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arXiv:2303.02307 · Physical Review A

Quantum steganography via coherent- and Fock-state encoding in an optical medium

Bruno Avritzer, Todd A. Brun

Published Mar 1, 2024• 9 citations
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Abstract

Steganography is an alternative to cryptography, where information is protected by secrecy (being disguised as innocent communication or noise) rather than being scrambled. In this work we develop schemes for steganographic communication using Fock and coherent states in optical channels based on disguising the communications as thermal noise, with a fidelity approaching 1. We derive bounds on their efficiency in terms of the communication rate and the required keyrate in the case of an all-powerful eavesdropper and provide explicit methods of encoding and error correction for the noiseless channel case.

DOI
10.1103/physreva.109.032401

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Steganography is an alternative to cryptography, where information is protected by secrecy (being disguised as innocent communication or noise) rather than being scrambled. In this work we develop schemes for steganographic communication using Fock and coherent states in optical channels based on disguising the communications as thermal noise, with a fidelity approaching 1. We derive bounds on their efficiency in terms of the communication rate and the required keyrate in the case of an all-powerful eavesdropper and provide explicit methods of encoding and error correction for the noiseless channel case.
Quantum steganography is the study of hiding secret quantum information by encoding it into what an eavesdropper would perceive as an innocent-looking message. Here we study an explicit steganographic encoding for Alice to hide her secret message in the syndromes of an error-correcting code, so that the encoding simulates a given noisy quantum channel. We calculate achievable rates of steganographic communication over noiseless quantum channels using this encoding. We give definitions of secrecy and reliability for the communication process, and with these assumptions derive upper bounds on the amount of steganographic communication possible and show that these bounds match the communication rates achieved with our encoding. This gives a steganographic capacity for a noiseless channel emulating a given noisy channel.
Steganography is the technique of hiding secret information by embedding it in a seemingly ``innocent'' message. We present protocols for hiding quantum information by disguising it as noise in a codeword of a quantum error-correcting code. The sender (Alice) swaps quantum information into the codeword and applies a random choice of unitary operation, drawing on a secret random key she shares with the receiver (Bob). Using the key, Bob can retrieve the information, but an eavesdropper (Eve) with the power to monitor the channel, but without the secret key, cannot distinguish the message from channel noise. We consider two types of protocols: one in which the hidden quantum information is stored locally in the codeword, and another in which it is embedded in the space of error syndromes. We analyze how difficult it is for Eve to detect the presence of secret messages, and estimate rates of steganographic communication and secret key consumption for specific protocols and examples of error channels. We consider both the case where there is no actual noise in the channel (so that all errors in the codeword result from the deliberate actions of Alice), and the case where the channel is noisy and not controlled by Alice and Bob.
In a previous work we have discussed a theoretical grounding for classical steganography using quantum Fock and coherent states in an optical channel, building on previous work by Wu et al. In that work, we discussed protocols which disguise communications to mimic the thermal state of a harmonic oscillator. In this work we will extend this to transmission of quantum information, and demonstrate the utility of steganographic entanglement sharing in practical contexts like nonclassical state teleportation, even with the presence of an active eavesdropper.
Quantum steganography is a powerful method for information security where communications between a sender and receiver are disguised as naturally occurring noise in a channel. A candidate resource state required for implementing quantum steganography is a weak coherent state engineered with modulated phase and amplitude values drawn from probability distributions that result in a mixed state indistinguishable from a thermal state. We experimentally demonstrate construction of this resource state by encoding the phase and amplitude of weak coherent laser states such that a third party monitoring the communications channel, measuring the flow of optical states through the channel, would see an amalgamation of states indistinguishable from thermal noise light such as that from spontaneous emission. Using quantum state tomography, we experimentally reconstructed the density matrices for the artificially engineered thermal states and spontaneous emission from an optical amplifier and verified a mean state fidelityF=0.98F=0.98F=0.98when compared with theoretical thermal states.
Characterizing secret communication over noisy quantum channels is an interesting problem from both a practical and theoretical perspective. Suppose Alice and Bob wish to communicate secret information so that an eavesdropper Eve will not suspect any type of encoded communication between the two. Classical or quantum cryptography will not suffice since it is always clear secret communication is taking place. Therefore Alice and Bob must execute what is known as a quantum steganographic protocol. Assuming Eve only has partial knowledge of the channel connecting Alice and Bob, we show that for the bit-flip and depolarizing channels Alice can use Eve's lack of knowledge of the channel parameter to encode quantum information steganographically. We give an explicit encoding procedure and calculate the rate at which Alice and Bob can communicate secretly. We also show that our encoding is optimal for nondegenerate quantum codes. We calculate the rate at which a secret key must be consumed. Finally, we discuss the possibility of steganographic communication over more general quantum channels and conjecture a general formula for the steganographic rate.
Steganography is the art of concealing secret information by embedding it in an apparently innocent-looking message. Quantum steganography applies the principles of quantum mechanics to traditional steganography and, compared to the latter, offers significant advantages, including heightened security, improved concealment, and increased data-hiding capacity. Traditionally, quantum steganography disguises the covert communication as channel noise, which is corrected using preshared classical randomness. This method requires the steganalytic eavesdropper Eve to overestimate the level of channel noise, so that the bounds on the stego channel capacity depend on this assumed gap in Eve's knowledge of the channel. In this work, we point out that by means of preshared quantum entanglement the secret message can be encoded into nonlocal correlations, obviating the need for such an assumption of Eve's ignorance. Consequently, the capacity bounds on the stego channel can then come from the channel capacity of the quantum communication channel. We introduce three such entanglement-based quantum steganographic protocols that make use of catalytic quantum error-correcting codes (QECCs), degenerate entanglement-assisted QECCs, or the phase bit of preshared entanglement. Here catalytic QECCs enable recycling entanglement, while entanglement assistance allows both sender and receiver to contribute to the protocol's secrecy. We derive upper and lower bounds on the secrecy capacity of each protocol, and demonstrate their practical robustness.