Pattern-based quantum text watermarking: Securing digital content with next-Gen quantum techniques

Summary

As pioneers of next-generation watermarking technologies, quantum methods offer advanced solutions for securing digital text copyright. Quantum text representation is a prerequisite for realizing quantum watermarking. Thus we propose a generalized quantum text representation (GQTR) model for English text. It can accurately represent and retrieve characters, words, and texts. Based on the proposed GQTR, a multi-scale pattern-based quantum text watermarking (MPQTW) scheme is proposed, which embeds multi-scale images into quantum text simultaneously to protect digital text copyrights. To evaluate the scheme, we design various metrics. The quantum circuits for GQTR and MPQTW are designed in detail. Finally, we evaluate the effectiveness and performance of the MPQTW scheme in terms of imperceptibility, robustness, and embedding rate. The results and analysis show that MPQTW has good performance.

Highlights

• •Explored quantum text encoding model GQTR for quantum text algorithms
• •Proposed quantum text watermarking scheme MPQTW to protect text copyright
• •Designed multiple evaluation metrics to analyze the performance of MPQTW
• •Quantum circuits for GQTR and MPQTW are provided and analyzed

Physics; Quantum physics

Introduction

In the current digital era, the wide range of electronic data of all kinds has brought unprecedented convenience, while also exposing new information security challenges.¹ In order to effectively protect multimedia copyrights, digital watermarking techniques are widely used. Digital watermarking is an information hiding technology that embeds specific watermark information into digital media (e.g., text, images, audio, or video) for the purposes of copyright protection,² content authentication,³ tracking, and secret communication.⁴ A watermarking system consists of two main processes: embedding the watermark into the original data, and extracting the watermark from the watermarked data or the attacked watermarked data. Digital watermarking technology has received widespread attention as one of the important means of information security. Watermarking technology not only protects copyright, but also plays an important role in data integrity verification and confidential information transmission. In recent years, researchers in different fields have explored the application and improvement of watermarking technology in depth. Gutub et al.⁵ emphasized the application of watermarking technology in copyright authentication in their study and proposed an innovative approach to enhance the intelligent trust and robustness of Arabic text. By comparing the two new approaches, the study not only improves the accuracy of watermarking, but also demonstrates its functionality and effectiveness in the face of potential threats, providing new perspectives and solutions to watermarking technology in the field of electronic writing. With the popularization of the internet and the advent of the information age, digital texts, as an important way of information storage and dissemination, account for a large proportion of electronic data. Moreover, Gutub’s research³ provides insights in the area of exploring how modern technology serves religious practices. The results of the study show that these apps play an important role in facilitating Hajj rituals, Umrah rituals and prayers, with English, Arabic, and Urdu being particularly prominent. How to protect electronic copyrights and prevent digital texts from being illegally copied, tampered with and plagiarized are of increasing concern. Traditional digital watermarking techniques have made significant progress in the field of images,² audio,⁶ and video,⁷ but the copyright protection of text data are still a challenge. The main problem in text watermarking research⁸ is how to embed watermarks into text without affecting its readability, making it robust and confidential. However, unlike other forms of watermarking such as image and audio, the research on text watermarking⁹ faces greater challenges. On the one hand, text is more intuitive and simple to edit and modify, and any changes may draw attention or interfere with the information in the original text, and on the other hand, text does not have redundant spatial and frequency domains.¹⁰ Text watermarking is used in a wide range of application scenarios, such as the detection of copyright protection, academic plagiarism, etc. In copyright protection, text watermarking can be embedded in texts and datasets to maintain their intellectual property rights; in the academic field, it helps to detect whether a text is generated by a language model or not, thus maintaining academic integrity. Therefore, designing a robust and feasible text watermarking algorithm is a challenging task.

With the rapid development of emerging quantum technology,¹¹ it offers advantages¹² that cannot be matched by traditional methods, such as the ultra-high efficiency of quantum computing^13,14 in handling complex algorithms and big data, and the unconditional confidentiality of quantum communications.¹⁵ These characteristics give quantum technology the potential to break through traditional limitations in a number of fields and drive innovation and progress in related industries. It is necessary to introduce the importance of quantum technologies in future watermarking techniques. Although traditional digital watermarking techniques have been remarkably effective in securing the copyright and integrity of media content, in view of the powerful capabilities of quantum information technology and possible potential quantum threats, it becomes crucial to study quantum watermarking techniques.¹⁶ The essential reason for researching quantum watermarking technology is exploitation and defense, which means that we need to both take advantage of powerful quantum technology and use it to defend against quantum threats that may arise in the future quantum era.¹⁷ Quantum watermarking technology utilizes special quantum properties such as the no-cloning theorem¹⁸ and phenomena such as quantum entanglement,¹⁹ which can provide higher watermark data security. It provides a more secure, efficient, and robust watermarking solution for the future quantum information era. In addition, quantum watermarking technology benefits from the superposition state²⁰ and entanglement state properties of the qubits, which can embed more watermark information compared to traditional methods, thus significantly increasing the capacity of data transmission.^21,22

