## Abstract

Let ψ be a 2-DNF formula on boolean variables x_{1},...,x _{n} ∈ {0,1}. We present a homomorphic public key encryption scheme that allows the public evaluation of ψ given an encryption of the variables x_{1},...,x_{n}. In other words, given the encryption of the bits x_{1},...,x_{n}, anyone can create the encryption of ψ(x_{1},...,x_{n}). 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.

Original language | English |
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Pages (from-to) | 325-341 |

Number of pages | 17 |

Journal | Lecture Notes in Computer Science |

Volume | 3378 |

DOIs | |

State | Published - 1 Jan 2005 |

Event | Second Theory of Cryptography Conference, TCC 2005 - Cambridge, MA, United States Duration: 10 Feb 2005 → 12 Feb 2005 |

## ASJC Scopus subject areas

- Theoretical Computer Science
- General Computer Science