Authentication documentation in Rest API - Time & Space Complexity

Time Complexity: Authentication documentation

O(n)

Understanding Time Complexity

When working with authentication in REST APIs, it's important to understand how the time to verify users grows as more requests come in.

We want to know how the system handles many login attempts and what affects the speed.

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

POST /login
Request Body: { username, password }

// Server side
user = findUserByUsername(username)
if user is None:
  return error
if verifyPassword(user.passwordHash, password):
  return success
else:
  return error
    

This code checks a username and password against stored data to authenticate a user.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Searching for the user by username in the database.
• How many times: Once per login request.

How Execution Grows With Input

As the number of users grows, finding a user can take longer if the search is not optimized.

Input Size (n)	Approx. Operations
10	About 10 checks to find a user
100	About 100 checks
1000	About 1000 checks

Pattern observation: The time to find a user grows roughly in direct proportion to the number of users if no special search method is used.

Final Time Complexity

Time Complexity: O(n)

This means the time to authenticate grows linearly with the number of users in the system.

Common Mistake

[X] Wrong: "Authentication time stays the same no matter how many users exist."

[OK] Correct: If the system searches users one by one, more users mean more time to find the right one.

Interview Connect

Understanding how authentication scales helps you design systems that stay fast as they grow, a key skill in real projects.

Self-Check

"What if we used a database index or hash map to find users? How would the time complexity change?"