As a matter of fact, quantum watermarking technology as an emerging and hot means of information security has been applied in a variety of scenarios, such as quantum image watermarking^23,24 and quantum audio watermarking.²⁵ Quantum image watermarking provides a new method for image copyright protection²⁶ and integrity verification by embedding watermark information in quantum images, and many quantum image representation models are available.^27,28 Quantum audio watermarking,²⁹ on the other hand, utilizes quantum audio representations³⁰ to embed watermarks in the quantum states of audio signals for audio content protection and verification. Although quantum watermarking technology has made some progress in these areas,²⁵ there are still many other potential watermarking scenarios that have not yet fully utilized quantum technology, such as quantum watermarking of the text content. Currently, there is still a gap in the research of quantum text watermarking, and there is an urgent need to adopt quantum watermarking technology to enhance the security level³¹ of text information.

Therefore, the study of quantum text watermarking is promising and meaningful. The prerequisite for realizing quantum text watermarking is the quantum representation of classical text information. However the quantum representation model for text has not been developed yet. Thus, we first propose a generalized quantum text representation (GQTR) model for English text. It enables precise quantum representation and retrieval of textual information. Subsequently, based on the GQTR, we propose a multi-scale pattern-based quantum text watermarking (MPQTW) scheme, which allows for the simultaneous embedding of multi-scale watermarks into the text to improve the embedding capacity and robustness. In this paper, we provide a detailed description about the definitions and expressions in the GQTR. We also design detailed quantum preparation circuits for GQTR and quantum watermarking circuits for the MPQTW. To evaluate the imperceptibility, robustness, and capacity of our proposed MPQTW, we carry out a series of evaluation experiments with satisfactory results. The significant contributions of the research in this paper are summarized and listed as follows.

• •A pioneering GQTR for text representation is proposed. Quantum encoding of English characters, words and text is realized. It lays the foundation for quantum text algorithms.
• •A MPQTW scheme for securing text copyright is proposed for the first time. It realizes embedding multiple image watermarks in significant text content. It has the advantages of blind extraction with no modification of the original text content.
• •Multiple metrics for evaluating quantum text watermarking with multiple watermarks are designed. The proposed MPQTW method is comprehensively evaluated through simulation experiments. The results show that it has good robustness against deletion, insertion, and substitution attacks.
• •Detailed quantum circuits for GQTR preparation and MPQTW watermarking are provided. The quantum circuits are also illustrated and analyzed.

The next is organized as follows. Section “related work” introduces the proposed GQTR model. Section “the MPQTW scheme” describes the proposed MPQTW scheme. Section “quantum circuits” provides detailed quantum circuits for GQTR preparation and MPQTW watermarking and analyzes the complexity. Section “results” gives simulation experimental results and analysis. Section “discussion” discusses the work and results. Section “conclusions and future work” summarizes the research in this paper.

Related work

Quantum signal representation is of crucial importance in the field of quantum information. In current research, a variety of quantum representation models for images and audio exist. These models provide effective ways for image and audio information to be processed and transmitted in the quantum regime, etc.

There are unique properties in quantum image representations that make different quantum image processing purposes achievable.³² At present, many achievements have been obtained to promote the development of this field. The Qubit Lattice³³ quantum image representation was proposed first by Venegas et al. After that, Latorre et al. put forward a quantum representation named Real Ket. Le et al. proposed a new flexible representation of quantum images (FRQI).³⁴ It should be noted that FRQI uses normalized states to store the positional and color information of each pixel in the image, so the number of qubits needed for quantum image preparation is small. Yan et al. released a survey on quantum image representation.²⁷ This survey summarizes eight typical quantum image representations and discusses the progress in this field until 2016. In addition, the similarities, differences, and applications of these quantum image representations are reviewed in the survey. Since then, a series of new quantum image representations have emerged. Su et al. issued a review on quantum image representation.²⁸ This review collects 23 quantum image representations, describes in detail the definitions and demonstrations of these quantum image representations, and also summarizes and compares the methods. Currently, quantum image representation involves normal arbitrary quantum superposition state (NAQSS),³⁵ quantum states for M colors and N coordinates of an image (QSMC and QSNC),³⁶ simple quantum representation of infrared images (SQR),³⁷ quantum log-polar images (QUALPI),³⁸ novel enhanced quantum representation (NEQR),³⁹ Caraiman’s quantum image representation (CQIR),⁴⁰ multi-channel quantum images (MCQI),⁴¹ improved NEQR (INEQR),⁴² a generalized model of NEQR (GNEQR),⁴³ a novel quantum representation of color digital images (NCQI),⁴⁴ a bitplane representation of quantum images (BRQI).⁴⁵

