A payment system implemented on a mobile device authorizes and processes transactions. The mobile device generates a public-private key pair and receives payment information. The private key and the payment information are split into a local and a remote fragment. The public key, a private key fragment, and a payment information fragment are sent to a secure payment system, and the other fragments are stored on the mobile device. When a transaction is received by the mobile device to authorize, the mobile device sends a payment fragment to the secure payment system and receives a private key fragment from the secure payment system. The mobile device authorizes the transaction using the private key, recovered from the private key fragments. The secure payment system verifies the transaction using the public key and processes the transaction using the recovered payment information. Additional techniques to process transactions using data splitting are disclosed.