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The Geometry of Lattice Cryptography

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Foundations of Security Analysis and Design VI (FOSAD 2011)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 6858))

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Abstract

Lattice cryptography is one of the hottest and fastest moving areas in mathematical cryptography today. Interest in lattice cryptography is due to several concurring factors. On the theoretical side, lattice cryptography is supported by strong worst-case/average-case security guarantees. On the practical side, lattice cryptography has been shown to be very versatile, leading to an unprecedented variety of applications, from simple (and efficient) hash functions, to complex and powerful public key cryptographic primitives, culminating with the celebrated recent development of fully homomorphic encryption. Still, one important feature of lattice cryptography is simplicity: most cryptographic operations can be implemented using basic arithmetic on small numbers, and many cryptographic constructions hide an intuitive and appealing geometric interpretation in terms of point lattices. So, unlike other areas of mathematical cryptology even a novice can acquire, with modest effort, a good understanding of not only the potential applications, but also the underlying mathematics of lattice cryptography.

In these notes, we give an introduction to the mathematical theory of lattices, describe the main tools and techniques used in lattice cryptography, and present an overview of the wide range of cryptographic applications. This material should be accessible to anybody with a minimal background in linear algebra and some familiarity with the computational framework of modern cryptography, but no prior knowledge about point lattices.

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  1. UC San Diego, USA

    Daniele Micciancio

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  1. Daniele Micciancio
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  1. Dipartimento di Scienze di Base e Fondamenti, Università degli Studi di Urbino “Carlo Bo”, Piazza della Repubblica 13, 61029, Urbino, Italy

    Alessandro Aldini

  2. Dipartimento di Scienze dell’Informazione, Università degli Studi di Bologna, Mura Anteo Zamboni 7, 40127, Bologna, Italy

    Roberto Gorrieri

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Micciancio, D. (2011). The Geometry of Lattice Cryptography. In: Aldini, A., Gorrieri, R. (eds) Foundations of Security Analysis and Design VI. FOSAD 2011. Lecture Notes in Computer Science, vol 6858. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23082-0_7

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