For communication over arbitrarily varying channels (AVC), common randomness is an important resource to establish reliable communication, especially if the AVC is symmetrizable. In this paper the arbitrarily varying wiretap channel (AVWC) with active wiretapper is studied. Here the wiretapper is active in the sense that it can exploit the knowledge about the common randomness to control the channel conditions of the legitimate users. The common randomness assisted secrecy capacity of the AVWC with active wiretapper is analyzed and is related to the corresponding secrecy capacity of the AVWC with passive wiretapper. If the active secrecy capacity is positive, it equals the corresponding passive secrecy capacity. The case of zero active capacity is also studied.
For communication over arbitrarily varying channels (AVC), common randomness is an important resource to establish reliable communication, especially if the AVC is symmetrizable. In this paper the arbitrarily varying wiretap channel (AVWC) with active wiretapper is studied. Here the wiretapper is active in the sense that it can exploit the knowledge about the common randomness to control the channel conditions of the legitimate users. The common randomness assisted secrecy capacity of the AVWC with active wiretapper is analyzed and is related to the corresponding secrecy capacity of the AVWC with passive wiretapper. If the active secrecy capacity is positive, it equals the corresponding passive secrecy capacity. The case of zero active capacity is also studied.
The classical wiretap channel models secure communication in the presence of a nonlegitimate wiretapper who has to be kept ignorant. Traditionally, the wiretapper is passive in the sense that he only tries to eavesdrop the communication using his received channel output. In this paper, more powerful active wiretappers are studied. In addition to eavesdropping, these wiretappers are able to influence the communication conditions of all users by controlling the corresponding channel states. Since legitimate transmitters and receivers do not know the actual channel realization or the wiretapper's strategy of influencing the channel states, they are confronted with arbitrarily varying channel (AVC) conditions. The corresponding secure communication scenario is, therefore, given by the arbitrarily varying wiretap channel (AVWC). In the context of AVCs, common randomness (CR) has been shown to be an important resource for establishing reliable communication, in particular, if the AVC is symmetrizable. But availability of CR also affects the strategy space of an active wiretapper as he may or may not exploit the common randomness for selecting the channel states. Several secrecy capacity results are derived for the AVWC. In particular, the CR-assisted secrecy capacity of the AVWC with an active wiretapper exploiting CR is established and analyzed in detail. Finally, it is demonstrated for active wiretappers how two orthogonal AVWCs, each useless for transmission of secure messages, can be super-activated to a useful channel allowing for secure communication at nonzero secrecy rates. To the best of our knowledge, this is not possible for passive wiretappers and, further, provides the first example of such super-activation, which has been expected to appear only in the area of quantum communication. Such knowledge is particularly important as it provides valuable insights for the design and the medium access control of future wireless communication systems.
Availability of channel state information, especially to non-legitimate users, is one major challenge for secure communication in wireless systems. For arbitrarily varying channels (AVC), coordination resources such as common randomness have been shown to be important for reliable communication; especially for symmetrizable AVCs. In this paper, the arbitrarily varying wiretap channel (AVWC) with active wiretapper is studied. Such an wiretapper may or may not exploit his knowledge about the coordination resources to control the channel conditions. Secrecy capacity results are derived for different forms of coordination resources including common randomness and correlated sources. Finally, it is demonstrated how two orthogonal AVWCs, each with zero secrecy capacity, i.e., useless for secure transmission, can be super-activated to a useful channel allowing for secure communication at non-zero secrecy rates.
The wiretap channel models secure communication in the presence of an eavesdropper who must be kept ignorant of transmitted messages. In this paper, the arbitrarily varying wiretap channel (AVWC), in which the channel may vary in an unknown and arbitrary manner from channel use to channel use, is considered. For arbitrarily varying channels (AVCs) the capacity might differ depending on whether deterministic or common randomness (CR) assisted codes are used. The AVWC has been studied for both coding strategies and the relation between the corresponding secrecy capacities has been established. However, a characterization of the CR-assisted secrecy capacity itself or even a general CR-assisted achievable secrecy rate remain open in general for weak and strong secrecy. Here, the secrecy measure of high decoding error at the eavesdropper is considered, where the eavesdropper is further assumed to know channel states and to adapt its decoding strategy accordingly. For this secrecy measure a general CR-assisted achievable secrecy rate is established. The relation between secrecy capacities for different secrecy measures is discussed: The weak and strong secrecy capacities are smaller than or equal to the one for high decoding error. It is conjectured that this relation can be strict for certain channels.
The wiretap channel models secure communication in the presence of a non-legitimate eavesdropper who has to be kept ignorant. In this paper, the arbitrarily varying wiretap channel (AVWC) is studied, in which the channel to both legitimate receiver and eavesdropper may vary in an unknown and arbitrary manner from channel use to channel use. It has been shown that for AVCs coordination between the transmitter and legitimate receiver based on common randomness (CR) is indispensable for reliable communication. Approaches taken so far yield CR-assisted strategies where the needed amount of CR increases unbounded with the block length. In this paper, it is shown that if we allow for a small but non-vanishing average probability of error and information leakage (in terms of weak secrecy), the amount of CR is always finite and independent of the block length. The corresponding secrecy capacity equals the one with asymptotically vanishing performance requirements. Furthermore, it is shown that the average decoding error at the eavesdropper can be made arbitrarily close to 1 regardless of the applied decoding strategy.
We consider a communication scenario in which the channel undergoes two different classes of attacks at the same time: a passive eavesdropper and an active jammer. This scenario is modelled by the concept of arbitrarily varying wiretap channels (AVWCs). In this paper, we derive a full characterization of the list secrecy capacity of the AVWC, showing that the list secrecy capacity is equivalent to the correlated random secrecy capacity if the list size L is greater than the order of symmetrizability of the AVC between the transmitter and the legitimate receiver. Otherwise, it is zero. Our result indicates that for a sufficiently large list size L, list codes can overcome the drawbacks of correlated and uncorrelated codes and provide a stable secrecy capacity for AVWCs. Furthermore, we investigate the effect of relaxing the reliability and secrecy constraints by allowing a non-vanishing error probability and information leakage on the list size L. We found that we can construct a list code whose rate is close to the correlated secrecy capacity using a finite list size L that only depends on the average error probability requested. Finally, we point out that our capacity characterization is an important step in investigating the analytical properties of the capacity function such as: the continuity behavior, Turing computability and super-activation of parallel AVWCs.
We investigate secure communication over a channel that undergoes two different classes of attacks at the same time: passive eavesdropping and active jamming. This scenario is perfectly modeled by the concept of arbitrarily varying wiretap channels (AVWCs). We derive a full characterization of the secrecy capacity of AVWCs under list decoding. We show that the list secrecy capacity is either equivalent to the correlated random secrecy capacity or zero depending on the order of symmetrizability of the legitimate AVC. Differently from correlated random codes, our coding scheme does not assume any restrictions on the communication between the eavesdropper and the jammer.