Asymmetric encryption (RSA, ECC) in Cybersecurity - 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 and what is it used for?

RSA stands for Rivest-Shamir-Adleman, the inventors of this encryption method. It is widely used for secure data transmission by encrypting data with a public key and decrypting with a private key.

intermediate

How does ECC differ from RSA?

ECC (Elliptic Curve Cryptography) uses smaller keys than RSA but provides similar security. This makes ECC faster and uses less computing power, ideal for mobile devices.

beginner

Why is the private key kept secret in asymmetric encryption?

The private key is kept secret because it is used to decrypt messages encrypted with the public key. If someone else gets the private key, they can read all encrypted messages.

beginner

What is a real-life example of asymmetric encryption use?

When you visit a secure website (https://), your browser uses asymmetric encryption to safely exchange a secret key with the website. This key then encrypts all data sent between you and the site.

Which key is used to encrypt data in asymmetric encryption?

A No key

B Private key

C Public key

D Both keys

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

What is a main advantage of ECC over RSA?

A Faster and uses less computing power

B Less secure

C Uses larger keys

D Only works on desktops

ECC uses smaller keys and is faster, making it more efficient especially for devices with limited resources.

What happens if someone obtains your private key?

A They can encrypt messages to you

B They can decrypt your encrypted messages

C They can only send emails

D Nothing happens

The private key decrypts messages encrypted with the public key, so if stolen, encrypted data can be read by others.

RSA encryption is named after:

A Rivest, Shamir, and Adleman

B Random Secure Algorithm

C Rapid Security Access

D Reliable Secure Application

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

Which of these is a common use of asymmetric encryption?

A Speeding up internet connection

B Encrypting files on your computer only

C Compressing data

D Securely exchanging keys over the internet

Asymmetric encryption is often used to securely exchange keys that will then be used for faster symmetric encryption.

Explain how asymmetric encryption works using the example of sending a secret message.

Think about how you can send a locked box that only the receiver can open.

Compare RSA and ECC in terms of key size and efficiency.

Consider which method is better for mobile devices.

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