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Evaluating 2-dnf formulas on ciphertexts (2005)
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| Venue: | In proceedings of TCC ’05, LNCS series |
| Citations: | 229 - 7 self |
BibTeX
@INPROCEEDINGS{Boneh05evaluating2-dnf,
author = {Dan Boneh and Eu-jin Goh and Kobbi Nissim},
title = {Evaluating 2-dnf formulas on ciphertexts},
booktitle = {In proceedings of TCC ’05, LNCS series},
year = {2005},
pages = {325--341}
}
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Abstract
Abstract. Let ψ be a 2-DNF formula on boolean variables x1,..., xn ∈ {0, 1}. We present a homomorphic public key encryption scheme that allows the public evaluation of ψ given an encryption of the variables x1,..., xn. In other words, given the encryption of the bits x1,..., xn, anyone can create the encryption of ψ(x1,..., xn). More generally, we can evaluate quadratic multi-variate polynomials on ciphertexts provided the resulting value falls within a small set. We present a number of applications of the system: 1. In a database of size n, the total communication in the basic step of the Kushilevitz-Ostrovsky PIR protocol is reduced from √ n to 3 √ n. 2. An efficient election system based on homomorphic encryption where voters do not need to include non-interactive zero knowledge proofs that their ballots are valid. The election system is proved secure without random oracles but still efficient. 3. A protocol for universally verifiable computation. 1
Keyphrases
2-dnf formula homomorphic encryption knowledge proof public evaluation boolean variable quadratic multi-variate polynomial small set random oracle basic step kushilevitz-ostrovsky pir protocol variable x1 efficient election system verifiable computation homomorphic public key encryption scheme total communication election system bit x1
