Moritz Wiese

The arbitrarily varying wiretap channel - secret randomness, stability and super-activation

We study the arbitrarily varying wiretap channel (AVWC) under average error criterion when external common randomness (CR) can be used between the legitimate parties. We consider three scenarios: In the first one the CR is known to the eavesdropper, in the second it is not known to her and in the third there is no CR available. For the second scenario, we prove a complete coding theorem. For the third scenario it is known that the capacity function is discontinuous. We prove that it is nonetheless stable in the sense of being continuous around its positivity points. We characterize the points of discontinuity in terms of continuous functions. We then give a complete characterization of those pairs of AVWCs whose capacity can be super-activated in the unassisted third case - in terms of the capacity function describing the first case.

A Channel Under Simultaneous Jamming and Eavesdropping Attack—Correlated Random Coding Capacities Under Strong Secrecy Criteria

We give a complete characterization of the correlated random coding secrecy capacity of arbitrarily varying wiretap channels (AVWCs). We apply two alternative strong secrecy criteria, which both lead to the same multi-letter formula. The difference of these criteria lies in the treatment of correlated randomness; they coincide in the case of uncorrelated 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, in contrast to the discontinuous uncorrelated coding secrecy capacity. 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 arbitrarily varying 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. 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.

The Arbitrarily Varying Wiretap Channel—Secret Randomness, Stability, and Super-Activation

We define the common randomness-assisted capacity of an arbitrarily varying wiretap channel (AVWC) when the eavesdropper is kept ignorant about the common randomness. We prove a multi-letter capacity formula for this model. We prove that, if enough common randomness is used, the capacity formula can be given a single-shot form again. We then consider the opposite extremal case, where no common randomness is available, and derive the capacity. It is known that the capacity of the system can be discontinuous under these circumstances. We prove here that it is still stable in the sense that it is continuous around its positivity points. We further prove that discontinuities can only arise if the legal link is symmetrizable and characterize the points where it is positive. These results shed new light on the design principles of communication systems with embedded security features. At last, we investigate the effect of super-activation of the message transmission capacity of AVWCs under the average error criterion. We give a complete characterization of those AVWCs that may be super-activated. The effect is thereby also related to the (conjectured) super-activation of the common randomness assisted capacity of AVWCs with an eavesdropper that gets to know the common randomness. Super-activation is based on the idea of wasting a few bits of non-secret messages in order to enable provably secret transmission of a large bulk of data, a concept that may prove to be of further importance in the design of communication systems. In this paper, we provide further insight into this phenomenon by providing a class of codes that is capacity achieving and does not convey any information to the eavesdropper.

An achievable region for the Wiretap multiple-access channel with common message

We derive a rate region which is achievable by the Wiretap MAC with Common Message under the strong secrecy criterion. We follow Devetaks approach to establishing strong secrecy. Using the concentration of the normed sum of bounded i.i.d. random variables around its mean, it is possible to show the existence of a code where the channel outputs at the eavesdropper are almost independent of the messages. The encoders may use a certain amount of common randomness. We give the example of a channel where the availability of common randomness is necessary for secret transmission.

Strong secrecy for multiple access channels

We show strongly secret achievable rate regions for two different wiretap multiple-access channel coding problems. In the first problem, each encoder has a private message and both together have a common message to transmit. The encoders have entropy-limited access to common randomness. If no common randomness is available, then the achievable region derived here does not allow for the secret transmission of a common message. The second coding problem assumes that the encoders do not have a common message nor access to common randomness. However, they may have a conferencing link over which they may iteratively exchange rate-limited information. This can be used to form a common message and common randomness to reduce the second coding problem to the first one. We give the example of a channel where the achievable region equals zero without conferencing or common randomness and where conferencing establishes the possibility of secret message transmission. Both coding problems describe practically relevant networks which need to be secured against eavesdropping attacks.

The Arbitrarily Varying Multiple-Access Channel With Conferencing Encoders

We derive the capacity region of arbitrarily varying multiple-access channels (AV-MACs) with conferencing encoders for both deterministic and random coding. For a complete description, it is sufficient that one conferencing capacity is positive. We obtain a dichotomy: either the channels deterministic capacity region is zero or it equals the 2-D random coding region. We determine exactly when either case holds. We also discuss the benefits of conferencing. We give the example of an AV-MAC which does not achieve any nonzero rate pair without encoder cooperation, but the 2-D random coding capacity region if conferencing is possible. Unlike compound multiple-access channels, arbitrarily varying multiple-access channels may exhibit a discontinuous increase of the capacity region when conferencing in at least one direction is enabled.

Strong Secrecy in Bidirectional Broadcast Channels With Confidential Messages

To increase the spectral efficiency of future wireless networks, it is important to wisely integrate multiple services at the physical layer. Here the efficient integration of confidential services in the three-node bidirectional relay channel is studied. A relay node establishes a bidirectional communication between two other nodes using a decode-and-forward protocol, which is also known as two-way relaying. In the broadcast phase, the relay transmits not only the two bidirectional messages it received in the previous multiple access phase, but also an additional confidential message to one node while keeping the other node completely ignorant of it. The concept of strong information theoretic secrecy is used to ensure that the nonlegitimate node cannot decode the confidential message no matter what its computational resources are. Moreover, this implies that the average decoding error at the nonlegitimate node goes exponentially fast to one for any decoding strategy it may use. This results in the study of the bidirectional broadcast channel with confidential messages for which the strong secrecy capacity region is established. Furthermore, it is shown that the efficient integration of confidential messages with strong secrecy extends to such scenarios, where the relay further transmits an additional common message to both nodes.

Uncertain wiretap channels and secure estimation

The zero-error secrecy capacity of uncertain wiretap channels is defined. If the sensor-estimator channel is perfect, it is also calculated. Further properties are discussed. The problem of estimating a dynamical system with nonstochastic disturbances is studied where the sensor is connected to the estimator and an eavesdropper via an uncertain wiretap channel. The estimator should obtain a uniformly bounded estimation error whereas the eavesdroppers error should tend to infinity. It is proved that the system can be estimated securely if the zero-error capacity of the sensor-estimator channel is strictly larger than the logarithm of the systems unstable pole and the zero-error secrecy capacity of the uncertain wiretap channel is positive.

The arbitrarily varying multiple-access channel with conferencing encoders

We characterize the capacity region of the arbitrarily varying multiple-access channel with conferencing encoders. This channel exhibits a dichotomy: either it is useless or its capacity region equals the region achievable with random coding. We determine exactly when either case holds. This model can be used to analyze downlink networks with cooperating base stations suffering from exterior interference.

The arbitrarily varying wiretap channel - communication under uncoordinated attacks

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.