- Ex. 5 in Supplemental material
- Ex. 7 in Supplemental material
- Ex.2.8
- Ex.2.9
*Extra Credit: Ex.2.10*- Ex. 3.24 (a: assigned, b:
*extra credit*) - Solve the following equalities (or prove that there is no solution):

*Note: "=" is used here in place of the 3-bar "congruence" symbol**15x + 21 = 2 (mod 31)**15x + 21 = 2 (mod 33)**15x + 21 = 3 (mod 33)**15x + 21 = 2 (mod 31)***AND***15x + 21 = 3 (mod 33)*[that is x must satisfy both]*2x+3 = 4 (mod 5)***AND***4x+3=2 (mod 7)***AND***8x+9=10 (mod 11)*

compute RSA public and private keys using the primes 11 and 13, and write Encrypt and Decrypt algorithms for it.*RSA:*- You can pick any
*e,d.*Test your result by encrypting and then decrypting 1, 2, 3, 5, 10, 100. - It is customary to fix
*e*to be something small and always the same, e.g., 3 or 5. What would be the corresponding*d*for each of these values of*e*? Can you use*e=4*? How about*e=7*? - Now, what would the public and secret key be if you use primes 101 and 113
instead?

Use the smallest possible value of*e*.

- You can pick any