Mathematics of cryptography...........

Exercise a) Alice and Bob wish to use the ElGamal public key cryptosystem. The prime p = 59 and the element g = 14 are made publicly known. Alice then chooses a private key and presents the public key A = 11. You find the ciphertext

c = (c1,c2) = (31,58). Use Shanks baby step-giant step algorithm to find Alices private key and the corresponding plaintext.

b) Shanks baby step-giant step algorithm takes O(log pp)-steps, which is a big advantage over the naive method. But there is another property of this algorithm that makes it problematic to use when p is large. What?

c) In view of the Pohlig-Hellman algorithm we should avoid certain types of primes when setting up the ElGamal public key cryptosystem. Which?