Elsevier

Measurement

Volume 73, September 2015, Pages 352-359
Measurement

Least significant qubit (LSQb) information hiding algorithm for quantum image

https://doi.org/10.1016/j.measurement.2015.05.038Get rights and content

Abstract

Quantum computation has the ability to solve some problems that are considered inefficient in classical computer. Research on Quantum image processing has been extensively exploited in recent decades. Quantum image information hiding can be divided into quantum image digital watermarking, quantum image steganography, anonymity and other branches. Least significant bit (LSB) information hiding plays an important role in classical world because many information hiding algorithms are designed based on it. In this paper, based on novel enhanced quantum representation (NEQR), the concrete least significant qubit (LSQb) information hiding algorithm for quantum image is given firstly. Because information hiding located on the frequency domain of an image can increase the security, we further discuss the frequency domain LSQb information hiding algorithm for quantum image based on quantum Fourier transform. In our algorithms, the corresponding unitary transformations are designed to realize the aim of embedding the secret information to the least significant qubit representing color of the quantum cover image. Finally, we illustrate the procedure of extracting the secret information. Quantum image LSQb information hiding algorithm can be applied in many fields according to different needs.

Introduction

Quantum computation has been a novel topic in recent information science owing to the advantages of quantum mechanics [1] overcoming the limitations of classical computation. A series of quantum information processing algorithm have been proposed in recent decades, such as Shor’s integer factoring algorithm [2], Grover’s search algorithm [3].

Digital image processing plays an important role in practical applications [4], correspondingly, quantum image processing has been a hot topic in recent years. Quantum image processing is a branch of quantum information processing, and it has attracted many researchers’ attention. Until now, most researches focus on the problems about quantum image representation, quantum image watermarking and quantum image encryption. Many quantum image representations have been proposed for the need of storing image information in quantum states, i.e., Qubit Lattice [5], Entangled Image [6], Real Ket [7], Flexible Representation of Quantum Images (FRQI) [8], Multi-Channel representation of quantum image (MCRQI) [9], quantum representation for log-polar images [10] and a new enhanced quantum image representation [11]. FRQI reduces the required number of qubits from 2n×2n of Qubit Lattice to 2n + 1 for 2n×2n image. Although the required qubits of NEQR increases to 2n + q, it is good for image processing because the gray coding is very similar like the bit plane of classical image.

Watermarking and steganography are two parts of information hiding. Image watermarking, as one of branches of information hiding, has been researched deeply in classical computer. Quantum watermarking is the technique which embeds the invisible quantum signal such as the owner’s identification into quantum multimedia data (such as audio, video and image) for copyright protection. Quantum image watermarking methods have been explored with many quantum image representations proposed. Based on FRQI, Iliyasu et al. proposed a secure, keyless, and blind watermarking and authentication strategy for quantum images based on restricted geometric transformations [14]. But the scheme can only be used to verify the identification of true owner of the carrier image. Then Zhang et al. designed a watermarking protocol [15] for quantum images. The scheme can be used to find out who is the real owner. Concrete quantum image watermarking method based on QFT has been proposed by Zhang et al. [16]. In their strategy, the watermark image is embedded into the Fourier coefficients of the quantum carrier image. Song et al. put forward a dynamic watermarking scheme for quantum images using quantum wavelet transform (QWT) [17] and quantum Hadamard transform [18], which has larger embedding capacity and good visual effect.

Information hiding embeds the additional secret information into media under the conditions of the carrier does not changing so much. Many information hiding methods for traditional images have been developed [19], [20], [21]. Classical LSB information hiding algorithm just substitutes the least significant bit of cover image using the secret information [22]. And LSB plays a significant part in digital image information hiding since many information hiding algorithms are based on it. Now the study of quantum image LSB information hiding algorithm is still in its infancy.

Most researches for quantum image security are based on FRQI representation. FRQI uses a superposition quantum state to store all pixels in an image. Color information is encoded by one qubit, and some simple image processing algorithms have been designed based on FRQI [12], [13]. Obviously, single qubit is not suitable for LSQb information hiding because of no least significant qubit. Therefore, when discussing LSB information hiding algorithms for quantum images, the color encoding should be in the form of the binary qubit. At this time, NEQR based on binary qubit is an ideal representation for quantum image.

