Suppose that Alice uses a stream cipher to encrypt plaintext P$,$ obtaining ciphertext C$,$ and Alice then sends C to Bob. Suppose that Trudy

happens to know the plaintext P$,$ but Trudy does not know the key K

that was used in the stream cipher.

a$.$ Show that Trudy can easily determine the keystream that was used

to encrypt P$.$

b$.$ Show that Trudy can, in effect, replace P with plaintext of her

choosing, say, P$\text{'}.$ That is$,$ show that Trudy can create a ciphertext

message C$"$ so that when Bob decrypts C$\text{'}$ he will obtain P$\text{'}.$