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arXiv:1708.09103 · Physical Review A

Secret-key expansion from covert communication

Juan Miguel Arrazola, Ryan Amiri

Published Feb 20, 2018• 13 citations
arXivHTMLPDF

Abstract

Covert communication allows the transmission of messages in such a way that it is not possible for adversaries to detect that the communication is occurring. This provides protection in situations where knowledge that two parties are talking to each other may be incriminating to them. In this work, we study how covert communication can be used for a different purpose: secret key expansion. First, we show that any message transmitted in a secure covert protocol is also secret and therefore unknown to an adversary. We then propose a covert communication protocol where the amount of key consumed in the protocol is smaller than the transmitted key, thus leading to secure secret key expansion. We derive precise conditions for secret key expansion to occur, showing that it is possible when there are sufficiently low levels of noise for a given security level. We conclude by examining how secret key expansion from covert communication can be performed in a computational security model.

DOI
10.1103/physreva.97.022325

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Covert communication allows the transmission of messages in such a way that it is not possible for adversaries to detect that the communication is occurring. This provides protection in situations where knowledge that two parties are talking to each other may be incriminating to them. In this work, we study how covert communication can be used for a different purpose: secret key expansion. First, we show that any message transmitted in a secure covert protocol is also secret and therefore unknown to an adversary. We then propose a covert communication protocol where the amount of key consumed in the protocol is smaller than the transmitted key, thus leading to secure secret key expansion. We derive precise conditions for secret key expansion to occur, showing that it is possible when there are sufficiently low levels of noise for a given security level. We conclude by examining how secret key expansion from covert communication can be performed in a computational security model.
Covert and secret quantum key distribution aims at generating information-theoretically secret bits between distant legitimate parties in a manner that remains provably undetectable by an adversary. We propose a framework in which to precisely define and analyze such an operation, and we show that covert and secret key expansion is possible. For fixed and known classical-quantum wiretap channels, we develop and analyze protocols based on forward and reverse reconciliation. The crux of our approach is the use of information reconciliation and privacy amplification techniques that are able to process the sparse signals required for covert operation and the Shannon entropy of which scales as the square root of their length. In particular, our results show that the coordination required between legitimate parties to achieve covert communication can be achieved with a negligible number of secret key bits.
We extend covert communication to the quantum regime by showing that covert quantum communication is possible over optical channels with noise arising either from the environment or from the sender's lab. In particular, we show that sequences of qubits can be transmitted covertly by using both a single photon and a coherent state encoding. We study the possibility of performing covert quantum key distribution (QKD) and show that positive key rates and covertness can be achieved simultaneously. Covert communication requires a secret key between the sender and receiver, which raises the problem of how this key can be regenerated covertly. We show that covert QKD consumes more secret bits than it can generate and propose instead a hybrid protocol for covert key regeneration that uses pseudorandom number generators (PRNGs) together with covert QKD to regenerate secret keys. The security of the new key is guaranteed by QKD while the security of the covert communication is at least as strong as the security of the PRNG.
We show that covert secret key expansion is possible against a restricted class of coherent attacks, which we characterize. Specifically, we propose a protocol based on pulse-position modulation and multi-level coding that allows one to use traditional quantum key distribution (QKD) protocols while ensuring covertness, in the sense that no statistical test by the adversary can detect the presence of communication better than a random guess. Covertness holds as long as there exists some noise in the channel that is not under the control of the adversary, which we model as a quantum channel preceding the adversary's apparatus.
In Chapter 3, we considered the transmission of information over a noisy broadcast channel subject to reliability and security constraints; we showed that appropriate coding schemes can exploit the presence of noise to confuse the eavesdropper and guarantee some amount of information-theoretic security. It is important to note that the wiretap channel model assumes that all communications occur over the channel, hence communications are inherently rate-limited and one-way. Consequently, the results obtained do not fully capture the role of noise for secrecy; in particular, for situations in which the secrecy capacity is zero, it is not entirely clear whether this stems from the lack of any “physical advantage” over the eavesdropper or the restrictions imposed on the communication schemes. The objective of this chapter is to study more precisely the fundamental role of noise in information-theoretic security. Instead of studying how we can communicate messages securely over a noisy channel, we now analyze how much secrecy we can extract from the noise itself in the form of a secret key. Specifically, we assume that the legitimate parties and the eavesdropper observe the realizations of correlated random variables and that the legitimate parties attempt to agree on a secret key unknown to the eavesdropper. To isolate the role played by noise, we remove restrictions on communication schemes and we assume that the legitimate parties can distill their key by communicating over a two-way, public, noiseless , and authenticated channel at no cost.
Information security has always been a critical issue in wireless networks. Apart from other secure techniques, covert communication emerges as a potential solution to security for wireless networks owing to its high-security level. In covert communication networks, the transmitter hides the transmitted signals into environmental or artificial noise by introducing randomness to avoid detection at the warden. By eliminating the existence of transmitted signals at the warden, information security can be preserved more solidly than other secure transmission techniques, i.e., without noticing the existence. Due to the promising security protection, covert communication has been successfully utilized in tremendous wireless communication scenarios. However, fundamental challenges in its practical implementation still exist, e.g., the effectiveness of randomness utilization, the low signal-to-interference-plus-noise ratio at legitimate users, etc. In this survey, we demonstrate a comprehensive review concentrating on the applications, solutions, and future challenges of covert communications. Specifically, the covert principle and research categories are first introduced. Then, the applications in the networks with different topologies and the effective covert techniques in the existing literature are reviewed. We also discuss the potential implementation of covert communications in future networks and the open challenges.
We study covert communication and covert secret key generation with positive rates over quantum state-dependent channels. Specifically, we consider fully quantum state-dependent channels when the transmitter shares an entangled state with the channel. We study this problem setting under two security metrics. For the first security metric, the transmitter aims to communicate covertly with the receiver while simultaneously generating a covert secret key, and for the second security metric, the transmitter aims to transmit a secure message covertly and generate a covert secret key with the receiver simultaneously. Our main results include one-shot and asymptotic achievable positive covert-secret key rate pairs for both security metrics. Our results recover as a special case the best-known results for covert communication over state-dependent classical channels. To the best of our knowledge, our results are the first instance of achieving a positive rate for covert secret key generation and the first instance of achieving a positive covert rate over a quantum channel. Additionally, we show that our results are optimal when the channel is classical and the state is available non-causally at both the transmitter and the receiver.