An innovative security system in which the need to "unlock" the system is eliminated if the system is awakened within a predetermined duration from its last use. In the preferred embodiment, when the user "logs onto" a system by activating it and entering his password, the time of login, plus a predetermined delay, is stored in nonvolatile memory. Thereafter, if the system is placed (or places itself) into a low-power mode, no password will be required to log onto the system if the logon is made before the time stored in nonvolatile memory. If the logon is attempted after this time, the user must go through the entire authorization procedure.