The Wiretap Channel with Feedback: Encryption over the Channel (0704.2259v1)

Abstract: In this work, the critical role of noisy feedback in enhancing the secrecy capacity of the wiretap channel is established. Unlike previous works, where a noiseless public discussion channel is used for feedback, the feed-forward and feedback signals share the same noisy channel in the present model. Quite interestingly, this noisy feedback model is shown to be more advantageous in the current setting. More specifically, the discrete memoryless modulo-additive channel with a full-duplex destination node is considered first, and it is shown that the judicious use of feedback increases the perfect secrecy capacity to the capacity of the source-destination channel in the absence of the wiretapper. In the achievability scheme, the feedback signal corresponds to a private key, known only to the destination. In the half-duplex scheme, a novel feedback technique that always achieves a positive perfect secrecy rate (even when the source-wiretapper channel is less noisy than the source-destination channel) is proposed. These results hinge on the modulo-additive property of the channel, which is exploited by the destination to perform encryption over the channel without revealing its key to the source. Finally, this scheme is extended to the continuous real valued modulo-$\Lambda$ channel where it is shown that the perfect secrecy capacity with feedback is also equal to the capacity in the absence of the wiretapper.

• The paper demonstrates that using noisy feedback over the same communication channel can significantly increase secrecy capacity in wiretap channels.
• Key results show that in discrete settings, noisy feedback allows the secrecy capacity to match the source-destination channel capacity even with a wiretapper present.
• The research implies that embedding encryption within the channel can lead to more robust secure systems and suggests new directions for future secure communication studies.

Implications of Noisy Feedback in Wiretap Channels

The paper "The Wiretap Channel with Feedback: Encryption over the Channel" contributes significantly to the discourse on secure communication through the innovative use of noisy feedback to enhance secrecy capacity in wiretap channels. Wiretap channels, a concept introduced by Wyner, are used to model scenarios where communication is subject to possible interception by an adversary. Traditionally, these channels have been utilized under the assumption of noiseless feedback, where feedback occurs over a separate and clean public communication channel. This paper, however, explores the notion of implementing feedback directly via the same noisy channel used for transmission, thus eliminating the need for a separate public discussion channel.

The authors introduce groundbreaking models where both feed-forward and feedback signals share the same noisy channel. This setup is shown to not only be implementable but also beneficial in increasing the secrecy capacity, a metric representing the maximum rate at which information can be securely transmitted from the source to the destination without revealing it to the wiretapper. In the discrete modulo-additive setting, the paper demonstrates that noisy feedback allows the secrecy capacity to match the capacity of the source-destination channel that would exist without any interception, a remarkable feat considering the presence of a wiretapper.

Key Results

The paper makes substantial numerical claims about increasing the perfect secrecy rate. Specific channel models, such as the Binary Symmetric Channel (BSC), illustrate situations where noisy feedback improves secrecy, surpassing the traditionally held view regarding the inevitably superior utility of noiselessness in discussions. For instance, with full-duplex nodes, the capacity achieved equals $1-H(\epsilon)$, where $\epsilon$ represents the noise affecting the destination. Notably, half-duplex feedback scenarios, where nodes cannot simultaneously transmit and receive, are also extensively analyzed, providing robust techniques to ensure positive secrecy rates even when the channel between the source and wiretapper becomes less noisy compared to the source-destination channel.

Implications and Future Directions

The implications of this research are manifold. Practically, the approach of embedding the encryption process within the channel itself may lead to more robust secure communication systems by alleviating the burden of secret key distribution. Theoretically, it questions the established norms that associate public discussion channels with higher secrecy capacities, particularly in wiretap channel models.

Future research could focus on expanding the proposed noisy feedback model to other communication scenarios, including wireless networks and multi-terminal setups. Exploration of different channel structures for encryption purposes and extending these methods to continuous channels, such as the Additive White Gaussian Noise (AWGN) channel, poses further challenges and opportunities for advancing secure communications.

In conclusion, this work opens up new avenues in exploring feedback mechanisms in wiretap channels, emphasizing that simplicity and directness in communication design can yield substantial benefits in secure data transmission. The intersection of information theory, cryptography, and channel coding observed herein blends foundational principles with innovative strategies, a valuable addition to existing literature on communication security.