Detection of algebraic manipulation with applications to robust secret sharing and fuzzy extractors
EUROCRYPT'08 Proceedings of the theory and applications of cryptographic techniques 27th annual international conference on Advances in cryptology
Asymptotic enumeration methods for analyzing LDPC codes
IEEE Transactions on Information Theory
Applications of LDPC Codes to the Wiretap Channel
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Interference channels with strong secrecy
Allerton'09 Proceedings of the 47th annual Allerton conference on Communication, control, and computing
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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 wire-tap code constructed from low density parity check (LDPC) code, randomly generated wire-tap code and for the Gaussian model the lattice code.