  We study the fundamental limits to secret key generation from an excited
distributed source (EDS). In an EDS a pair of terminals observe dependent
sources of randomness excited by a pre-arranged signal. We first determine the
secret key capacity for such systems with one-way public messaging. We then
characterize a tradeoff between the secret key rate and exponential bounds on
the probability of key agreement failure and on the secrecy of the key
generated. We find that there is a fundamental tradeoff between reliability and
secrecy.
  We then explore this framework within the context of reciprocal wireless
channels. In this setting, the users transmit pre-arranged excitation signals
to each other. When the fading is Rayleigh, the observations of the users are
jointly Gaussian sources. We show that an on-off excitation signal with an
SNR-dependent duty cycle achieves the secret key capacity of this system.
Furthermore, we characterize a fundamental metric -- minimum energy per key bit
for reliable key generation -- and show that in contrast to conventional AWGN
channels, there is a non-zero threshold SNR that achieves the minimum energy
per key bit. The capacity achieving on-off excitation signal achieves the
minimum energy per key bit at any SNR below the threshold. Finally, we build
off our error exponent results to investigate the energy required to generate a
key using a finite block length. Again we find that on-off excitation signals
yield an improvement when compared to constant excitation signals. In addition
to Rayleigh fading, we analyze the performance of a system based on binary
channel phase quantization.
