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Über dieses Buch

The objective of this book is to provide the reader with a comprehensive survey of the topic compressed sensing in information retrieval and signal detection with privacy preserving functionality without compromising the performance of the embedding in terms of accuracy or computational efficiency. The reader is guided in exploring the topic by first establishing a shared knowledge about compressed sensing and how it is used nowadays. Then, clear models and definitions for its use as a cryptosystem and a privacy-preserving embedding are laid down, before tackling state-of-the-art results for both applications. The reader will conclude the book having learned that the current results in terms of security of compressed techniques allow it to be a very promising solution to many practical problems of interest. The book caters to a broad audience among researchers, scientists, or engineers with very diverse backgrounds, having interests in security, cryptography and privacy in information retrieval systems. Accompanying software is made available on the authors’ website to reproduce the experiments and techniques presented in the book. The only background required to the reader is a good knowledge of linear algebra, probability and information theory.

Inhaltsverzeichnis

Frontmatter

Chapter 1. Introduction

Abstract
Information processing systems have been revolutionized by recent advances in several technological areas, like device miniaturization, wireless transmission, network infrastructure. Traditional information sources have been replaced by a multitude of devices with sensing capabilities, the so-called Internet of Things (IoT), including smart home devices, cars with autonomous driving functions, portable medical devices. Meanwhile, single processing and storage units have been replaced by cloud services, leading to interconnected systems that share and process huge amount of data. While this provides endless opportunities to tackle different societal needs, it poses several problems regarding the security and privacy of the involved data. This chapter introduces the challenges and the techniques discussed in the literature to address them and serves as an overview of the book.
Matteo Testa, Diego Valsesia, Tiziano Bianchi, Enrico Magli

Chapter 2. Compressed Sensing and Security

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.
Matteo Testa, Diego Valsesia, Tiziano Bianchi, Enrico Magli

Chapter 3. Compressed Sensing as a Cryptosystem

Abstract
This chapter presents the most relevant results on Compressed Sensing (CS) used as a cryptosystem. First, we analyze the statistical properties of CS measurements, showing that they always convey at least the energy of the sensed signal. Then, we discuss the secrecy achievable by different sensing matrix constructions. For sensing matrices made of Gaussian i.i.d. entries, we have the highest secrecy guarantees, where only the energy of the signal can be revealed. This particular case is analyzed by introducing a secrecy metric that depends on the ability to estimate the signal energy by an adversary who observes only the signal measurements. The secrecy achievable by generic sensing matrices is analyzed by introducing a distinguishability metric inspired by the standard statistical secrecy definition used in cryptography. Results are provided for matrices made of i.i.d entries with generic distributions and circulant matrices. At the end of the chapter, we discuss several issues connected with the practical implementation of a CS cryptosystem, including sensing matrix generation and quantization of sensing matrix entries.
Matteo Testa, Diego Valsesia, Tiziano Bianchi, Enrico Magli

Chapter 4. Privacy-Preserving Embeddings

Abstract
In this chapter, we illustrate main results on privacy-preserving embeddings. Here, security properties of embeddings are analyzed by considering two possible scenarios for their use. In the first case, a client submits a query containing sensitive information to a server, which should respond to the query without gaining access to the private information. This is discussed describing an authentication system in which a client submit an embedding of a physical characteristic of a device, and a verification server is able to match the embedding without revealing the actual physical characteristic. Interestingly, in this case the security properties of the embedding permit to combine it with existing biometric template mechanisms, enhancing the security of the system. In the second case, a large amount of sensitive data is stored in the cloud and a user should be able to make specific queries to the cloud without gaining access to the data. Here, we describe a universal embedding that preserves distances only locally. If data are stored in the cloud using this embedding, a user is able to retrieve data close to the query, but the complete geometry of the dataset remains hidden by the embedding and data cannot be recovered.
Matteo Testa, Diego Valsesia, Tiziano Bianchi, Enrico Magli

Chapter 5. Conclusions

Abstract
Compressed sensing has drawn remarkable attention because of its appealing compress-while-sampling property. Nonetheless, its noteworthy properties as privacy-preserving framework are among its lesser known aspects. This book enlightened this latter perspective by summarizing state-of-the-art results of CS as a cryptosystem and CS as a privacy-preserving embedding.
Matteo Testa, Diego Valsesia, Tiziano Bianchi, Enrico Magli
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