2.1 NEQR

It is worth pointing out that the protection of network information, especially the increasing number of multimedia information on the network, has attracted researcher's attention. Thus information hiding was came into being a hot issue, which utilizes the sensory redundancy of the human sense organ to the digital signal, hiding a message in another ordinary message without changing the essential

Similarly, quantum information hiding also includes steganography and watermarking, which have been gradually studied as the two main branches of quantum information hiding technology. In 2012, Iliyasu et al. proposed a quantum image watermarking algorithm based on restricted geometric transformations [27]. Zhang et al. introduced a protocol in 2013, that the watermark image was embedded into the Fourier coefficients of the quantum carrier image [28]. Later on, a dynamic watermarking scheme for quantum images based on Hadamard transform was proposed by Song et al. [29]. Two blind steganography algorithms based on LSB were proposed by Jiang et al. [30]. Miyake proposed a quantum watermarking scheme using simple and small-scale quantum circuits [31]. In this algorithm, the gray scale image was first used as a secret image. A watermarking scheme through Arnold scrambling and LSB was proposed by Zhou et al. [32], in which the quantum equal circuit was demonstrated. In 2017, Abd-El-Atty et al. proposed a new steganography scheme with Hadamard transformation [33]. In this scheme, the quantum text message was hided into the cover image. In addition, some algorithms that adopt color image as cover image have also been reported [34–37]. Wherein, a quantum copyright protection method based on a new quantum representation of

In order to reduce the qubits of the representation of text in literature [34], we introduce an improved quantum representation of text. Then, the quantum text will be embedded in cover image through utilizing Gray code and quantum gates. Furthermore, the extracting procedure is absolutely blind and without any other

The physical implementation of qubits and gates is difficult, for the same reasons that quantum phenomena are hard to observe in everyday life. One approach is to implement the quantum computers in superconductors, where the quantum effects become macroscopic, though at a price of extremely low operation

In a superconductor, the basic charge carriers are pairs of electrons (known as Cooper pairs), rather than the single electrons in a normal conductor. At every point of a superconducting electronic circuit (that is a network of electrical elements), the condensate wave function describing the charge flow is well-defined by a specific complex probability amplitude. In a normal conductor electrical circuit, the same quantum description is true for individual charge carriers, however the various wave functions are averaged in the macroscopic analysis, making it impossible to observe quantum effects. The condensate wave function allows designing and measuring macroscopic quantum effects. And successive generations of IBM Q processors have demonstrated the potential of superconducting transmon qubits as the basis for electrically controlled solid-state quantum computers. But in this chapter, we focus on the theoretical design of quantum steganography scheme and

The rest of the chapter is organized as follows. Section 2 gives fundamental knowledge of NEQR, Gray code and quantum equal circuit. The improved quantum representation of text is provided in Section 3. The proposed embedding and extracting procedures are depicted in Section 4. In Section 5, simulations and analysis that include visual quality, capacity, robustness, and computational complexity are provided. Finally, the conclusion is drawn in Section 6.

characteristics and use value of the ordinary message.

Advances in Quantum Communication and Information

text was presented by Heidari et al. [34].

help from classical computer.

describe it in the remaining sections.

temperatures.

12

For a gray scale image, a novel enhanced quantum representation of digital images (NEQR) was proposed in 2013 [7]. A quantum image can be described by the NEQR model as follows:

$$|I\rangle = \frac{1}{\mathcal{Z}^{\mathfrak{n}}} \sum\_{Y=0}^{\mathfrak{n}} \sum\_{X=0}^{\mathfrak{n}-1} |C\_{YX}\rangle |Y\rangle |X\rangle = \frac{1}{\mathcal{Z}^{\mathfrak{n}}} \sum\_{YX=0}^{\mathfrak{n}-1} \bigotimes\_{i=0}^{q-1} C\_{YX}^{i} \otimes |YX\rangle \tag{1}$$

where, j i YX represents the position information and Ci YX � � � encodes the color information.

$$\begin{aligned} \left| \left| Y \right> = \left| Y \right> \left| X \right> &= \left| y\_{n-1} y\_{n-2} ... y\_0 \right> \left| x\_{n-1} x\_{n-2} ... x\_0 \right>, y\_j, x\_i \in \{0, 1\}, i = 0, 1, ..., n-1 \\ \left| \mathbf{C}\_{YX} \right> &= \left| \mathbf{C}\_{YX}^{q-1} \mathbf{C}\_{YX}^{q-2} ... \mathbf{C}\_{yx}^0 \right>, \mathbf{C}\_{YX}^i \in \{0, 1\}, i = 0, 1, ..., q-1 \end{aligned} \tag{2}$$

Thus, there are q þ 2n qubits being employed to store image information into a NEQR state for an 2<sup>n</sup> � <sup>2</sup><sup>n</sup> image with gray range 0; <sup>2</sup><sup>q</sup> ½ �. An example of an 2 � <sup>2</sup> image with ranged 0; 28 � <sup>1</sup> � �, i.e., <sup>n</sup> = 2, <sup>q</sup> = 8 is demonstrated in Figure 1, in which the equation indicates that NEQR model stores the whole image in the superposition of the two entangled qubit sequences, encoding the color and position information, respectively.

