[Cryptography] Privacy-preserving wireless communication?

[Henry Baker]

[The following discussion is intended to be 100% *theoretical*.
I'm *not* interested in a technical discussion of a particular
protocol -- e.g., Bluetooth -- as the complexity introduced
thereby completely obscures the theoretical issues I'm trying
to understand.]

Suppose I have a device -- e.g., my smartphone -- that wants
to talk *securely* and *privately* to another device -- e.g.,
my car.

I'm willing to go to significant initialization/precomputation
effort (aka "pairing"), in order to make sure that when the
time comes for actual communication/talking between the two
devices:

1.  My smartphone talks *only* with *my* car;
2.  My car talks *only* with *my* smartphone;
3.  No passive observer of the communications between my phone
and my car will reveal any information which will enable later
impersonation of either my phone or my car;
4.  No passive observer of the communications between my phone
and my car will reveal either the identity of my phone or the
identity of my car;
5.  No active observer can do anything other than simply jam
the channel;
6.  Either my phone or my car can decide to terminate the
communication relationship in such a way that only *repairing*
will re-enable the communication.

But here's the real kicker:

7.  From time to time, my phone and my car may not be able to
communicate for an unknown period of time -- e.g., my phone
may have gone out of range, my car may be turned off, passive
or active jamming could make communications impossible, etc.
During the period of non-communication, I don't want the
battery in either my phone or my car to be run down by constant
polling; I don't want any polling by either my phone or my
car to identify my phone or my car; I'd rather not have my
phone or my car even reveal that it IS polling.

Let's assume that my phone and my car might perform the
pairing process via non-wireless means -- e.g., simply
plugging them together via USB -- so that we don't have
to worry about protecting the pairing process itself.

Are there any simple protocols that could achieve these
goals?

I'm particularly interested in what happens during the
period of non-communication: what "messages" are sent
by either device; what does such a "message" look like?
how often are such messages emitted (e.g., Ethernet
backoff protocol ?), etc.