## Abstract

We put forward a new notion, function privacy, in identity-based encryption and, more generally, in functional encryption. Intuitively, our notion asks that decryption keys reveal essentially no information on their corresponding identities, beyond the absolute minimum necessary. This is motivated by the need for providing predicate privacy in public-key searchable encryption. Formalizing such a notion, however, is not straightforward as given a decryption key it is always possible to learn some information on its corresponding identity by testing whether it correctly decrypts ciphertexts that are encrypted for specific identities. In light of such an inherent difficulty, any meaningful notion of function privacy must be based on the minimal assumption that, from the adversary's point of view, identities that correspond to its given decryption keys are sampled from somewhat unpredictable distributions. We show that this assumption is in fact sufficient for obtaining a strong and realistic notion of function privacy. Loosely speaking, our framework requires that a decryption key corresponding to an identity sampled from any sufficiently unpredictable distribution is indistinguishable from a decryption key corresponding to an independently and uniformly sampled identity. Within our framework we develop an approach for designing function-private identity-based encryption schemes, leading to constructions that are based on standard assumptions in bilinear groups (DBDH, DLIN) and lattices (LWE). In addition to function privacy, our schemes are also anonymous, and thus yield the first public-key searchable encryption schemes that are provably keyword private: A search key sk_{w} enables to identify encryptions of an underlying keyword w, while not revealing any additional information about w beyond the minimum necessary, as long as the keyword w is sufficiently unpredictable.

Original language | American English |
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Title of host publication | Advances in Cryptology, CRYPTO 2013 - 33rd Annual Cryptology Conference, Proceedings |

Pages | 461-478 |

Number of pages | 18 |

Edition | PART 2 |

DOIs | |

State | Published - 2013 |

Externally published | Yes |

Event | 33rd Annual International Cryptology Conference, CRYPTO 2013 - Santa Barbara, CA, United States Duration: 18 Aug 2013 → 22 Aug 2013 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Number | PART 2 |

Volume | 8043 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 33rd Annual International Cryptology Conference, CRYPTO 2013 |
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Country/Territory | United States |

City | Santa Barbara, CA |

Period | 18/08/13 → 22/08/13 |