Replace the entirety of this text with the main body of your chapter. The main body is where the author explains experiments, presents and interprets data of one's research. Authors are free to decide how the main body will be structured. However, you are required to have at least one heading. Please ensure that either British or American English is used consistently in your chapter.

### 2.2 Gray code

The typical binary Gray Code, called the Gray Code, was originally proposed by Frank Gray in 1953 for communication purposes and is now commonly used in analog-to-digital and position-to-digital conversion. In a group of Gray codes, there is only one different binary number between any two adjacent codes, as well as in the maximum and minimum numbers. By Gray code transform, the binary code can be converted into Gray code [21]. Denote n qð Þ¼ nq�<sup>1</sup>nq�<sup>2</sup>…n1n<sup>0</sup> as a q-bit binary code, where ni is a binary bit, the definition of Gray code transform is as follows:

$$\begin{aligned} \left| \begin{array}{c} \vert I \rangle = \frac{1}{2} \langle \vert 0 \rangle \otimes \vert 00 \rangle + \vert 100 \rangle \otimes \vert 01 \rangle + \vert 200 \rangle \otimes \vert 10 \rangle + \vert 25 \rangle \otimes \vert 11 \rangle \rangle \end{array} \right\rangle \\ = \frac{1}{2} \begin{pmatrix} \vert 000000000 \rangle \otimes \vert 00 \rangle + \vert 01100100 \rangle \otimes \vert 01 \rangle \\ + \vert 110010000 \rangle \otimes \vert 10 \rangle + \vert 111111111 \rangle \otimes \vert 11 \rangle \end{pmatrix} \end{aligned} $$

Figure 1. A 2 � 2 example image and its representative expression in NEQR.

gq�<sup>1</sup> <sup>¼</sup> nq�<sup>1</sup>

A Novel Quantum Steganography Scheme Based on ASCII

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

ni <sup>¼</sup> giþ<sup>1</sup> <sup>⊕</sup> gi

nq�<sup>1</sup> <sup>¼</sup> gq�<sup>1</sup>

which compares j i YX and j i AB , where j i YX <sup>¼</sup> j i <sup>Y</sup> j i <sup>X</sup> <sup>¼</sup> yn�<sup>1</sup>…y<sup>0</sup>

output. If j ic ¼ j i1 , j i YX = j i AB , otherwise, j i YX ¼6 j i AB .

3. The improved representation of quantum text

and its inverse transform is:

2.3 Quantum equal circuit

j i AB ¼ j i A j i B ¼ j i an�<sup>1</sup>…a<sup>0</sup> j i bn�<sup>1</sup>…b<sup>0</sup> , yi

Figure 3.

15

Figure 4.

Quantum equal circuit.

gi ¼ ni ⊕ niþ<sup>1</sup>, i ¼ 0, 1, …q � 2

their corresponding quantum circuits are illustrated in Figure 2a and b.

two qubit sequences are equal or not. The quantum circuit is shown in Figure 4,

ASCII (American Standard Code for Information Interchange) is a Latin alphabet-based computerized coding system that is the most versatile single-byte coding system available today [38]. The ASCII code uses the specified combination of 7-bit or 8-bit binary sequence to represent 128 or 256 possible characters. A standard ASCII code that uses 7-bit binary sequence (a total 8-bit sequence and the remaining 1-bit is 0) to represent all uppercase and lowercase letters, Arabic numerals, punctuation marks, and special control characters used in American

The transformed binary code g qð Þ¼ gq�<sup>1</sup> gq�<sup>2</sup>… <sup>g</sup><sup>1</sup> <sup>g</sup><sup>0</sup> is defined as the q-bit Gray code of n qð Þ. An example of Gray code where the bit number q = 1, 2, 3 is shown in

In literature [32], Zhou et al. provided a quantum equal circuit to determine whether

 

, xi, ai, bi ∈0, 1, i ¼ n � 1, …, 0. Qubit j ic is

, i ¼ 0, 1, …q � 2

(3)

(4)

j i xn�<sup>1</sup>…x<sup>0</sup> and

Quantum circuits of (a) Gray code transform and (b) inverse Gray code transform.

Figure 3. 1-bit, 2-bit and 3-bit Gray codes.

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

Figure 4. Quantum equal circuit.

Figure 2.

Figure 3.

14

1-bit, 2-bit and 3-bit Gray codes.

Quantum circuits of (a) Gray code transform and (b) inverse Gray code transform.

Advances in Quantum Communication and Information

$$\begin{aligned} \mathbf{g}\_{q-1} &= n\_{q-1} \\ \mathbf{g}\_i &= n\_i \oplus n\_{i+1}, \ i = \mathbf{0}, \mathbf{1}, \ldots q-2 \end{aligned} \tag{3}$$

and its inverse transform is:

$$\begin{aligned} n\_i &= \mathcal{g}\_{i+1} \oplus \mathcal{g}\_i, & i &= 0, 1, \ldots q-2 \\ n\_{q-1} &= \mathcal{g}\_{q-1} \end{aligned} \tag{4}$$

their corresponding quantum circuits are illustrated in Figure 2a and b.

