Quantum steganographic protocols using degenerate and entanglement-assisted quantum codes

Abstract

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.