Authorization code flow in Rest API - Time & Space Complexity

Time Complexity: Authorization code flow

O(n)

Understanding Time Complexity

We want to understand how the time needed to complete the authorization code flow changes as more users or requests happen.

Specifically, how does the process scale when handling multiple authorization requests?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

POST /authorize
  - User sends request with client_id and redirect_uri
  - Server validates client and user credentials
  - Server generates authorization code

POST /token
  - Client sends authorization code
  - Server validates code and issues access token

This code snippet shows the main steps of the authorization code flow in a REST API.

Identify Repeating Operations

Look for repeated actions that affect time.

• Primary operation: Validating user and client data, and generating tokens for each request.
• How many times: Once per authorization request and once per token request.

How Execution Grows With Input

Each authorization request requires a fixed set of steps.

Input Size (n)	Approx. Operations
10 requests	About 10 sets of validation and token generation
100 requests	About 100 sets of validation and token generation
1000 requests	About 1000 sets of validation and token generation

Pattern observation: The time grows directly with the number of requests, doubling requests roughly doubles the work.

Final Time Complexity

Time Complexity: O(n)

This means the time needed grows linearly with the number of authorization requests.

Common Mistake

[X] Wrong: "The authorization code flow takes the same time no matter how many requests happen."

[OK] Correct: Each request requires separate validation and token generation, so more requests mean more work and more time.

Interview Connect

Understanding how the authorization code flow scales helps you design APIs that handle many users efficiently and reliably.

Self-Check

"What if the server cached validation results for clients? How would that affect the time complexity?"

Practice

1. What is the main purpose of the authorization code in the Authorization Code Flow?

easy

A. To exchange it for an access token securely

B. To directly access user data

C. To authenticate the user with a password

D. To refresh the access token automatically

Solution

1. Step 1: Understand the role of the authorization code

   The authorization code is a temporary code given after user consent, not the token itself.

2. Step 2: Identify what the app does with the code

   The app sends this code to the authorization server to get an access token securely.

3. Final Answer:

   To exchange it for an access token securely -> Option A

4. Quick Check:

   Authorization code = temporary code for token exchange [OK]

Hint: Authorization code is a temporary code, not a token [OK]

Common Mistakes:

• Thinking the code directly accesses data
• Confusing code with user password
• Assuming code refreshes tokens

2. Which HTTP method is typically used by the app to exchange the authorization code for an access token?

easy

A. DELETE

B. GET

C. PUT

D. POST

Solution

1. Step 1: Recall the token exchange request

   The app sends the authorization code to the token endpoint to get an access token.

2. Step 2: Identify the HTTP method used

   This request uses POST because it sends data securely in the request body.

3. Final Answer:

   POST -> Option D

4. Quick Check:

   Token exchange uses POST method [OK]

Hint: Token exchange sends data securely, so use POST [OK]

Common Mistakes:

• Using GET which exposes data in URL
• Confusing PUT or DELETE with token exchange
• Assuming token exchange is a simple GET request

3. Given this simplified token exchange request in Python:

import requests
response = requests.post('https://auth.example.com/token', data={
    'code': 'abc123',
    'client_id': 'myapp',
    'client_secret': 'secret',
    'redirect_uri': 'https://myapp.com/callback',
    'grant_type': 'authorization_code'
})
print(response.json().get('access_token'))

What will this code print if the exchange is successful?

medium

A. The authorization code 'abc123'

B. The access token string from the server

C. An error message about invalid client

D. None

Solution

1. Step 1: Understand the request purpose

   The code sends a POST request to exchange the authorization code for an access token.

2. Step 2: Analyze the printed output

   If successful, the server returns JSON with an 'access_token' key, which is printed.

3. Final Answer:

   The access token string from the server -> Option B

4. Quick Check:

   response.json()['access_token'] = access token [OK]

Hint: Successful exchange returns access token, not code [OK]

Common Mistakes:

• Printing the code instead of token
• Expecting error message on success
• Not accessing JSON correctly

4. In the Authorization Code Flow, a developer wrote this code snippet to exchange the code:

response = requests.get('https://auth.example.com/token', params={
    'code': 'abc123',
    'client_id': 'myapp',
    'client_secret': 'secret',
    'redirect_uri': 'https://myapp.com/callback',
    'grant_type': 'authorization_code'
})

What is the main issue with this code?

medium

A. Incorrect redirect URI format

B. Missing the authorization code parameter

C. Using GET instead of POST for token exchange

D. Client secret should not be sent

Solution

1. Step 1: Check HTTP method for token exchange

   The token exchange requires a POST request to send sensitive data securely.

2. Step 2: Identify the problem in the code

   The code uses GET with query parameters, which is insecure and not standard for this flow.

3. Final Answer:

   Using GET instead of POST for token exchange -> Option C

4. Quick Check:

   Token exchange must use POST, not GET [OK]

Hint: Token exchange always uses POST, not GET [OK]

Common Mistakes:

• Using GET exposes secrets in URL
• Forgetting to send client secret
• Assuming redirect URI format is wrong

5. A web app uses Authorization Code Flow with PKCE (Proof Key for Code Exchange). Which additional step does PKCE add to improve security?

hard

A. The app sends a code verifier with the token request to prove it initiated the flow

B. The app uses client secret only without authorization code

C. The user enters their password twice during login

D. The app skips the authorization code and uses implicit flow

Solution

1. Step 1: Understand PKCE purpose

   PKCE adds a code verifier and challenge to prevent interception of the authorization code.

2. Step 2: Identify the added step in the flow

   The app sends the code verifier with the token request to prove it started the flow and prevent attacks.

3. Final Answer:

   The app sends a code verifier with the token request to prove it initiated the flow -> Option A

4. Quick Check:

   PKCE adds code verifier step for security [OK]

Hint: PKCE adds code verifier to token request for security [OK]

Common Mistakes:

• Thinking PKCE removes authorization code
• Confusing PKCE with password prompts
• Assuming PKCE uses implicit flow