### Abstract

Non-malleable codes, introduced by Dziembowski, Pietrzak and Wichs [DPW10], provide a useful message integrity guarantee in situations where traditional error-correction (and even error-detection) is impossible; for example, when the attacker can completely overwrite the encoded message. Informally, a code is non-malleable if the message contained in a modified codeword is either the original message, or a completely "unrelated value". Although such codes do not exist if the family of "tampering functions" F allowed to modify the original codeword is completely unrestricted, they are known to exist for many broad tampering families F. The family which received the most attention [DPW10, LL12, DKO13, ADL14, CG14a, CG14b] is the family of tampering functions in the so called (2-part) split-state model: here the message x is encoded into two shares L and R, and the attacker is allowed to arbitrarily tamper with each L and R individually. Despite this attention, the following problem remained open: Build efficient, information-theoretically secure non-malleable codes in the split-state model with constant encoding rate: |L| = |R| = O(|x|). In this work, we resolve this open problem. Our technique for getting our main result is of independent interest. We (a) develop a generalization of non-malleable codes, called non-malleable reductions; (b) show simple composition theorem for non-malleable reductions; (c) build a variety of such reductions connecting various (independently interesting) tampering families F to each other; (d) construct several new non-malleable codes in the split-state model by applying the composition theorem to a series of easy to understand reductions. Most importantly, we show several "independence amplification" reductions, showing how to reduce split-state tampering of very few parts to an easier question of split-state tampering with a much larger number of parts. In particular, our final, constant-rate, non-malleable code composes one of these reductions with the very recent, "9-split-state" code of Chattopadhyay and Zuckerman [CZ14].

Original language | English (US) |
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Title of host publication | STOC 2015 - Proceedings of the 2015 ACM Symposium on Theory of Computing |

Publisher | Association for Computing Machinery |

Pages | 459-468 |

Number of pages | 10 |

ISBN (Electronic) | 9781450335362 |

DOIs | |

State | Published - Jun 14 2015 |

Event | 47th Annual ACM Symposium on Theory of Computing, STOC 2015 - Portland, United States Duration: Jun 14 2015 → Jun 17 2015 |

### Publication series

Name | Proceedings of the Annual ACM Symposium on Theory of Computing |
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Volume | 14-17-June-2015 |

ISSN (Print) | 0737-8017 |

### Other

Other | 47th Annual ACM Symposium on Theory of Computing, STOC 2015 |
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Country | United States |

City | Portland |

Period | 6/14/15 → 6/17/15 |

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### ASJC Scopus subject areas

- Software

### Cite this

*STOC 2015 - Proceedings of the 2015 ACM Symposium on Theory of Computing*(pp. 459-468). (Proceedings of the Annual ACM Symposium on Theory of Computing; Vol. 14-17-June-2015). Association for Computing Machinery. https://doi.org/10.1145/2746539.2746544