NDLI: On Ideal Lattices and Learning with Errors over Rings

Content Provider	ACM Digital Library
Author	Lyubashevsky, Vadim Peikert, Chris Regev, Oded
Copyright Year	2013
Abstract	The “learning with errors” (LWE) problem is to distinguish random linear equations, which have been perturbed by a small amount of noise, from truly uniform ones. The problem has been shown to be as hard as worst-case lattice problems, and in recent years it has served as the foundation for a plethora of cryptographic applications. Unfortunately, these applications are rather inefficient due to an inherent quadratic overhead in the use of LWE. A main open question was whether LWE and its applications could be made truly efficient by exploiting extra algebraic structure, as was done for lattice-based hash functions (and related primitives). We resolve this question in the affirmative by introducing an algebraic variant of LWE called $\textit{ring-LWE},$ and proving that it too enjoys very strong hardness guarantees. Specifically, we show that the ring-LWE distribution is pseudorandom, assuming that worst-case problems on ideal lattices are hard for polynomial-time quantum algorithms. Applications include the first truly practical lattice-based public-key cryptosystem with an efficient security reduction; moreover, many of the other applications of LWE can be made much more efficient through the use of ring-LWE.
Starting Page	1
Ending Page	35
Page Count	35
File Format	PDF
ISSN	00045411
e-ISSN	1557735X
DOI	10.1145/2535925
Journal	Journal of the ACM (JACM)
Volume Number	60
Issue Number	6
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2013-11-01
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Lattice Average-case hardness Cryptography Public key encryption Quantum computation
Content Type	Text
Resource Type	Article
Subject	Hardware and Architecture Information Systems Control and Systems Engineering Artificial Intelligence Software

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