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Characterization of the secrecy of a common key constructed via data transmission over the two-way AND channel

Vladimir B. Balakirsky, A. Barbé, E. van der Meulen, Peter Vanroose

Published Jan 1, 1999• 0 citations
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On Forward Secrecy in One-Round Key Exchange

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Lecture notes in computer science•Jan 1, 2011•35 citations
This paper investigates the secure data transmission in the broadcast channel with noiseless feedback by using the information-theoretic method. We consider transmitting a private message and a common message to two receivers, of which the common message is to be decoded by both receivers while the private message is only for the intended receiver. The channel to the intended receiver is assumed to be independent of that to the other receiver. Feedback from the output of the intended receiver is used as a shared secret key to enhance the secrecy in the transmission. The capacity-equivocation region and the secrecy capacity of this new model are obtained. We find the secrecy capacity is enhanced by using feedback, even in the case that the other receiver is in a better position than the intended receiver. In addition, our results generalize the secrecy capacity of the degraded wiretap channel with secure feedback, and the capacity region of the degraded broadcast channel.
We study a discrete memoryless two-way wiretap channel under strong one-sided secrecy, where User 1's message is confidential and User 2's message is not required to be secret. We develop non-adaptive and key-assisted adaptive inner bounds from a common resolvability estimate for selected index components. For the adaptive construction, we prove a multiround leakage theorem that accounts both for information revealed about a key before its later use and for the possibility that an encoder uses an incorrectly decoded key. The proof includes an ideal-to-implemented coupling, deterministic codebook selection, and a growing-round argument that removes the initialization-rate loss. We eliminate the internal component rates exactly and characterize the adaptive gain at each fixed auxiliary distribution. For an open two-parameter family of binary channels, we also prove a converse for arbitrary non-adaptive stochastic codes and obtain an operational adaptive-versus-non-adaptive separation. For one representative channel, the complete non-adaptive strong one-sided secrecy capacity region is identified exactly.
We determine the secrecy capacities of AVQCs (arbitrarily varying quantum channels). Both secrecy capacity with average error probability and with maximal error probability are derived. Both derivations are based on one common code construction. The code we construct fulfills a stringent secrecy requirement, which is called the strong code concept. We determine when the secrecy capacity is a continuous function of the system parameters and completely characterize its discontinuity points both for average error criterion and for maximal error criterion. Furthermore, we prove the phenomenon “super-activation” for secrecy capacities of AVQCs, i.e., two quantum channels both with zero secrecy capacity, which, if used together, allow secure transmission with positive capacity. We also discuss the relations between the entanglement distillation capacity, the entanglement generating capacity, and the strong subspace transmission capacity for AVQCs.