  Many security protocols rely on the assumptions on the physical properties in
which its protocol sessions will be carried out. For instance, Distance
Bounding Protocols take into account the round trip time of messages and the
transmission velocity to infer an upper bound of the distance between two
agents. We classify such security protocols as Cyber-Physical. Time plays a key
role in design and analysis of many of these protocols. This paper investigates
the foundational differences and the impacts on the analysis when using models
with discrete time and models with dense time. We show that there are attacks
that can be found by models using dense time, but not when using discrete time.
We illustrate this with a novel attack that can be carried out on most Distance
Bounding Protocols. In this attack, one exploits the execution delay of
instructions during one clock cycle to convince a verifier that he is in a
location different from his actual position. We additionally present a
probabilistic analysis of this novel attack. As a formal model for representing
and analyzing Cyber-Physical properties, we propose a Multiset Rewriting model
with dense time suitable for specifying cyber-physical security protocols. We
introduce Circle-Configurations and show that they can be used to symbolically
solve the reachability problem for our model, and show that for the important
class of balanced theories the reachability problem is PSPACE-complete. We also
show how our model can be implemented using the computational rewriting tool
Maude, the machinery that automatically searches for such attacks.