The research on quantum audio representation is still in the exploratory stage, and some quantum audio methods have been proposed. In 2016, Wang proposed the quantum representation of digital audio (QRDA).⁴⁶ The amplitude information is represented as an integer in the QRDA model, and the negative amplitude numbers are shifted to positive numbers by translation. In 2018, Yan et al. proposed flexible representation of quantum audio (FRQA).⁴⁷ The FRQA is very similar to the QRDA model, with the difference that the FRQA model represents negative amplitude values as two’s complement. In 2019, Şahin and Yılmaz proposed a quantum representation of multichannel audio (QRMA)³⁰ model inspired by the quantum image representation. The amplitude information in the QRMA model is stored in the same way as in the FRQA model, where negative integers are stored in binary notation. However, when the amplitude of the signal is represented as an integer, it is not possible to operate with decimal numbers. In the same year, Li et al. proposed a quantum representation of digital signals (QRDS)⁴⁸ similar to FRQA. The amplitude values are represented as floating point numbers rather than just integers. The quantum state of the amplitude information consists of one quantum bit (sign qubit), m qubits (integer part) and ($n-m$)-qubits (fractional part). In 2020, Zhang et al. proposed generalized floating point representation of quantum signals (GFPRQS),⁴⁹ which is represented in floating point format of IEEE-754. Quantum states with amplitude information require $\left(p+q\right)$-qubits. In QRDA, FRQA, and QRMA models, the amplitude information is stored in integer form. In the QRDS and GFPRQS models, the amplitude information is represented as floating point numbers. Both the QRDS and GFPRQS models allow the amplitude information to be represented by a wide range of decimal numbers.

Proposed methods

The GQTR model

The composition of the English language consists mainly of components such as letters, words, phrases, sentences and paragraphs. A word is a basic unit made up of one or more letters, while a phrase is a unit of language made up of one or more words, which is usually a combination of complete meaning. A sentence is a unit of language consisting of several words and phrases. It is used to express a complete thought or message. A paragraph is a unit of text consisting of a group of related sentences that are organized to present a series of ideas or points of view. In the proposed GQTR, we first proposed the encoding method of English letters, numbers and two important symbols (placeholder and separator signs) in order to accurately represent any English text. Then, the quantum representation of arbitrary words is realized by entangling the letter quantum states with the quantum information of the spelling order of the words. The representation of English words is proposed. Finally, based on the representation of English words, the quantum representation of sentences or texts is realized by quantum entanglement of a series of words with quantum information of a particular order.

First, we present the quantum coding of the English alphabet. In the GQTR, we propose a set of codes with a total of 64 symbols including 52 case-sensitive alphabets, 10 Arabic numerals and two common significant symbols. Table 1 shows the encoding rules. Since the classical encoding of each character is 6 bits, we use 6 qubits to carry the corresponding character information. For example, the classical code of “D” is 001000, then its quantum form is $|001000⟩$.

Table 1.

GQTR alphabet, Arabic numerals and character coding

Symbol	Code	Symbol	Code	Symbol	Code	Symbol	Code
_	000000	’	000001	A	000010	a	000011
B	000100	b	000101	C	000110	c	000111
D	001000	d	001001	E	001010	e	001011
F	001100	f	001101	G	001110	g	001111
H	010000	h	010001	I	010010	i	010011
J	010100	j	010101	K	010110	k	010111
L	011000	l	011001	M	011010	m	011011
N	011100	n	011101	O	011110	o	011111
P	100000	p	100001	Q	100010	q	100011
R	100100	r	100101	S	100110	s	100111
T	101000	t	101001	U	101010	u	101011
V	101100	v	101101	W	101110	w	101111
X	110000	x	110001	Y	110010	y	110011
Z	110100	z	110101	0	110110	1	110111
2	111000	3	111001	4	111010	5	111011
6	111100	7	111101	8	111110	9	111111

The ‘_’ indicates a placeholder, which is a space in the text.

