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Secret-Key Generation Using Compound Sources and One-Way Public Communication

Nima Tavangaran

Published Feb 1, 2018• 22 citations
Publisher

Abstract

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.

DOI
10.1109/tifs.2016.2611484

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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.
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.
We investigate the problem of generating common randomness (CR) from a finite compound source aided by unidirectional communication over a rate-limited perfect channel. The two communicating parties observe independent and identically distributed (i.i.d.) samples of a finite compound source and aim to agree on a common random variable with high probability for every possible state. Both parties know the set of source states as well as their statistics. However, they don’t know the actual state. We establish a single-letter formula for the compound CR capacity in the presence of communication over the channel and study key properties of the compound CR capacity: superadditivity, concavity, and continuity. We also consider the case where there is no communication between the terminals, and only the source outputs observed by the terminal at the receiving end of the perfect channel are state-dependent. In this setting, we establish single-letter bounds on the compound CR capacity. The single-letter lower bound is derived under the assumption that the source distributions are pairwise distinct for all states. Finally, within the same setting, we propose a CR generation scheme for a two-state binary source example. Notably, this scheme does not depend on the previously mentioned assumption.
Secret key generation at two terminals is considered. Each terminal observes one of the outputs of a two component source. The two source outputs are correlated. Additionally one terminal can send a message to the second terminal via a noiseless public channel. It is assumed that this message is rate constrained. An eavesdropper with access to the public communication should be kept ignorant of the secret key. The maximum secret key rate that can be achieved such that the key is uniformly distributed and meets the perfect secrecy requirement is determined. This result is established for a compound source model.