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 language | English (US) |
|---|---|
| Title of host publication | Advances in Cryptology, EUROCRYPT 2013 - 32nd Annual International Conference on the Theory and Applications of Cryptographic Techniques, Proceedings |
| Pages | 35-54 |
| Number of pages | 20 |
| Volume | 7881 LNCS |
| DOIs | |
| State | Published - 2013 |
| Event | 32nd Annual International Conference on the Theory and Applications of Cryptographic Techniques, EUROCRYPT 2013 - Athens, Greece Duration: May 26 2013 → May 30 2013 |
Publication series
| Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
|---|---|
| Volume | 7881 LNCS |
| ISSN (Print) | 03029743 |
| ISSN (Electronic) | 16113349 |
Other
| Other | 32nd Annual International Conference on the Theory and Applications of Cryptographic Techniques, EUROCRYPT 2013 |
|---|---|
| Country | Greece |
| City | Athens |
| Period | 5/26/13 → 5/30/13 |
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ASJC Scopus subject areas
- Computer Science(all)
- Theoretical Computer Science
Cite this
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 proceeding › Conference contribution
}
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 -