Custom authentication tokens in Firebase - Time & Space Complexity

Time Complexity: Custom authentication tokens

O(n)

Understanding Time Complexity

When using custom authentication tokens in Firebase, it's important to understand how the time to create and verify these tokens changes as you handle more users.

We want to know: how does the work grow when we generate tokens for many users?

Scenario Under Consideration

Analyze the time complexity of the following operation sequence.

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

async function createCustomTokens(userIds) {
  const tokens = [];
  for (const uid of userIds) {
    const token = await admin.auth().createCustomToken(uid);
    tokens.push(token);
  }
  return tokens;
}

This code creates a custom authentication token for each user ID in a list.

Identify Repeating Operations

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

• Primary operation: Calling createCustomToken(uid) for each user.
• How many times: Once per user ID in the input list.

How Execution Grows With Input

Each user requires one token creation call, so the total work grows directly with the number of users.

Input Size (n)	Approx. API Calls/Operations
10	10 token creations
100	100 token creations
1000	1000 token creations

Pattern observation: The number of operations increases evenly as the input size grows.

Final Time Complexity

Time Complexity: O(n)

This means the time to create tokens grows in direct proportion to the number of users.

Common Mistake

[X] Wrong: "Creating one token is slow, so creating many tokens will take the same time as one."

[OK] Correct: Each token creation is a separate operation, so more users mean more work and more time.

Interview Connect

Understanding how your code scales with more users shows you can build systems that handle growth smoothly and predict performance.

Self-Check

"What if we batch user IDs and create tokens in parallel? How would the time complexity change?"

Practice

1. What is the main purpose of Firebase custom authentication tokens?

easy

A. To store user data in Firebase Realtime Database

B. To sign in users from your own system to Firebase

C. To send notifications to users

D. To create Firebase projects automatically

Solution

1. Step 1: Understand the role of custom tokens

   Custom tokens are used to authenticate users from an external system with Firebase.

2. Step 2: Identify the correct purpose

   They allow users to sign in securely using tokens generated on your server.

3. Final Answer:

   To sign in users from your own system to Firebase -> Option B

4. Quick Check:

   Custom tokens = sign in users [OK]

Hint: Custom tokens = external user sign-in method [OK]

Common Mistakes:

• Confusing tokens with data storage
• Thinking tokens send notifications
• Assuming tokens create projects

2. Which Firebase Admin SDK method is used to create a custom authentication token?

easy

A. admin.auth().createCustomToken(uid)

B. admin.database().createToken(uid)

C. firebase.auth().signInWithCustomToken(uid)

D. admin.storage().generateToken(uid)

Solution

1. Step 1: Identify the correct Admin SDK service

   Custom tokens are created using the Authentication service, not database or storage.

2. Step 2: Match the correct method

   The method to create a custom token is createCustomToken(uid) under admin.auth().

3. Final Answer:

   admin.auth().createCustomToken(uid) -> Option A

4. Quick Check:

   Custom token creation = admin.auth().createCustomToken [OK]

Hint: Use admin.auth().createCustomToken to generate tokens [OK]

Common Mistakes:

• Using database or storage methods incorrectly
• Confusing signInWithCustomToken with token creation
• Calling methods on firebase instead of admin SDK

3. What will the following code output if uid is 'user123' and no errors occur?

const admin = require('firebase-admin');
admin.initializeApp();

admin.auth().createCustomToken('user123')
  .then(token => console.log(typeof token))
  .catch(error => console.error(error));

medium

A. 'object'

B. An error message

C. 'undefined'

D. 'string'

Solution

1. Step 1: Understand createCustomToken return type

   The method returns a Promise that resolves to a string token.

2. Step 2: Check console.log output

   Logging typeof token will print 'string' because the token is a string.

3. Final Answer:

   'string' -> Option D

4. Quick Check:

   createCustomToken returns string token [OK]

Hint: createCustomToken returns a string token inside a Promise [OK]

Common Mistakes:

• Expecting an object instead of string
• Confusing token with undefined
• Assuming an error without cause

4. Identify the error in this code snippet for generating a custom token:

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

admin.auth().createCustomToken('12345')
  .then(token => console.log(token))
  .catch(error => console.error(error));

medium

A. Missing admin.initializeApp() call

B. Incorrect method name, should be generateCustomToken

C. createCustomToken does not return a Promise

D. UID must be a string, not a number

Solution

1. Step 1: Check initialization of Firebase Admin SDK

   The admin SDK must be initialized with admin.initializeApp() before use.

2. Step 2: Verify other parts

   The UID '12345' is a valid string, createCustomToken returns a Promise, and method name is correct.

3. Final Answer:

   Missing admin.initializeApp() call -> Option A

4. Quick Check:

   Initialize admin SDK before calling methods [OK]

Hint: Always call admin.initializeApp() before using admin SDK [OK]

Common Mistakes:

• Passing number instead of string UID
• Assuming createCustomToken is synchronous
• Using wrong method name

5. You want to add extra user info like role: 'admin' in a custom token. Which code snippet correctly adds this claim?

hard

A. admin.auth().setCustomUserClaims(uid, { role: 'admin' })

B. admin.auth().createCustomToken(uid).setClaims({ role: 'admin' })

C. admin.auth().createCustomToken(uid, { role: 'admin' })

D. admin.auth().createCustomToken(uid, { claims: { role: 'admin' } })

Solution

1. Step 1: Understand how to add extra claims in custom tokens

   The createCustomToken method accepts a second argument with additional claims as a plain object.

2. Step 2: Evaluate each option

   admin.auth().createCustomToken(uid, { role: 'admin' }) correctly passes extra claims as second argument. admin.auth().createCustomToken(uid).setClaims({ role: 'admin' }) is invalid chaining. admin.auth().setCustomUserClaims(uid, { role: 'admin' }) sets claims on user but not in token creation. admin.auth().createCustomToken(uid, { claims: { role: 'admin' } }) nests claims incorrectly.

3. Final Answer:

   admin.auth().createCustomToken(uid, { role: 'admin' }) -> Option C

4. Quick Check:

   Extra claims go as second argument in createCustomToken [OK]

Hint: Pass extra claims as second argument to createCustomToken [OK]

Common Mistakes:

• Trying to chain setClaims on token creation
• Using setCustomUserClaims instead of token claims
• Nesting claims inside another object