Week 14

Question 1

Appreciate that, in practice, public-key encryption is largely used for the encryption of symmetric keys

(Outline how Alice sends a message to Bob using a hybrid approach - 4 steps)

Answer 1

Yes appreciate 🙏

1. Alice encrypts her message with a symmetric encryption scheme, using the key k to produce ciphertext c
2. Bob provides Alice with his public encryption key, e, and public param, n, so she can encrypt k using the RSA encryption scheme, producing ciphertext k^e (mod n)
3. Once Bob receives c and k^e (mod n), he can use his private decryption key d to find **(k^e)^d≡ k (mod n) **
4. k is the symmetric scheme key, so Bob can then decrypt c with it and recover the message

Question 2

Define the One-Way goal for attacking a public-key encryption scheme

Question 3

Give an informal definition of semantic security of a public-key encryption scheme

Question 4

Define a chosen plaintext attack on a public-key encryption scheme

Question 5

Define a chosen ciphertext attack on a public-key encryption scheme

Question 6

Appreciate that RSA is One-Way secure against chosen plaintext attacks provided that the RSA problem is difficult to solve

Question 7

Prove that RSA is not One-Way secure against chosen ciphertext attacks

Question 8

Demonstrate how to compute the Jacobi symbol of a of a message m modulo an RSA modulus n, given only n, e and m^e (mod n)

Question 9

Describe why a Fermat Prime makes a convenient choice for an RSA encryption key