I'm taking a course in Cryptography, and I came across this question:
Let Alice and Bob use Hill Cipher to encrypt the message $m$ as $km$ for $k\in \mathbb{Z}^*_{41}$. Let $G=\mathbb{Z}^*_{83}$ and $5$ be the generator of $G$. Alic and Bob generate a shared key as $g^{ab}=52$. Find the decryption of cipher text $9$. Also, find the value of $a,b,g^a,g^b$.
Now, I know that this shared key is created using the Diffe-Hellman Key Exchange Protocol. This is all the information I have. This chapter only talks about the Massey-Omura Cryptosystem and the ElGamal Cryptosystem. I'm not sure if the information given in the question is enough to find the required quantities. Also, I'm not sure if and how the shared key is being used in this encryption. Please guide me on how to proceed with this. This is not a homework or exam problem. Thanks.