Does anyone know where I can find a calculation of the likelihood of a collision of two randomly generated private keys?
if it was truly random generated then it is simply the size of the bit space of the hash function 2^256 for a single sha256 over ecdsa then - any short cuts the devs have taken to produce those keys in a realistic time frame e.g limiting the curve to reduce the time taken to generate the said key pair, and you would produce a pair not just a private key.
but I think the issues is that no computer can really do true random its always pseudo random like with the "SecureRandom" function in java/android and this has shown that a functions weakness is not in the bit space its in the way it has been implemented
read some of this to get a better idea as this has been asked quite a few times on this forums in more than 1 post/section Gavin has also talked about collisions
https://bitcointalk.org/?topic=62.0but like I have said its not about the function and bit space as 2^256/2^255 is quite secure and if brute forced would take longer than the dinosaurs walked the earth to create a collision
Quote: molecular
"take an average of 1,618,542,460,620,902,128,345,579,373 years to generate a collision"
it is more about how the devs have used said function and if that function has any exploits or weakness that would allow an attacker to shortcut this time