Question $4$: Difife$-$Hellman Key Exchange $(25$ points$)$

a$.$ For Difie$-$Hallman key exchange algorithm, explain the assumptions under which Itis secure$.($spoints$)$

b$.$ Whout the assumptions mentioned in quastion $($o$),$ will it be winerable to a certain kind of athack? What is this attack? Describe it in dotall. $(10$ points$)$

c$.$ During the key exchange, the sender and recolver can calculate the final shared key. Please prove that the calculated shared keys K of the sender and receiver are the same. $(10$ points$)$

Question $5$: Message Authentication $(15$ points$)$

Wo assuma user A intends to send a mossage to muliplo reciptonts, B$,$ through $B_n.$ Whllo maintaining socurily is not a priority; onsuring integity ts cructal. This means that reciplonts By to Bn must havo coniddonca that the massage thay recelvo oigigatas from user A To achlove this, user A opts to employ a Massaga Amthenteation Codo $($MAC$)$

Assume all parties $($ A and $B_1$ to $B_n)$ share a secret koy $R_{.\text{U}\text{s}\text{e}\text{r}}^A$ is using the secret key $k$ to