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 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 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.
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.
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 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 explore covert entanglement generation over the lossy thermal-noise bosonic channel, which is a quantummechanical model of many practical settings, including optical, microwave, and radio-frequency (RF) channels. Covert communication ensures that an adversary is unable to detect the presence of transmissions, which are concealed in channel noise. While covert communication of classical bits is well studied, covert quantum communication and entanglement generation remain largely unexplored. Here, we first show that a square root law (SRL) for covert classical secret communication over the lossy thermal-noise bosonic channel, defining the optimal rate and covert capacityLsec . The achievable construction relies on position-based coding, sequential decoding, and quadrature phase-shift keying. Furthermore, we adapt the code used in covert secret communication to show that a square root law (SRL) for covert entanglement generation similar to that for classical:LEGnentangled bits (ebits) can be generated covertly and reliably overnuses of a bosonic channel. We report a single-letter expression for optimalLEGas well as an achievable method. We additionally analyze the performance of covert entanglement generation using single- and dual-rail photonic qubits for varying channel parameters. Despite a performance gap compared to the optimal strategy, these encodings may be more practical for physical implementation.
The rate at which a secure key can be generated in a quantum key distribution (QKD) protocol is limited by the channel loss and the quantum bit-error rate (QBER). Increases to the QBER can stem from detector noise, channel noise, or the presence of an eavesdropper, Eve. Eve is capable of obtaining information of the unsecure key by performing an attack on the quantum channel or by listening to all discussion performed via a noiseless public channel. Conventionally a QKD protocol will perform the information reconciliation over the authenticated public channel, revealing the parity bits used to correct for any quantum bit errors. In this invited paper, the possibility of limiting the information revealed to Eve during the information reconciliation is considered. Using a covert communication channel for the transmission of the parity bits, secure key rates are possible at much higher QBERs. This is demonstrated through the simulation of a polarization based QKD system implementing the BB84 protocol, showing significant improvement of the SKRs over the conventional QKD protocols.