The transformed binary code g qð Þ¼ gq�<sup>1</sup> gq�<sup>2</sup>… <sup>g</sup><sup>1</sup> <sup>g</sup><sup>0</sup> is defined as the q-bit Gray code of n qð Þ. An example of Gray code where the bit number q = 1, 2, 3 is shown in Figure 3.

#### 2.3 Quantum equal circuit

In literature [32], Zhou et al. provided a quantum equal circuit to determine whether two qubit sequences are equal or not. The quantum circuit is shown in Figure 4, which compares j i YX and j i AB , where j i YX <sup>¼</sup> j i <sup>Y</sup> j i <sup>X</sup> <sup>¼</sup> yn�<sup>1</sup>…y<sup>0</sup> j i xn�<sup>1</sup>…x<sup>0</sup> and j i AB ¼ j i A j i B ¼ j i an�<sup>1</sup>…a<sup>0</sup> j i bn�<sup>1</sup>…b<sup>0</sup> , yi , xi, ai, bi ∈0, 1, i ¼ n � 1, …, 0. Qubit j ic is output. If j ic ¼ j i1 , j i YX = j i AB , otherwise, j i YX ¼6 j i AB .

## 3. The improved representation of quantum text

ASCII (American Standard Code for Information Interchange) is a Latin alphabet-based computerized coding system that is the most versatile single-byte coding system available today [38]. The ASCII code uses the specified combination of 7-bit or 8-bit binary sequence to represent 128 or 256 possible characters. A standard ASCII code that uses 7-bit binary sequence (a total 8-bit sequence and the remaining 1-bit is 0) to represent all uppercase and lowercase letters, Arabic numerals, punctuation marks, and special control characters used in American

English. Zero to thirty one and 127 (33 in total) are special characters for control or communication, and the rest are displayable characters. Figure 5 shows a table of characters that can be displayed.

j i <sup>T</sup> <sup>¼</sup> <sup>1</sup> 2<sup>n</sup>þm=<sup>2</sup>

dure will now be described.

information is prepared in j i ψ 1.

Figure 6.

17

∑ <sup>2</sup>n�<sup>1</sup> Y¼0

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

∑ <sup>2</sup>m�<sup>1</sup> X¼0

A Novel Quantum Steganography Scheme Based on ASCII

initial state j i ψ <sup>0</sup> can be expressed as in Eq. (6):

j i f Yð Þ ;<sup>X</sup> j i <sup>Y</sup> j i <sup>X</sup> <sup>¼</sup> <sup>1</sup>

2<sup>n</sup>þm=<sup>2</sup>

Figure 6 illustrates an example of a 2 � 4 text and its representative expression, where eight qubits are desired to store the text message and three qubits to store the position information. Therefore, this model just needs 8 þ n þ m qubits to represent a 2<sup>n</sup> � <sup>2</sup><sup>m</sup> text, namely there are 2nþ<sup>m</sup> symbols be stored. It is can be captured according to [34] which fifty-six qubits and 7 � <sup>2</sup>nþ<sup>m</sup> qubits are required to represent the text in this example and a text of 2nþ<sup>m</sup> symbols, respectively. In order to embed the text information into quantum image, firstly, the text information needs to be transformed into a quantum state. The preparation proce-

Step 1: this step is to prepare 8 þ n þ m qubits that all are with state 0j i. The

Step 2: two single-qubit gates, I and H (shown in Eq. (7)), are used to transform j i ψ <sup>0</sup> to the intermediate state j i ψ 1, which is the superposition of all the characters of

> 2 <sup>p</sup> <sup>=</sup> 1 1 1 �1

<sup>⊗</sup>ð Þ <sup>H</sup>j i <sup>0</sup> <sup>⊗</sup>ð Þ <sup>n</sup>þ<sup>m</sup>

j i <sup>0</sup> <sup>⊗</sup><sup>8</sup>

j iji h j ji ! <sup>þ</sup> <sup>Ω</sup>YX⊗j i YX h j YX (10)

j i YX

⊗ ∑ <sup>2</sup>nþm�<sup>1</sup> i¼0 j ii

0 1 � �, H <sup>¼</sup> <sup>1</sup> ffi

The operation U<sup>1</sup> is setting on the j i ψ <sup>0</sup> as shown in Eq. (9), and the position

j i <sup>0</sup> <sup>⊗</sup><sup>8</sup>

∑ <sup>2</sup>n�<sup>1</sup> Y¼0 ∑ <sup>2</sup>m�<sup>1</sup> X¼0

Step 3: In this step, 2<sup>n</sup>þ<sup>m</sup> sub-operations used to store the text message value for

U<sup>1</sup> ¼ I

� � <sup>¼</sup> ð Þ <sup>I</sup>j i <sup>0</sup> <sup>⊗</sup><sup>8</sup>

<sup>¼</sup> <sup>1</sup> 2<sup>n</sup>þm=<sup>2</sup>

<sup>¼</sup> <sup>1</sup> 2<sup>n</sup>þm=<sup>2</sup>

¼ j i ψ <sup>1</sup>

every position. In position ð Þ Y;X , the unitary operation UYX is shown below:

∑ 2m�<sup>1</sup>

ji6¼YX

2n�<sup>1</sup> <sup>j</sup>¼<sup>0</sup>,i¼<sup>0</sup>

an empty text. The unitary operation U<sup>1</sup> can be written in Eq. (8):

<sup>I</sup> <sup>¼</sup> 1 0

U<sup>1</sup> j i ψ <sup>0</sup>

UYX ¼ I⊗ ∑

A 2 � 4 text and its representative expression.

