On zero-testable homomorphic encryption and publicly verifiable non-interactive arguments

Omer Paneth, Guy N. Rothblum

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

We define and study zero-testable homomorphic encryption (ZTHE) – a semantically secure, somewhat homomorphic encryption scheme equipped with a weak zero test that can identify trivial zeros. These are ciphertexts that result from homomorphically evaluating an arithmetic circuit computing the zero polynomial over the integers. This is a relaxation of the (strong) zero test provided by the notion of graded encodings, which identifies all encodings of zero. We show that ZTHE can suffice for powerful applications. Based on any ZTHE scheme that satisfies the additional properties of correctness on adversarial ciphertexts and multi-key homomorphism, we construct publicly verifiable non-interactive arguments for delegating computation. Such arguments were previously constructed from indistinguishability obfuscation or based on so-called knowledge assumptions. The arguments we construct are adaptively sound, based on an efficiently falsifiable assumption, and only make black-box use of the underlying cryptographic primitives. We also show that a ZTHE scheme that is sufficient for our application can be constructed based on an efficiently-falsifiable assumption over so-called “clean” graded encodings.

Original languageEnglish
Title of host publicationTheory of Cryptography - 15th International Conference, TCC 2017, Proceedings
EditorsYael Kalai, Leonid Reyzin
PublisherSpringer Verlag
Pages283-315
Number of pages33
ISBN (Print)9783319705026
DOIs
StatePublished - 2017
Externally publishedYes
Event15th International Conference on Theory of Cryptography, TCC 2017 - Baltimore, United States
Duration: 12 Nov 201715 Nov 2017

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10678 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference15th International Conference on Theory of Cryptography, TCC 2017
Country/TerritoryUnited States
CityBaltimore
Period12/11/1715/11/17

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