2. Alice is using the one-time pad encryption scheme described in class (and in the book). Her message space, ciphertext space and keyspace are all {0,1}3 (that is, 3 bits long). She samples her key at random and finds that it is 000. After encrypting her message, she sees that the ciphertext is the same as the plaintext! This seems problematic to her, so she re-samples the key, effectively changing the key distribution. (a) Prove that the resulting encryption scheme, with a key chosen uniformly from {0,1}3 \ {000), is not perfectly secret. (That is, show that the requirement stated in the definition of perfect secrecy is not met.) (b) Intuitively, why is it OK to use key 000 for the one-time pad? 2. Alice is using the one-time pad encryption scheme described in class (and in the book). Her message space, ciphertext space and keyspace are all {0,1}3 (that is, 3 bits long). She samples her key at random and finds that it is 000. After encrypting her message, she sees that the ciphertext is the same as the plaintext! This seems problematic to her, so she re-samples the key, effectively changing the key distribution. (a) Prove that the resulting encryption scheme, with a key chosen uniformly from {0,1}3 \ {000), is not perfectly secret. (That is, show that the requirement stated in the definition of perfect secrecy is not met.) (b) Intuitively, why is it OK to use key 000 for the one-time pad