∑ <sup>2</sup>nþm�<sup>1</sup> YX¼0

⊗ 7 i¼0 Ti

j i <sup>ψ</sup> <sup>0</sup> <sup>¼</sup> j i <sup>0</sup> <sup>⊗</sup>nþmþ<sup>8</sup> (6)

� � (7)

(9)

<sup>⊗</sup><sup>8</sup>⊗H⊗ð Þ <sup>n</sup>þ<sup>m</sup> (8)

YX⊗j i YX (5)

Through analysis of the quantum text representation model proposed in literature [34], it is known that the model uses a seven-qubit sequence to store one character in the text message. In our proposed scheme, an improved quantum representation of text based on ASCII is proposed. Like NEQR model, the model including text message and position information. The text message f Yð Þ ;X on the corresponding coordinates ð Þ Y;X is encoded using ASCII of 8-bit binary sequence T7 YXT<sup>6</sup> YX⋯T<sup>2</sup> YXT<sup>1</sup> YXT<sup>0</sup> YX, T<sup>i</sup> YX ∈f g 0; 1 , i ¼ 0, 1, …, 7, this quantum textrepresentation model can be expressed as in Eq. (5) for a 2<sup>n</sup> � <sup>2</sup><sup>m</sup> text.


Figure 5. ASCII of displayable characters.

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

English. Zero to thirty one and 127 (33 in total) are special characters for control or communication, and the rest are displayable characters. Figure 5 shows a table of

Through analysis of the quantum text representation model proposed in litera-

YX ∈f g 0; 1 , i ¼ 0, 1, …, 7, this quantum text-

ture [34], it is known that the model uses a seven-qubit sequence to store one character in the text message. In our proposed scheme, an improved quantum representation of text based on ASCII is proposed. Like NEQR model, the model including text message and position information. The text message f Yð Þ ;X on the corresponding coordinates ð Þ Y;X is encoded using ASCII of 8-bit binary sequence

representation model can be expressed as in Eq. (5) for a 2<sup>n</sup> � <sup>2</sup><sup>m</sup> text.

characters that can be displayed.

Advances in Quantum Communication and Information

T7 YXT<sup>6</sup>

Figure 5.

16

ASCII of displayable characters.

YX⋯T<sup>2</sup>

YXT<sup>1</sup> YXT<sup>0</sup> YX, T<sup>i</sup>

$$|T\rangle = \frac{1}{\mathfrak{Z}^{\* + n/2}} \sum\_{Y=0}^{2^n - 1} \sum\_{X=0}^{2^n - 1} |f(Y, X)\rangle |Y\rangle |X\rangle = \frac{1}{\mathfrak{Z}^{\* + n/2}} \sum\_{YX=0}^{2^{n+n} - 1} \bigotimes\_{i=0}^7 T\_{YX}^i \otimes |YX\rangle \tag{5}$$

Figure 6 illustrates an example of a 2 � 4 text and its representative expression, where eight qubits are desired to store the text message and three qubits to store the position information. Therefore, this model just needs 8 þ n þ m qubits to represent a 2<sup>n</sup> � <sup>2</sup><sup>m</sup> text, namely there are 2nþ<sup>m</sup> symbols be stored. It is can be captured according to [34] which fifty-six qubits and 7 � <sup>2</sup>nþ<sup>m</sup> qubits are required to represent the text in this example and a text of 2nþ<sup>m</sup> symbols, respectively.

In order to embed the text information into quantum image, firstly, the text information needs to be transformed into a quantum state. The preparation procedure will now be described.

Step 1: this step is to prepare 8 þ n þ m qubits that all are with state 0j i. The initial state j i ψ <sup>0</sup> can be expressed as in Eq. (6):

$$|\psi\rangle\_0 = |\mathbf{0}\rangle^{\otimes n+m+8} \tag{6}$$

Step 2: two single-qubit gates, I and H (shown in Eq. (7)), are used to transform j i ψ <sup>0</sup> to the intermediate state j i ψ 1, which is the superposition of all the characters of an empty text. The unitary operation U<sup>1</sup> can be written in Eq. (8):

$$I = \begin{bmatrix} \mathbf{1} & \mathbf{0} \\ \mathbf{0} & \mathbf{1} \end{bmatrix}, \qquad H = {}^{1}\!/\_{\sqrt{\mathbb{Z}}} \begin{bmatrix} \mathbf{1} & \mathbf{1} \\ \mathbf{1} & -\mathbf{1} \end{bmatrix} \tag{7}$$

$$U\_1 = I^{\otimes \\$} \otimes H^{\otimes (n+m)} \tag{8}$$

The operation U<sup>1</sup> is setting on the j i ψ <sup>0</sup> as shown in Eq. (9), and the position information is prepared in j i ψ 1.

