### Abstract

"Hash then encrypt" is an approach to message authentication, where first the message is hashed down using an ε-universal hash function, and then the resulting k-bit value is encrypted, say with a block-cipher. The security of this scheme is proportional to εq^{2}, where q is the number of MACs the adversary can request. As ε is at least 2^{-k}, the best one can hope for is O(q^{2} /2^{k}) security. Unfortunately, such small ε is not achieved by simple hash functions used in practice, such as the polynomial evaluation or the Merkle-Damgård construction, where ε grows with the message length L. The main insight of this work comes from the fact that, by using randomized message preprocessing via a short random salt p (which must then be sent as part of the authentication tag), we can use the "hash then encrypt" paradigm with suboptimal "practical" ε-universal hash functions, and still improve its exact security to optimal O(q^{2}/2^{k}). Specifically, by using at most an 0(logL)-bit salt p, one can always regain the optimal exact security O(q^{2}/2^{k}), even in situations where ε grows polynomially with L. We also give very simple preprocessing maps for popular "suboptimal" hash functions, namely polynomial evaluation and the Merkle-Damgård construction. Our results come from a general extension of the classical Carter-Wegman paradigm, which we believe is of independent interest. On a high level, it shows that public randomization allows one to use the potentially much smaller "average-case" collision probability in place of the "worst-case" collision probability ε.

Original language | English (US) |
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Title of host publication | Fast Software Encryption - 14th International Workshop, FSE 2007 |

Pages | 414-433 |

Number of pages | 20 |

State | Published - Dec 1 2007 |

Event | 14th International Workshop on Fast Software Encryption, FSE 2007 - Luxembourg, Luxembourg Duration: Mar 26 2007 → Mar 28 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 | 4593 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 14th International Workshop on Fast Software Encryption, FSE 2007 |
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Country | Luxembourg |

City | Luxembourg |

Period | 3/26/07 → 3/28/07 |

### Fingerprint

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Fast Software Encryption - 14th International Workshop, FSE 2007*(pp. 414-433). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4593 LNCS).