How to create REST authentication for iOS and Android mobile applications

I am creating an application with a version of iOS and Android. I want to create or implement an existing REST validation process that can be used by both applications. I know that I can accomplish this with a simple Get service, but this will pass the password in a clear way. Is there any API that handles authentication for mobile apps?

I do not want to use OAuth because I do not want the user to have to take an extra step to allow access to their data. I want the user to smoothly enter the username and password and authenticate as in most mobile applications that I used.