$$\begin{split} U\_1(|\boldsymbol{\psi}\rangle\_0) &= (I|\mathbf{0}\rangle)^{\otimes 8} \otimes (H|\mathbf{0}\rangle)^{\otimes (n+m)} \\ &= \frac{1}{2^{\*+n/2}} |\mathbf{0}\rangle^{\otimes 8} \otimes \sum\_{i=0}^{2^{\*+n}-1} |i\rangle \\ &= \frac{1}{2^{\*+n/2}} \sum\_{Y=0}^{2^\*-1} \sum\_{X=0}^{2^\*-1} |\mathbf{0}\rangle^{\otimes 8} |YX\rangle \\ &= |\boldsymbol{\psi}\rangle\_1 \end{split} \tag{9}$$

Step 3: In this step, 2<sup>n</sup>þ<sup>m</sup> sub-operations used to store the text message value for every position. In position ð Þ Y;X , the unitary operation UYX is shown below:

$$U\_{YX} = \left( I \otimes \sum\_{j=0,\,i=0}^{2^{n-1}} \sum\_{j\neq i\neq YX}^{2^{m-1}} |ji\rangle\langle ji| \right) + \Delta\_{YX} \otimes |YX\rangle\langle YX| \tag{10}$$

$$\begin{aligned} \left| \begin{array}{c} |T\rangle \right\rangle &= \frac{1}{2^3} \left( \left| \begin{matrix} |\mathbf{G}\rangle \langle 000 \rangle + |\mathbf{R}\rangle \langle 001 \rangle + |\mathbf{A}\rangle \langle 010 \rangle + |\mathbf{Y}\rangle \langle 011 \rangle \right\rangle \right) \\ + \left| \begin{matrix} |100\rangle + |o\rangle \langle 101 \rangle + |d\rangle \langle 1101\rangle + |e\rangle \langle 1110\rangle + |e\rangle \end{matrix} \right) \end{aligned} \right\} \\ = \frac{1}{2^3} \left( \left| \begin{matrix} |010001111\rangle \\ + \left| \begin{matrix} 010001111\end{matrix} \right\rangle \left| 0000\right\rangle + \left| \begin{matrix} 0110100101\end{matrix} \right\rangle \left| 010\right\rangle + \left| \begin{matrix} 011011001\end{matrix} \right\rangle \left| 011\right\rangle \right) \right) \\ + \left| \begin{matrix} 010100011\end{matrix} \right| \left| 100\right\rangle + \left| \begin{matrix} 0110011001\end{matrix} \right\rangle \left| 011\right\rangle \end{aligned} \right)$$

Figure 6.

A 2 � 4 text and its representative expression.

where, ΩYX is a unitary operation as shown in Eq. (11), which is manipulating on j i ψ <sup>1</sup> for altering digital representation of characters to the quantum state.

$$\begin{aligned} \boldsymbol{\mathfrak{Q}\_{YX}} &= \underset{i=\mathbf{0}}{\boldsymbol{\mathfrak{Q}\_{YX}}} \mathbf{1}\_{\mathbf{Y}X} \\ \boldsymbol{\mathfrak{Q}\_{YX}^{i}} &: |\mathbf{0}\rangle \to |\mathbf{0} \oplus T\_{YX}^{i}\rangle \end{aligned} \tag{11}$$

j i <sup>C</sup> <sup>¼</sup> <sup>1</sup>

A Novel Quantum Steganography Scheme Based on ASCII

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

j i¼ <sup>T</sup> <sup>1</sup> 22<sup>n</sup>�3=<sup>2</sup>

are similarly for the receiver.

4.1 Embedding procedure

transforming method.

Figure 7.

19

The general framework of the proposed scheme.

<sup>2</sup><sup>n</sup> <sup>∑</sup> <sup>2</sup>2n�<sup>1</sup> YX¼0 ⊗ 7 i¼0 Ci

> ∑ <sup>2</sup>2n�3�<sup>1</sup> YX¼0

The embedding procedure in the proposed scheme is as follows.

<sup>2</sup><sup>n</sup>�<sup>2</sup> � <sup>2</sup><sup>n</sup>�<sup>1</sup> into a quantum text j i <sup>T</sup> by ASCII expression.

2. Scramble the secret text j i <sup>T</sup> to be a meaningless text <sup>T</sup>^

secret text will be divided into eight bit-planes.

1. Transform a classical cover image with 2<sup>n</sup> � <sup>2</sup><sup>n</sup> size and eight bits gray scale into a quantum image j i C by NEQR, and transform a secret text with size

3. The cover image will be divided into eight blocks of the same size and the

4.The divided eight bit-planes are embedded into eight blocks one by one.

