Curriculum: Logical/Formal Methods in Security
I suggest familiarizing the students with the following logics:


Epistemic logic: Used to model the knowledge of various parties participating in the protocol, and prove that an adversary cannot gain knowledge of some secret.
BAN logic: An old logic for proving various properties of authentication protocols. (Other belief logics are appropriate as well.)
Logics for transition systems: This includes logics like LTL, CTL, and LTL*. (such logics act on Kripke-like models of the protocol.)
Process Algebras: Several process algebras, like Spi-calculus (or CSP, and its security-related tool, Casper) are useful for modeling security protocols.
Introducing tools like AVISPA of NuSMV are very useful.
I also suggest Formal Correctness of Security Protocols as one of the course textbooks.


A friend of mine, Morteza Amini, has recently got his Ph.D. on modeling access control with logic. He devised a new logic, named $MA(DL)^2$, which stands for "multi-authority deontic logic and description logic." As the name suggests, it combines two non-classical logics (deontic logic + description logic) to decide whether an entity has access to an object. If you like, I can encourage him to provide more information.