On the Optimality of Secret Key Agreement via Omniscience

Chung Chan; Manuj Mukherjee; Navin Kashyap; Qiaoqiao Zhou

doi:10.1109/TIT.2018.2802546

On the Optimality of Secret Key Agreement via Omniscience

Chung Chan, Manuj Mukherjee, Navin Kashyap, Qiaoqiao Zhou

Research output: Contribution to journal › Article › peer-review

15 Scopus citations

Abstract

For the multiterminal secret key agreement problem under a private source model, it is known that the maximum key rate, i.e., the secrecy capacity, can be achieved through communication for omniscience, but the omniscience strategy can be strictly suboptimal in terms of minimizing the public discussion rate. While a single-letter characterization is not known for the minimum discussion rate needed for achieving the secrecy capacity, we derive single-letter lower bounds that yield some simple conditions for omniscience to be discussion-rate optimal. These conditions turn out to be enough to deduce the optimality of omniscience for a large class of sources, including the hypergraphical sources. We also extend our results to more general class of multiterminal sources with helpers and silent users.

Original language	English
Pages (from-to)	2371-2389
Number of pages	19
Journal	IEEE Transactions on Information Theory
Volume	64
Issue number	4
DOIs	https://doi.org/10.1109/TIT.2018.2802546
State	Published - Apr 2018
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2017 IEEE.

Funding

Manuscript received February 23, 2017; revised January 4, 2018; accepted January 27, 2018. Date of publication February 5, 2018; date of current version March 15, 2018. C. Chan was supported by the University Grants Committee of the Hong Kong Special Administrative Region, China, under Project 14200714. Q. Zhou was supported by the University Grants Committee of Hong Kong Special Administrative Region, China, under Project AoE/E-02/08. N. Kashyap was supported by the Swarnajayanti Fellowship through the Department of Science and Technology, Government of India. This paper was presented in part at the 2016 IEEE International Symposium on Information Theory and the 2016 IEEE Information Theory Workshop.

Funders	Funder number
University Grants Committee of Hong Kong Special Administrative Region	AoE/E-02/08
University Grants Committee	14200714
Department of Science and Technology, Government of Kerala

Keywords

Gács-Körner common information
Secret key agreement
Wyner common information
multivariate mutual information
omniscience

Access to Document

10.1109/TIT.2018.2802546

Cite this

@article{16de96b498e446a5be88bb389492299a,

title = "On the Optimality of Secret Key Agreement via Omniscience",

abstract = "For the multiterminal secret key agreement problem under a private source model, it is known that the maximum key rate, i.e., the secrecy capacity, can be achieved through communication for omniscience, but the omniscience strategy can be strictly suboptimal in terms of minimizing the public discussion rate. While a single-letter characterization is not known for the minimum discussion rate needed for achieving the secrecy capacity, we derive single-letter lower bounds that yield some simple conditions for omniscience to be discussion-rate optimal. These conditions turn out to be enough to deduce the optimality of omniscience for a large class of sources, including the hypergraphical sources. We also extend our results to more general class of multiterminal sources with helpers and silent users.",

keywords = "G{\'a}cs-K{\"o}rner common information, Secret key agreement, Wyner common information, multivariate mutual information, omniscience",

author = "Chung Chan and Manuj Mukherjee and Navin Kashyap and Qiaoqiao Zhou",

note = "Publisher Copyright: {\textcopyright} 2017 IEEE.",

year = "2018",

month = apr,

doi = "10.1109/TIT.2018.2802546",

language = "אנגלית",

volume = "64",

pages = "2371--2389",

journal = "IEEE Transactions on Information Theory",

issn = "0018-9448",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

number = "4",

}

TY - JOUR

T1 - On the Optimality of Secret Key Agreement via Omniscience

AU - Chan, Chung

AU - Mukherjee, Manuj

AU - Kashyap, Navin

AU - Zhou, Qiaoqiao

PY - 2018/4

Y1 - 2018/4

N2 - For the multiterminal secret key agreement problem under a private source model, it is known that the maximum key rate, i.e., the secrecy capacity, can be achieved through communication for omniscience, but the omniscience strategy can be strictly suboptimal in terms of minimizing the public discussion rate. While a single-letter characterization is not known for the minimum discussion rate needed for achieving the secrecy capacity, we derive single-letter lower bounds that yield some simple conditions for omniscience to be discussion-rate optimal. These conditions turn out to be enough to deduce the optimality of omniscience for a large class of sources, including the hypergraphical sources. We also extend our results to more general class of multiterminal sources with helpers and silent users.

AB - For the multiterminal secret key agreement problem under a private source model, it is known that the maximum key rate, i.e., the secrecy capacity, can be achieved through communication for omniscience, but the omniscience strategy can be strictly suboptimal in terms of minimizing the public discussion rate. While a single-letter characterization is not known for the minimum discussion rate needed for achieving the secrecy capacity, we derive single-letter lower bounds that yield some simple conditions for omniscience to be discussion-rate optimal. These conditions turn out to be enough to deduce the optimality of omniscience for a large class of sources, including the hypergraphical sources. We also extend our results to more general class of multiterminal sources with helpers and silent users.

KW - Gács-Körner common information

KW - Secret key agreement

KW - Wyner common information

KW - multivariate mutual information

KW - omniscience

UR - http://www.scopus.com/inward/record.url?scp=85041499718&partnerID=8YFLogxK

U2 - 10.1109/TIT.2018.2802546

DO - 10.1109/TIT.2018.2802546

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:85041499718

SN - 0018-9448

VL - 64

SP - 2371

EP - 2389

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

IS - 4

ER -

On the Optimality of Secret Key Agreement via Omniscience

Abstract

Bibliographical note

Funding

Keywords

Access to Document

Other files and links

Fingerprint

Cite this