5. Simulations and analysis

In this section, some simulations and analysis of the results and properties of the proposed scheme are demonstrated. All the simulations are based on a classical computer equipped with software Matlab R2014b. The secret text of size 64 128 used in our proposed scheme is full of "Quantum Text and Quantum Image." And all the cover images are with size of 256 256, and shown in Figure 13.

In general quantum image steganography scheme, the peak-signal-to-noise ratio (PSNR) is one of the most employed techniques to compare the fidelity of the stego image and the cover image. However, Iliyasu et al. explained that these available classical metrics are insufficient and/or ill-suited to effectively quantify the fidelity between two or more quantum images [39]. And in Refs. [39, 40], a wholly quantum-based metric to assess fidelity between quantum images (QIFM) is proposed. By using a statistical analysis they established that the proposed QIFM metric had a better correlation with digital image quality assessments of congruity than the other quantum image quality measures. And the formulation of the QIFM metric is the important in ensuring that applications sensitive to the peculiarities of quantum computation are formulated for effective quantum image processing (QIP). Before this, inspired to Ref. [41] that proposed a method to analyze the similarity between two quantum images of the same size based on the flexible representation of quantum images, a quantum image matching algorithm was introduced in [26], which sums up all the grayscale differences between two quantum images. In this chapter, we use the above two algorithms to assess the similarity of two images.

5.2 Robustness

Table 1.

following equation:

ID c or s ð Þ ¼

where BER denotes the bit error rate.

Here, the notations n<sup>b</sup>

cover and stego images.

quantified by equation:

25

In a noise-free environment, the proposed scheme can extract an intact secret text. However, the text extracting procedure is not always performed in a noiseless environment. The fidelity of the extracted text from the stego image under noise (simulate with salt and pepper noise) is verified, that is, using the QIFM metric. In this chapter, we give an outline of the steps of QIFM metric. For more details of the

Cover image Stego image Sum of differences Lena Stego-Lena 4,026,525 Airplane Stego-airplane 4,260,325 Cameraman Stego-cameraman 4,455,338 Pepper Stego-pepper 4,461,076

Γ ¼ IDc � IDs (17)

ð Þ c or s 6¼ <sup>n</sup><sup>w</sup>

ð Þ c or s

<sup>s</sup> and n<sup>w</sup>

<sup>8</sup><sup>N</sup> (19)

� 100 (20)

:

(18)

<sup>s</sup> for the stego

concepts and principles of QIFM, the reader can referred to [40].

Sum of all the grayscale differences between cover image and stego image.

A Novel Quantum Steganography Scheme Based on ASCII

DOI: http://dx.doi.org/10.5772/intechopen.86413

detail between cover image Ic and stego image Is is evaluated using the

where the ID c or s ð Þ for an N ¼ n � n pixel image is defined in:

ð Þ c or s � nw ð Þ c or s � �

ð Þ c or s � nw ð Þ c or s � �

image, which are referred to the number of white (0) and black (1) pixels in the

<sup>N</sup> ; if nb

<sup>c</sup> for the cover image and n<sup>b</sup>

Next, we count the number of pixel correspondences, D, which is defined as the number of pixels in cover image corresponding with pixels in stego image. And

<sup>B</sup> <sup>¼</sup> <sup>∑</sup>BER

Finally, the fidelity of two images expressed in the form of a percentage is

As can be found from Table 2, four frequently-used cover images are used here as examples, when the value of the noise densities is set to 0.1. The average value of

<sup>F</sup> <sup>¼</sup> <sup>D</sup> <sup>þ</sup> ð Þ� <sup>1</sup> � <sup>B</sup> <sup>Γ</sup> N

<sup>N</sup> <sup>þ</sup> 1; otherwise

∑ nb

8 >>>><

>>>>:

∑ nb

<sup>c</sup> and n<sup>w</sup>

then, the total pixel-wise variation B is computed by the equation:

Based on a pixel threshold (p) that assigns a value of zero or one to the pixel when 0 ≤p < 127 or 128 ≤p < 255, respectively. The content of both the cover and stego image is converted into their binary versions. Then the binary

## 5.1 Visual quality

To verify the visual quality of the proposed scheme, we use the algorithm introduced in [26] to compare the congruity of the stego image and the cover image. Here, we briefly describe the algorithm as follows and the details can be acquired in [26].

