new block.

Has someone actually made some figures comparing the average revenue of mining vs. the chance of generating the key of a very rich address?

**Tags:** security, mining-profitability

> **Comments:**
> **username_1**: possible duplicate of [Is it possible to brute force bitcoin address creation in order to steal money?](http://bitcoin.stackexchange.com/questions/22/is-it-possible-to-brute-force-bitcoin-address-creation-in-order-to-steal-money)  
> **username_0**: Not a duplicate, as I explained in my comments to @username_1's answer.  

---

## 2 answers

### Answer by username_3 on 2012-05-15. Score: 12 | Accepted answer

The chance of generating the key of a very rich address is effectively zero. That is, in the entire history of humanity, nobody has come anywhere close to accomplishing such a feat.

Let's consider 1 Bitcoin a score. Since there can never be more than 21 million bitcoins or so, you need to hit on one of at most 21 million accounts. Let's say you could try 2 trillion accounts per second. Your odds of matching an account in a hundred years are approximately one in 11 billion billion.

Good luck.

> **Comments:**
> **username_1**: You're thinking that you need to find the same private key to steal funds, but you don't.  You only need to find a private key that hashes to the same (160 bit) bitcoin address.  So it's 2^(256-160) times easier than you thought, and so your odds are really approximately one in 11 billion billion - a much safer bet!  
> **username_1**: To get username_3's number, "pow(2,256) / (21*pow(10,6) * 2*pow(10,12) * 60 * 60 * 24 * 365.25 * 100 * pow(pow(10,9), 5))".  To get mine: "pow(2,160) / (21*pow(10,6) * 2*pow(10,12) * 60 * 60 * 24 * 365.25 * 100 * pow(pow(10,9), 2))".  Both typed at a Python prompt.  
> **username_4**: @username_1 We can currently have up to 2100 trillion accounts since there's 2100 trillion units. So instead of 1 in 11 billion billion, we now have 1 in 110k.  
> **username_1**: @username_4 if you could test all 2100 trillion accounts in the time it took username_3 to test one account (ie. one 2 trillionth of a second) then OK.  If your computer gets 2100 trillion times faster, your odds get about 2100 trillion times better.  
> **username_4**: @username_1 Right, I'm just pointing out the cap of 21 million accounts is wrong.  
> **username_1**: @username_4 Fair enough, but I think the original point was that it's not worth spending so many billions of years if you're not going to be able to steal at least one bitcoin.  

---

### Answer by username_1 on 2012-05-15. Score: 3

[Is it possible to brute force bitcoin address creation in order to steal money?](https://bitcoin.stackexchange.com/q/22/659) is the same question, and has an argument about what "possible" means in which a majority of people seem to think that something can have a greater than zero probability and also be impossible at the same time. Check it out!

> **Comments:**
> **username_0**: I was aware of that question, thanks :) Here I was asking specifically if its profitability could change due to some addresses containing a substantial amount of money.  
> **username_1**: Oh, I see.  So are you happy with your answer?  It's "not really, no", because the substantial reward is offset by the much-more-than-substantial difficulty in stealing money the way you describe.  
> **username_2**: Incidentally, you can also have something with zero probability that is possible. See http://en.wikipedia.org/wiki/Almost_surely.  
> **username_0**: @username_1 yes I'm totally satisfied, in fact I accepted it.  

---

