## 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 < ε > there exists a log * n-round protocol for authenticating n-bit messages, in which only 2log (1/ε) + 0(1) bits are manually authenticated, and any adversary (even computationally unbounded) has probability of at most ε 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/ε) - )(1) 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.We apply the proof technique above to obtain a lower bound of log (1/∈ - O (1) on the required Shannon entropy of the shared key. This settles an open question posed by Gemmell and Naor (Advances in Cryptology-CRYPTO '93, pp. 355-367, 1993). Finally, we prove that one-way functions are necessary (and sufficient) for the existence of protocols breaking the above lower bounds in the computational setting.

Original language | American English |
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Pages (from-to) | 2408-2425 |

Number of pages | 18 |

Journal | IEEE Transactions on Information Theory |

Volume | 54 |

Issue number | 6 |

DOIs | |

State | Published - Jun 2008 |

Externally published | Yes |

### Bibliographical note

Funding Information:Manuscript received February 11, 2007; revised October 16, 2007. The material in this paper was presented in part at Advances in Cryptology–CRYPTO ’06, University of California, Santa Barbara, August 2006. This work was supported in part by a grant from the Israel Science Foundation. This work was performed at the Weizmann Institute of Science, Rehovot, Israel, and supported by the Louis L. and Anita M. Perlman postdoctoral fellowship.

## Keywords

- Authentication
- Cryptographic protocols
- Lower bounds
- Unconditional security