Problem 1: Two-Time Pad? Alice is sure that One-Time Pad would work just fine for messages that are longer than the key. To convince everyone else in her class, Alice decides to come up with her own "clever" ways of re-using a single key k of size n bits to encrypt messages of size 2n bits. Alice comes up with three different ways (lI denotes concatenation) . c = Enc(k,Tn)= me(kollkollkilkII Ilk-Ilk-1), where ki is the the i-th b it of k (i.e., each bit of k is duplicated in place) . c = Enc(k, m) = (mL k)!! (mlekmR), where m1 denotes the leftmost n bits of m and mR the rightmost n bits in m (i.e., m mLlmR). For each item, show how Eve can obtain some function of the plaintext message m by looking just at ciphertext c? (Assume that Eve knows the encryption algorithms, but not k) NOTE: Any bit mi of the plaintext m is a function of m mimj, where mi and mj are two distinc toi min m, is a function of m. Problem 1: Two-Time Pad? Alice is sure that One-Time Pad would work just fine for messages that are longer than the key. To convince everyone else in her class, Alice decides to come up with her own "clever" ways of re-using a single key k of size n bits to encrypt messages of size 2n bits. Alice comes up with three different ways (lI denotes concatenation) . c = Enc(k,Tn)= me(kollkollkilkII Ilk-Ilk-1), where ki is the the i-th b it of k (i.e., each bit of k is duplicated in place) . c = Enc(k, m) = (mL k)!! (mlekmR), where m1 denotes the leftmost n bits of m and mR the rightmost n bits in m (i.e., m mLlmR). For each item, show how Eve can obtain some function of the plaintext message m by looking just at ciphertext c? (Assume that Eve knows the encryption algorithms, but not k) NOTE: Any bit mi of the plaintext m is a function of m mimj, where mi and mj are two distinc toi min m, is a function of m