Question 1. Find integer x such that 3*x = 1 (mod 23). Question 2 Using Fermat's theorem to compute 3(139) mod 11. Question 3 Compute the Euler Totient function of 200, i.e., (200). Question 4 Compute the Euler Totient function of 720, i.e., o(720). Question 5 Compute @ (45); Compute 748 mod 45 using Euler's Theorem. Question 6 Let Zn* = {x| 1==x = n-1, where GCD(x, n)=1 }. Z20* =7 Question 7 Consider the RSA algorithm. Let the two prime numbers, p=7 and g=5. You need to derive appropriate public key (e,n) and private key (d,n). (a) Can we pick e=3? If yes, what will be the corresponding (d,n)? (b) Can we pick e=5? If yes, what will be the corresponding (d,n)? (c) Use e=5, how to encrypt the number 3? What is the encrypted value? Question 8 Question for Graduate Students) Is PU=(7, 77) and PR=(43,77) a valid RSA public key and private key pair? Show your work