Cryptology ePrint Archive: Report 2016/049

Implementing a Toolkit for Ring-LWE Based Cryptography in Arbitrary Cyclotomic Number Fields

Christoph M. Mayer

Abstract: Recent research in the field of lattice-based cryptography, especially on the topic of the ring-based primitive ring-LWE, provided efficient and practical ring-based cryptographic schemes, which can compete with more traditional number-theoretic ones. In the case of ring-LWE these cryptographic schemes operated mainly in power-of-two cyclotomics, which vastly restricted the variety of possible applications. Due to the toolkit for ring-LWE of Lyubashevsky, Peikert and Regev, there are now cryptographic schemes that operate in arbitrary cyclotomics, with no loss in their underlying hardness guarantees, and only little loss computational efficiency. Next to some further refinements and explanations of the theory and additional implementation notes, we provide the - as far as we know - first implementation of the toolkit of Lyubashevsky, Peikert and Regev. This includes a complete framework with fast and modular algorithms that can be used to build cryptographic schemes around ring-LWE. Our framework is easy to use, open source and has only little third party dependencies. For demonstration purposes we implemented two public-key cryptographic schemes using our framework. The complete source code is available at

Category / Keywords: implementation / ring-LWE, lattices, implementation, lattice-based cryptography, algebraic number theory, applications, arbitrary cyclotomic number fields

Date: received 19 Jan 2016, last revised 25 Jan 2016

Contact author: c m mayer at gmx de

Available format(s): PDF | BibTeX Citation

Note: Added citation to Crocketts and Peikerts "LOL" paper. Some minor changes in the introduction.

Version: 20160125:100435 (All versions of this report)

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