Disclaimer: You should probably talk to your advisor about this rather than the internet since your advisor will be responsable for supporting your project and judging it's results.
Disclaimer2: My answer is probably more appropriate for a Computer Science or Mathematics Major. PulpSpy's answer is more on target for developing an ece portfolio.
The SHA3 cryptographic hash function contest is still ongoing. A fun project would be to choose the hash function of your choice and attempt to break a reduce-round varient.
The SHA3 zoo has a list of the finalists and public research on them.
- Choose one.
- Attempt to break a single round of a finalist of your choice.
- Once successful apply that attack to the function allowing slightly more rounds.
- Rinse/repeat step 3 until the attack n longer works or you break a finalist (unlikely).
In terms of breaking any of the finalists, I would suggest either trying a meet-in-the-middle attack or a differential attack. If your attack isn't working try modifying the hash function to make it less secure. Try to determine what design choices make the hash function resilient to your attacks and what part of the design makes it weak. How can you modify a standard attack to avoid the strong parts of the function? How could you modify the hash function to make it stronger?