1. Introduction

With the advantage of quantum physics, quantum computer has demonstrated a bright prospect over than the classic computer, especially in Grover's database searching algorithm [1] and Shor's prime factor decomposition algorithm [2].

Over the past few decades, teams of researchers have been noticed by quantum image processing that is a young emerging cross-discipline of image processing and quantum mechanics. The investigation in this direction is how to construct the quantum representations to represent images on quantum computer at first. So various quantum representations have been proposed, such as, Qubit Lattice [3], entangled image [4], real ket [5], flexible representation of quantum images (FRQI) [6], a novel enhanced quantum representation of digital images (NEQR) [7], multichannel representation for quantum images (MCRQI) [8], a normal arbitrary quantum superposition state (NAQSS) [9], and a novel quantum representation for color digital images (NCQI) [10]. Secondly, many kinds of quantum image processing algorithms were developed, such as geometric transformations [11, 12], image translation [13–15], image scaling [16–18], image scrambling [19–21], image segmentation [22], feature extraction [23], edge detection [24], and image matching [25, 26].

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 characteristics and use value of the ordinary message.

2. Preliminaries

the NEQR model as follows:

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

j i YX <sup>¼</sup> j i <sup>Y</sup> j i <sup>X</sup> <sup>¼</sup> yn�<sup>1</sup>yn�<sup>2</sup>…y<sup>0</sup> �

> YX Cq�<sup>2</sup> YX …C<sup>0</sup> yx

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

A Novel Quantum Steganography Scheme Based on ASCII

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

where, j i YX represents the position information and Ci

� �

E , C<sup>i</sup>

or American English is used consistently in your chapter.

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

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

j i CYX j i <sup>Y</sup> j i <sup>X</sup> <sup>¼</sup> <sup>1</sup>

j i xn�<sup>1</sup>xn�<sup>2</sup>…x<sup>0</sup> , yi

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,

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

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

YX ∈ f g 0; 1 , i ¼ 0, 1, …, q � 1

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

⊗ q�1 i¼0 Ci

> YX � � �

, xi ∈ f g 0; 1 , i ¼ 0, 1, …, n � 1

YX⊗j i YX (1)

encodes the color

(2)

2.1 NEQR

information.

respectively.

2.2 Gray code

follows:

Figure 1.

13

j i <sup>C</sup>YX <sup>¼</sup> <sup>C</sup><sup>q</sup>�<sup>1</sup>

� � �

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

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 help from classical computer.

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 temperatures.

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 describe it in the remaining sections.

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.