 

by Gray code

⊗ 7 i¼0 Ti

The general framework for the proposed scheme is shown in Figure 7, from which we can see that it is delineated into the classical and quantum domains. The preparation interface can transform classic image data into quantum states, which realizes the function of preparing the quantum image [7]. After the quantum image is stored in quantum states, our proposed quantum image steganography scheme can be implemented to transform the original quantum states to the desired states through the designed embedding circuits. Then, the quantum measurement operation is utilized to retrieve the processed image information. And once identified, the stego image is sent to the receiver by the public channel. The extraction operations

YX⊗j i YX , Ci

YX⊗j i YX , T<sup>i</sup>

YX ∈f g 0; 1 (15)

YX ∈f g 0; 1 (16)

And if T<sup>i</sup> YX <sup>¼</sup> 1, <sup>Ω</sup><sup>i</sup> YX is a (n+m)-CNOT gate, otherwise if T<sup>i</sup> YX <sup>¼</sup> 0 then <sup>Ω</sup><sup>i</sup> YX is a quantum identity gate. Therefore, the text message value in position (Y, X) is preparing by employing unitary operationΩYX:

$$\left| \mathfrak{Q}\_{\text{YX}} | \mathbf{0} \right\rangle^{\otimes \mathfrak{B}} = \underset{i=0}{\overset{7}{\otimes}} \left( \mathfrak{Q}\_{\text{YX}}^{i} | \mathbf{0} \right) = \underset{i=0}{\overset{7}{\otimes}} \left| \mathbf{0} \oplus T\_{\text{YX}}^{i} \right\rangle = \underset{i=0}{\overset{7}{\otimes}} \left| T\_{\text{YX}}^{i} \right\rangle = \left| f(\mathbf{Y}, \mathbf{X}) \right\rangle \tag{12}$$

Applying UYX on intermediate state j i ψ 1, the transformation is shown in Eq. (13).

$$\begin{split} U\_{\mathbf{Y}\mathbf{X}}\left(|\boldsymbol{\mu}\rangle\_{1}\right) &= U\_{\mathbf{Y}\mathbf{X}}\left(\frac{1}{2^{n}}\sum\_{j=0}^{2^{n-1}}\sum\_{i=0}^{2^{n-1}}|\mathbf{0}\rangle^{\otimes\mathsf{8}}|j i\rangle\right) \\ &= \frac{1}{2^{n}}U\_{\mathbf{Y}\mathbf{X}}\left(\sum\_{j=0}^{2^{n-1}}\sum\_{i=0}^{2^{n-1}}|\mathbf{0}\rangle^{\otimes\mathsf{8}}|j i\rangle + |\mathbf{0}\rangle^{\otimes\mathsf{8}}|\mathbf{Y}\mathbf{X}\rangle\right) \\ &= \frac{1}{2^{n}}\left(\sum\_{j=0}^{2^{n-1}}\sum\_{i=0}^{2^{n-1}}|\mathbf{0}\rangle^{\otimes\mathsf{8}}|j i\rangle + \Omega\_{\mathbf{Y}\mathbf{X}}|\mathbf{0}\rangle^{\otimes\mathsf{8}}|\mathbf{Y}\mathbf{X}\rangle\right) \\ &= \frac{1}{2^{n}}\left(\sum\_{j=0}^{2^{n}}\sum\_{i=0}^{2^{n-1}}|\mathbf{0}\rangle^{\otimes\mathsf{8}}|j i\rangle + |f(\mathbf{Y},\mathbf{X})\rangle|\mathbf{Y}\mathbf{X}\rangle\right) \end{split} \tag{13}$$

To store all the values to the quantum state, the whole operation U that consists of 2<sup>n</sup>þ<sup>m</sup> sub-operations and shown in Eq. (14) is necessary. The final state j i <sup>ψ</sup> <sup>2</sup> that is transformed from j i ψ <sup>1</sup> is the improved representation of quantum text.

$$\begin{aligned} U &= \prod\_{Y=0}^{2^n - 12^n - 1} \prod\_{X=0}^{2^n - 1} U\_{YX} \\ U(\left| \boldsymbol{\nu} \right>\_1) &= U \left( \frac{1}{2^n} \sum\_{j=0}^{2^{n-1} - 2^{n-1}} \left| \mathbf{0} \right|^{\otimes 8} \left| Y \mathbf{X} \right> \right) \\ &= \frac{1}{2^n} \sum\_{j=0}^{2^{n-1} - 2^{n-1}} \sum\_{i=0}^{2^n - 1} \Omega\_{\mathbf{Y}X} |\mathbf{0} \rangle^{\otimes 8} |Y \mathbf{X} \rangle \\ &= \frac{1}{2^n} \sum\_{j=0}^{2^{n-1} - 2^{n-1}} \left| f(\left| Y, X \right>) \right| |Y \mathbf{X} \rangle = \left( |\boldsymbol{\nu} \rangle\_2 \right) \end{aligned} \tag{14}$$

### 4. Proposed scheme

This section will discuss the particulars of embedding and extracting procedures about the proposed steganography scheme that hides a secret text into a cover grayscale image. Assume that the sizes for cover image and secret text are 2<sup>n</sup> � <sup>2</sup><sup>n</sup> and 2<sup>n</sup>�<sup>2</sup> � <sup>2</sup><sup>n</sup>�<sup>1</sup> , respectively, the quantum representation can be formulated in Eqs. (15) and (16).