Quantum stego image is directly mapped with quantum cover image, i.e., the quantum register representing each corresponding pixel of the quantum template image is subtracted from that of the quantum reference image by running a quantum subtractor. According to the quantum measurement results, all the grayscale difference can be summed. The smaller the sum, the higher the similarity between two quantum images, that is, the better visual quality of the stego image.

Table 1 shows the sum of all the grayscale differences between the stego image and the cover image, in which the secret text 1 is embedded.

Compared with the value 5,189,090 of Lena with watermark in Ref. [26], we can see that the values of the sum all the grayscale differences between cover image and stego image in our proposed scheme are smaller.

Figure 13. Cover images used in the proposed scheme.

A Novel Quantum Steganography Scheme Based on ASCII DOI: http://dx.doi.org/10.5772/intechopen.86413


Table 1.

5. Simulations and analysis

Advances in Quantum Communication and Information

5.1 Visual quality

acquired in [26].

Figure 13.

24

Cover images used in the proposed scheme.

In this section, some simulations and analysis of the results and properties of the

In general quantum image steganography scheme, the peak-signal-to-noise ratio (PSNR) is one of the most employed techniques to compare the fidelity of the stego image and the cover image. However, Iliyasu et al. explained that these available classical metrics are insufficient and/or ill-suited to effectively quantify the fidelity between two or more quantum images [39]. And in Refs. [39, 40], a wholly quantum-based metric to assess fidelity between quantum images (QIFM) is proposed. By using a statistical analysis they established that the proposed QIFM metric had a better correlation with digital image quality assessments of congruity than the other quantum image quality measures. And the formulation of the QIFM metric is the important in ensuring that applications sensitive to the peculiarities of quantum computation are formulated for effective quantum image processing (QIP). Before this, inspired to Ref. [41] that proposed a method to analyze the similarity between two quantum images of the same size based on the flexible representation of quantum images, a quantum image matching algorithm was introduced in [26], which sums up all the grayscale differences between two quantum images. In this chapter,

proposed scheme are demonstrated. All the simulations are based on a classical computer equipped with software Matlab R2014b. The secret text of size 64 128 used in our proposed scheme is full of "Quantum Text and Quantum Image." And

all the cover images are with size of 256 256, and shown in Figure 13.

we use the above two algorithms to assess the similarity of two images.

To verify the visual quality of the proposed scheme, we use the algorithm introduced in [26] to compare the congruity of the stego image and the cover image. Here, we briefly describe the algorithm as follows and the details can be

Quantum stego image is directly mapped with quantum cover image, i.e., the quantum register representing each corresponding pixel of the quantum template image is subtracted from that of the quantum reference image by running a quantum subtractor. According to the quantum measurement results, all the grayscale difference can be summed. The smaller the sum, the higher the similarity between

Table 1 shows the sum of all the grayscale differences between the stego image

Compared with the value 5,189,090 of Lena with watermark in Ref. [26], we can see that the values of the sum all the grayscale differences between cover image and

two quantum images, that is, the better visual quality of the stego image.

and the cover image, in which the secret text 1 is embedded.

stego image in our proposed scheme are smaller.

Sum of all the grayscale differences between cover image and stego image.

### 5.2 Robustness

In a noise-free environment, the proposed scheme can extract an intact secret text. However, the text extracting procedure is not always performed in a noiseless environment. The fidelity of the extracted text from the stego image under noise (simulate with salt and pepper noise) is verified, that is, using the QIFM metric. In this chapter, we give an outline of the steps of QIFM metric. For more details of the concepts and principles of QIFM, the reader can referred to [40].

Based on a pixel threshold (p) that assigns a value of zero or one to the pixel when 0 ≤p < 127 or 128 ≤p < 255, respectively. The content of both the cover and stego image is converted into their binary versions. Then the binary detail between cover image Ic and stego image Is is evaluated using the following equation:

$$
\Gamma = I\_{D\mathfrak{c}} - I\_{D\mathfrak{s}} \tag{17}
$$

where the ID c or s ð Þ for an N ¼ n � n pixel image is defined in:

$$I\_{D(c\ or s)} = \begin{cases} \frac{\sum\left(n^b\_{(c\ or s)} - n^w\_{(c\ or s)}\right)}{N} ; \text{if } n^b\_{(c\ or s)} \neq n^w\_{(c\ or s)}\\\frac{\sum\left(n^b\_{(c\ or s)} - n^w\_{(c\ or s)}\right)}{N} + \mathbf{1}; \text{otherwise} \end{cases} . \tag{18}$$

Here, the notations n<sup>b</sup> <sup>c</sup> and n<sup>w</sup> <sup>c</sup> for the cover image and n<sup>b</sup> <sup>s</sup> and n<sup>w</sup> <sup>s</sup> for the stego image, which are referred to the number of white (0) and black (1) pixels in the cover and stego images.

