## Abstract

We construct the first public-key encryption scheme that is proven secure (in the standard model, under standard assumptions) even when the attacker gets access to encryptions of arbitrary efficient functions of the secret key. Specifically, under either the DDH or LWE assumption, and for arbitrary but fixed polynomials L and N, we obtain a public-key encryption scheme that resists key-dependent message (KDM) attacks for up to N(k) public keys and functions of circuit size up to L(k), where k denotes the size of the secret key. We call such a scheme bounded KDM secure. Moreover, we show that our scheme suffices for one of the important applications of KDM security: ability to securely instantiate symbolic protocols with axiomatic proofs of security. We also observe that any fully homomorphic encryption scheme that additionally enjoys circular security and circuit privacy is fully KDM secure in the sense that its algorithms can be independent of the polynomials L and N as above. Thus, the recent fully homomorphic encryption scheme of Gentry (STOC 2009) is fully KDM secure under certain non-standard hardness assumptions. Finally, we extend an impossibility result of Haitner and Holenstein (TCC 2009), showing that it is impossible to prove KDM security against a family of query functions that contains exponentially hard pseudorandom functions if the proof makes only a black-box use of the query function and the adversary attacking the scheme. This shows that the non-black-box use of the query function in our proof of security is inherent.

Original language | English |
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Title of host publication | Advances in Cryptology - Eurocrypt 2010, 29th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Proceedings |

Pages | 423-444 |

Number of pages | 22 |

DOIs | |

State | Published - 2010 |

Externally published | Yes |

Event | 29th in the Series of EuropeanConferences on the Theory and Application of Cryptographic Techniques, Eurocrypt 2010 - French Riviera, France Duration: 30 May 2010 → 3 Jun 2010 |

### 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 | 6110 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 29th in the Series of EuropeanConferences on the Theory and Application of Cryptographic Techniques, Eurocrypt 2010 |
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Country/Territory | France |

City | French Riviera |

Period | 30/05/10 → 3/06/10 |

## Keywords

- KDM/clique/circular security
- formal security
- fully homomorphic encryption