Asymmetric encryption (RSA) in Computer Networks - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to identify the key used for encryption in RSA.

Computer Networks

encrypted_message = encrypt(message, [1])

Drag options to blanks, or click blank then click option'

Apublic_key

Bprivate_key

Cshared_key

Dsession_key

Attempts:

3 left

💡 Hint

Common Mistakes

Confusing the private key with the public key for encryption.

Thinking that a shared or session key is used in RSA encryption.

In RSA, the public key is used to encrypt messages so that only the holder of the private key can decrypt them.

2fill in blank

medium

Complete the code to identify the key used for decryption in RSA.

Computer Networks

decrypted_message = decrypt(encrypted_message, [1])

Drag options to blanks, or click blank then click option'

Asession_key

Bpublic_key

Cprivate_key

Dshared_key

Attempts:

3 left

💡 Hint

Common Mistakes

Using the public key for decryption instead of the private key.

Confusing shared or session keys with RSA keys.

In RSA, the private key is used to decrypt messages that were encrypted with the public key.

3fill in blank

hard

Fix the error in the RSA key generation code by selecting the correct prime number.

Computer Networks

p = [1]  # First prime number for RSA key generation

Drag options to blanks, or click blank then click option'

A17

B15

C21

D20

Attempts:

3 left

💡 Hint

Common Mistakes

Choosing a composite number instead of a prime number.

Not verifying the primality of the number before using it.

RSA requires prime numbers for key generation. Among the options, 17 is a prime number, while 15, 20, and 21 are not.

4fill in blank

hard

Fill both blanks to complete the RSA public key generation formula.

Computer Networks

public_key = ([1], [2])  # (e, [2])

Drag options to blanks, or click blank then click option'

Ae

Bn

Cd

Dp

Attempts:

3 left

💡 Hint

Common Mistakes

Confusing the private exponent 'd' with the public exponent 'e'.

Using prime numbers directly instead of the modulus 'n'.

The RSA public key consists of e (the public exponent) and n (the modulus).

5fill in blank

hard

Fill all three blanks to complete the RSA decryption formula.

Computer Networks

decrypted_message = ([1] ** [2]) % [3]

Drag options to blanks, or click blank then click option'

Aencrypted_message

Bd

Cn

De

Attempts:

3 left

💡 Hint

Common Mistakes

Using the public exponent 'e' instead of the private exponent 'd' for decryption.

Forgetting to use the modulus operation.

RSA decryption uses the formula: message = (encrypted_message ^ d) mod n, where d is the private key exponent and n is the modulus.

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