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dc.contributor.authorBrakerski, Zvika
dc.contributor.authorVaikuntanathan, Vinod
dc.date.accessioned2018-05-18T13:31:11Z
dc.date.available2018-05-18T13:31:11Z
dc.date.issued2014-04
dc.date.submitted2012-03
dc.identifier.issn0097-5397
dc.identifier.issn1095-7111
dc.identifier.urihttp://hdl.handle.net/1721.1/115488
dc.description.abstractA fully homomorphic encryption (FHE) scheme allows anyone to transform an encryption of a message, m, into an encryption of any (efficient) function of that message, f(m), without knowing the secret key. We present a leveled FHE scheme that is based solely on the (standard) learning with errors (LWE) assumption. (Leveled FHE schemes are initialized with a bound on the maximal evaluation depth. However, this restriction can be removed by assuming “weak circular security.”) Applying known results on LWE, the security of our scheme is based on the worst-case hardness of “short vector problems” on arbitrary lattices. Our construction improves on previous works in two aspects: 1. We show that “somewhat homomorphic” encryption can be based on LWE, using a new relinearization technique. In contrast, all previous schemes relied on complexity assumptions related to ideals in various rings. 2. We deviate from the “squashing paradigm” used in all previous works. We introduce a new dimension-modulus reduction technique, which shortens the ciphertexts and reduces the decryption complexity of our scheme, without introducing additional assumptions. Our scheme has very short ciphertexts, and we therefore use it to construct an asymptotically efficient LWE-based single-server private information retrieval (PIR) protocol. The communication complexity of our protocol (in the public-key model) is k·polylog(k)+log |DB| bits per single-bit query, in order to achieve security against 2k-time adversaries (based on the best known attacks against our underlying assumptions). Key words. cryptology, public-key encryption, fully homomorphic encryption, learning with errors, private information retrievalen_US
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)en_US
dc.relation.isversionofhttp://dx.doi.org/10.1137/120868669en_US
dc.rightsArticle is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.en_US
dc.sourceSIAMen_US
dc.titleEfficient Fully Homomorphic Encryption from (Standard) LWEen_US
dc.typeArticleen_US
dc.identifier.citationBrakerski, Zvika, and Vinod Vaikuntanathan. “Efficient Fully Homomorphic Encryption from (Standard) LWE.” SIAM Journal on Computing, vol. 43, no. 2, Jan. 2014, pp. 831–71. © The Authorsen_US
dc.contributor.departmentMassachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratoryen_US
dc.contributor.departmentMassachusetts Institute of Technology. Department of Electrical Engineering and Computer Scienceen_US
dc.contributor.mitauthorVaikuntanathan, Vinod
dc.relation.journalSIAM Journal on Computingen_US
dc.eprint.versionFinal published versionen_US
dc.type.urihttp://purl.org/eprint/type/JournalArticleen_US
eprint.statushttp://purl.org/eprint/status/PeerRevieweden_US
dc.date.updated2018-05-10T16:45:09Z
dspace.orderedauthorsBrakerski, Zvika; Vaikuntanathan, Vinoden_US
dspace.embargo.termsNen_US
dc.identifier.orcidhttps://orcid.org/0000-0002-2666-0045
mit.licensePUBLISHER_POLICYen_US


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