Authorization through WordPress site

I recommend to look at this plugin from wordpress

https://ru.wordpress.org/plugins/json-api-user/

This is an extended authorization feature using the REST JSON API.

just look here:

• https://code.tutsplus.com/tutorials/wp-rest-api-setting-up-and-using-oauth-10a-authentication--cms-24797
• https://github.com/Automattic/android-wordpress-com-rest/blob/master/WordPressComRest/src/main/java/com/wordpress/rest/Oauth.java