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

$$|\mathbf{C}\rangle = \frac{1}{2^{\pi}} \sum\_{\mathbf{Y}X=0}^{2^{2n}-1} \bigotimes\_{i=0}^{\mathcal{I}} \mathbf{C}\_{\mathbf{Y}X}^{i} \otimes |\mathbf{Y}X\rangle, \quad \mathbf{C}\_{\mathbf{Y}X}^{i} \in \{0, 1\} \tag{15}$$

$$|T\rangle = \frac{1}{2^{\aleph-\beta/2}} \sum\_{\mathbf{YX}=0}^{2^{\aleph-\beta}-1} \bigotimes\_{i=0}^{7} T\_{\mathbf{YX}}^{i} \otimes |Y\mathbf{X}\rangle, \quad T\_{\mathbf{YX}}^{i} \in \{0, 1\} \tag{16}$$

The general framework for the proposed scheme is shown in Figure 7, from which we can see that it is delineated into the classical and quantum domains. The preparation interface can transform classic image data into quantum states, which realizes the function of preparing the quantum image [7]. After the quantum image is stored in quantum states, our proposed quantum image steganography scheme can be implemented to transform the original quantum states to the desired states through the designed embedding circuits. Then, the quantum measurement operation is utilized to retrieve the processed image information. And once identified, the stego image is sent to the receiver by the public channel. The extraction operations are similarly for the receiver.

### 4.1 Embedding procedure

where, ΩYX is a unitary operation as shown in Eq. (11), which is manipulating on

YX : j i <sup>0</sup> ! <sup>0</sup> <sup>⊕</sup> <sup>T</sup><sup>i</sup>

quantum identity gate. Therefore, the text message value in position (Y, X) is

0 ⊕ T<sup>i</sup> YX

Applying UYX on intermediate state j i ψ 1, the transformation is shown in

i¼0

∑ 2m�<sup>1</sup>

ji6¼YX

∑ 2m�<sup>1</sup>

ji6¼YX

is transformed from j i ψ <sup>1</sup> is the improved representation of quantum text.

UYX

2n�<sup>1</sup> <sup>j</sup>¼<sup>0</sup>,i¼<sup>0</sup>

!

j i <sup>0</sup> <sup>⊗</sup><sup>8</sup> j iji

> ∑ 2m�<sup>1</sup>

j i <sup>0</sup> <sup>⊗</sup><sup>8</sup>

!

!

!

j iji <sup>þ</sup> j i <sup>0</sup> <sup>⊗</sup><sup>8</sup>

j iji þ j i f Yð Þ ;X j i YX

j iji <sup>þ</sup> <sup>Ω</sup>YXj i <sup>0</sup> <sup>⊗</sup><sup>8</sup>

j i YX

j i YX

ji6¼YX

j i <sup>0</sup> <sup>⊗</sup><sup>8</sup>

j i <sup>0</sup> <sup>⊗</sup><sup>8</sup>

To store all the values to the quantum state, the whole operation U that consists of 2<sup>n</sup>þ<sup>m</sup> sub-operations and shown in Eq. (14) is necessary. The final state j i <sup>ψ</sup> <sup>2</sup> that

j i <sup>0</sup> <sup>⊗</sup><sup>8</sup>

!

<sup>Ω</sup>YXj i <sup>0</sup> <sup>⊗</sup><sup>8</sup>

This section will discuss the particulars of embedding and extracting procedures

about the proposed steganography scheme that hides a secret text into a cover grayscale image. Assume that the sizes for cover image and secret text are 2<sup>n</sup> � <sup>2</sup><sup>n</sup>

j i YX

j i YX

j i f Yð Þ ;X j i YX ¼ j i ψ <sup>2</sup>

, respectively, the quantum representation can be formulated in

� �

� �

�

YX is a (n+m)-CNOT gate, otherwise if T<sup>i</sup>

YX

¼ ⊗ 7 i¼0 Ti YX � � � (11)

YX is a

(13)

(14)

YX <sup>¼</sup> 0 then <sup>Ω</sup><sup>i</sup>

¼ j i f Yð Þ ;X (12)

� �

j i ψ <sup>1</sup> for altering digital representation of characters to the quantum state.

ΩYX ¼ ⊗ 7 i¼0 Ωi YX

> 7 i¼0

1 <sup>2</sup><sup>n</sup> <sup>∑</sup> 2n�<sup>1</sup>

<sup>2</sup><sup>n</sup> UYX <sup>∑</sup>

<sup>2</sup><sup>n</sup> <sup>∑</sup> 2n�<sup>1</sup> <sup>j</sup>¼<sup>0</sup>,i¼<sup>0</sup>

<sup>2</sup><sup>n</sup> <sup>∑</sup> 2n�<sup>1</sup> <sup>j</sup>¼<sup>0</sup>,i¼<sup>0</sup>

> 2 Ym�1 X¼0

<sup>2</sup><sup>n</sup> <sup>∑</sup> 2n�<sup>1</sup>

j¼0 ∑ 2m�<sup>1</sup>

j¼0 ∑ 2m�<sup>1</sup>

j¼0 ∑ 2m�<sup>1</sup>

i¼0

i¼0

i¼0

j¼0 ∑ 2m�<sup>1</sup>

�

Ωi

YXj i <sup>0</sup> � � <sup>¼</sup> <sup>⊗</sup>

And if T<sup>i</sup>

Eq. (13).

