Secret Key Generation From Correlated Sources

Nima Tavangaran, Holger Boche, Rafael F. Schaefer

In the classical Secret-Key generation model, Common Randomness is generated by two terminals based on the observation of correlated components of a common source, while keeping it secret from a non-legitimate observer. It is assumed that the statistics of the source are known to all participants. In this work, the Secret-Key generation model based on a compound source is studied where the source realization is unknown. The protocol should guarantee the security and reliability of the generated Secret-Key, simultaneously for all possible realizations of the compound source. A single-letter lower-bound of the Secret-Key capacity is derived for the case where the public communication rate is limited. Furthermore, a multi-letter capacity formula is computed for the case where the public communication is unconstrained.

Onur Günlü

Wenwen Tu, Lifeng Lai

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.

Jun Muramatsu

van Me Marten Dijk

Nima Tavangaran

In the classical secret-key generation model, common randomness is generated by two terminals based on the observation of correlated components of a common source, while keeping it secret from a non-legitimate observer. It is assumed that the statistics of the source are known to all participants. In this paper, the secret-key generation based on a compound source is studied where the realization of the source statistic is unknown. The protocol should guarantee the security and reliability of the generated secret-key, simultaneously for all possible realizations of the compound source. A single-letter lower-bound of the secret-key capacity for a finite compound source is derived as a function of the public communication rate constraint. A multi-letter capacity formula is further computed for a finite compound source for the case in which the public communication is unconstrained. Finally, a single-letter capacity formula is derived for a degraded compound source with an arbitrary (possibly infinite) set of source states and a finite set of marginal states.