## Abstract

We put forth a new notion of distributed public key functional encryption. In such a functional encryption scheme, the secret key for a function f will be split into shares skif. Given a ciphertext ct that encrypts a message x, a secret key share skif, one can evaluate and obtain a shared value y_{i}. Adding all the shares up can recover the actual value of f(x), while partial shares reveal nothing about the plaintext. More importantly, this new model allows us to establish function privacy which was not possible in the setting of regular public key functional encryption. We formalize such notion and construct such a scheme from any public key functional encryption scheme together with learning with error assumption. We then consider the problem of hosting services in the untrusted cloud. Boneh, Gupta, Mironov, and Sahai (Eurocrypt 2014) first studied such application and gave a construction based on indistinguishability obfuscation. Their construction had the restriction that the number of corrupted clients has to be bounded and known. They left an open problem how to remove such restriction. We resolve this problem by applying our function private (distributed) public key functional encryption to the setting of hosting service in multiple clouds. Furthermore, our construction provides a much simpler and more flexible paradigm which is of both conceptual and practical interests. Along the way, we strengthen and simplify the security notions of the underlying primitives, including function secret sharing.

Original language | English (US) |
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Title of host publication | Public-Key Cryptography - PKC 2018 - 21st IACR International Conference on Practice and Theory of Public-Key Cryptography, Proceedings |

Editors | Michel Abdalla, Ricardo Dahab |

Publisher | Springer Verlag |

Pages | 218-244 |

Number of pages | 27 |

ISBN (Print) | 9783319765778 |

DOIs | |

State | Published - 2018 |

Event | 21st IACR International Conference on Practice and Theory of Public-Key Cryptography, PKC 2018 - Rio de Janeiro, Brazil Duration: Mar 25 2018 → Mar 29 2018 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 10770 10769 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 21st IACR International Conference on Practice and Theory of Public-Key Cryptography, PKC 2018 |
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Country/Territory | Brazil |

City | Rio de Janeiro |

Period | 3/25/18 → 3/29/18 |

## All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- General Computer Science