Semantic-Security Capacity for the Physical Layer via Information Theory

Ziv Goldfeld, Paul Cuff, Haim H. Permuter

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

2 Scopus citations

Abstract

Physical layer security can ensure secure communication over noisy channels in the presence of an eavesdropper with unlimited computational power. We adopt an information theoretic variant of semantic-security (SS) (a cryptographic gold standard), as our secrecy metric and study the open problem of the type II wiretap channel (WTC II) with a noisy main channel is, whose secrecy-capacity is unknown even under looser metrics than SS. Herein the secrecy-capacity is derived and shown to be equal to its SS capacity. In this setting, the legitimate users communicate via a discrete-memory less (DM) channel in the presence of an eavesdropper that has perfect access to a subset of its choosing of the transmitted symbols, constrained to a fixed fraction of the block length. The secrecy criterion is achieved simultaneously for all possible eavesdropper subset choices. On top of that, SS requires negligible mutual information between the message and the eavesdropper's observations even when maximized over all message distributions. A key tool for the achievability proof is a novel and stronger version of Wyner's soft covering lemma. Specifically, the lemma shows that a random codebook achieves the soft-covering phenomenon with high probability. The probability of failure is doubly-exponentially small in the block length. Since the combined number of messages and subsets grows only exponentially with the block length, SS for the WTC II is established by using the union bound and invoking the stronger soft-covering lemma. The direct proof shows that rates up to the weak-secrecy capacity of the classic WTC with a DM erasure channel (EC) to the eavesdropper are achievable. The converse follows by establishing the capacity of this DM wiretap EC as an upper bound for the WTC II. From a broader perspective, the stronger soft-covering lemma constitutes a tool for showing the existence of codebooks that satisfy exponentially many constraints, a beneficial ability for many other applications in information theoretic security.

Original languageEnglish
Title of host publicationProceedings - 2016 IEEE International Conference on Software Science, Technology and Engineering, SwSTE 2016
PublisherInstitute of Electrical and Electronics Engineers
Pages17-27
Number of pages11
ISBN (Electronic)9781509010189
DOIs
StatePublished - 18 Jul 2016
Event2016 IEEE International Conference on Software Science, Technology and Engineering, SwSTE 2016 - Beer Sheva, Israel
Duration: 23 Jun 201624 Jun 2016

Publication series

NameProceedings - 2016 IEEE International Conference on Software Science, Technology and Engineering, SwSTE 2016

Conference

Conference2016 IEEE International Conference on Software Science, Technology and Engineering, SwSTE 2016
Country/TerritoryIsrael
CityBeer Sheva
Period23/06/1624/06/16

Keywords

  • Erasure wiretap channel
  • information theoretic security
  • physical-layer security
  • semantic-security
  • soft-covering lemma
  • wiretap channel of type II
  • wiretap codes

ASJC Scopus subject areas

  • Modeling and Simulation
  • Software

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