The Wiretap Channel with Feedback: Encryption over the Channel

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.

Submitted to IEEE Transactions on Information Theory

References in corpus (5)

• Discrete Memoryless Interference and Broadcast Channels with Confidential Messages: Secrecy Rate Regions
• Relay Channels with Confidential Messages
• Wireless Information-Theoretic Security - Part I: Theoretical Aspects
• Wireless Information-Theoretic Security - Part II: Practical Implementation
• The Gaussian Multiple Access Wire-Tap Channel

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• Strongly Secure Communications Over the Two-Way Wiretap Channel
• Providing Secrecy With Structured Codes: Tools and Applications to Two-User Gaussian Channels
• Secret Communication with Feedback
• On the Secure Degrees of Freedom in the K-User Gaussian Interference Channel
• Coding for Cryptographic Security Enhancement using Stopping Sets
• A Survey of Physical Layer Security Techniques for 5G Wireless Networks and Challenges Ahead
• The Wiretap Channel with Generalized Feedback: Secure Communication and Key Generation
• Increasing Physical Layer Security through Scrambled Codes and ARQ
• Secrecy Rate Region of the Broadcast Channel with an Eavesdropper
• Secrecy Capacity of the Wiretap Channel with Noisy Feedback
• Degraded Broadcast Channel with Side Information, Confidential Messages and Noiseless Feedback
• Secret Sharing over Fast-Fading MIMO Wiretap Channels
• On Secret-Message Transmission by Echoing Encrypted Probes
• Secure Capacity Region for Erasure Broadcast Channels with Feedback
• Secret Communication over Broadcast Erasure Channels with State-feedback
• The Two-Way Wiretap Channel: Achievable Regions and Experimental Results
• Individual secrecy for broadcast channels with receiver side information
• Adversarial Wiretap Channel with Public Discussion
• Relay Broadcast Channel with Confidential Messages
• A Simplified Coding Scheme for the Broadcast Channel With Complementary Receiver Side Information Under Individual Secrecy Constraints
• Effects of Feedback on the One-sided Secrecy of Two-way Wiretap through Multiple Transmissions
• Feedback-Based Collaborative Secrecy Encoding over Binary Symmetric Channels
• Information-Theoretical Security for Several Models of Multiple-Access Channel
• Two-hop Secure Communication Using an Untrusted Relay
• Control of Wireless Networks with Secrecy
• Providing Secrecy with Lattice Codes
• Randomization for Security in Half-Duplex Two-Way Gaussian Channels