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.
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 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 investigate covert communication over general memoryless classical-quantum channels with fixed finite-size input alphabets. We show that the square root law (SRL) governs covert communication in this setting when product a ofninput states is used:LSRLn+o(n)covert bits (but no more) can be reliably transmitted innuses of classical-quantum channel, whereLSRL>0is a channel-dependent constant that we callcovert capacity. We also show that ensuring covertness requiresJSRLn+o(n)bits secret key shared by the communicating parties prior to transmission, whereJSRL≥0is a channel-dependent constant. We assume a quantum-powerful adversary that can perform an arbitrary joint (entangling) measurement on allnchannel uses. We determine the single-letter expressions forLSRLandJSRL, and establish conditions whenJSRL=0(i.e., no pre-shared secret key is needed). Finally, we evaluate scenarios where covert communication is not governed by the SRL.
Recently, the fundamental limits of covert, i.e., reliable-yet-undetectable, communication have been established for general memoryless channels and for lossy-noisy bosonic (quantum) channels with a quantum-limited adversary. The key import of these results was the square-root law (SRL) for covert communication, which states that O(√n) covert bits, but no more, can be reliably transmitted over n channel uses with O(√n) bits of secret pre-shared between communicating parties. Here we prove the achievability of the SRL for a general memoryless classical-quantum channel, showing that SRL covert communication is achievable over any quantum communication channel with a product-state transmission strategy. We leave open the converse, which, if proven, would show that even using entangled transmissions and entangling measurements, the SRL for covert communication cannot be surpassed over an arbitrary quantum channel.
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.
We establish the fundamental limits of covert communication over quantum channels, focusing on both finite-dimensional classical-quantum (CQ) channels and the infinite-dimen\-sional lossy thermal-noise bosonic channel. For general memoryless CQ channels, we characterize when covert communication is possible and prove a square root law (SRL): at most Ln+o(n) bits can be reliably transmitted covertly over n uses of the channel where L is the channel-dependent covert capacity. We derive a single-letter expression for L and show that the required pre-shared secret key also scales as n under mild conditions. We also identify and characterize corner cases where either constant-rate or zero-rate covert communication is possible. For the bosonic channel, we prove that the SRL holds and derive exact covert capacities under different resource assumptions. In particular, we show that the covert secrecy and covert entanglement generation capacities both equal the covert classical capacity without entanglement-assistance, Lno-EA, and show that the required pre-shared classical secret key scales as n. We also find that quadrature phase-shift keying (QPSK) achieves the optimal covert capacity, outperforming binary modulation in contrast to the classical channel setting. When Alice and Bob instead share entanglement, the covert classical capacity improves to LEAnlogn+o(nlogn), though this scaling is sensitive to noise in the entangled resource. Finally, we propose a practical covert transceiver and simulate its performance compared to recently experimentally-tested transceivers under realistic conditions.
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.