Next, we count the number of pixel correspondences, D, which is defined as the number of pixels in cover image corresponding with pixels in stego image. And then, the total pixel-wise variation B is computed by the equation:

$$B = \frac{\sumBER}{8N} \tag{19}$$

where BER denotes the bit error rate.

Finally, the fidelity of two images expressed in the form of a percentage is quantified by equation:

$$F = \frac{D + (1 - B) \times \Gamma}{N} \times 100\tag{20}$$

As can be found from Table 2, four frequently-used cover images are used here as examples, when the value of the noise densities is set to 0.1. The average value of Advances in Quantum Communication and Information


Acknowledgements

Conflict of interest

Author details

China

27

Ri-Gui Zhou1,2 and Jia Luo1,2\*

Intelligent Computing, Shanghai, China

provided the original work is properly cited.

\*Address all correspondence to: luojia@stu.shmtu.edu.cn

This work is supported by the National Key R&D Plan under Grant No. 2018YFC1200200 and 2018YFC1200205, National Natural Science Foundation of China under Grant No. 61463016 and "Science and technology innovation action

1 College of Information Engineering, Shanghai Maritime University, Shanghai,

© 2019 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

2 The Research Center of Intelligent Information Processing and Quantum

plan" of Shanghai in 2017 under Grant No. 17510740300.

The authors declare no conflict of interest.

A Novel Quantum Steganography Scheme Based on ASCII

DOI: http://dx.doi.org/10.5772/intechopen.86413

Table 2.

QIFM values of the extracted text and their original secret text.

QIFM values is around 91, which is considered that the extracted text have a good fidelity.

#### 5.3 Circuit complexity

The circuit complexity depends on the number of the elementary quantum gates. Thus, we take C-NOT gate as the basic unit. For our proposed scheme, the circuit complexity consists of two parts: embedding and extracting. In embedding part, the scrambling circuit complexity is 7. The embedding circuit is composed of eight QE circuits with three control qubits and eight embedding blocks with one control qubit. As the literature [42] pointed out, only 4ð Þ k � 8 2-C-NOT gates are needed to construct one k-C-NOT gate. Again, one SWAP gate is equivalent to three C-NOT gates. The complexity of embedding circuit is:

$$\begin{aligned} 8 \times [4n \times (4 \times 4 - 8) + (4 \times 2n - 8)] + 8 \times [16 \times 3 \times (4 \times 5 - 8)] \\ = 320n - 64 + 4608 = 320n + 4544 \end{aligned} \tag{21}$$

In extracting part, the complexity of descrambling circuit is 7, and the extracting circuit is consist of eight QE circuits with three control qubits and eight extracting blocks with one control qubit. The complexity of extracting circuit is:

$$\begin{aligned} 8 \times [4n \times (4 \times 4 - 8) + (4 \times 2n - 8)] + 8 \times [8 \times (4 \times 5 - 8)] \\ = 320n - 64 + 768 = 320n + 704 \end{aligned} \tag{22}$$

Therefore, the circuit complexity of the proposed scheme is 640 ð Þ n þ 5262 , i.e., Oð Þ n .

## 6. Conclusion

This chapter proposes a new grayscale image steganography scheme which using NEQR representation to represent a 2<sup>n</sup> � <sup>2</sup><sup>n</sup> cover image and presenting an improved representation of quantum text to store secret text with 2<sup>n</sup>�1þn�<sup>2</sup> symbols. The Gray code of the highest three qubits of the gray value of the cover image is used as a judgment condition in embedded procedure. The acquisition of secret text is a process of extracting and reorganizing and inversely scrambling eight bit-planes, and it is worth mentioning that the process is absolutely blind. In addition, simulation results about the visibility quality and robustness of the proposed scheme are provided. And the circuit complexity is analyzed at last.
