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Physical and Data-Link Security Techniques for Future Communication Systems pp 145–162Cite as

Security Aspects of Compressed Sensing

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Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 358))

Abstract

In this chapter, we will consider the security achievable by the compressed sensing (CS) framework under different constructions of the sensing matrix. CS can provide a form of data confidentiality when the signals are sensed by a random matrix composed of i.i.d. Gaussian variables. However, alternative constructions, based either on different distribution or on circulant matrices, which have similar CS recovery performance as Gaussian random matrices and admit faster implementations, are more suitable for practical CS systems. Compared to Gaussian matrices, which leak only the energy of the sensed signal, we show that generic matrices leak also some information about the structure of the sensed signal. In order to characterize this information leakage, we propose an operational definition of security linked to the difficulty of distinguishing equal energy signals and we propose practical attacks to test this definition. The results provide interesting insights on the security of generic sensing matrices, showing that a properly randomized partial circulant matrix can provide a weak encryption layer irrespective of the signal sparsity and the sensing domain.

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Notes

  1. 1.

    Actually, since KL divergence is not symmetric, a stricter bound is given as \(\delta (\mathbb {P}_1,\mathbb {P}_2) \le \sqrt{\min \left( D(\mathbb {P}_1||\mathbb {P}_2),D(\mathbb {P}_2||\mathbb {P}_2)\right) /2}\). In the following sections, for the sake of conciseness, we will always consider a single KL divergence. However, experimental results are based on the stricter bound.

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Acknowledgments

The research leading to these results has received funding from the European Research Council under the European Community’s Seventh Framework Programme (FP7/2007-2013) / ERC Grant agreement no. 279848.

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Authors and Affiliations

  1. Politecnico di Torino, Corso Duca Degli Abruzzi 24, 10129, Torino, Italy

    Tiziano Bianchi & Enrico Magli

Authors
  1. Tiziano Bianchi
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  2. Enrico Magli
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Correspondence to Tiziano Bianchi .

Editor information

Editors and Affiliations

  1. Department of Information Engineering, Università Politecnica delle Marche, Ancona, Italy

    Marco Baldi

  2. Department of Information Engineering, University of Padova, Padova, Italy

    Stefano Tomasin

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Bianchi, T., Magli, E. (2016). Security Aspects of Compressed Sensing. In: Baldi, M., Tomasin, S. (eds) Physical and Data-Link Security Techniques for Future Communication Systems. Lecture Notes in Electrical Engineering, vol 358. Springer, Cham. https://doi.org/10.1007/978-3-319-23609-4_9

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  • DOI: https://doi.org/10.1007/978-3-319-23609-4_9

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-23608-7

  • Online ISBN: 978-3-319-23609-4

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