What is the relationship between a Bitcoin Private Key / Public Key / Address? What is the relationship between a Bitcoin Private Key / Public Key / Address?  I see that a private key / public key pair is generated, but is there a possibility of generating a private key already in use?  And, also I'm assuming that a wallet address is a bitcoin address?  Does each wallet address have a one-one relationship with a private key?
Thanks
Using Elliptical Curve Digital Signature Algorithm (ECDSA), the private key is used to generate the public key, a secure hash function is then applied to the public key and a checksum appended to produce a Base58 formatted bitcoin address.
A private key collision is theoretically possible, but practically impossible due to the sheer number of them available on the network (quadrillions+).