1. One-time pad without the identity element in the key space (10 points). Recall that in the lecture, we defined one-time pad encryption scheme over a group (G ). The encryption algorithm works as follows Encak (m) = m o sk. Let e be the identity element of the group G. One observes that when using the one-time pad key sk = e, the ciphertext is identical to the plaintext because c = Encsk(m) = moe=m. It has been, therefore, suggested to modify the scheme by only encrypting with ske, in other words, to have Gen choose sk uniformly at random from the set of G {e}. Prove that this modified scheme is nol secure. 1. One-time pad without the identity element in the key space (10 points). Recall that in the lecture, we defined one-time pad encryption scheme over a group (G ). The encryption algorithm works as follows Encak (m) = m o sk. Let e be the identity element of the group G. One observes that when using the one-time pad key sk = e, the ciphertext is identical to the plaintext because c = Encsk(m) = moe=m. It has been, therefore, suggested to modify the scheme by only encrypting with ske, in other words, to have Gen choose sk uniformly at random from the set of G {e}. Prove that this modified scheme is nol secure