What if a bitcoin clients could create identical private keys

Question

What would happen if in rarest of condition a bitcoin wallet could create conflicting private keys. If this could happen what would happen??

Answer 1

If this happens, then Person B will be able to spend person A's bitcoins. However, there are only two ways this can happen:

a) Person B generates the same keypair (private key) as person A

or b) Person B generates a different keypair, which (public key) hashes to person A's address (a hash collision)

Take a look at the specification for at bitcoin address: https://en.bitcoin.it/wiki/Technical_background_of_Bitcoin_addresses

Answer 2

The private key is random number so large that it is impossible to generate another equal number. Private and public keys could be created using different algorithms. The RSA works taking in combination of two prime numbers.

So basically it is easy to calculate in one sense, but difficult to do so in opposite sense. Basically it is a one way function. The number or a hash generated from the algorithms are random and unique. ANd it is almost impossible to generate two unique keys.