Secure HTTP trigger for Cloud Functions for Firebase

Since the question asks for auth-based access (1) within, or (2) before a function, here's an method for the "before" case: >

Since every Firebase Project is also a Google Cloud Project -- and GCP allows for "private" functions, you can set project-wide or per-function permissions outside the function(s), so that only authenticated users can cause the function to fire.

Unauthorized users will be rejected before function invocation, even if they try to hit the endpoint.

Here's documentation on setting permissions and authenticating users. As of writing, I believe using this method requires users to have a Google account to authenticate.

Yes. You will need to send the Firebase ID token along with the request (for example in the Authorization header of an AJAX request), then verify it using the Firebase Admin SDK. There is an in-depth example in the Cloud Functions for Firebase samples repository. It looks something like this (made shorter for SO post):

const functions = require('firebase-functions');
const admin = require('firebase-admin');
const cors = require('cors')();

const validateFirebaseIdToken = (req, res, next) => {
  cors(req, res, () => {
    const idToken = req.headers.authorization.split('Bearer ')[1];
    admin.auth().verifyIdToken(idToken).then(decodedIdToken => {
      console.log('ID Token correctly decoded', decodedIdToken);
      req.user = decodedIdToken;
      next();
    }).catch(error => {
      console.error('Error while verifying Firebase ID token:', error);
      res.status(403).send('Unauthorized');
    });
  });
};

exports.myFn = functions.https.onRequest((req, res) => {
  validateFirebaseIdToken(req, res, () => {
    // now you know they're authorized and `req.user` has info about them
  });
});