Novel quantum steganography with large payload
Introduction
Steganography is the art of covert communication via classical channel. Corresponding to quantum channel, quantum steganography was introduced to achieve covert communication of quantum or classical messages. It integrates steganography and quantum cryptography, and has formed a brand new research field in quantum communication, which has been the concern of many experts and scholars recently. Taking its functions into considerations, three key parameters, capacity, imperceptibility and security must be addressed for various applications. In detail, capacity characterizes maximum quantity of secret messages transmitted per round of covert communication. Imperceptibility means that the hidden channel can't be detected or is hardly detected to prevent supervisors or attackers from damaging it. And security refers to that the protocol can defend most of the possible quantum attacks from eavesdropping on secret messages.
From the functional point of view, quantum steganography can be separated into two categories. One is called QMS (Quantum Multi-secret Sharing) [1], [2], [3], [4], [5], [6], [7], [8] which can be generalized to hide the bits in multipartite quantum states for sharing secret messages. This type of quantum steganography embeds the bits in the way that some parties can recover the bit via local operations and classical communication. And the other is called QDH (Quantum Data Hiding) [9], [10], [11], [12], [13] which builds up hidden channel within normal quantum channel to transmit secret messages. Comparing with QMS, QDH is more close to the classical steganography and can more effectively transmit secret messages. In 2002, J. G. Banacloche [9] adopted QECC (Quantum Error-Correcting Code) to hide secret messages as errors in arbitrary quantum data files. In this protocol, secret messages could also act as watermarks to secure authenticity or integrity of the data. In 2004, G. G. Worley III [10] proposed a new quantum watermarking, which embedded digital watermark by introducing errors in measurement results based on QKD (Quantum Key Distribution), BB84 protocol [14]. In 2007, K. Matin [11] presented a novel quantum steganographic communication protocol. The protocol was also based on the BB84 protocol. It analyzed imperceptibility and security in detail, and accurately calculated capacity of this type of hidden channel. Based on quantum teleportation, G. Mogos [12] proposed another new quantum steganography in 2008. It used three-dimensional qubits to represent RGB (Red, Green and Blue) pixels for transmitting the quantum secret messages in digital color images. As a result, it successfully extended steganography from classical channel to quantum channel. After that, G. Mogos [13] made further improvements on this algorithm in 2009.
However, most of these protocols mentioned above have the defect of small capacity, meanwhile there are also some other defects in them more or less. For example, capacities of most QMS protocols [1], [2], [3], [4], [5], [6], [7], [8] are small, about one bit per round of covert communications. In contrast, the capacity of Ref. [9] is one bit or one qubit, moreover, the protocol's security isn't very reliable. Once the hidden channel is detected, secret messages embedded in QECC will be easily removed by correcting errors. As for Ref. [10], even if amounts of quantum resources are consumed, its capacity is still only one bit. For Ref. [11], although the proofs about imperceptibility and security are well given, its capacity is only one bit capacity per round covert communication yet. The protocols of Ref. [12] and Ref. [13] own efficient transmission of one qubit per round by consuming only two key particles and one RGB pixel particle. However, its capacity is still unchanged, only one bit per round.
In this paper, following QDH, we present a novel quantum steganography with large payload based on IBF (improved ping-pong protocol) [16] for improving hidden channel's capacity. The new protocol integrates entanglements swapping of Bell states and super-dense coding to transmit secret messages. With the aid of QSDC's (Quantum Secure Direct Communication) merits, its capacity is greatly extended to four bits, four times that of the previous algorithms. Moreover, the hidden channel built up in IBF is imperceptible and hard to detect, because distributions of carrier information and secret messages can be treated as random or pseudo-random distribution, and the possibility of detecting the hidden channel can be arbitrarily reduced by increasing the Bell states' number. With regard to its security, BF (ping-pong protocol) [15] or IBF can guarantee the new protocol to effectively prevent from intercept–resend attack, auxiliary particle attack and man-in-the-middle attack, regardless of whether the hidden channel has been detected or not.
The rest of this paper is organized as follows. Section 2 presents the novel quantum steganography protocol in detail. The analysis about imperceptibility, capacity and security, is given in Section 3. In Section 4, the extended applications of our protocol are introduced and illuminated. Section 5 concludes this paper.
Section snippets
Quantum steganography protocol
The BF [15] is one of famous QSDC protocols [18], [19], [20], [21], which transmits information in a deterministic way [17]. IBF further improved its security in noisy condition. There are two major reasons considered to choose QSDC as the basis of our new protocol. The first, because QSDC protocols often adopt super-dense coding to enlarge its capacity such as IBF, the capacity of the hidden channel based on them can be easily increased, as a result. The second, comparing with QKD and QSS
Capacity
From Section 2, we know that both A′mB′m and A′m + 1B′m + 1 are used to transmit secret messages by entanglement swapping. As a matter of fact, the information carried by A′mB′m is recovered, while A′m + 1B′m + 1 is consumed, finally. In this case, the protocol actually transmits two bits secret messages by transferring one qubit and consuming one Bell state. From this point of view, the way used in our protocol is a kind of super-dense coding. As a result, the capacity of hidden channel in our
Applications
The main application of our quantum steganography is covert communication, including classical secret messages and quantum secret messages. Based on its superposition channel, the proposed protocol can also be used to distribute information or files with different security-level simultaneously. For example, the files access to managers and employees are often with different security-level in a company. It will be a good application to distribute these files to them simultaneously. Moreover, our
Discussions and conclusions
As mentioned above, the new protocol's best advantage is super large capacity of hidden channel. Although IBF's capacity is large in various quantum communication protocols due to super-dense coding, the capacity of hidden channel in our protocol is twice that of it. On the surface, our protocol's super large capacity is a little unreasonable according to quantum theory of super-dense coding. However, considering the present protocol's implementation carefully, we can conclude that the
Acknowledgements
Project supported by the National Basic Research Program of China (973 Program) (No. 2007CB311203), Specialized Research Fund for the Doctoral Program of Higher Education (No. 20070013007), the National Natural Science Foundation of China (Nos. 61003287, U0835001, 60821001), the Fundamental Research Funds for the Central Universities (No. BUPT2009RC0220), and the 111 Project (No. B08004).
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