Consider these resources:
The concept behind this would be to send a randomly generated string to the mobile phone number that the user enters, store it as a transient, and ask the user to enter it to send him his/her password via e-mail.
wp-login.php?action=register already does half of the job - sending he password to the registered person, you would only have to stop lay this process off until the password from the SMS is provided.
So an options would be:
- User registers, entering his phone number along with his e-mail
- E-mail with random password is not sent
- Random code is generated and sent using any SMS gateway API and stored in transients along with the user ID
- User enters code and any pending transients matching that code and user ID will release the registration e-mail with the password
Alternatively you can:
- Stop e-mail from going out with the password
- Send password through SMS gateway instead
The second option is very very simple, most gateways provide PHP libraries that you can use to interface with the API, override the
wp_mail() pluggable to send the password through the gateway.