Phone number authentication in Firebase - Time & Space Complexity

Time Complexity: Phone number authentication

O(n)

Understanding Time Complexity

We want to understand how the time needed to verify phone numbers changes as more users try to sign in.

How does the system handle more requests and how does that affect speed?

Scenario Under Consideration

Analyze the time complexity of the following operation sequence.

const phoneNumber = "[phone]";
const appVerifier = window.recaptchaVerifier;

firebase.auth().signInWithPhoneNumber(phoneNumber, appVerifier)
  .then(confirmationResult => {
    // User receives SMS code
    const code = prompt('Enter the verification code');
    return confirmationResult.confirm(code);
  })
  .then(userCredential => {
    // User signed in
  })
  .catch(error => {
    // Handle errors
  });

This code sends a verification SMS to the user and then confirms the code they enter to sign them in.

Identify Repeating Operations

Identify the API calls, resource provisioning, data transfers that repeat.

• Primary operation: Sending SMS verification via Firebase API.
• How many times: Once per user sign-in attempt.

How Execution Grows With Input

Each new user triggers one SMS send and one verification check.

Input Size (n)	Approx. Api Calls/Operations
10	10 SMS sends + 10 code verifications
100	100 SMS sends + 100 code verifications
1000	1000 SMS sends + 1000 code verifications

Pattern observation: The number of operations grows directly with the number of users trying to sign in.

Final Time Complexity

Time Complexity: O(n)

This means the time needed grows linearly as more users try to authenticate with their phone numbers.

Common Mistake

[X] Wrong: "Sending one SMS code will handle multiple users at once, so time stays the same."

[OK] Correct: Each user needs their own SMS and verification, so the system must do separate work for each user.

Interview Connect

Understanding how authentication scales helps you design systems that stay fast and reliable as more people use them.

Self-Check

"What if we batch phone number verifications instead of sending SMS one by one? How would the time complexity change?"

Practice

1. What is the main purpose of phone number authentication in Firebase?

easy

A. To sign in users using SMS codes without passwords

B. To store phone numbers in the database

C. To send marketing messages to users

D. To verify email addresses

Solution

1. Step 1: Understand and identify the main purpose of phone number authentication

   It allows users to sign in by receiving a code on their phone via SMS instead of using a password. The main goal is to authenticate users securely and easily using their phone number and SMS code.

2. Final Answer:

   To sign in users using SMS codes without passwords -> Option A

3. Quick Check:

   Phone number authentication = SMS sign-in [OK]

Hint: Phone auth uses SMS codes to sign in, not emails [OK]

Common Mistakes:

• Confusing phone auth with email verification
• Thinking it stores phone numbers only
• Assuming it sends marketing SMS

2. Which Firebase method is used to start phone number authentication by sending an SMS code?

easy

A. signInWithEmailAndPassword()

B. signInWithPhoneNumber()

C. sendPasswordResetEmail()

D. verifyPhoneNumber()

Solution

1. Step 1: Identify the method for phone auth SMS sending and exclude unrelated methods

   Firebase provides signInWithPhoneNumber() to send the SMS code to the user. signInWithEmailAndPassword() is for email login, sendPasswordResetEmail() is for password reset, and verifyPhoneNumber() is not a Firebase client method.

2. Final Answer:

   signInWithPhoneNumber() -> Option B

3. Quick Check:

   Send SMS code = signInWithPhoneNumber() [OK]

Hint: Phone auth starts with signInWithPhoneNumber() [OK]

Common Mistakes:

• Using email sign-in methods for phone auth
• Confusing password reset with phone auth
• Assuming verifyPhoneNumber() is a Firebase method

3. What will happen if you try to sign in with phone number authentication without setting up reCAPTCHA verifier in Firebase web?

medium

A. The phone number will be stored but no SMS sent

B. The SMS code will be sent without any issues

C. The user will be signed in automatically

D. Firebase will throw an error requiring reCAPTCHA verification

Solution

1. Step 1: Understand reCAPTCHA role and predict behavior without it in Firebase phone auth

   Firebase requires reCAPTCHA on web to prevent abuse and verify the user is human before sending SMS. If reCAPTCHA is not set up, Firebase will block the SMS sending and throw an error demanding reCAPTCHA verification.

2. Final Answer:

   Firebase will throw an error requiring reCAPTCHA verification -> Option D

3. Quick Check:

   Missing reCAPTCHA = error thrown [OK]

Hint: Web phone auth needs reCAPTCHA or it errors [OK]

Common Mistakes:

• Assuming SMS sends without reCAPTCHA
• Thinking user signs in automatically
• Believing phone number stores without SMS

4. Given this code snippet, what is the error?

const confirmationResult = await signInWithPhoneNumber(auth, phoneNumber, appVerifier);
const userCredential = await confirmationResult.confirm(code);

medium

A. phoneNumber should be an email string

B. Using confirm() instead of verify() method

C. Missing reCAPTCHA verifier initialization

D. code variable should be a number, not string

Solution

1. Step 1: Check parameters and identify common mistake in signInWithPhoneNumber code

   The third parameter must be a valid reCAPTCHA verifier instance (appVerifier) initialized properly. If appVerifier is not initialized or missing, the code will fail even if confirm() is called correctly.

2. Final Answer:

   Missing reCAPTCHA verifier initialization -> Option C

3. Quick Check:

   Missing appVerifier init = error [OK]

Hint: Always initialize reCAPTCHA verifier before signInWithPhoneNumber() [OK]

Common Mistakes:

• Confusing confirm() with verify() method
• Passing email instead of phone number
• Assuming code must be number type

5. You want to implement phone number authentication in a React app using Firebase. Which sequence correctly describes the steps to sign in a user?

hard

A. Initialize reCAPTCHA verifier -> call signInWithPhoneNumber() -> send SMS -> confirm code -> sign in user

B. Call signInWithPhoneNumber() -> confirm code -> initialize reCAPTCHA verifier -> sign in user

C. Confirm code -> initialize reCAPTCHA verifier -> call signInWithPhoneNumber() -> sign in user

D. Sign in user -> initialize reCAPTCHA verifier -> call signInWithPhoneNumber() -> confirm code

Solution

1. Step 1: Outline the correct sequence for implementing phone auth

   Initialize reCAPTCHA verifier first to prevent abuse and required before sending SMS. Call signInWithPhoneNumber() next to send the code to the user's phone. Confirm the code received by user using confirmationResult.confirm(code) to verify and sign in the user.

2. Final Answer:

   Initialize reCAPTCHA verifier -> call signInWithPhoneNumber() -> send SMS -> confirm code -> sign in user -> Option A

3. Quick Check:

   reCAPTCHA -> send SMS -> confirm code = correct flow [OK]

Hint: Always start with reCAPTCHA, then send SMS, then confirm code [OK]

Common Mistakes:

• Calling signInWithPhoneNumber before reCAPTCHA setup
• Confirming code before SMS sent
• Trying to sign in before confirmation