API key authentication in Rest API - Time & Space Complexity

Time Complexity: API key authentication

O(n)

Understanding Time Complexity

When checking API key authentication, we want to know how the time to verify a key changes as more keys exist.

We ask: How does the process scale when the number of stored API keys grows?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

// Example: Check if provided API key is valid
function isValidApiKey(providedKey, storedKeys) {
  for (let key of storedKeys) {
    if (key === providedKey) {
      return true;
    }
  }
  return false;
}
    

This code checks each stored API key one by one to find a match with the provided key.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Looping through the list of stored API keys.
• How many times: Up to once for each stored key until a match is found or all keys checked.

How Execution Grows With Input

As the number of stored keys grows, the time to check can grow roughly the same amount.

Input Size (n)	Approx. Operations
10	Up to 10 key checks
100	Up to 100 key checks
1000	Up to 1000 key checks

Pattern observation: The time grows directly with the number of keys; doubling keys roughly doubles checks.

Final Time Complexity

Time Complexity: O(n)

This means the time to verify an API key grows linearly with the number of stored keys.

Common Mistake

[X] Wrong: "Checking an API key always takes the same time no matter how many keys there are."

[OK] Correct: Because the code may need to look through many keys before finding a match or deciding none match, so more keys usually mean more work.

Interview Connect

Understanding how checking API keys scales helps you design faster and smarter authentication systems, a useful skill in many real projects.

Self-Check

"What if we stored the API keys in a hash map instead of a list? How would the time complexity change?"