## Abstract

Transforming private-key encryption schemes into public-key encryption schemes is an interesting application of program obfuscation. The idea is that, given a private-key encryption scheme, an obfuscation of an encryption program with a private key embedded is used as a public key and the private key is used for decryption as it is. The security of the resulting public-key encryption scheme would be ensured because obfuscation is unintelligible and the public key is expected to leak no information on the private key. This paper investigates the possibility of general-purpose obfuscators for such a transformation, i.e., obfuscators that can transform an arbitrary private-key encryption scheme into a secure public-key encryption scheme. Barak et al. have shown a negative result, which says that there is a deterministic private-key encryption scheme that is unobfuscatable in the sense that, given any encryption program with a private key embedded, one can efficiently compute the private key. However, it is an open problem whether their result extends to probabilistic encryption schemes, where we should consider a relaxed notion of obfuscators, i.e., sampling obfuscators. Programs obfuscated by sampling obfuscators do not necessarily compute the same function as the original program, but produce the same distribution as the original program. In this paper, we show that there is a probabilistic private-key encryption scheme that can not be transformed into a secure public-key encryption scheme by sampling obfuscators which have a special property regarding input-output dependency of encryption programs. Our intention is not to claim that the required special property is reasonable. Rather, we claim that general-purpose obfuscators for the transformation, if they exist, must be a sampling obfuscator which does NOT have the special property.

Original language | English |
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Title of host publication | Advances in Information and Computer Security - Second International Workshop on Security, IWSEC 2007, Proceedings |

Publisher | Springer Verlag |

Pages | 1-12 |

Number of pages | 12 |

ISBN (Print) | 9783540756507 |

DOIs | |

Publication status | Published - 2007 |

Event | 2nd International Workshop on Security, IWSEC 2007 - Nara, Japan Duration: Oct 29 2007 → Oct 31 2007 |

### 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 | 4752 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 2nd International Workshop on Security, IWSEC 2007 |
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Country/Territory | Japan |

City | Nara |

Period | 10/29/07 → 10/31/07 |

## All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- General Computer Science