Alice is going to use an ElGamal public key.

(a) If she announces (p = 13, g = 7, A = 11), find secret key using brute force.

(b) If she announces (p = 101, g = 2, A = 49), find secret key using Shanks Babystep Giant-step Algorithm.

(c) If Eve has a computer that can do 1,000,000,000 multiplications per second, estimate how large should p be to make sure Alices key would take at least one year to break with Shanks Algorithm on Eves computer? Give your answer in number of bits.