TY - GEN

T1 - Secure communication with a byzantine relay

AU - He, Xiang

AU - Yener, Aylin

PY - 2009/11/19

Y1 - 2009/11/19

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=70449463810&partnerID=8YFLogxK

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U2 - 10.1109/ISIT.2009.5205271

DO - 10.1109/ISIT.2009.5205271

M3 - Conference contribution

AN - SCOPUS:70449463810

SN - 9781424443130

T3 - IEEE International Symposium on Information Theory - Proceedings

SP - 2096

EP - 2100

BT - 2009 IEEE International Symposium on Information Theory, ISIT 2009

T2 - 2009 IEEE International Symposium on Information Theory, ISIT 2009

Y2 - 28 June 2009 through 3 July 2009

ER -