ARP spoofing in Computer Networks - Time & Space Complexity

Time Complexity: ARP spoofing

O(n)

Understanding Time Complexity

Analyzing time complexity helps us understand how the effort to perform ARP spoofing grows as the network size increases.

We want to know how the number of operations changes when more devices are on the network.

Scenario Under Consideration

Analyze the time complexity of the following ARP spoofing process.

for device in local_network:
    send_fake_arp_reply(target=device, spoofed_ip=router_ip)
    wait_for_response()
    if response_received:
        record_mac_address(device)

This code sends fake ARP replies to every device on the local network to trick them into associating the attacker's MAC address with the router's IP.

Identify Repeating Operations

Look at what repeats as the network grows.

• Primary operation: Sending fake ARP replies to each device.
• How many times: Once for every device on the network.

How Execution Grows With Input

As the number of devices increases, the number of fake ARP replies sent grows at the same rate.

Input Size (n)	Approx. Operations
10	10 fake ARP replies sent
100	100 fake ARP replies sent
1000	1000 fake ARP replies sent

Pattern observation: The effort grows directly with the number of devices; doubling devices doubles the work.

Final Time Complexity

Time Complexity: O(n)

This means the time to perform ARP spoofing increases linearly as more devices join the network.

Common Mistake

[X] Wrong: "Sending one fake ARP reply is enough to spoof the entire network instantly."

[OK] Correct: Each device must be targeted individually because ARP works device by device, so effort grows with network size.

Interview Connect

Understanding how ARP spoofing scales helps you think about network security and the challenges attackers face as networks grow.

Self-Check

"What if the attacker only targets a subset of devices instead of all? How would the time complexity change?"