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International Conference on Communications

Secret-key capacity of infinite compound sources with communication rate constraint

Nima Tavangaran, Holger Boche, Rafael F. Schaefer

Published May 1, 2017• 1 citation
Publisher

Abstract

For secret-key generation by using a compound source, the actual statistics of the source are unknown to the participants. It is assumed that the probability distribution of the source belongs to a set which is known to the participants. The secret-key generation protocol should guarantee in this case the reliability and security of the generated secret-key simultaneously for all possible source statistics which belong to this set. At the same time, the communication rate between the legitimate users should not exceed a given communication rate parameter. In this work, this problem is studied for the case where the set of source states is arbitrary (possibly infinite) and the set of marginals (transmitter's states) is finite. The secret-key capacity is completely characterized as a function of the forward communication rate parameter between the legitimate users.

DOI
10.1109/icc.2017.7996617

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For secret-key generation by using a compound source, the actual statistics of the source are unknown to the participants. It is assumed that the probability distribution of the source belongs to a set which is known to the participants. The secret-key generation protocol should guarantee in this case the reliability and security of the generated secret-key simultaneously for all possible source statistics which belong to this set. At the same time, the communication rate between the legitimate users should not exceed a given communication rate parameter. In this work, this problem is studied for the case where the set of source states is arbitrary (possibly infinite) and the set of marginals (transmitter's states) is finite. The secret-key capacity is completely characterized as a function of the forward communication rate parameter between the legitimate users.
In secret-key generation using a compound source, the actual statistics of the source are unknown to the participants. It is assumed rather that the actual source belongs to a set (compound set) which is known to the participants. The secret-key generation protocol should guarantee in this case reliability and security of the generated secret-key simultaneously for all elements of the compound set. In this paper, secret-key generation based on a three-party compound source is studied in which an eavesdropper's side information is also taken into account and strong secrecy is guaranteed. At the same time, the public communication rate constraint between the legitimate users is part of the secret-key generation protocol. In this setting, the achievable secret-key rates for finite compound sources are first reformulated as a region of secret-key rate versus communication rate constraint pairs. It is shown that this region is in general convex, even if the compound set is infinite. Based on this, the secret-key capacity results are extended to be valid for arbitrary (possibly infinite) compound sources with a finite set of marginals. In this case, the secret-key capacity is completely characterized as a function of the forward communication rate parameter between the legitimate users.
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.
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.
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.
This paper investigates the secret key generation from multiple cooperative sources. We assume that the public communication between the legitimate users has unlimited capacity. In this case, the secret key rate is the upper bound of a practical system with limited public communication. The random signals from the multiple helpers can help to create correlated Gaussian sources for the legitimate users to generate secret key, and only local channel state information (CSI) is needed by the helpers to cooperate with others. The power allocation between the helpers is studied with a total transmit power constraint, which results in a non-convex optimization problem. A high efficiency sub-optimal solution is proposed. And even when the legitimate users have no idea about the eavesdropper, the scheme still can help the system to achieve fairly good performance.
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.