I have a site which is essentially a blog carrying alerts to Doctors. The idea is that the Doctors will get an SMS alerting them to the fact that a new alert has been posted and a link to the alert. The alert will contain images. It is public, hidden from SE but might contain some sensitive info. I was wondering if there was any way of authenticating a user by mobile phone number, or any easy way for a mobile phone user to log in to a Wordpress site?
This is complex and considering the sensitive nature of the application and the usage "doctor alerts" I would really consider not using a blog platform.
There are a lot of systems out there that support secure sms with options for media.
If you must for some reason use WordPress, to authenticate users have a look at some of the HTTP authentication plugins, OAuth, XML-RPC, or just regular logins with cookie support and a mobile friendly theme.
ps. You cannot get a mobile number unless the user gives it to you.