There exists a message authentication code such that its tag does not

provide secrecy$.$

Particularly, you need to describe $(1)$ a secure message authentication

code KeyGen$(),$Tag$(),$ Verify$().(2)$ An adversary$$s strategy in the semantic

security game of encryption: he provides m$0,$ m$1$ and gets C $=$ Tag$($mb$)$

where b is a uniform bit from $\{0,1\}.$ From the ciphertext C$,$ adversary is

going to send another bit b

$$ and wins if b $=$ b

$$

$.$ Your adversary should be

able to win with probability better than $0\mathrm{.}5,$ significantly.