Task 1:
In a public-key system using RSA, you intercept the ciphertext C = 13 sent to a user whose public key is e = 23, n = 143. What is the plaintext M? Verify the correctness of your decryption.
Task 2:
Consider a Diffie-Hellman scheme with a common prime q = 11 and a primitive root α =2.
a. show that 2 is a primitive root of 11.
b. If user A has public key YA = 9, what is A's private key XA?
c. If user B has public key YB = 3, what is the shared secret key K?
Task 3:
Given x = 6 mod 13 and x = 2 mod 17, find x.