Achieving SK capacity in the source model: When must all terminals talk?

Mukherjee, Manuj; Kashyap, Navin; Sankarasubramaniam, Yogesh

doi:10.1109/isit.2014.6875014

Cited by 15 publications

(30 citation statements)

References 11 publications

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“…The finest optimal partition is unique and, in general, is different from the principal partition of random variables in [40]. The divergence expression and the optimal partitions are useful in the study of other related problems such as the data clustering algorithm in [28], [44], and [45], the data exchange problem in [26] and [27], the strong converse proof of secret-key agreement in [29], and the omnivocality in [30]. h APPENDIX A…”

Section: Discussionmentioning

confidence: 99%

“…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: 90%

“…The tightness result will also be derived from a more general result of Fujishige [32] on cointersecting submodular functions (Appendix B). In Appendix C, we will demonstrate how the informationtheoretic properties derived in this work can be applied to the problem of omnivocality and resolve a conjecture in [30]. 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.…”

Section: Motivation From Secret-key Agreementmentioning

confidence: 96%

“…The tightness result can be used in related information-theoretic problems. It is used in the work of Tyagi and Narayan [29] in simplying the proof of the strong converse of the secret-key agreement problem, and in the work of Mukherjee et al [30] in deriving a sufficient condition for omnivocality, i.e., the case when every user must speak in public to attain the secrecy capacity. It is also used in [26] to devise the divideand-conquer solution for the communication for omniscience.…”

Section: Motivation From Secret-key Agreementmentioning

confidence: 99%

“…In this section, we not only want to show that the MMI (4.1) is a natural extension of Shannon's mutual information to the multivariate case, but we will also derive meaningful interpretations and properties of the MMI and the optimal partitions. The properties are useful for data clustering [44], [45] and other related problems such as the problem of omnivocality [30] described in Appendix C.…”

Section: Interpretations and Propertiesmentioning

confidence: 99%

See 4 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: Discussionmentioning

confidence: 99%

Section: Motivation From Secret-key Agreementmentioning

confidence: 90%

Section: Motivation From Secret-key Agreementmentioning

confidence: 96%

Section: Motivation From Secret-key Agreementmentioning

confidence: 99%

Section: Interpretations and Propertiesmentioning

confidence: 99%

See 3 more Smart Citations

Multivariate Mutual Information Inspired by Secret-Key Agreement

Chan¹,

Al-Bashabsheh²,

Ebrahimi³

et al. 2015

Proc. IEEE

179

View full text Add to dashboard Cite

show abstract

Secret key capacity: Talk or keep silent?

Zhang

Liang

Lai

2015

2015 IEEE International Symposium on Information Theory (ISIT)

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The communication complexity of achieving SK capacity in a class of PIN models

Mukherjee

Kashyap

2015

2015 IEEE International Symposium on Information Theory (ISIT)

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The communication complexity of achieving secret key (SK) capacity in the multiterminal source model of Csiszár and Narayan is the minimum rate of public communication required to generate a maximal-rate SK. It is well known that the minimum rate of communication for omniscience, denoted by R CO , is an upper bound on the communication complexity, denoted by R SK . A source model for which this upper bound is tight is called R SK -maximal. In this paper, we establish a sufficient condition for R SK -maximality within the class of pairwise independent network (PIN) models defined on hypergraphs. This allows us to compute R SK exactly within the class of PIN models satisfying this condition. On the other hand, we also provide a counterexample that shows that our condition does not in general guarantee R SK -maximality for sources beyond PIN models. I. INTRODUCTIONCsiszár and Narayan [6] introduced the problem of secret key (SK) generation within the multiterminal i.i.d. source model. In this model, there are multiple terminals, each of which observes a distinct component of a source of correlated randomness. The goal is for the terminals to agree on a shared SK via communication over an insecure noiseless public channel. The SK is to be secured from passive eavesdroppers with access to the public channel. The maximum rate of such an SK, i.e. the SK capacity, was characterized in [6], and a protocol for attaining SK capacity was given, which involved communication for omniscience, i.e., all terminals recovering the entire information of all the other terminals. However, it was pointed out (see remark following Theorem 1 in [6]) that omniscience is not always necessary for achieving SK capacity. A question that naturally arises is the following (see [6, Section VI] and [12, Section V]): what is the minimum rate of public communication required to achieve SK capacity? We call this minimum rate of public communication the communication complexity 1 of achieving SK capacity, and denote it by R SK . The protocol from [6] shows that R SK is upper bounded by the minimum rate of public communication required for omniscience, denoted by R CO . We refer to sources for which this upper bound is tight as R SK -maximal.There have been a few attempts at characterizing R SK . In [13, Theorem 3] Tyagi has completely characterized the † M. Mukherjee and N. Kashyap are with the 1 Our use of "communication complexity" differs from the use prevalent in the theoretical computer science literature where, following [15], it refers to the total amount of communication, in bits, required to perform some distributed computation. communication complexity for two terminals in terms of an interactive common information, a type of Wyner common information [14]. Our previous work [10] involved extension of Tyagi's results to the case of m > 2 terminals. Specifically, we gave a lower bound [10, Theorem 2] on the communication complexity using a multiterminal variant of Tyagi's interactive common information. We were able to evaluate this lower bou...

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Achieving SK capacity in the source model: When must all terminals talk?

Cited by 15 publications

References 11 publications

Multivariate Mutual Information Inspired by Secret-Key Agreement

Multivariate Mutual Information Inspired by Secret-Key Agreement

Secret key capacity: Talk or keep silent?

The communication complexity of achieving SK capacity in a class of PIN models

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