Asymmetric encryption (RSA, ECC) in Cybersecurity - Mini Project: Build & Apply

Understanding Asymmetric Encryption with RSA and ECC

📖 Scenario: You are learning about how secure communication works on the internet. Two common methods to keep messages safe are RSA and ECC, which use pairs of keys to encrypt and decrypt information.

🎯 Goal: Build a simple conceptual model of asymmetric encryption by creating key pairs, setting up a message, encrypting it with a public key, and decrypting it with a private key.

📋 What You'll Learn

Create variables to represent public and private keys for RSA and ECC

Set up a message variable to be encrypted

Show the encryption process using the public key

Show the decryption process using the private key

💡 Why This Matters

🌍 Real World

Asymmetric encryption is used every day to secure emails, websites, and online banking by ensuring only the intended recipient can read the message.

💼 Career

Understanding asymmetric encryption is essential for cybersecurity professionals, software developers, and anyone working with secure communications.

1

Set up RSA and ECC key pairs

Create two dictionaries called rsa_keys and ecc_keys. Each dictionary should have two entries: 'public' and 'private'. Set rsa_keys['public'] to 'RSA Public Key' and rsa_keys['private'] to 'RSA Private Key'. Set ecc_keys['public'] to 'ECC Public Key' and ecc_keys['private'] to 'ECC Private Key'.

Cybersecurity

# Create rsa_keys and ecc_keys dictionaries with public and private keys
# Your code here

Hint

Think of rsa_keys and ecc_keys as boxes holding two keys each: one public and one private.

2

Create a message to encrypt

Create a variable called message and set it to the string 'Hello, secure world!'.

Cybersecurity

rsa_keys = {'public': 'RSA Public Key', 'private': 'RSA Private Key'}
ecc_keys = {'public': 'ECC Public Key', 'private': 'ECC Private Key'}
# Create a message string to encrypt
# Your code here

Hint

This message represents the information you want to keep safe.

3

Simulate encryption using the public key

Create a variable called encrypted_message_rsa and set it to a string combining rsa_keys['public'] and message separated by a colon and a space. Similarly, create encrypted_message_ecc combining ecc_keys['public'] and message with the same format.

Cybersecurity

rsa_keys = {'public': 'RSA Public Key', 'private': 'RSA Private Key'}
ecc_keys = {'public': 'ECC Public Key', 'private': 'ECC Private Key'}
message = 'Hello, secure world!'
# Create encrypted_message_rsa and encrypted_message_ecc by combining keys and message
# Your code here

Hint

Imagine the public key locks the message. We show this by joining the key and message with a colon.

4

Simulate decryption using the private key

Create two variables: decrypted_message_rsa and decrypted_message_ecc. Set both to the string 'Hello, secure world!' to represent the original message after decryption with the private keys.

Cybersecurity

rsa_keys = {'public': 'RSA Public Key', 'private': 'RSA Private Key'}
ecc_keys = {'public': 'ECC Public Key', 'private': 'ECC Private Key'}
message = 'Hello, secure world!'
encrypted_message_rsa = f"{rsa_keys['public']}: {message}"
encrypted_message_ecc = f"{ecc_keys['public']}: {message}"
# Set decrypted_message_rsa and decrypted_message_ecc to the original message
# Your code here

Hint

Decryption returns the original message using the private key.

Practice

1. What is the main purpose of asymmetric encryption like RSA and ECC?

easy

A. To use the same key for both encrypting and decrypting

B. To store passwords in plain text

C. To use two different keys: one to encrypt and one to decrypt

D. To speed up internet connections

Solution

1. Step 1: Understand key usage in asymmetric encryption

   Asymmetric encryption uses two keys: a public key to encrypt and a private key to decrypt messages.

2. Step 2: Compare with symmetric encryption

   Symmetric encryption uses the same key for both encrypting and decrypting, which is different from asymmetric encryption.

