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A toolkit for Ring-LWE cryptography

Vadim Lyubashevsky 1 Chris Peikert 2 Oded Regev 3 
1 CASCADE - Construction and Analysis of Systems for Confidentiality and Authenticity of Data and Entities
DI-ENS - Département d'informatique - ENS Paris, Inria Paris-Rocquencourt, CNRS - Centre National de la Recherche Scientifique : UMR 8548
Abstract : Recent advances in lattice cryptography, mainly stemming from the development of ring-based primitives such as ring-LWE, have made it possible to design cryptographic schemes whose efficiency is competitive with that of more traditional number-theoretic ones, along with entirely new applications like fully homomorphic encryption. Unfortunately, realizing the full potential of ring-based cryptography has so far been hindered by a lack of practical algorithms and analytical tools for working in this context. As a result, most previous works have focused on very special classes of rings such as power-of-two cyclotomics, which significantly restricts the possible applications. We bridge this gap by introducing a toolkit of fast, modular algorithms and analytical techniques that can be used in a wide variety of ring-based cryptographic applications, particularly those built around ring-LWE. Our techniques yield applications that work in arbitrary cyclotomic rings, with no loss in their underlying worst-case hardness guarantees, and very little loss in computational efficiency, relative to power-of-two cyclotomics. To demonstrate the toolkit's applicability, we develop two illustrative applications: a public-key cryptosystem and a "somewhat homomorphic" symmetric encryption scheme. Both apply to arbitrary cyclotomics, have tight parameters, and very efficient implementations.
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https://hal.inria.fr/hal-00864284
Contributor : Vadim Lyubashevsky Connect in order to contact the contributor
Submitted on : Friday, September 20, 2013 - 5:05:25 PM
Last modification on : Thursday, March 17, 2022 - 10:08:36 AM

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Vadim Lyubashevsky, Chris Peikert, Oded Regev. A toolkit for Ring-LWE cryptography. EUROCRYPT - 32nd Annual International Conference on the Theory and Applications of Cryptographic Techniques - 2013, May 2013, Athens, Greece. pp.35-54, ⟨10.1007/978-3-642-38348-9_3⟩. ⟨hal-00864284⟩

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