IAM deny policies in GCP - Time & Space Complexity

Time Complexity: IAM deny policies

O(n)

Understanding Time Complexity

We want to understand how the time to evaluate IAM deny policies changes as we add more policies or rules.

Specifically, how does checking permissions grow when there are many deny rules?

Scenario Under Consideration

Analyze the time complexity of evaluating deny policies during an access request.

// Pseudocode for IAM deny policy evaluation
for each denyPolicy in denyPolicies:
  for each denyRule in denyPolicy.rules:
    if denyRule matches request:
      deny access
allow access if no deny rules matched

This sequence checks all deny rules in all deny policies to decide if access should be denied.

Identify Repeating Operations

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

• Primary operation: Checking each deny rule against the access request.
• How many times: Once for every deny rule in all deny policies.

How Execution Grows With Input

As the number of deny rules increases, the system must check more rules one by one.

Input Size (n)	Approx. API Calls/Operations
10	10 rule checks
100	100 rule checks
1000	1000 rule checks

Pattern observation: The number of checks grows directly with the number of deny rules.

Final Time Complexity

Time Complexity: O(n)

This means the time to evaluate deny policies grows linearly with the number of deny rules.

Common Mistake

[X] Wrong: "Adding more deny policies won't affect evaluation time much because they run in parallel."

[OK] Correct: In reality, all deny rules must be checked one after another, so more rules mean more checks and longer evaluation time.

Interview Connect

Understanding how deny policies scale helps you design secure and efficient access controls in cloud environments.

Self-Check

"What if deny rules were grouped and checked using a fast lookup instead of one by one? How would the time complexity change?"