Asymmetric encryption (RSA) in Computer Networks - Practice Problems & Coding Challenges

Challenge - 5 Problems

🧠 Conceptual

intermediate

How RSA Uses Two Keys

In RSA encryption, what is the main purpose of having a public key and a private key?

A Both keys are used only for encrypting messages, not decrypting.

B Both keys encrypt and decrypt messages interchangeably without restrictions.

C The public key encrypts messages, and only the private key can decrypt them.

D The private key encrypts messages, and the public key decrypts them.

💡 Hint

Think about who should be able to read the message after encryption.

In RSA, the public key is shared openly to encrypt messages. Only the private key, kept secret, can decrypt those messages, ensuring security.

📋 Factual

intermediate

Key Components of RSA

Which two mathematical components are essential in generating RSA keys?

A Two large prime numbers

B Two random integers

C Two even numbers

D Two Fibonacci numbers

💡 Hint

These numbers must be special and hard to factor.

RSA keys are generated using two large prime numbers. Their product forms part of the public key, and their properties ensure security.

🔍 Analysis

advanced

Why RSA Encryption is Secure

Why is it difficult for someone to break RSA encryption without the private key?

A Because the keys change every second automatically.

B Because factoring the product of two large primes is very hard.

C Because the encryption uses simple addition and subtraction.

D Because the private key is shared publicly.

💡 Hint

Focus on the math problem behind the encryption.

The security of RSA relies on the difficulty of factoring a very large number made by multiplying two large primes. Without factoring, the private key cannot be found easily.

❓ Comparison

advanced

Difference Between Symmetric and Asymmetric Encryption

Which statement correctly compares symmetric encryption with RSA asymmetric encryption?

A Symmetric uses one key for both encrypting and decrypting; RSA uses two different keys.

B Symmetric encryption is slower than RSA encryption.

C RSA uses the same key for encryption and decryption, symmetric uses two keys.

D Both symmetric and RSA use two keys but for different purposes.

💡 Hint

Think about how many keys each method uses and their roles.

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

❓ Reasoning

expert

Understanding RSA Key Length Impact

What is the main effect of increasing the key length in RSA encryption?

A It makes encryption faster but reduces security.

B It makes decryption impossible even with the private key.

C It has no effect on security or speed.

D It makes encryption and decryption slower but increases security.

💡 Hint

Longer keys mean more work for computers but better protection.

Longer RSA keys increase the difficulty of breaking the encryption, improving security. However, they require more computing power, slowing down encryption and decryption.

Practice

1. What is the main purpose of the private key in RSA asymmetric encryption?

easy

A. To share with anyone for secure communication

B. To encrypt messages for everyone to read

C. To decrypt messages encrypted with the public key

D. To generate the public key

Solution

1. Step 1: Understand RSA key roles

   In RSA, the public key encrypts data, and the private key decrypts it.

2. Step 2: Identify private key function

   The private key is kept secret and used to decrypt messages encrypted by the public key.

3. Final Answer:

   To decrypt messages encrypted with the public key -> Option C

4. Quick Check:

   Private key = decrypt [OK]

Hint: Private key always decrypts what public key encrypts [OK]

Common Mistakes:

• Confusing encryption and decryption roles
• Thinking private key is shared publicly
• Assuming private key encrypts messages

2. Which of the following is the correct way to describe RSA keys?

easy

A. Both keys are identical and interchangeable

B. Public key encrypts, private key decrypts

C. Private key is public, public key is private

D. Keys are randomly generated but not related

Solution

1. Step 1: Recall RSA key relationship

   RSA uses a pair of keys where the public key encrypts and the private key decrypts.

2. Step 2: Evaluate options

   Only Public key encrypts, private key decrypts correctly states the roles of the keys in RSA encryption.

3. Final Answer:

   Public key encrypts, private key decrypts -> Option B

4. Quick Check:

   Public encrypt, private decrypt [OK]

Hint: Public encrypts, private decrypts in RSA [OK]

Common Mistakes:

• Thinking keys are the same
• Mixing up public and private key roles
• Believing keys are unrelated

3. Consider this simplified RSA scenario:
Public key: (e=3, n=33)
Private key: (d=7, n=33)
Message m = 4
What is the encrypted message c using c = m^e mod n?

medium

A. 31

B. 12

C. 16

D. 4

Solution

1. Step 1: Calculate encryption formula

   Compute c = 4^3 mod 33 = 64 mod 33.

2. Step 2: Find remainder

   64 divided by 33 leaves remainder 64 - 33*1 = 31, so 64 mod 33 = 31.

3. Step 3: Re-check calculation

   Actually, 4^3 = 64, 64 mod 33 = 31, so c = 31.

4. Final Answer:

   31 -> Option A

5. Quick Check:

   4^3 mod 33 = 31 [OK]

Hint: Calculate power then mod for encryption [OK]

Common Mistakes:

• Forgetting to apply modulo
• Calculating power incorrectly
• Mixing up encryption and decryption formulas

4. In an RSA implementation, a developer wrote:
c = (m ** d) % n
to encrypt a message. Why is this incorrect?

medium

A. Because d is the private key exponent used for decryption, not encryption

B. Because m should be raised to e for decryption

C. Because modulo n should not be used in RSA

D. Because exponentiation operator ** is invalid in Python

Solution

1. Step 1: Understand RSA key usage

   Encryption uses the public exponent e, decryption uses private exponent d.

2. Step 2: Identify error in code

   The code uses d to encrypt, which is incorrect; it should use e.

3. Final Answer:

   Because d is the private key exponent used for decryption, not encryption -> Option A

4. Quick Check:

   Encrypt with e, decrypt with d [OK]

Hint: Encrypt with e, decrypt with d [OK]

Common Mistakes:

• Using private key exponent for encryption
• Confusing exponentiation operator validity
• Ignoring modulo operation necessity

5. A company wants to use RSA to securely send a 128-bit message. Which of the following is the best practice to ensure security and efficiency?

hard

A. Encrypt the entire 128-bit message directly with RSA public key

B. Share the private key with the recipient to speed up encryption

C. Use the private key to encrypt the message and public key to decrypt

D. Use RSA to encrypt a symmetric key, then use that key to encrypt the message

Solution

1. Step 1: Understand RSA limitations

   RSA is slow and inefficient for large data encryption like 128-bit messages directly.

2. Step 2: Identify best practice

   Common practice is to encrypt a symmetric key with RSA, then use that key for fast message encryption.

3. Final Answer:

   Use RSA to encrypt a symmetric key, then use that key to encrypt the message -> Option D

4. Quick Check:

   Hybrid encryption = RSA + symmetric key [OK]

Hint: Encrypt keys with RSA, data with symmetric cipher [OK]

Common Mistakes:

• Encrypting large data directly with RSA
• Sharing private key publicly
• Reversing encryption/decryption key roles