On secret key generation from finite source observations

All existing secret key generation schemes assume that the users have access to infinite number of source observations. Motivated by applications in wireless networks, we consider the problem of generating secret keys from a finite number of correlated observations under the source model. We investigate the relationship among the achievable secret key rate, the decoding error probability, and the number of observations. Based on the connection between secret key generation and distributed source coding problems, we present two key generation schemes. In the first scheme, length of the generated key varies depending on the the realization of the source sequence, and the generated key is conditionally perfectly secure. We characterize the penalty, due to the finiteness of the number of observations, in the key rate compared to that of the scheme with infinite number of observations. In the second scheme, length of the generated key is fixed, and the key is unconditionally perfectly secure. We characterize the additional penalty associated with these additional features in the achievable key rate.