yas been chosen? 8.18. We investigate the weaknesses that arise in Elgamal encryption if a public key of small order is used. We look at the following example. Assume Bob uses the group Zo with the primitive element α = 2. His public key is ẞ = 28. 1. What is the order of the public key? 2. Which masking keys kм are possible? 3. Alice encrypts a text message. Every character is encoded according to the simple rule a→ 0,..., Z→ 25. There are three additional ciphertext symbols: ä→ 26, ö-27, ü→ 28. She transmits the following 11 ciphertexts (KE,y): (3, 15), (19, 14), (6, 15), (1,24), (22, 13), (4,7), (13,24), (3,21), (18, 12), (26,5), (7,12) Decrypt the message without computing Bob's private key. Just look at the ci- phertext and use the fact that there are only very few masking keys and a bit of guesswork.