Adding noise is not going to help much. You can just run the test many times and you can use statistics. The only thing helping is deterministic noise: For ever

Adding noise is not going to help much. You can just run the test many times and you can use statistics. The only thing helping is deterministic noise: For every security-related thing, you have a deterministic delay. That way you can not apply statistics. Unfortunately that won't work here, at least I don't know how it could.