Securing Raspberry Pi (SSH keys, firewall) - Time & Space Complexity

Time Complexity: Securing Raspberry Pi (SSH keys, firewall)

O(n)

Understanding Time Complexity

When securing a Raspberry Pi using SSH keys and firewall rules, it is important to understand how the time to apply these security steps grows as the number of devices or rules increases.

We want to know how the work needed changes when we add more keys or firewall rules.

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

import os

# Add multiple SSH public keys to authorized_keys
for key in ssh_keys:
    with open('/home/pi/.ssh/authorized_keys', 'a') as file:
        file.write(key + '\n')

# Apply firewall rules from a list
for rule in firewall_rules:
    os.system(f"sudo ufw allow {rule}")
    

This code adds each SSH key to the authorized keys file and applies each firewall rule one by one.

Identify Repeating Operations

• Primary operation: Two loops that each run through lists of keys and firewall rules.
• How many times: Each loop runs once for every item in its list.

How Execution Grows With Input

As the number of SSH keys or firewall rules grows, the time to add or apply them grows in a straight line.

Input Size (n)	Approx. Operations
10	About 20 operations (10 keys + 10 rules)
100	About 200 operations
1000	About 2000 operations

Pattern observation: Doubling the number of keys and rules roughly doubles the work needed.

Final Time Complexity

Time Complexity: O(n)

This means the time to secure the Raspberry Pi grows directly with the number of keys and firewall rules you add.

Common Mistake

[X] Wrong: "Adding more SSH keys or firewall rules won't affect the time much because each step is quick."

[OK] Correct: Even if each step is fast, doing many steps adds up, so more keys or rules mean more total time.

Interview Connect

Understanding how security setup time grows helps you plan and explain your approach clearly in real projects or interviews.

Self-Check

"What if we batch all firewall rules into one command instead of running one command per rule? How would the time complexity change?"

Practice

1. What is the main benefit of using SSH keys instead of passwords to access your Raspberry Pi?

easy

A. It improves security by avoiding password guessing attacks.

B. It makes the Raspberry Pi run faster.

C. It allows multiple users to share the same password.

D. It disables the firewall automatically.

Solution

1. Step 1: Understand SSH key authentication

   SSH keys use a pair of cryptographic keys to authenticate users without sending passwords over the network.

2. Step 2: Compare with password authentication

   Password authentication can be vulnerable to guessing or brute force attacks, while SSH keys are much harder to crack.

3. Final Answer:

   It improves security by avoiding password guessing attacks. -> Option A

4. Quick Check:

   SSH keys = better security [OK]

Hint: SSH keys stop password guessing attacks fast [OK]

Common Mistakes:

• Thinking SSH keys make the device faster
• Believing SSH keys share passwords
• Assuming SSH keys disable firewall

2. Which command correctly generates an SSH key pair on your Raspberry Pi?

easy

A. ssh-keygen --firewall

B. ssh-keygen -p rsa

C. ssh-keygen -t rsa

D. firewall-cmd --generate-key

Solution

1. Step 1: Identify the SSH key generation command

   The standard command to create SSH keys is ssh-keygen with the -t option to specify the type, e.g., rsa.

2. Step 2: Check options for correctness

   -p changes the passphrase, --firewall and firewall-cmd are unrelated to SSH keys.

3. Final Answer:

   ssh-keygen -t rsa -> Option C

4. Quick Check:

   ssh-keygen -t rsa = generate SSH keys [OK]

Hint: Use ssh-keygen with -t to specify key type [OK]

Common Mistakes:

• Using -p instead of -t for key generation
• Confusing firewall commands with SSH key commands
• Trying to generate keys with firewall tools

3. Given the following commands run on a Raspberry Pi, what will be the output of sudo ufw status?

sudo ufw enable
sudo ufw allow ssh
sudo ufw deny 80

medium

A. Error: ufw command not found

B. Status: inactive

C. Status: active
No rules defined

D. Status: active
To Action From
-- ------ ----
22/tcp ALLOW Anywhere
80 DENY Anywhere

Solution

1. Step 1: Analyze the firewall commands

   sudo ufw enable activates the firewall. sudo ufw allow ssh opens port 22 (SSH). sudo ufw deny 80 blocks HTTP port 80.

2. Step 2: Understand the status output

   The status shows active firewall with rules allowing SSH (port 22) and denying port 80.

3. Final Answer:

   Status: active To Action From -- ------ ---- 22/tcp ALLOW Anywhere 80 DENY Anywhere -> Option D

4. Quick Check:

   Firewall enabled with SSH allow and port 80 deny = Status: active To Action From -- ------ ---- 22/tcp ALLOW Anywhere 80 DENY Anywhere [OK]

Hint: Enable ufw then add rules to see them in status [OK]

Common Mistakes:

• Assuming firewall is inactive after enabling
• Expecting no rules after adding allow/deny
• Confusing port numbers with service names

4. You tried to add your SSH public key to ~/.ssh/authorized_keys but still get password prompts. What is the most likely cause?

medium

A. The authorized_keys file has incorrect permissions.

B. The Raspberry Pi firewall is disabled.

C. You forgot to restart the SSH service.

D. You used the wrong SSH key type.

Solution

1. Step 1: Check SSH key authentication requirements

   SSH requires strict permissions on ~/.ssh and authorized_keys files to allow key login.

2. Step 2: Identify common permission issues

   If permissions are too open, SSH ignores the keys and falls back to password login.

3. Final Answer:

   The authorized_keys file has incorrect permissions. -> Option A

4. Quick Check:

   Wrong permissions block SSH key login [OK]

Hint: Check .ssh and authorized_keys permissions first [OK]

Common Mistakes:

• Thinking firewall affects SSH key login
• Restarting SSH service unnecessarily
• Assuming wrong key type without checking permissions

5. You want to secure your Raspberry Pi by allowing SSH access only from a specific IP address 192.168.1.100 and blocking all other SSH attempts. Which ufw commands achieve this?

hard

A. sudo ufw allow from any to any port 22
sudo ufw deny from 192.168.1.100

B. sudo ufw allow from 192.168.1.100 to any port 22
sudo ufw deny 22

C. sudo ufw deny ssh
sudo ufw allow 22

D. sudo ufw allow ssh
sudo ufw deny from 192.168.1.100 to any port 22

Solution

1. Step 1: Allow SSH only from the specific IP

   Use sudo ufw allow from 192.168.1.100 to any port 22 to permit SSH from that IP.

2. Step 2: Deny all other SSH connections

   Use sudo ufw deny 22 to block SSH from all other IPs.

3. Final Answer:

   sudo ufw allow from 192.168.1.100 to any port 22 sudo ufw deny 22 -> Option B

4. Quick Check:

   Allow specific IP then deny all others = sudo ufw allow from 192.168.1.100 to any port 22 sudo ufw deny 22 [OK]

Hint: Allow specific IP first, then deny all others [OK]

Common Mistakes:

• Allowing SSH globally before denying specific IP
• Denying the allowed IP instead of others
• Using wrong port numbers or commands