### Abstract

We consider a communication scenario where the source and the destination can communicate only via a relay node who is both an eavesdropper and a Byzantine attacker. Hence for secure communication, two requirements must be met simultaneously: the transmitted message must be kept secret, and a Byzantine attack must be detected reliably. Both a discrete noiseless adder model with the relay receiving the real sum of two signals and a Gaussian model are considered. In both models, the loss in rate due to Byzantine detection can be made arbitrarily small. For the discrete adder model, we show that the probability that the adversary wins decreases exponentially with the number of channel uses. For the Gaussian model, we show that this probability decreases exponentially with the square root of the number of channel uses. The rate derived in this paper is the strong secrecy rate, and the rate loss incurred due to the untrusted and Byzantine relay is measured with respect to the achievable secrecy rate when the relay is untrusted but honest. The result is obtained via a careful combination of the algebraic manipulation detection (AMD) code, the linear wiretap code constructed from low density parity check (LDPC) code, randomly generated wire-tap code and for the Gaussian model the lattice code.

Original language | English (US) |
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Title of host publication | 2009 IEEE International Symposium on Information Theory, ISIT 2009 |

Pages | 2096-2100 |

Number of pages | 5 |

DOIs | |

State | Published - Nov 19 2009 |

Event | 2009 IEEE International Symposium on Information Theory, ISIT 2009 - Seoul, Korea, Republic of Duration: Jun 28 2009 → Jul 3 2009 |

### Publication series

Name | IEEE International Symposium on Information Theory - Proceedings |
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ISSN (Print) | 2157-8102 |

### Other

Other | 2009 IEEE International Symposium on Information Theory, ISIT 2009 |
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Country | Korea, Republic of |

City | Seoul |

Period | 6/28/09 → 7/3/09 |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Information Systems
- Modeling and Simulation
- Applied Mathematics

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## Cite this

*2009 IEEE International Symposium on Information Theory, ISIT 2009*(pp. 2096-2100). [5205271] (IEEE International Symposium on Information Theory - Proceedings). https://doi.org/10.1109/ISIT.2009.5205271