If you want to password protect the map you could use regular windows file security or alternatively consider creating an "Extension Add-in" which you would then deploy as part of an Application Configuration. This Extension Add-in gives you the chance to run some code as the application is starting - in which you could validate the logged in user against an Access Control List, or hook into your enterprise security approach perhaps. Or you could display a prompt asking the user for their credentials then again do the validation against your list/user database. See http://help.arcgis.com/en/arcgisexplorer/1500/sdk/componenthelp/index.html#/d/0003000003tv000000.htm for more information.
