$4\mathrm{.}11$ A message authentication code can be produced by using a block cipher in CFB mode instead of CBC mode. Given a sequence of plaintext blocks, x$\_(1)$cdotsx$\_($n$),$ suppose we define the initialization vector IV to be x$\_(1).$ Then encrypt the sequence

x$\_(2)$cdotsx$\_($n$)$ using key K in CFB mode, obtaining the ciphertext sequence y$\_(1)$cdotsy$\_($n$-1)$n$-1$ ciphertext blockse$\_($K$)($y$\_($n$-1)).$ Prove that this MAC is identical to CBC$-$MAC, which was presented

in Section $4\mathrm{.}4\mathrm{.}2.$