Please show work.

4. ECC El Gamal. In order to communicate securely, Alice and Bob use the ElGamal cryptosystem with the elliptic curve E : y2-13 + 162 + 14(mod 29) and the point P = (7, 11). (a.) (3 points) Alice chooses the secret key NA 4. Compute her public keyQ NAP (b.) (5 points) Bob wants to send the message M (12,7) to Alice using Alices public points that Bob sends to Alice. c.) (5 points) Eve also wants to communicate with Alice. She uses the public key QE to encode her message and sends Alice the pair Yi = (8,25) and Y2 = (8,4). Decrypt Eves message. 4. ECC El Gamal. In order to communicate securely, Alice and Bob use the ElGamal cryptosystem with the elliptic curve E : y2-13 + 162 + 14(mod 29) and the point P = (7, 11). (a.) (3 points) Alice chooses the secret key NA 4. Compute her public keyQ NAP (b.) (5 points) Bob wants to send the message M (12,7) to Alice using Alices public points that Bob sends to Alice. c.) (5 points) Eve also wants to communicate with Alice. She uses the public key QE to encode her message and sends Alice the pair Yi = (8,25) and Y2 = (8,4). Decrypt Eves message