Secret key capacity: Talk or keep silent?

Zhang, Huishuai; Liang, Y. T.; Lai, Lifeng

doi:10.1109/isit.2015.7282463

Cited by 12 publications

(14 citation statements)

References 9 publications

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“…4 3 Although the divergence is asymmetric and does not satisfy the triangle inequality, it is positive definite and is used in Pinsker's inequality to upper bound the variational distance. 4 After the submission of our work, we learned of a recent work [33] that also resolves the conjecture in [30]. Zhang et al [33] asked the more refined question of whether a user can keep silent in secret-key agreement without diminishing the capacity.…”

Section: Motivation From Secret-key Agreementmentioning

confidence: 89%

“…4 After the submission of our work, we learned of a recent work [33] that also resolves the conjecture in [30]. Zhang et al [33] asked the more refined question of whether a user can keep silent in secret-key agreement without diminishing the capacity. We note that this question can be answered systematically under the current framework using the general properties derived for the MMI such as Corollary 5.3.…”

Section: Motivation From Secret-key Agreementmentioning

confidence: 89%

“…We note that this question can be answered systematically under the current framework using the general properties derived for the MMI such as Corollary 5.3. In particular, the conjecture in [33] can be resolved in the positive using the data processing inequality in Theorem 5.5, and the achievable secrecy capacity when a user s keeps silent can be characterized meaningfully by the MMI as minfIðZ V Þ; IðZ Vnfsg Þg, which is related intimately to a special case of the successive omniscience problem in [31]. In the language of [31], the capacity can be achieved through any minimal successive omniscience communication by the local group V n fsg.…”

Section: Motivation From Secret-key Agreementmentioning

confidence: 99%

See 2 more Smart Citations

Multivariate Mutual Information Inspired by Secret-Key Agreement

Chan¹,

Al-Bashabsheh²,

Ebrahimi³

et al. 2015

Proc. IEEE

179

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This paper motivates the multiterminal secret-key capacity as a useful measure of multivariate mutual information, develops information-theoretic properties of this measure, and makes comparisons with other existing multivariate correlation measures.ABSTRACT | The capacity for multiterminal secret-key agreement inspires a natural generalization of Shannon's mutual information from two random variables to multiple random variables. Under a general source model without helpers, the capacity is shown to be equal to the normalized divergence from the joint distribution of the random sources to the product of marginal distributions minimized over partitions of the random sources. The mathematical underpinnings are the works on co-intersecting submodular functions and the principle lattices of partitions of the Dilworth truncation. We clarify the connection to these works and enrich them with information-theoretic interpretations and properties that are useful in solving other related problems in information theory as well as machine learning.

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Section: Motivation From Secret-key Agreementmentioning

confidence: 89%

Section: Motivation From Secret-key Agreementmentioning

confidence: 89%

Section: Motivation From Secret-key Agreementmentioning

confidence: 99%

See 1 more Smart Citation

Multivariate Mutual Information Inspired by Secret-Key Agreement

Chan¹,

Al-Bashabsheh²,

Ebrahimi³

et al. 2015

Proc. IEEE

179

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show abstract

“…Unfortunately, a counterexample has been given by Chan et al [12] that shows that the condition is not necessary for four or more terminals [12]. This has also been independently observed by Zhang et al in [13].…”

mentioning

confidence: 86%

On the Public Communication Needed to Achieve SK Capacity in the Multiterminal Source Model

Mukherjee

Kashyap

Sankarasubramaniam

2016

IEEE Trans. Inform. Theory

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The focus of this paper is on the public communication required for generating a maximal-rate secret key (SK) within the multiterminal source model of Csiszár and Narayan. Building on the prior work of Tyagi for the twoterminal scenario, we derive a lower bound on the communication complexity, RSK, defined to be the minimum rate of public communication needed to generate a maximal-rate SK. It is well known that the minimum rate of communication for omniscience, denoted by RCO, is an upper bound on RSK. For the class of pairwise independent network (PIN) models defined on uniform hypergraphs, we show that a certain "Type S" condition, which is verifiable in polynomial time, guarantees that our lower bound on RSK meets the RCO upper bound. Thus, PIN models satisfying our condition are RSK-maximal, meaning that the upper bound RSK ≤ RCO holds with equality. This allows us to explicitly evaluate RSK for such PIN models. We also give several examples of PIN models that satisfy our Type S condition. Finally, we prove that for an arbitrary multiterminal source model, a stricter version of our Type S condition implies that communication from all terminals ("omnivocality") is needed for establishing a SK of maximum rate.For three-terminal source models, the converse is also true: omnivocality is needed for generating a maximal-rate SK only if the strict Type S condition is satisfied. Counterexamples exist that show that the converse is not true in general for source models with four or more terminals.

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“…The theoretical underpinning of the MMI is a mathematical structure called the principal sequence of partitions (PSP) [60]. On the one hand, this structure enables the MMI and the clusters to be computed in strongly polynomial time [59,60] (see also [61]), and adds a new dimension to multi-terminal information theory [54][55][56][57][58][62][63][64][65][66]. On the other hand, the MMI enriches the abstract mathematical structure with informationtheoretic meanings.…”

Section: B Contributionsmentioning

confidence: 99%

Info-Clustering: A Mathematical Theory for Data Clustering

Chan

Al-Bashabsheh

Zhou

et al. 2016

IEEE Trans. Mol. Biol. Multi-Scale Commun.

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Abstract-We formulate an info-clustering paradigm based on a multivariate information measure, called multivariate mutual information, that naturally extends Shannon's mutual information between two random variables to the multivariate case involving more than two random variables. With proper model reductions, we show that the paradigm can be applied to study the human genome and connectome in a more meaningful way than the conventional algorithmic approach. Not only can infoclustering provide justifications and refinements to some existing techniques, but it also inspires new computationally feasible solutions.

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Secret key capacity: Talk or keep silent?

Cited by 12 publications

References 9 publications

Multivariate Mutual Information Inspired by Secret-Key Agreement

Multivariate Mutual Information Inspired by Secret-Key Agreement

On the Public Communication Needed to Achieve SK Capacity in the Multiterminal Source Model

Info-Clustering: A Mathematical Theory for Data Clustering

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