Quote from: bitfromit on July 12, 2013, 07:22:49 PM

read : http://download.wpsoftware.net/bitcoin-birthday.pdf

Going to quote another recent thread. Because this is a stupid argument as well. If you can really generate that many addresses, the collision that you'll find, will be with one of your own addresses (which would be empty) And the reward of finding a block is so much higher than the probability of finding a collision and the difference between the two happening is so small that you guys really don't understand how many zeros are on these numbers and what that means.

Quote from: netrin on July 05, 2011, 11:16:07 PM

Quote from: joepie91 on July 05, 2011, 06:30:44 PM

So, I was thinking about the address generation scheme that is used for Bitcoin. Please note I did not do any math here yet to see if it is likely to happen, it's just a concept.

From what I understand, the keys are 256 bits (10^77) and there are what? 1 billion keys?

http://en.wikipedia.org/wiki/Birthday_paradox
http://en.wikipedia.org/wiki/Universally_Unique_Identifier#Random_UUID_probability_of_duplicates

1-e^(-(n^2)/2x)

EDIT:

1-e^(-(1000000000^2)/(2^256)) =
1-e^(-(10^18)/(10^77)) =
1-e^(-1/(10^59)) =
10^(-60)

Current Block Probability: ~ 10^(-16)

So, getting the block is 10^45 times more likely than a single collision. An attacker would have to hope for colliding with wallets containing trillions of times more coins than will ever have been created. But if an attacker can change the value of 'n' to 10^39 (duodecillion attempts) then he'll likely be quite profitable... but then again he'll only be colliding with his own keys.

and for good measure:

Quote from: theymos on July 06, 2011, 01:03:38 AM

This has been discussed so many times already...

Quote from: theymos on March 24, 2011, 03:33:23 AM

There are currently 329,993 addresses in the Bitcoin network. Say that this number of addresses are created every day for the next 140 years. That's 16,862,642,300 addresses.

The chance that at least two of those addresses collided is about 9.7x10^-29, using the formula here. Calculation.

Quote from: theymos on November 14, 2010, 07:52:33 AM

If every person on Earth makes ten addresses per second for 20 years (2x10¹⁸ total addresses), then the probability that two of these addresses collide is about 1.57x10^-12.

Quote from: theymos on February 19, 2011, 08:27:06 PM

UUIDs have 2¹²⁸ possible identifiers. They are also designed to be collision-proof. Wikipedia says:

Quote

To put these numbers into perspective, one's annual risk of being hit by a meteorite is estimated to be one chance in 17 billion, that means the probability is about 0.00000000006 (6 × 10−11), equivalent to the odds of creating a few tens of trillions of UUIDs in a year and having one duplicate. In other words, only after generating 1 billion UUIDs every second for the next 100 years, the probability of creating just one duplicate would be about 50%. The probability of one duplicate would be about 50% if every person on earth owns 600 million UUIDs.

Compare this to Bitcoin's 2¹⁶⁰ possible addresses. Bitcoin has:
1461501637330902918203684832716283019655932542976 addresses
UUIDs have:
340282366920938463463374607431768211456 identifiers

And...

Quote from: theymos on July 01, 2011, 01:27:31 AM

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