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Compressed Sensing and Security

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Compressed Sensing for Privacy-Preserving Data Processing

Part of the book series: SpringerBriefs in Electrical and Computer Engineering ((BRIEFSSIGNAL))

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Abstract

In this chapter we briefly review the Compressed Sensing (CS) framework, discussing the acquisition model, the conditions under which the signal can be recovered, and the main reconstruction algorithms. Then, we show how CS is essentially analogous to a private key cryptosystem if signal acquisition, signal recovery, and sensing matrix generation are interpreted as encryption, decryption, and key generation functions respectively. The basic security properties of this CS cryptosystem under different attack scenarios are discussed according to standard security definitions. This sets the basis for the identification of the attack scenarios that will be analyzed more in depth in Chap. 3. In the second part of this chapter, we introduce the concept of signal embeddings, which can be seen as a generalization of CS measurements. The properties of some of the most common embeddings are briefly reviewed, followed by a discussion on how embeddings can provide privacy-preserving functionalities in particular settings.

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Notes

  1. 1.

    Exact reconstruction is possible if \({\mathbf {x}}\) is k-sparse, as described earlier in this section.

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Authors and Affiliations

  1. Department of Electronics and Telecommunications, Politecnico di Torino, Turin, Italy

    Matteo Testa, Diego Valsesia, Tiziano Bianchi & Enrico Magli

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  1. Matteo Testa
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  2. Diego Valsesia
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  3. Tiziano Bianchi
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  4. Enrico Magli
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Correspondence to Enrico Magli .

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Testa, M., Valsesia, D., Bianchi, T., Magli, E. (2019). Compressed Sensing and Security. In: Compressed Sensing for Privacy-Preserving Data Processing. SpringerBriefs in Electrical and Computer Engineering(). Springer, Singapore. https://doi.org/10.1007/978-981-13-2279-2_2

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  • DOI: https://doi.org/10.1007/978-981-13-2279-2_2

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