A Construction of Traceability Set Systems with Polynomial Tracing Algorithm

Elena Egorova, Marcel Fernandez, Grigory Kabatiansky

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

3 Citations (Scopus)

Abstract

A family F of w-subsets of a finite set X is called a set system with the identifiable parent property if for any w-subset contained in the union of some t sets, called traitors, of F at least one of these sets can be uniquely determined, i.e. traced. A set system with traceability property (TSS, for short) allows to trace at least one traitor by minimal distance decoding of the corresponding binary code, and hence the complexity of tracing procedure is of order O(M), where M is the number of users or the code's cardinality. We propose a new construction of TSS which is based on the old Kautz-Singleton concatenated construction with algebraic-geometry codes as the outer code and Guruswami-Sudan decoding algorithm. The resulting codes (set systems) have exponentially many users (codevectors) M and polylog(M) complexity of code construction and decoding, i.e. tracing traitors. This is the first construction of traceability set systems with such properties.

Original languageEnglish
Title of host publication2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages2739-2742
Number of pages4
ISBN (Electronic)9781538692912
DOIs
Publication statusPublished - Jul 2019
Event2019 IEEE International Symposium on Information Theory, ISIT 2019 - Paris, France
Duration: 7 Jul 201912 Jul 2019

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
Volume2019-July
ISSN (Print)2157-8095

Conference

Conference2019 IEEE International Symposium on Information Theory, ISIT 2019
Country/TerritoryFrance
CityParis
Period7/07/1912/07/19

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