Asymmetric encryption (RSA, ECC) in Cybersecurity - Practice Problems & Coding Challenges

Challenge - 5 Problems

🧠 Conceptual

intermediate

How does asymmetric encryption differ from symmetric encryption?

Which statement best explains the key difference between asymmetric and symmetric encryption?

A Asymmetric encryption uses two different keys, while symmetric encryption uses the same key for both encryption and decryption.

B Asymmetric encryption is faster than symmetric encryption because it uses simpler algorithms.

C Asymmetric encryption uses the same key for encryption and decryption, while symmetric encryption uses two different keys.

D Asymmetric encryption does not require keys, while symmetric encryption requires keys.

💡 Hint

Think about how keys are used in each encryption type.

Asymmetric encryption uses a pair of keys: one public and one private. Symmetric encryption uses a single shared key for both encrypting and decrypting data.

📋 Factual

intermediate

Key size comparison between RSA and ECC

Which of the following correctly compares the typical key sizes of RSA and ECC for similar security levels?

A Key size does not affect security in RSA or ECC.

B ECC keys are generally much larger than RSA keys for the same security level.

C RSA and ECC keys are usually the same size for the same security level.

D RSA keys are generally much larger than ECC keys for the same security level.

💡 Hint

Consider which algorithm is known for smaller keys with strong security.

ECC achieves similar security with much smaller key sizes compared to RSA, making RSA keys larger for equivalent security.

🚀 Application

advanced

Choosing encryption for a mobile app

You are designing a mobile app that requires secure communication but has limited processing power and battery life. Which asymmetric encryption method is best suited?

A RSA, because it is widely used and easy to implement.

B Neither RSA nor ECC; symmetric encryption is better for mobile apps.

C ECC, because it provides strong security with smaller keys and less computation.

D Use both RSA and ECC together to maximize security.

💡 Hint

Think about efficiency and resource use on mobile devices.

ECC is preferred for devices with limited resources because it uses smaller keys and requires less processing power than RSA.

🔍 Analysis

advanced

Security risk of private key exposure

What is the main security risk if the private key in an RSA or ECC system is exposed?

A An attacker can decrypt messages meant only for the key owner and can impersonate the owner.

B The public key becomes invalid and cannot be used anymore.

C Only the encrypted messages sent before exposure are at risk, not future messages.

D The encryption algorithm automatically changes keys to prevent risk.

💡 Hint

Consider what the private key controls in asymmetric encryption.

The private key is secret and used to decrypt messages and create digital signatures. Exposure allows attackers to read messages and impersonate the owner.

❓ Reasoning

expert

Why is ECC preferred over RSA in modern cryptography?

Which reason best explains why ECC is increasingly preferred over RSA in modern cryptographic systems?

A ECC is easier to implement correctly than RSA, reducing programming errors.

B ECC offers equivalent security with smaller keys, leading to faster computations and lower power consumption.

C RSA keys are no longer secure against modern attacks, while ECC keys are unbreakable.

D ECC does not require a private key, simplifying key management.

💡 Hint

Think about efficiency and security trade-offs in cryptography.

ECC provides strong security with smaller keys, which means faster processing and less power use, making it ideal for modern devices and applications.

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