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3 - Secure Source Coding

from Part I - Theoretical Foundations

Published online by Cambridge University Press:  28 June 2017

P. Cuff
Affiliation:
Department of Electrical Engineering, Princeton University
C. Schieler
Affiliation:
Lincoln Laboratory, Massachusetts Institute of Technology
Rafael F. Schaefer
Affiliation:
Technische Universität Berlin
Holger Boche
Affiliation:
Technische Universität München
Ashish Khisti
Affiliation:
University of Toronto
H. Vincent Poor
Affiliation:
Princeton University, New Jersey
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Summary

This chapter assumes that a limited amount of secret key and reliable communication are available for use in encoding and transmitting a stochastic signal. The chapter starts at the beginning, with a more general proof of Shannon's “key must be as large as the message” result that holds even for stochastic encoders.

Three directions are explored. First, for lossless compression and perfect secrecy, variable length codes or key regeneration allow for a tradeoff between efficiency of compression and efficiency of secret key usage. Second, the relaxation to imperfect secrecy is studied. This is accomplished by measuring the level of secrecy either by applying a distortion metric to the eavesdropper's best possible reconstruction or by considering the eavesdropper's ability to guess the source realization. Finally, an additional relaxation is made to allow the compression of the source to be lossy.

The chapter concludes by showing how the oft-used equivocation metric for information theoretic secrecy is a particular special case of the rate–distortion theory contained herein.

Introduction

Source coding is the process of encoding information signals for transmission through digital channels. Since efficiency is a primary concern in this process, the phrase “source coding” is often used interchangeably with “data compression.” The relationship between source coding and channel coding is that channel coding produces digital resources from natural resources (e.g., a physical medium), and source coding consumes digital resources to accomplish a task involving information, often simply moving it from one point to another.

The channel coding side of information theoretic security is referred to as physical layer security. This usually involves designing a communication system for a physical wiretap channel, introduced by Wyner in [1], which produces a provably secure digital communication link. Another important challenge in physical layer security is the production of a secret key based on common observations, such as channel fading parameters or prepared quantum states. Although a key agreement protocol does not necessarily involve a channel, it is consistent with the spirit of channel coding in that the objective is the production of digital resources.

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Chapter
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Publisher: Cambridge University Press
Print publication year: 2017

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References

[1] A. D., Wyner, “The wire-tap channel,” Bell Syst. Tech. J., vol. 54, pp. 1355–1387, Oct. 1975.Google Scholar
[2] C. E., Shannon, “Communication theory of secrecy systems,” Bell Syst. Tech. J., vol. 28, no. 4, pp. 656–715, Oct. 1949.Google Scholar
[3] Y., Kaspi and N., Merhav, “Zero-delay and causal secure source coding,” IEEE Trans. Inf. Theory, vol. 61, no. 11, pp. 6238–6250, Nov. 2015.Google Scholar
[4] C., Uduwerelle, S.-W., Ho, and T., Chan, “Design of error-free perfect secrecy system by prefix codes and partition codes,” in Proc. IEEE Int. Symp. Inf. Theory, Cambridge, MA, USA, Jul. 2012, pp. 1593–1597.
[5] C. E., Shannon, “A mathematical theory of communication,” Bell Syst. Tech. J., vol. 27, pp. 379–423, 623–656, Jul., Oct. 1948.Google Scholar
[6] C., Schieler and P., Cuff, “Rate-distortion theory for secrecy systems,” IEEE Trans. Inf. Theory, vol. 60, no. 12, pp. 7584–7605, Dec. 2014.Google Scholar
[7] C., Schieler and P., Cuff, “The henchman problem: Measuring secrecy by the minimum distortion in a list,” IEEE Trans. Inf. Theory, vol. 62, no. 6, pp. 3436–3450, Jun. 2016.Google Scholar
[8] N., Merhav and E., Arikan, “The Shannon cipher system with a guessing wiretapper,” IEEE Trans. Inf. Theory, vol. 45, no. 6, pp. 1860–1866, Sep. 1999.Google Scholar
[9] E., Arıkan, “An inequality on guessing and its application to sequential decoding,” IEEE Trans. Inf. Theory, vol. 42, no. 1, pp. 99–105, Jan. 1996.Google Scholar
[10] N., Merhav, “A large-deviations notion of perfect secrecy,” IEEE Trans. Inf. Theory, vol. 49, no. 2, pp. 506–508, Feb. 2003.Google Scholar
[11] T. A., Courtade and T., Weissman, “Multiterminal source coding under logarithmic loss,” IEEE Trans. Inf. Theory, vol. 60, no. 1, pp. 740–761, Jan. 2014.Google Scholar
[12] E. C., Song, P., Cuff and H. V., Poor, “The Likelihood Encoder for Lossy Compression,” in IEEE Trans. Inf. Theory, vol. 62, no. 4, pp. 1836–1849, April 2016.Google Scholar

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  • Secure Source Coding
    • By P. Cuff, Department of Electrical Engineering, Princeton University, C. Schieler, Lincoln Laboratory, Massachusetts Institute of Technology
  • Edited by Rafael F. Schaefer, Technische Universität Berlin, Holger Boche, Technische Universität München, Ashish Khisti, University of Toronto, H. Vincent Poor, Princeton University, New Jersey
  • Book: Information Theoretic Security and Privacy of Information Systems
  • Online publication: 28 June 2017
  • Chapter DOI: https://doi.org/10.1017/9781316450840.004
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  • Secure Source Coding
    • By P. Cuff, Department of Electrical Engineering, Princeton University, C. Schieler, Lincoln Laboratory, Massachusetts Institute of Technology
  • Edited by Rafael F. Schaefer, Technische Universität Berlin, Holger Boche, Technische Universität München, Ashish Khisti, University of Toronto, H. Vincent Poor, Princeton University, New Jersey
  • Book: Information Theoretic Security and Privacy of Information Systems
  • Online publication: 28 June 2017
  • Chapter DOI: https://doi.org/10.1017/9781316450840.004
Available formats
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Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Secure Source Coding
    • By P. Cuff, Department of Electrical Engineering, Princeton University, C. Schieler, Lincoln Laboratory, Massachusetts Institute of Technology
  • Edited by Rafael F. Schaefer, Technische Universität Berlin, Holger Boche, Technische Universität München, Ashish Khisti, University of Toronto, H. Vincent Poor, Princeton University, New Jersey
  • Book: Information Theoretic Security and Privacy of Information Systems
  • Online publication: 28 June 2017
  • Chapter DOI: https://doi.org/10.1017/9781316450840.004
Available formats
×