Reliable Deniable Communication: Hiding Messages in Noise (1304.6693v2)

Abstract: A transmitter Alice may wish to reliably transmit a message to a receiver Bob over a binary symmetric channel (BSC), while simultaneously ensuring that her transmission is deniable from an eavesdropper Willie. That is, if Willie listening to Alice's transmissions over a "significantly noisier" BSC than the one to Bob, he should be unable to estimate even whether Alice is transmitting. We consider two scenarios. In our first scenario, we assume that the channel transition probability from Alice to Bob and Willie is perfectly known to all parties. Here, even when Alice's (potential) communication scheme is publicly known to Willie (with no common randomness between Alice and Bob), we prove that over 'n' channel uses Alice can transmit a message of length O(sqrt{n}) bits to Bob, deniably from Willie. We also prove information-theoretic order-optimality of this result. In our second scenario, we allow uncertainty in the knowledge of the channel transition probability parameters. In particular, we assume that the channel transition probabilities for both Bob and Willie are uniformly drawn from a known interval. Here, we show that, in contrast to the previous setting, Alice can communicate O(n) bits of message reliably and deniably (again, with no common randomness). We give both an achievability result and a matching converse for this setting. Our work builds upon the work of Bash et al on AWGN channels (but with common randomness) and differs from other recent works (by Wang et al and Bloch) in two important ways - firstly our deniability metric is variational distance (as opposed to Kullback-Leibler divergence), and secondly, our techniques are significantly different from these works.

• The paper establishes information-theoretic rate limits for reliable deniable communication, showing that the achievable rate for hiding messages depends on channel knowledge.
• When channel parameters are known, the paper proves an achievable rate of exit{O}( exit{n}) bits over exit{n} uses, while uncertain channels allow a higher rate of exit{O}( exit{n}) bits.
• The study utilizes new techniques, including variational distance for deniability, and its findings offer insights for designing covert communication systems where privacy is crucial.

Deniable and Reliable Communication in Noisy Channels: A Formal Overview

The paper "Reliable Deniable Communication: Hiding Messages in Noise" by Pak Hou Che, Mayank Bakshi, and Sidharth Jaggi, focuses on a sophisticated challenge in the field of secure communication: enabling a communication system to simultaneously transmit information reliably between a transmitter (Alice) and a receiver (Bob) while ensuring that the transmission remains deniable with respect to an eavesdropper (Willie).

The paper addresses this challenge in the context of binary symmetric channels (BSC) under two distinct scenarios: channels with known transition probabilities and those with uncertain transition probabilities. The dual goals in this communication model are to achieve deniability, ensuring an eavesdropper cannot detect whether transmission is occurring, and reliability, ensuring that Bob receives Alice's messages accurately.

Key Contributions

1. Known Channel Scenario:
   • In this scenario, channel parameters between Alice and Bob, and Alice and Willie are perfectly known. The paper proves that Alice can reliably and deniably transmit approximately $\mathcal{O}(\sqrt{n})$ bits over $n$ channel uses. This aligns with the "Square Root Law" commonly referenced in steganography literature.
   • This result is significant as it establishes the information-theoretic limits (order-optimality) of deniable communication without requiring shared randomness between Alice and Bob.
2. Uncertain Channel Scenario:
   • Here, the channel transition probabilities for both Bob and Willie are drawn from known intervals. The paper demonstrates a more robust scenario where the achievable communication rate scales linearly with $n$, allowing Alice to transmit $\mathcal{O}(n)$ bits.
   • This outcome contrasts with the known parameters scenario, indicating the substantial advantages of leveraging channel uncertainty in certain practical situations.
3. Novel Approach to Deniability:
   • The paper diverges from previous works primarily in two areas: the choice of deniability metric and the employed techniques. Deviating from the traditional Kullback-Leibler divergence, the research uses the variational distance to quantify deniability, indicating a different perspective on what constitutes secure communications.
   • The authors also developed new analytical techniques, such as leveraging concentration inequalities and typicality arguments, to demonstrate the achievability of the bound under varying conditions.

Implications and Future Directions

This paper contributes to the theoretical foundations of deniable communication by rigorously demonstrating how different assumptions about channel knowledge affect achievable levels of communication security and reliability. The results have several implications:

• Practical Systems Design: The findings provide guidelines for designing communication systems where privacy and deniability are crucial, especially in environments with inherent uncertainty.
• Theoretical Advancements: Further theoretical exploration could aim to generalize these models to arbitrary discrete memoryless channels or to environments with more complex adversarial settings.
• Applications in Covert Communications: By demonstrating conditions under which high rates of communication remain undetectable, this work can influence the development of advanced steganographic and cryptographic systems in sensitive applications such as espionage and secure data transmission in adversarial settings.
• Impact on Cryptography and Information Theory: The results may stimulate broader interest and further research in cryptographic protocols that eliminate the need for shared secret keys, thus reducing system complexity without compromising on security.

In summary, the exploration of both deterministic and probabilistic channel models in this paper opens new avenues for ensuring deniability in noisy communications, blending the concepts from classical information theory with innovative contemporary needs for privacy and security. Speculating forward, this research could lead toward more sophisticated strategies for covert communications, potentially with applications extending beyond current technological capabilities.