step by step all 2 and 3

2) (a) Find a primitive root mod 181 (b) Determine if 5 is a primitive root mod 21163 (which is prime) (c) Show that there are no primitive roots mod 30. ( 3) Alice wants to send Bob a secret message using an ElGamal scheme . (a) Bob announces his public key is (m 83, a5,b 78). You are sure Bob picked one of his three favorite numbers (7, 11, and 42) as his secret exponent e. Which one did he pick? (b) Alice sends Bob the encrypted message (c 45, d 79). What was her plaintext message? 2) (a) Find a primitive root mod 181 (b) Determine if 5 is a primitive root mod 21163 (which is prime) (c) Show that there are no primitive roots mod 30. ( 3) Alice wants to send Bob a secret message using an ElGamal scheme . (a) Bob announces his public key is (m 83, a5,b 78). You are sure Bob picked one of his three favorite numbers (7, 11, and 42) as his secret exponent e. Which one did he pick? (b) Alice sends Bob the encrypted message (c 45, d 79). What was her plaintext message