As for security field of research (excluding cryptography) I can recommend you the following universities that are outside of top-20 or on 20-th place:
UCSB (but their security group is extremely strong and it's very hard into it), Purdue (these guys don't like to give funding for incoming students), WashU, UC Irvine, Stony Brook, UNC, Rice, JHU. All these universities have strong research in the security area and they are stronger that some from top-10 such as MIT, Princeton or Cornell.
Also there are some universities with very low ranking, but with strong security groups. For example UTSA or Northeastern.