### Abstract

We address the message authentication problem in two seemingly different communication models. In the first model, the sender and receiver are connected by an insecure channel and by a low-bandwidth auxiliary channel, that enables the sender to "manually" authenticate one short message to the receiver (for example, by typing a short string or comparing two short strings). We consider this model in a setting where no computational assumptions are made, and prove that for any 0 < ∈ < 1 there exists a log* n-round protocol for authenticating n-bit messages, in which only 2 log(1/∈) + O(1) bits are manually authenticated, and any adversary (even computationally unbounded) has probability of at most ∈ to cheat the receiver into accepting a fraudulent message. Moreover, we develop a proof technique showing that our protocol is essentially optimal by providing a lower bound of 2 log(1/∈) - 6 on the required length of the manually authenticated string. The second model we consider is the traditional message authentication model. In this model the sender and the receiver share a short secret key; however, they are connected only by an insecure channel. Once again, we apply our proof technique, and prove a lower bound of 2 log(1/∈) - 2 on the required Shannon entropy of the shared key. This settles an open question posed by Gemmell and Naor (CRYPTO '93). Finally, we prove that one-way functions are essential (and sufficient) for the existence of protocols breaking the above lower bounds in the computational setting.

Original language | English (US) |
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Title of host publication | Advances in Cryptology - CRYPTO 2006 - 26th Annual International Cryptology Conference, Proceedings |

Publisher | Springer Verlag |

Pages | 214-231 |

Number of pages | 18 |

ISBN (Print) | 3540374329, 9783540374329 |

State | Published - Jan 1 2006 |

Event | 26th Annual International Cryptology Conference, CRYPTO 2006 - Seattle, WA, United States Duration: Aug 20 2006 → Aug 24 2006 |

### 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 | 4117 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 26th Annual International Cryptology Conference, CRYPTO 2006 |
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Country | United States |

City | Seattle, WA |

Period | 8/20/06 → 8/24/06 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Advances in Cryptology - CRYPTO 2006 - 26th Annual International Cryptology Conference, Proceedings*(pp. 214-231). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4117 LNCS). Springer Verlag.