TY - GEN

T1 - On zero-testable homomorphic encryption and publicly verifiable non-interactive arguments

AU - Paneth, Omer

AU - Rothblum, Guy N.

N1 - Publisher Copyright:
© 2017, International Association for Cryptologic Research.

PY - 2017

Y1 - 2017

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85033791793&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-70503-3_9

DO - 10.1007/978-3-319-70503-3_9

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AN - SCOPUS:85033791793

SN - 9783319705026

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

SP - 283

EP - 315

BT - Theory of Cryptography - 15th International Conference, TCC 2017, Proceedings

A2 - Kalai, Yael

A2 - Reyzin, Leonid

PB - Springer Verlag

T2 - 15th International Conference on Theory of Cryptography, TCC 2017

Y2 - 12 November 2017 through 15 November 2017

ER -