## Abstract

We propose generic constructions of public-key encryption schemes, satisfying key-dependent message (KDM) security for projections and different forms of key-leakage resilience, from CPA-secure private-key encryption schemes with two main abstract properties: (1) a form of (additive) homomorphism with respect to both plaintexts and randomness, and (2) reproducibility, providing a means for reusing encryption randomness across independent secret keys. More precisely, our construction transforms a private-key scheme with the stated properties (and one more mild condition) into a public-key one, providing:–KDM-projection security, an extension of circular security, where the adversary may also ask for encryptions of negated secret key bits;–a (1− o(1)) resilience rate in the bounded-memory leakage model of Akavia et al. (TCC 2009); and–Auxiliary-input security against subexponentially-hard functions. We introduce homomorphic weak pseudorandom functions, a homomorphic version of the weak PRFs proposed by Naor and Reingold (FOCS’95) and use them to realize our base encryption scheme. We in turn obtain homomorphic weak PRFs from homomorphic hash-proof systems (HHPS). We also show how the base encryption scheme may be realized using subgroup indistinguishability (implied, in particular, by quadratic residuosity (QR) and decisional composite residuosity (DCR)). As corollaries of our results, we obtain (1) the first multiple-key projection-secure bit-encryption scheme (as well as the first scheme with a (1 − o(1)) resilience rate) based solely on the HHPS assumption, and (2) a unifying approach explaining the results of Boneh et al. (CRYPTO’08) and Brakerski and Goldwasser (CRYPTO’10). Finally, by observing that Applebaum’s KDM amplification method (EUROCRYPT’11) preserves both types of leakage resilience, we obtain schemes providing at the same time high leakage resilience and KDM security against any fixed polynomial-sized circuit family.

Original language | English (US) |
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Title of host publication | Public-Key Cryptography – PKC 2016 - 19th IACR International Conference on Practice and Theory in Public-Key Cryptography, Proceedings |

Editors | Chen-Mou Cheng, Kai-Min Chung, Bo-Yin Yang, Giuseppe Persiano |

Publisher | Springer Verlag |

Pages | 129-158 |

Number of pages | 30 |

ISBN (Print) | 9783662493861 |

DOIs | |

State | Published - 2016 |

Event | 19th IACR International Conference on Practice and Theory in Public-Key Cryptography, PKC 2016 - Taipei, Taiwan, Province of China Duration: Mar 6 2016 → Mar 9 2016 |

### 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 | 9615 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 19th IACR International Conference on Practice and Theory in Public-Key Cryptography, PKC 2016 |
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Country | Taiwan, Province of China |

City | Taipei |

Period | 3/6/16 → 3/9/16 |

## All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)