Methods and systems for controlling certificate-based open payment transactions involving a merchant and a customer utilizing various types of networks and terminals. Prior to accessing a merchant POS terminal or, for example, a merchant website, a customer obtains a certificate from a service provider (SP), such as a bank, certifying his identification (ID) and his relevant financial information, in a form that is understandable by the SP. The SP is capable of performing multiple functions. For example, the SP is capable of acting as a certificate authority when it issues the customer's certificates, an authenticator when it receives private-key encrypted certificates from the customers to be decrypted using the corresponding public-key, and an authorizing authority when it checks the value available in a customer' chosen payment account against the requested purchase or transfer amount.