firebase 创建用户 promise

Question

I'm trying to create users in Firebase and add some data in the database using real-time datase. I'm protecting the database with a rule only allowing the current user to insert data in his table. Even I'm using the promise I got a message saying "PERMISION DENIED". This is my code:

firebase.auth().createUserWithEmailAndPassword(email, password)
 .then( user => {
        const db = firebase.database();
        const customer = db.ref().child('customers');
        const key = firebase.auth().currentUser.uid;

        customer.child(key).set({
            name : email,
            pwd : password,
            isRegistered : false,       
        });

How can I modify the data right after the user is created?

Thanks folks

Edit2: these are the rules

{
  "rules": {
    "customers": {
      "$uid": {
        ".read": "auth.uid === $uid",
        ".write": "auth.uid === $uid"
      }
    }
  }
}

Answer 1

Considering the edit you made are after Doug's comment, your security rules should look more like:

{
  "rules": {
    "customers": {
      "$uid": {
        ".read": "auth.uid === $uid",
        ".write": "auth.uid === $uid"
      }
    }
  }
}