Alice and Bob were two cryptographers tasked with establishing a secure communication channel across an unsafe network using the DiffieHellman key exchange protocol. They employ the prime number p: $97$ and the Generator number $$:$2.$ The private keys in question are Bob's private key b: $27$ and Alice's private key a: $13.$ Calculate their common secret key.

Also, justify why Diffie$-$Hellman key exchange is more secure than traditional methods of key exchange

please solve it correctly with detailed explanation