When a Bitcoin user wants to use the 2-Way Peg, he sends a transaction to a multisig wallet whose funds are secured by the Federation. The same public key associated with the source bitcoins in this transaction is used on the RSK chain to store the Smart Bitcoins. This means that the private key that controlled the Bitcoins in the Bitcoin blockchain can be used to control an account on the RSK chain. Although both public and private keys are similar, each blockchain encodes the address in a different format. This means that the addresses on both blockchains are different.