Asymmetric encryption (RSA) in Computer Networks - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is asymmetric encryption?

Asymmetric encryption uses two different keys: a public key to encrypt data and a private key to decrypt it. This allows secure communication without sharing the private key.

beginner

What does RSA stand for in RSA encryption?

RSA stands for Rivest, Shamir, and Adleman, the three scientists who invented this encryption method in 1977.

intermediate

How does RSA encryption ensure security?

RSA relies on the difficulty of factoring large numbers into primes. The public key is based on a large number, and only the private key can decrypt messages because it knows the prime factors.

beginner

What are the two keys used in RSA encryption called?

The two keys are called the public key (shared openly) and the private key (kept secret). The public key encrypts data, and the private key decrypts it.

beginner

Why is RSA important for secure internet communication?

RSA allows people to send private messages over the internet without sharing secret keys beforehand. It helps protect passwords, credit card info, and other sensitive data.

What key is used to encrypt data in RSA?

A Private key

B Public key

C Secret key

D Symmetric key

In RSA, the public key is used to encrypt data, while the private key is used to decrypt it.

What makes RSA encryption secure?

A Encrypting with the private key only

B Using very short keys

C Factoring large numbers is hard

D Sharing private keys openly

RSA's security depends on the difficulty of factoring large numbers into primes.

Who invented RSA encryption?

A Rivest, Shamir, and Adleman

B Newton, Einstein, and Tesla

C Turing, Shannon, and Hopper

D Bell, Morse, and Marconi

RSA is named after its inventors: Rivest, Shamir, and Adleman.

Which key must be kept secret in RSA?

A Private key

B Public key

C Encryption key

D Session key

The private key must be kept secret to ensure only the owner can decrypt messages.

What is a common use of RSA encryption?

A Speeding up internet

B Compressing files

C Creating graphics

D Protecting online passwords

RSA is widely used to protect sensitive data like passwords during online communication.

Explain how RSA encryption uses two keys to secure communication.

Think about how you can send a locked message that only one person can open.

Describe why factoring large numbers is important for RSA security.

Consider why breaking RSA is hard for computers.

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