Problem 2. Suppose (Gen, Enc, Dec) is a PKE scheme which supports encryptions of one-bit messages. Prove that the following bit-by-bit encryption is a PKE scheme (Gen,Enc,Dec) which supports encryptions of two-bit messages. This extends naturally also to longer messages, but you do not have to show this. Gen(): Draw and output (pk, sk) Gen(). Enc(msg, pk): Parse msg = msg(1) msg(2) for msg(1), msg(2) {0, 1}. For i = 1, 2, draw ct(i) Gen(msg(i), pk) and output ct = ct(1) ct(2). Dec(ct, sk): Parse ct = ct(1) ct(2), compute for i = 1, 2, msg(i) = Dec(ct(i), sk) and output msg = msg(1) msg(2).