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IEEE International Symposium on Information Theory (ISIT)

Strong Secrecy of Arbitrarily Varying Wiretap Channels with Constraints by Stochastic Code

Yiqi Chen, Dan Nong He, Chenhao Ying, Yuan Luo

Published Jul 12, 2021• 2 citations
Publisher

Abstract

The strong secrecy transmission problem of arbitrarily varying wiretap channel (AVWC) with input and state constraints is investigated in this paper. A stochastic code lower bound of the secrecy capacity is established by applying the type argument and Csiszár's almost independent coloring lemma, which includes the result of the ordinary AVWC as special case. Our codebook generation without the i.i.d. assumption of the soft covering lemma is to ensure the reliable communication over the AVWC with constraints. It is proved that the 0good codebooks for the strong secrecy transmission can be generated by choosing codewords randomly from a given type set, which is critical in this model.

DOI
10.1109/isit45174.2021.9517973

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The strong secrecy transmission problem of arbitrarily varying wiretap channel (AVWC) with input and state constraints is investigated in this paper. A stochastic code lower bound of the secrecy capacity is established by applying the type argument and Csiszár's almost independent coloring lemma, which includes the result of the ordinary AVWC as special case. Our codebook generation without the i.i.d. assumption of the soft covering lemma is to ensure the reliable communication over the AVWC with constraints. It is proved that the 0good codebooks for the strong secrecy transmission can be generated by choosing codewords randomly from a given type set, which is critical in this model.
The strong secrecy transmission problem of the arbitrarily varying wiretap channel (AVWC) with input and state constraints is investigated in this paper. First, a stochastic-encoder code lower bound of the strong secrecy capacity is established by applying the type argument and Csiszár’s almost independent coloring lemma. Then, a superposition stochastic-encoder code lower bound of the secrecy capacity is provided. The superposition stochastic-encoder code lower bound can be larger than the ordinary stochastic-encoder code lower bound. Random code lower and upper bounds of the secrecy capacity of the AVWC with constraints are further provided. Based on these results, we further consider a special case of the model, namely severely less noisy AVWC, and give the stochastic-encoder code and random code capacities. It is proved that the stochastic-encoder code capacity of the AVWC with constraints is either equal to or strictly smaller than the corresponding random code capacity, which is consistent with the property of the ordinary AVC. Finally, some numerical examples are presented to better illustrate our capacity results. Compared to the soft covering lemma that requires the codewords to be generated i.i.d., our method has more relaxed requirements regarding codebooks. It is proved that the good codebooks for secure transmission can be generated by choosing codewords randomly from a given type set, which is critical when considering the AVWC with constraints.
In this work the arbitrarily varying wiretap channel AVWC under the average error criterion and the strong secrecy criterion is studied. We show that in the case of a non-symmetrisable channel to the legitimate receiver the deterministic code secrecy capacity equals the random code secrecy capacity and thus we establish a result for the AVWC similar to that of Ahlswede's dichotomy for ordinary AVCs. We derive a lower bound on the random code secrecy capacity in the case of a best channel to the eavesdropper. We further prove upper bounds on the deterministic code secrecy capacity, which in special cases results in explicit expressions of the secrecy capacity.
The secrecy capacity problems over the general arbitrarily varying wiretap channel (AVWC), with respect to the maximal decoding error probability and strong secrecy criterion, are considered, where the channel state sequence may be known or unknown at the receiver. In the mean time, it is always assumed that the channel state sequence is known at the eavesdropper and unknown at the transmitter. Capacity results of both stochastic code (with random encoder and deterministic decoder) and random code (with random encoder and decoder) are discussed. This model includes the previous models of classic AVWC as special cases. Single-letter lower bounds on the secrecy capacities are given, which are proved to be the secrecy capacities when the main channel is less noisy than the wiretap channel. The coding scheme is based on Csiszar's almost independent coloring scheme and Ahlswede's elimination technique. Moreover, a new kind of typical sequence with respect to states is defined for this coding scheme. It is concluded that the secrecy capacity of stochastic code is identical to that of random code when the receiver knows the state sequence. Meanwhile, random code may achieve larger secrecy capacity when the state sequence is unknown by the receiver.
We give a complete characterization of the secrecy capacity of arbitrarily varying wiretap channels (AVWCs) with correlated random coding. We apply two alternative strong secrecy criteria, which both lead to the same formula and which coincide in the case of deterministic codes. On the basis of the derived formula, we show that the correlated random coding secrecy capacity is continuous as a function of the AVWC. We show that the deterministic coding secrecy capacity of the AVWC either equals 0 or the correlated random coding secrecy capacity. For the case that only a weak secrecy criterion is applied, we derive a complete characterization of the corresponding secrecy capacity for deterministic codes. In the proof of the secrecy capacity formula for correlated random codes, we apply an auxiliary channel which is compound from the sender to the intended receiver and varies arbitrarily from the sender to the eavesdropper.
We give a complete characterization of the secrecy capacity of arbitrarily varying wiretap channels (AVWCs) with correlated random coding under a strong secrecy criterion where the eavesdropper may also know the correlated randomness. We obtain that the correlated random coding secrecy capacity is continuous as a function of the AVWC. We show that the deterministic coding secrecy capacity of the AVWC either equals 0 or the correlated random coding secrecy capacity. For the case that only a weak secrecy criterion is applied, a complete characterization of the corresponding secrecy capacity for deterministic codes is possible. In the proof of the secrecy capacity formula for correlated random codes, we apply an auxiliary channel which is compound from the sender to the intended receiver and varies arbitrarily from the sender to the eavesdropper. We discuss the relation between the usual mutual information secrecy criterion and a criterion formulated in terms of total variation distance, and investigate the robustness of the AVWC model.
This paper investigates the strong secrecy capacity of the arbitrarily varying multiple access channel (AVMAC). First, Csiszár's almost independent coloring lemma is generalized to establish an achievable secrecy rate region of the AVMAC with an eavesdropper, which includes existing results on both the arbitrarily varying wiretap channel and the multiple access wiretap channel. We then determine the capacity for a special case named semi-noiseless wiretap channel. In addition, a multi-letter outer bound is also presented. Finally, the results of this paper are further explained via a binary example with a numerical inner bound.