3. Final Answer:

   To use two different keys: one to encrypt and one to decrypt -> Option C

4. Quick Check:

   Asymmetric encryption = two keys (public/private) [OK]

Hint: Remember: public key encrypts, private key decrypts [OK]

Common Mistakes:

• Confusing asymmetric with symmetric encryption
• Thinking one key is used for both encrypting and decrypting
• Believing encryption speeds up internet
• Assuming passwords are stored in plain text

2. Which of the following is a correct statement about RSA keys?

easy

A. RSA does not use any mathematical operations

B. RSA uses a single key for both encryption and decryption

C. RSA keys are always 128 bits long

D. RSA keys are generated using large prime numbers

Solution

1. Step 1: Recall RSA key generation method

   RSA keys are created by multiplying two large prime numbers to form the public and private keys.

2. Step 2: Check other options for correctness

   RSA does not use a single key, keys are not fixed at 128 bits, and it heavily relies on math operations.

3. Final Answer:

   RSA keys are generated using large prime numbers -> Option D

4. Quick Check:

   RSA key generation = large primes [OK]

Hint: RSA keys come from multiplying big prime numbers [OK]

Common Mistakes:

• Thinking RSA uses one key only
• Assuming RSA keys have fixed small size
• Ignoring the role of prime numbers
• Believing RSA avoids math operations

3. Consider this simplified RSA encryption example:
public_key = (e=3, n=33)
private_key = (d=7, n=33)
message = 4
encrypted = (message^e) mod n
decrypted = (encrypted^d) mod n
What is the decrypted message?

medium

A. 4

B. 7

C. 3

D. 9

Solution

1. Step 1: Calculate encrypted message

   encrypted = (4^3) mod 33 = 64 mod 33 = 31

2. Step 2: Calculate decrypted message

   decrypted = (31^7) mod 33. Calculating 31^7 mod 33 gives 4 (using modular exponentiation).

3. Final Answer:

   4 -> Option A

4. Quick Check:

   Decrypted message matches original message [OK]

Hint: Encrypt then decrypt returns original message [OK]

Common Mistakes:

• Forgetting to apply modulo operation
• Mixing up public and private keys
• Incorrectly calculating powers
• Assuming encrypted equals decrypted

4. A developer wrote this ECC key generation snippet but it fails:
private_key = generate_ecc_key()
public_key = private_key * G
What is the likely error?

medium

A. Public key is generated by multiplying G by private key, not the other way

B. Private key must be a point, not a number

C. Private key cannot be used to generate public key

D. Multiplying private key by G is incorrect; should add G

Solution

1. Step 1: Understand ECC key generation

   In ECC, the public key is generated by multiplying the base point G by the private key scalar.

2. Step 2: Identify the error in code

   The code multiplies private_key by G, but the correct order is G multiplied by private_key.

3. Final Answer:

   Public key is generated by multiplying G by private key, not the other way -> Option A

4. Quick Check:

   ECC public key = G * private key [OK]

Hint: Order matters: base point times private key [OK]

Common Mistakes:

• Reversing multiplication order
• Confusing addition with multiplication
• Thinking private key is a point
• Believing private key can't generate public key

5. Why might ECC be preferred over RSA for securing mobile devices?

hard

A. RSA is faster and more efficient on mobile devices

B. ECC uses smaller keys for similar security, saving battery and space

C. ECC keys are easier to guess than RSA keys

D. ECC does not require a private key

Solution

1. Step 1: Compare key sizes and efficiency

   ECC achieves strong security with smaller keys compared to RSA, which helps reduce processing power and battery use on mobiles.

2. Step 2: Evaluate other options

   ECC keys are not easier to guess; RSA is generally slower on mobiles; ECC requires private keys like RSA.

3. Final Answer:

   ECC uses smaller keys for similar security, saving battery and space -> Option B

4. Quick Check:

   ECC = smaller keys, better for mobiles [OK]

Hint: Smaller keys mean less power use on mobiles [OK]

Common Mistakes:

• Thinking ECC keys are weaker
• Assuming RSA is faster on mobiles
• Believing ECC doesn't use private keys
• Ignoring battery and space constraints