An improved monetary system using electronic media to exchange economic value securely and reliably is disclosed. The system provides a complete monetary system having electronic money that is interchangeable with conventional paper money. Also disclosed is a system for open electronic commerce having a customer trusted agent securely communicating with a first money module, and a merchant trusted agent securely communicating with a second money module. Both trusted agents are capable of establishing a first cryptographically secure session, and both money modules are capable of establishing a second cryptographically secure session. The merchant trusted agent transfers electronic merchandise to the customer trusted agent, and the first money module transfers electronic money to the second money module. The money modules inform their trusted agents of the successful completion of payment, and the customer may use the purchased electronic merchandise.