a. [5 points] Given p=23, q=7, and e=5, generate the public key (n,e) and the private key (n,d) using RSA Key generation algorithm.
b. (5 points) Given Bob's public key of (85, 7) and private key of (85, 55), show how Alice can encrypt m=10 to send to Bob. Show the ciphertext.
c. (5 points) Given Bob's public key of (85, 7) and private key of (85, 55), show how Bob can decrypt the ciphertetx y=8 received from Alice. Show the plaintext.
d. [5 points] Using the fast exponentiation method (page 182), determine $3^{25} \mod 37$. Show your work.