Reference no: EM133423657

Question: Consider a group of 30 people in a room who wish to be able to establish pairwise secure communications in the future. How many keys need to be exchanged in total: (a) Using symmetric cryptography? (b) Using public key cryptography?

The following question has you use RSA. You may use a program that you write or any other computer program to help you solve this problem.

Let p = 9, 497 and q = 7, 187 and e = 3. •

What is N? What is Φ(N)? •

Verify that e is relatively prime to Φ(N). What method did you use to verify this?

Compute d as the inverse of e mod Φ(N). What is d?

Encrypt the value P = 22446688 with the RSA primitive and the values for N and e above. Let C be the resulting ciphertext. What is C?

Verify that you can decrypt C using d as the private exponent to get back P. What method did you use to verify this?

Decrypt the value C ′ = 11335577 using the RSA primitive and your values for N and d above. Let P ′ be the resulting plaintext. What is P ′ ?

Verify that you can encrypt P ′ using e as the public exponent to get back C ′ . What method did you use to verify this?

Consider a Diffie-Hellman key exchange with p = 29 and g = 2. Suppose that Alice picks x = 3 and Bob picks y = 5. What will each party send to the other, and what shared key will they agree on? Show your details