## Abstract

In a seminal paper, Dolev et al. [15] introduced the notion of non-malleable encryption (NM-CPA). This notion is very intriguing since it suffices for many applications of chosen-ciphertext secure encryption (IND-CCA), and, yet, can be generically built from semantically secure (IND-CPA) encryption, as was shown in the seminal works by Pass et al. [29] and by Choi et al. [9], the latter of which provided a black-box construction. In this paper we investigate three questions related to NM-CPA security: 1. Can the rate of the construction by Choi et al. of NM-CPA from IND-CPA be improved? 2. Is it possible to achieve multi-bit NM-CPA security more efficiently from a single-bit NM-CPA scheme than from IND-CPA? 3. Is there a notion stronger than NM-CPA that has natural applications and can be achieved from IND-CPA security? We answer all three questions in the positive. First, we improve the rate in the scheme of Choi et al. by a factor O(λ), where λ is the security parameter. Still, encrypting a message of size O(λ) would require ciphertext and keys of size O(λ^{2}) times that of the IND-CPA scheme, even in our improved scheme. Therefore, we show a more efficient domain extension technique for building a λ-bit NM-CPA scheme from a single-bit NM-CPA scheme with keys and ciphertext of size O(λ) times that of the NM-CPA one-bit scheme. To achieve our goal, we define and construct a novel type of continuous non-malleable code (NMC), called secret-state NMC, as we show that standard continuous NMCs are not enough for the natural “encode-then-encrypt-bit-by-bit” approach to work. Finally, we introduce a new security notion for public-key encryption that we dub non-malleability under (chosen-ciphertext) self-destruct attacks (NM-SDA). After showing that NM-SDA is a strict strengthening of NM-CPA and allows for more applications, we nevertheless show that both of our results—(faster) construction from IND-CPA and domain extension from one-bit scheme—also hold for our stronger NM-SDA security. In particular, the notions of IND-CPA, NM-CPA, and NM-SDA security are all equivalent, lying (plausibly, strictly?) below IND-CCA security.

Original language | English (US) |
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Title of host publication | Theory of Cryptography - 13th International Conference, TCC 2016-A, Proceedings |

Editors | Eyal Kushilevitz, Tal Malkin |

Publisher | Springer Verlag |

Pages | 306-335 |

Number of pages | 30 |

ISBN (Print) | 9783662490952 |

DOIs | |

State | Published - 2016 |

Event | 13th International Conference on Theory of Cryptography, TCC 2016 - Tel Aviv, Israel Duration: Jan 10 2016 → Jan 13 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 | 9562 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 13th International Conference on Theory of Cryptography, TCC 2016 |
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Country/Territory | Israel |

City | Tel Aviv |

Period | 1/10/16 → 1/13/16 |

## ASJC Scopus subject areas

- Theoretical Computer Science
- General Computer Science