Then, we propose the quantum representation of English words. We denote the quantum form of the word $W_p$ as $|W_p⟩$, its expression is as follows.

$$|W_p⟩=\frac{1}{\sqrt{2^a}}\sum _{r=0}^{2^a-1}\left|c\left(r\right)⟩\right|r$$ (Equation 1)

where $c\left(r,h\right)$ is the codes of characters in Table1, and r is the characters order information. The $r=r_{a-1}{r}_{a-2}\dots r_i\dots r_0$, and $r_i\in \left\{0,1\right\}$. The a is the number of qubits needed to represent the longest word with length of $l_w$. In addition, $c\left(r,h\right)$ requires 6 qubits, so it takes $a+6$ qubits to represent a word. Note that $a=\lceil {\log }_2{l}_w\rceil$.

Since the length $l_w$ of the word is random, due to the quantum superposition and quantum entanglement in quantum representation, if $l_w$ is not an integer power of 2, then redundant information is generated. Therefore, in the proposed GQTR, we fill all these redundant positions to the right with the placeholders in Table 1. Then, the quantum representation is carried out according to the definition of Equation 1. For easy understanding, we take the word “quantum” as an example to explain. Figure 1 shows the representation of the “quantum”. First, the length of “quantum” is 7, so 3 qubits are needed. However, 3 qubits produce 8 order information, so there is a redundant order filled with a placeholder. Then, it is sufficient to derive the quantum representation of the word “quantum” from the expression in Equation 1 (also seen in Equation 2).

$$|\text{Quantum}⟩=\frac{1}{2\sqrt{2}}\left(|100010⟩|000⟩+\left|101011⟩\right|001⟩+\left|000011⟩\right|010⟩+\left|011101⟩\right|011⟩+\left|101001⟩\right|100⟩+\left|101011⟩\right|101⟩+\left|011011⟩\right|110⟩+\left|000000⟩\right|111⟩\right)$$ (Equation 2)

Figure 1.

Demonstration of the quantum representation of the word using the GQTR for “Quantum”

We have realized the quantum representation of words, and then next, we elaborate the quantum representation of sentences. As a matter of fact, an English text is composed of many words organized in a particular order. Therefore, we simply use a set of qubits for representing order information of words and then entangle them with the qubits sequence of words. The quantum representation for the sentence evolving from Equation 1 is shown in the further text.

$$|T⟩=\frac{1}{\sqrt{2^{a+b}}}\sum _{h=0}^{2^b-1}\sum _{r=0}^{2^a-1}|c\left(r,h\right)⟩|\mathrm{r}⟩|\mathrm{h}$$ (Equation 3)

where h is the order of words in a sentence, $h=h_{b-1}{h}_{b-2}\dots h_i\dots h_0$, and $h_i\in \left\{0,1\right\}$. The b is the number of qubits needed to encode the length $l_s$ and $b=\lceil {\log }_2{l}_s\rceil$.

To clearly explain the quantum form of sentences in our text model, we show the quantum representation of the sentence “quantum text model research” in Figure 2. It can be seen that the text is in fact constructed in the form of a matrix in terms of characters, the redundant positions are filled with placeholders. Each row is a word. Its quantum representation is shown in Equation 4, the complete unfolding is simply a matter of bringing in the representation of each word according to Equation 1.

$$|Text⟩=\frac{1}{2}\left(\left|\text{Quantum}⟩\right|00⟩+\left|\text{Text}⟩\right|01⟩+|\text{Model}⟩|10⟩+\left|\text{Research}⟩\right|11⟩\right)$$ (Equation 4)

In terms of quantum cost under the premise of considering only characters, it can be seen from the previous definition that the quantum cost required to represent a text containing $l_w\times l_s$ characters in GQTR is no more than $a+b+6$ qubits. This shows that quantum information technology brings great potential in storage and computation.

Figure 2.

Demonstration of the quantum representation for the sentence “Quantum Text Model Research” using the GQTR

To retrieving the text from GQTR $|T⟩$ in Equation 3, we define an observable operator to obtain the text information. Assume that we want to get the text information of the r-th character of the h-th word, deboted as $|T_{rh}⟩$.

$$\mathrm{\Psi }=\sum _{rh=0}^{2^{a+b}-1}{I}^{\otimes 6}\otimes \left|\text{rh}⟩⟨\text{rh}\right|$$ (Equation 5)

$$|T_{rh}⟩=\left|c\left(r,h\right)⟩\right|rh$$ (Equation 6)

