We give an example of the ELGamal Cryptosystem implemented in GF(3) using x + 2x? + 1 as the irreducible polynomial. We can associate the 26 letters of the alphabet with the 26 nonzero field elements, and thus encrypt ordinary text. The associations are given on below. Suppose Bob uses the polynomial r as the generator (g in the notes) and uses 11 as the random power (x in the notes, and a in the slides). Show how Bob will decrypt the following string of ciphertext: (K,H) (P,X) (N, K) (H,R) (T,F) (V,Y) (E,H)(F,A) (T,W) (J,D) (U,J) I would advise writing a small program for this. Although it might be quicker to do by hand, it would be quite tedious. Also writing a program will help you understand how to implement the Galois Field operations. A 1 2 1+ x? 2+ x? J 1+ 2x? 2 + 2x2 S K T x + x? M 1+x + x? 2 + x + x? 2x + x? C L U x + 2x? 2 D 1+x 1+x + 2x? W 2+x + 2.x? V E 2+ x N F 2x 1+ 2x + x? Q 2+ 2x +x? 2x + 2x? 1+ 2x + 2x2 2 + 2x + 2x2 G 1+ 2x Y H 2+ 2x I R 2x2