YX <sup>¼</sup> 1, <sup>Ω</sup><sup>i</sup>

<sup>Ω</sup>YXj i <sup>0</sup> <sup>⊗</sup><sup>8</sup> <sup>¼</sup> <sup>⊗</sup>

preparing by employing unitary operationΩYX:

Advances in Quantum Communication and Information

� � <sup>¼</sup> UYX

¼ 1

¼ 1

¼ 1

U ¼ 2 Yn�1 Y¼0

� � <sup>¼</sup> <sup>U</sup> <sup>1</sup>

¼ 1 <sup>2</sup><sup>n</sup> <sup>∑</sup> 2n�<sup>1</sup>

¼ 1 <sup>2</sup><sup>n</sup> <sup>∑</sup> 2n�<sup>1</sup>

U j i ψ <sup>1</sup>

4. Proposed scheme

and 2<sup>n</sup>�<sup>2</sup> � <sup>2</sup><sup>n</sup>�<sup>1</sup>

18

Eqs. (15) and (16).

7 i¼0 Ωi

UYX j i ψ <sup>1</sup>

The embedding procedure in the proposed scheme is as follows.


Figure 7. The general framework of the proposed scheme.

then 2n�<sup>2</sup> � <sup>2</sup>n�<sup>1</sup> pixels in the top-left corner, that is, the first block <sup>B</sup><sup>000</sup> is designated. For quantum text, the binary length of text message is eight, i.e., the text can be separated into eight bit-planes. Assume that the highest bit is embedded in B000, the second highest bit is embedded in B001, and so on. An example of partition with cover image size of 23 � <sup>2</sup><sup>3</sup> and secret text size of 21 � 22 is illustrated in

After dividing the cover image, the quantum equal (QE) circuit is used to compare the coordinates of a block and quantum text. Then, the stego image j iS is obtained after embedding process. More specifically, taking one of the blocks as an

where the function GRAY ið Þ is the Gray code value of i, and the function SWAP ið Þ ; j is to swap the value of i and j. The corresponding embed block circuit is shown in Figure 10a and b presents the integrated embedding circuit that contains the selection of the block of cover image, the comparison of the coordinates, and the embedding process of the bit-planes of secret text into the LSB of

Like all the information hiding papers, only the receiver can extract the message. But it is worth pointing out the receiver only uses the stego image to extract the secret text in our scheme that means it is a blind scheme. The extracting procedure

by using inverse Gray code transform in order to obtain

1. Extract and reorganize the bit plane from the stego image to obtain the

� �

j i xn�<sup>2</sup>xn�3…x<sup>0</sup> of j i C is equal to the

by the following pseudo-code.

� �

is embedded in C<sup>0</sup> �

Figure 9.

4.1.3 Embedding

coordinates of T^

If GRAY C<sup>7</sup>

SWAP C<sup>0</sup>

SWAP C<sup>0</sup>

If GRAY C<sup>7</sup>

SWAP C<sup>0</sup>

SWAP C<sup>0</sup>

End

cover image.

End If <sup>T</sup>^<sup>i</sup> � � � E = 0j i

If <sup>T</sup>^<sup>i</sup> � � � E = 1j i

� � � , <sup>T</sup>^<sup>i</sup> � � � E

YXC<sup>6</sup> YXC<sup>5</sup> YX � � is even

YXC<sup>6</sup> YXC<sup>5</sup> YX � � is even

YX; <sup>1</sup> � � Else if GRAY C<sup>7</sup>

YX; <sup>0</sup> � �

YX; <sup>0</sup> � � Else if GRAY C<sup>7</sup>

YX; <sup>1</sup> � �

4.2 Extraction procedure

can be described as follows.

disordered text T^

2. Descramble T^

21

� � � .

� � �

original secret textj i T .

illustration, if the coordinates yn�<sup>3</sup>yn�4…y<sup>0</sup>

A Novel Quantum Steganography Scheme Based on ASCII

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

YXC<sup>6</sup> YXC<sup>5</sup> YX � � is odd

YXC<sup>6</sup> YXC<sup>5</sup> YX � � is odd

�

### 4.1.1 Scrambling

For purpose of improving the security of secret text, the text message of j i T will be scrambled by Gray code transform before the embedding procedure. As mentioned in Subsection 2.2, in the eight qubits which store the text message, seven CNOT gates are used according to Gray code transform method, while the qubits representing for position information are not changed by quantum gates, the corresponding circuit is demonstrated in Figure 8.

#### 4.1.2 Partitioning

In the proposed scheme, the 2<sup>n</sup> � <sup>2</sup><sup>n</sup> cover image is divided into 4 � 2 blocks sized 2<sup>n</sup>�<sup>2</sup> � <sup>2</sup><sup>n</sup>�<sup>1</sup> . We define these blocks as Bij, where ji¼ <sup>i</sup> yn yn�<sup>1</sup> and j i¼ j j i xn are called control coordinates because if they are restricted as a specific value, then one of blocks will be selected. For example, if their values are equal to 00 j i and 0j i,

Figure 9. An example of partition.
