A Toolkit for Ring-LWE Cryptography

  • Vadim Lyubashevsky
  • Chris Peikert
  • Oded Regev
Conference paper

DOI: 10.1007/978-3-642-38348-9_3

Part of the Lecture Notes in Computer Science book series (LNCS, volume 7881)
Cite this paper as:
Lyubashevsky V., Peikert C., Regev O. (2013) A Toolkit for Ring-LWE Cryptography. In: Johansson T., Nguyen P.Q. (eds) Advances in Cryptology – EUROCRYPT 2013. EUROCRYPT 2013. Lecture Notes in Computer Science, vol 7881. Springer, Berlin, Heidelberg


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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Copyright information

© International Association for Cryptologic Research 2013

Authors and Affiliations

  • Vadim Lyubashevsky
    • 1
  • Chris Peikert
    • 2
  • Oded Regev
    • 3
  1. 1.INRIA and École Normale SupérieureParisFrance
  2. 2.Georgia Institute of TechnologyUSA
  3. 3.Courant InstituteNew York UniversityUSA

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