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IEEE Transactions on Information Theory

Covert and Secret Key Expansion Over Quantum Channels Under Collective Attacks

Mehrdad Tahmasbi, Matthieu R. Bloch

Published Sep 3, 2020• 8 citations
Publisher

Abstract

We consider an enhanced measure of security for a quantum key distribution protocol, in which we require that the adversary not only obtains no information about the key but also remains unaware that a key generation protocol has been executed. When the adversary applies the same quantum channel independently to each transmitted quantum state, akin to a collective attack in the quantum key distribution literature, we propose a protocol that achieves covert and secret key expansion under mild restrictions. A crucial component of the protocol is a covert estimation stage, which is then combined with universal channel coding for reliability and resolvability in the covert regime.

DOI
10.1109/tit.2020.3021595

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We consider an enhanced measure of security for a quantum key distribution protocol, in which we require that the adversary not only obtains no information about the key but also remains unaware that a key generation protocol has been executed. When the adversary applies the same quantum channel independently to each transmitted quantum state, akin to a collective attack in the quantum key distribution literature, we propose a protocol that achieves covert and secret key expansion under mild restrictions. A crucial component of the protocol is a covert estimation stage, which is then combined with universal channel coding for reliability and resolvability in the covert regime.
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.
We show that covert secret key expansion is possible using a public authenticated classical channel and a quantum channel largely under control of an adversary, which we precisely define. We also prove a converse result showing that, under the golden standard of quantum key distribution by which the adversary completely controls the quantum channel, no covert key generation is possible. 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. When run over a bosonic channel, our protocol can leverage existing discrete-modulated continuous variable protocols. Since existing techniques to bound Eve's information do not directly apply, we develop a new bound that results in positive throughput for a range of channel parameters.
We propose a protocol based on pulse-position modulation and multi-level coding that allows one to bootstrap traditional quantum key distribution protocols while ensuring covertness, in the sense that no statistical test by the adversary can detect the presence of communication over the quantum channel better than a random guess. When run over a bosonic channel, our protocol can leverage existing discrete-modulated continuous-variable protocols. Since existing techniques to bound Eve's information do not directly apply, we develop a new bound that results in positive, although very low, throughput for a range of channel parameters. The analysis of the protocol performance shows that covert secret key expansion is possible using a public authenticated classical channel and a quantum channel largely but not fully under the control of an adversary, which we precisely define. We also establish a converse result showing that, under the golden standard of quantum key distribution, by which the adversary completely controls the quantum channel, no covert key generation is possible.
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.
The goal of quantum key distribution (QKD) is to establish a secure key between two parties connected by an insecure quantum channel. To use a QKD protocol in practice, one has to prove that a finite size key is secure against general attacks: no matter the adversary's attack, they cannot gain useful information about the key. A much simpler task is to prove security against collective attacks, where the adversary is assumed to behave identically and independently in each round. In this work, we provide a formal framework for general QKD protocols and show that for any protocol that can be expressed in this framework, security against general attacks reduces to security against collective attacks, which in turn reduces to a numerical computation. Our proof relies on a recently developed information-theoretic tool called generalised entropy accumulation and can handle generic prepare-and-measure protocols directly without switching to an entanglement-based version.
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.