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Foundations in signal processing, communications and networking

Identification via Discrete Memoryless Wiretap Channels

Rudolf Ahlswede

Published Jan 1, 2021• 0 citations
Publisher
DOI
10.1007/978-3-030-65072-8_6

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An upper bound to the identification capacity of discrete memoryless wiretap channels is derived under the requirement of semantic effective secrecy, combining semantic secrecy and stealth constraints. A previously established lower bound is improved by applying it to a prefix channel, formed by concatenating an auxiliary channel and the actual channel. The bounds are tight if the legitimate channel is more capable than the eavesdropper’s channel. An illustrative example is provided for a wiretap channel that is composed of a point-to-point channel, and a parallel, reversely degraded wiretap channel. A comparison with results for message transmission and for identification with only secrecy constraint is provided.
Studies two problems in the theory of identification via channels. The first problem concerns the identification via channels with noisy feedback. Whereas for Shannon's transmission problem the capacity of a discrete memoryless channel does not change with feedback, it is known that the identification capacity is affected by feedback. The authors study its dependence on the feedback channel. They prove both, a direct and a converse coding theorem. Although a gap exists between the upper and lower bounds provided by these two theorems, the known result for channels without feedback and the known result for channels with complete feedback, are both special cases of these two new theorems, because in these cases the bounds coincide. The second problem is the identification via wiretap channels. A secrecy identification capacity is defined for the wiretap channel. A "dichotomy theorem" is proved which says that the second-order secrecy identification capacity is the same as Shannon's capacity for the main channel as long as the secrecy transmission capacity of the wiretap channel is not zero, and zero otherwise. Equivalently, one can say that the identification capacity is not lowered by the presence of a wiretapper as long as 1 bit can be transmitted (or identified) correctly with arbitrarily small error probability. This is in strong contrast to the case of transmission.>
We study the identification capacity of classical-quantum channels (“cq-channels”) under channel uncertainty and privacy constraints. To be precise, we first consider compound memoryless cq-channels and determine their identification capacity; then we add an eavesdropper by considering compound memoryless wiretap cqq-channels, and determine their secret identification capacity. In the first case (without privacy), we find the identification capacity always equal to the transmission capacity. In the second case, we find a dichotomy: either the secrecy capacity (also known as private capacity) of the channel is zero, and then the secrecy identification capacity is also zero, or the secrecy capacity is positive and then the secrecy identification capacity equals the transmission capacity of the main channel without the wiretapper. We perform the same analysis for the case of arbitrarily varying wiretap cqq-channels (cqq-AVWC) with analogous findings, and make several observations regarding the continuity and super-additivity of the identification capacity in the latter case.