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 contribution

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 (US)
Title of host publicationProceedings - 2016 IEEE International Conference on Software Science, Technology and Engineering, SwSTE 2016
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages17-27
Number of pages11
ISBN (Electronic)9781509010189
DOIs
StatePublished - Jul 18 2016
Event2016 IEEE International Conference on Software Science, Technology and Engineering, SwSTE 2016 - Beer Sheva, Israel
Duration: Jun 23 2016Jun 24 2016

Publication series

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

Other

Other2016 IEEE International Conference on Software Science, Technology and Engineering, SwSTE 2016
CountryIsrael
CityBeer Sheva
Period6/23/166/24/16

All Science Journal Classification (ASJC) codes

  • Modeling and Simulation
  • Software

Keywords

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

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  • Cite this

    Goldfeld, Z., Cuff, P., & Permuter, H. H. (2016). Semantic-Security Capacity for the Physical Layer via Information Theory. In Proceedings - 2016 IEEE International Conference on Software Science, Technology and Engineering, SwSTE 2016 (pp. 17-27). [7515406] (Proceedings - 2016 IEEE International Conference on Software Science, Technology and Engineering, SwSTE 2016). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/SWSTE.2016.12