A user inputs a password at a user device whose processor receives the password, retrieves a stored derived value resulting from a derivation function, preferably a cryptographic one-way function, applied to a reference password, scrambles the received password using a function taking the derived value as a variable to obtain a scrambled password, and sends the scrambled password to an authentication server. In case the stored derived value cannot be retrieved, the processor uses the derivation function to generate a derived value from the received password. In case the password is received during generation of a new password, the processor generates and stores a derived value from the new password. In an embodiment, the apparatus comprises the authentication server.