In lattice cryptography there are many parameters. Many, if not all useful theorems require certain bounds on these parameters. Examples for these parameters are the length of some vectors under the L2 norm or the infinity norm, the spectral norm of matrices of certain distributions, or the so-called smoothing parameter.
When instantiating cryptographic schemes based on lattices, one has to decide on values for these parameters, such that security still holds. However, theoretical bounds can often be quite conservative, leading to not-so efficient schemes.
The question now is whether there are heuristics with which one could choose values for the parameters and how much these heuristics could improve the efficiency of the cryptographic schemes.
Your task is to identify interesting parameters, to create and implement heuristic tests for bounds and to compare the heuristics to the theoretical bounds. Afterwards you compare the efficiency of instantiations of some cryptographic schemes based on your heuristics and theoretical bounds.
A Decade of Lattice Cryptography: https://eprint.iacr.org/2015/939.pdf A good starting point to learn about lattices.
Supervisor: Laurens Porzenheim Mail