Abstract: An authentication system of a terminal on a public switched telephone network provides a security node associated with a local exchange and a network terminal. For one-way authentication, the terminal responds to a call initiation by sending a unique authentication code comprising a number and a secret key encrypted according to a first algorithm, the secret key being specific to the terminal. The security node constructs the expected authentication code from the number, using the first algorithm and a second key which is a function of a terminal identification number, and compares the expected code with the received code. In two-way authentication, the security node responds to the call initiation by sending a transaction number to the terminal encrypted according to a second algorithm. The terminal generates the authentication code as a function of the first algorithm, the secret key and the transaction number. The authentication code is sent back to the security node.