In this paper, based on NEQR, we propose quantum image LSQb information hiding algorithm, and the LSQb information hiding algorithm in quantum Fourier transformed domain for quantum image. Owning to the color information and position information are entangled together in NEQR, so in the procedure of the algorithm, we design the unitary transformation acting on the quantum image state. Through the unitary operations, we can realize the aim of embedding the secret message into the quantum cover image.

The rest of the paper is organized as follows. A brief introduction about NEQR representation, Quantum Fourier Transform, two quantum bit comparator and Classical LSB information hiding algorithm is presented in Section 2. The LSQb information hiding algorithm based on NEQR representation is proposed in Section 3. Based on Quantum Fourier transform of quantum image information hiding algorithm is shown in Section 4. Experimental results are shown in Section 5. Finally, a conclusion is given in Section 6.

Section snippets

Classical least significant bit (LSB) information hiding method

Information hiding can achieve the functions of covert communication and copyright protection and so on. LSB information hiding is one of the significant methods of information hiding. It is proposed firstly by Tirkel in 1993 [22]. It substitutes the least significant bit of cover image with the secret information. When extract the secret information, only need to operate the stego image (the embedded cover image). It has the merits of easy to operate. Meanwhile, the stego image not changed so

Proposed quantum LSB image information hiding algorithm

Just like described in Section 2.1, the principle of classical LSB information hiding is embedding the secret message into the least significant bit of cover image. Appropriately, we can define quantum LSQb information hiding. Quantum LSQb information hiding can be described in this way: substituting the last qubit of cover image encoding color with the secret information. We must notice that no matter what kind of the secret information is, it can be encoded into a binary qubit stream.

Quantum image LSQb steganography algorithm in frequency domain

Researches on frequency domain of classical image LSB information hiding algorithm are meaningful. Correspondingly, we can define the quantum image frequency domain LSQb information hiding algorithm. It embeds the secret message to frequency domain of the quantum image. Next we will give the example quantum image LSQb information hiding algorithm in the QFT frequency domain.

Experimental results

There are some difference between quantum image and classical image. And until now, there is no concrete evaluation index for quantum image’s visual quality. But we can change quantum image to the classical image to evaluate. Just like section B described, when NEQR image changes into classical image, only need to turn its binary color information qubit into an integer. In classical LSB algorithm, we use PSNR to evaluate its hidden effect. Here, we also use PSNR to evaluate the visual effect of

Conclusion

In this paper, based on NEQR, firstly, we designed the concrete quantum image LSQb information hiding algorithm. LSQb information hiding embedded the secret message qubit stream in the last qubit of color of quantum cover image. Moreover, information hiding is researched on the frequency domain which can increase the security of quantum cover image. Concretely, we also discuss the quantum image Fourier frequency domain LSQb information hiding algorithm. In algorithms, the corresponding unitary

Acknowledgment

This work is supported by the National Science Foundation of China (61301099, 61361166006 and 61471141).

References (23)

  • Y. Zhang et al.

    NEQR: a novel enhanced quantum representation of digital images

    Quantum Inf. Process

    (2013)
  • H.C. Huang et al.

    Hierarchy-based reversible data hiding

    Expert Syst. Appl.

    (2013)
  • D. Deutsch

    Quantum theory, the Church-Turing principle and the universal quantum computer

    Proc. Roy. Soc. Lond.

    (1985)
  • P.W. Shor, Algorithms for quantum computation discrete logarithms and factoring, in: S. Goldwasser (Ed.), Pro of the...
  • L.K. Grove

    Quantum computers can search arbitrarily large databases by a single query

    Phys. Rev. Lett.

    (1977)
  • R.C. Gozalez et al.

    Digital Image Processing

    (2002)
  • S.E. Venegas-Andraca et al.

    Storing, processing and retrieving an image using quantum mechanics

    Proc. SPIE Conf. Quantum Inf. Comput.

    (2003)
  • S.E. Venegas-Andraca et al.

    Processing images in entangled quantum systems

    Quantum Inf. Process.

    (2010)
  • J.I. Latorre, Image compression and entanglement. arXiv: quant-ph/ 0510031,...
  • P.Q. Le et al.

    A flexible representation of quantum images for polynomial preparation, image compression and processing operations

    Quantum Inf. Process.

    (2010)
  • B. Sun, P.Q. Le, A.M. Iliyasu, J. Adrian Garcia, F. Yan, J.F. Dong, K. Hirota, A multi-channel representation for...
  • View full text