| \paragraph{Problem 3 (18 points)} | |
| Let us briefly recall the Diffie-Hellman key exchange: Alice and Bob want to establish a shared secret key. Alice has a secret $x$ and sends Bob $g^x$, Bob has a secret $y$ and sends Alice $g^y$. At the end, their shared secret is $g^{xy}$. | |
| This question asks you to give a formal definition of a secure key exchange (not just for the Diffie-Hellman key exchange, but for secure key exchange schemes in general). | |
| Please provide the syntax and the requirements of correctness and security. | |
| Your definition does not have to be equivalent to ``the'' standard definition of a key exchange protocol. Any definition that captures any reasonable security of key exchange is acceptable (you are welcome to add a few sentences explaining why your definition captures some reasonable security of a key exchange protocol). | |