What if someone generates the same address/key as you?

[nicepumper]

All these math are making my brain hurt, thanks.

[kittycatbtc]

So by what i understood, another reason BTC is superior to credit cards 

[thecast]

So you have more chances at winning the lottery? 

[DannyHamilton]

So you have more chances at winning the lottery? 

I suppose that depends on the lottery.  Different lotteries have different odds.  However, any lottery that has the same odds of winning as the odds of generating the same bitcoin address as someone else would be a lottery that nobody would play (since nobody would ever win).


As an example, lets assume that it's after the year 2140 and all the bitcoins that will ever exist have already been mined.

To demonstrate how unlikely it is, lets assume that nobody ever lost any private keys and no bitcoins have ever been permanently lost, so ALL bitcoins are accessible.  Then lets assume that all the bitcoins are spread out into the smallest possible outputs.  That would result in 2,099,999,997,690,000 addresses each with exactly 0.00000001 BTC in them.  This gives you the largest possible set of bitcoin addresses that could ever exist with bitcoins in them.

Given that you are trying to find any one of 2,099,999,997,690,000 different addresses out of a total of approximately 1.46 X 10⁴⁸ possible addresses, your odds of "winning" on any given attempt are approximately 1 in 6.96 X 10³²

Looking at the Mega Millions lottery that is popular in the United States, the odds of winning the jackpot with a single set of 6 numbers are:
1 in 258,890,850

If I haven't messed up my math, the odds of winning the Mega Millions lottery jackpot twice in a row with that same set of numbers are therefore:
1 in 6.7 X 10¹⁶

The odds of winning the Mega Millions lottery jackpot three times in a row with that same set of numbers are then:
1.7 X 10²⁵

We finally have better odds of finding a bitcoin address that has a balance if we compare to the odds of winning the Mega Millions lottery jackpot four times in a row with the same exact set of 6 numbers every time: 4.5 X 10³³

Of course there aren't actually 2,099,999,997,690,000 different addresses that are holding a bitcoin balance (and there never will be due to lost bitcoins and the fact that people will generally store more than 0.00000001 BTC per adddress).  If we use a more realistic number (perhaps something like 2,100,000,000 addresses with a balance) we find that:

You have better odds of winning the Mega Millions lottery jackpot all four times on your next four attempts with the exact same set of 6 numbers each time than you will ever have of have of generating a bitcoin address that already exists in a single attempt.

[Vortex20000]

I can get an account cracked... in, according to my computer, E-988985950 years.

[bitkilo]

First of all, does every public key have a corresponding private key or can more than one public key correspond to just one private key?

Every public key is calculated directly from its corresponding private key.  There are slightly less than 2²⁵⁶ possible public/private key pairs.

yes I don't think it will happen anytime soon because that is 1 big fuckin number of possibilities, something like
1.157920893×10^77. Well that's what a mate told me it was and he is pretty smart. I can't claim I worked that out.
Can't see it happening in my lifetime.

[cassimares]

I dont get it, you mean there is a chance the private key would be same?

[Kluge]

I dont get it, you mean there is a chance the private key would be same?

Absolutely, but it's millions times more likely your dad's actually your maternal grandpa.

[DannyHamilton]

Can't see it happening in my lifetime.

As long as the private keys are randomly generated with proper entropy, I can't see if happening in the lifetime of any human being that will ever exist on the face of the earth.

I dont get it, you mean there is a chance the private key would be same?

Only if the wallet is using a faulty random number generator.  As long as the private key is randomly generated with sufficient entropy, it won't ever happen.

If there is a bug in some wallet software, then it is possible that it will generate an insufficiently random number resulting in another copy of that software generating the same random number for someone else.

[BurtW]

First of all, does every public key have a corresponding private key or can more than one public key correspond to just one private key?

Every public key is calculated directly from its corresponding private key.  There are slightly less than 2²⁵⁶ possible public/private key pairs.

yes I don't think it will happen anytime soon because that is 1 big fuckin number of possibilities, something like
1.157920893×10^77. Well that's what a mate told me it was and he is pretty smart. I can't claim I worked that out.
Can't see it happening in my lifetime.

10^x = 2²⁵⁶

ln(10^x) = ln(2²⁵⁶)

x(ln(10)) = 256(ln(2))

x = 256(ln(2))/(ln(10))

x = 77.06367888997918597471715704947

2²⁵⁶ = 10^{77.06367888997918597471715704947}
      = 10^{(0.06367888997918597471715704947 + 77)}
      = (10^{0.06367888997918597471715704947})(10⁷⁷)
      = 1.1579208923731619542357098500863 * 10⁷⁷

Math is fun.

[DannyHamilton]

Math is fun.

Agreed.

However, if you trust Google to be able to handle basic mathematics properly, you can also just enter:

2^256

into the Google search text box and click the "Google Search" button.

[BurtW]

That is not as much fun.  I can also just put 2²⁵⁶ into my calculator, still not a much fun.

[BitCoinDream]

I think moat people understand it will take billions of years to brute force an address, but it is still an extremely thin chance someone else can generate a key to your address. It just makes you feel insecure.

If you understand how incredibly low the chance is, you shouldn't feel insecure.

Here is what DannyHamilton responded to a very similar question a few months ago.
 

It is also possible that all the air in the room will spontaneously collect in one corner suffocating everyone in the room.  The chance is extremely low, so low it is like impossible, but extremely low chance does not equal impossible.

Now ask any lay person if they think that it is possible for all the air in the room to suddenly collect tightly in a corner leaving everyone to suffocate, and we'll see if "impossible" in general use means what you think it means.

EDIT: Oops, DannyHamilton mentioned that analogy faster than me.

Interestingly I asked the question then...

[g29wheel]

Probably now you have understood that it's almost impossible to generate an existing address therefore don't worry about that

[Buo]

This is a doubt which pop up every week or so, generating the same key is out of the question and there are math proofs for this.

[cookiemonsterwhat]

If they have the same key, they would have access to your bitcoin..

But the odds of this ever happening is very slim.