A toolkit for ring-LWE cryptography

Vadim Lyubashevsky, Chris Peikert, Oded Regev

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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.

Original languageEnglish (US)
Title of host publicationAdvances in Cryptology, EUROCRYPT 2013 - 32nd Annual International Conference on the Theory and Applications of Cryptographic Techniques, Proceedings
Pages35-54
Number of pages20
Volume7881 LNCS
DOIs
StatePublished - 2013
Event32nd Annual International Conference on the Theory and Applications of Cryptographic Techniques, EUROCRYPT 2013 - Athens, Greece
Duration: May 26 2013May 30 2013

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7881 LNCS
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other32nd Annual International Conference on the Theory and Applications of Cryptographic Techniques, EUROCRYPT 2013
CountryGreece
CityAthens
Period5/26/135/30/13

Fingerprint

Cryptography
Cyclotomic
Ring
Computational efficiency
Homomorphic Encryption
Public-key Cryptosystem
Homomorphic
Arbitrary
Hardness
Efficient Implementation
Computational Efficiency
Encryption
Demonstrate

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Lyubashevsky, V., Peikert, C., & Regev, O. (2013). A toolkit for ring-LWE cryptography. In Advances in Cryptology, EUROCRYPT 2013 - 32nd Annual International Conference on the Theory and Applications of Cryptographic Techniques, Proceedings (Vol. 7881 LNCS, pp. 35-54). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7881 LNCS). https://doi.org/10.1007/978-3-642-38348-9_3

A toolkit for ring-LWE cryptography. / Lyubashevsky, Vadim; Peikert, Chris; Regev, Oded.

Advances in Cryptology, EUROCRYPT 2013 - 32nd Annual International Conference on the Theory and Applications of Cryptographic Techniques, Proceedings. Vol. 7881 LNCS 2013. p. 35-54 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7881 LNCS).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Lyubashevsky, V, Peikert, C & Regev, O 2013, A toolkit for ring-LWE cryptography. in Advances in Cryptology, EUROCRYPT 2013 - 32nd Annual International Conference on the Theory and Applications of Cryptographic Techniques, Proceedings. vol. 7881 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 7881 LNCS, pp. 35-54, 32nd Annual International Conference on the Theory and Applications of Cryptographic Techniques, EUROCRYPT 2013, Athens, Greece, 5/26/13. https://doi.org/10.1007/978-3-642-38348-9_3
Lyubashevsky V, Peikert C, Regev O. A toolkit for ring-LWE cryptography. In Advances in Cryptology, EUROCRYPT 2013 - 32nd Annual International Conference on the Theory and Applications of Cryptographic Techniques, Proceedings. Vol. 7881 LNCS. 2013. p. 35-54. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-642-38348-9_3
Lyubashevsky, Vadim ; Peikert, Chris ; Regev, Oded. / A toolkit for ring-LWE cryptography. Advances in Cryptology, EUROCRYPT 2013 - 32nd Annual International Conference on the Theory and Applications of Cryptographic Techniques, Proceedings. Vol. 7881 LNCS 2013. pp. 35-54 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
@inproceedings{aee5cc4fd2a7418abd1b7cfa43573eb4,
title = "A toolkit for ring-LWE cryptography",
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.",
author = "Vadim Lyubashevsky and Chris Peikert and Oded Regev",
year = "2013",
doi = "10.1007/978-3-642-38348-9_3",
language = "English (US)",
isbn = "9783642383472",
volume = "7881 LNCS",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
pages = "35--54",
booktitle = "Advances in Cryptology, EUROCRYPT 2013 - 32nd Annual International Conference on the Theory and Applications of Cryptographic Techniques, Proceedings",

}

TY - GEN

T1 - A toolkit for ring-LWE cryptography

AU - Lyubashevsky, Vadim

AU - Peikert, Chris

AU - Regev, Oded

PY - 2013

Y1 - 2013

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84883318384&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84883318384&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-38348-9_3

DO - 10.1007/978-3-642-38348-9_3

M3 - Conference contribution

AN - SCOPUS:84883318384

SN - 9783642383472

VL - 7881 LNCS

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 35

EP - 54

BT - Advances in Cryptology, EUROCRYPT 2013 - 32nd Annual International Conference on the Theory and Applications of Cryptographic Techniques, Proceedings

ER -