According to the definition of GNETR-PT, it is known that the character information is stored in the first qubits sequence $|c\left(r,h\right)⟩$ in the $|T_{rh}⟩$. Next, we use projection measurements to retrieve the character code from the quantum state.

$$\mathbb{M}=\sum _{m=0}^{5}m|\mathrm{m}⟩⟨\mathrm{m}|$$ (Equation 7)

$$⟨c\left(r,h\right)\left|\mathbb{M}\right|c\left(r,h\right)⟩=\sum _{m=0}^{5}m⟨c\left(r,h\right)\Vert \mathrm{m}⟩⟨\mathrm{m}\Vert c\left(r,h\right)⟩=c\left(r,h\right)$$ (Equation 8)

With our defined quantum measurement operation, the exact code of each character can be obtained from the quantum text. And then the plaintext characters can be obtained according to the code table (see Table 1). Eventually, when all the characters are recovered, the words can be obtained, and then all the words can be obtained to get the whole text content.

The quantum representation of text has been solved by the previous GQTR. But this is only the quantum state encoding of the textual information without including additional textual attributes. However, in practical applications, text has many important attributes other than information, such as font formatting, color, size, thickness, etc. to express unique artistic effects. This information can also be expressed by means similar to character encoding, thus allowing quantum text to be processed to utilize more information. Ultimately, we give the generalized expression of GQTR as follows:

$$|GT⟩=\frac{1}{\sqrt{2^{a+b}}}\sum _{h=0}^{2^b-1}\sum _{r=0}^{2^a-1}|\mathrm{A}\left(\mathrm{r},\mathrm{h}\right)⟩|\mathrm{c}(\mathrm{r},\mathrm{h})⟩\left|\mathrm{r}⟩\right|\mathrm{h}⟩$$ (Equation 9)

where $|A\left(r,h\right)⟩$ is a text attribute that carries various extra information about each character. Note that $|A\left(r,h\right)⟩$ can be customized and set according to actual needs. Its quantum encoding process can be referred to the previous character encoding method.

The MPQTW scheme

With the development of large language modeling, text watermarking technology has received attention. To prevent text misuse and protect intellectual property. It can be used for watermark embedding of sensitive text, including identification of generated text by large language models. Text watermarking techniques involve embedding additional information in text data that is normally imperceptible to the reader, but can be detected and recognized by watermark detection systems. This embedding process does not significantly change the visual effect or readability of the text, but can provide a mechanism for proving ownership of the text, ensuring the integrity of the content, etc. Text watermarking has a wide range of applications including, but not limited to, digital copyright management, and anti-counterfeiting verification of documents. In this way, text watermarking provides strong support for the security and authenticity of electronic texts.

GQTR preparation

In the proposed quantum text watermarking scheme, we need to use the color attribute of the text. The color information of a character is a grayscale value ranging from 0 to 255, its visual variation is shown in the Figure 3. Grayscale values in the range 0–255 have 8 bits in classic binary form. Whereas in quantum representation, due to quantum entanglement and quantum superposition properties, we only need four qubits. We use one qubit to encode the color information, the remaining three qubits are used to represent the order information of the grayscale binary sequence. We define the quantum representation $g\left(x\right)$ for grayscale values as follows:

$$g\left(x\right)=\frac{1}{2\sqrt{2}}\sum _{x=0}^7|\mathrm{v}⟩|\mathrm{x}⟩$$ (Equation 10)

where v is the color qubit, and $v\in \left\{0,1\right\}$. The $x\in Z$ is the order value of 8 bits in grayscale binary form and x ranges from 0 to 7. We take the grayscale value “15” as an example, its binary form is “00001111”. The quantum representation is as follows according to Equation 10.

$$|15⟩=\frac{1}{2\sqrt{2}}\left(\left|1⟩\right|000⟩+\left|1⟩\right|001⟩+\left|1⟩\right|010⟩+\left|1⟩\right|011⟩+\left|0⟩\right|100⟩+\left|0⟩\right|101⟩+\left|0⟩\right|110⟩+\left|0⟩\right|111⟩\right)$$ (Equation 11)

Figure 3.

The color variation of text in GQTR

Finally, based on Equation 9, we get the required GQTR expression as follows.

$$|GT⟩=\frac{1}{\sqrt{2^{a+b+3}}}\sum _{h=0}^{2^b-1}\sum _{x=0}^7\sum _{r=0}^{2^a-1}|\mathrm{c}\left(\mathrm{r},\mathrm{h},\mathrm{x}\right)⟩|\mathrm{v}\left(\mathrm{r},\mathrm{h},\mathrm{x}\right)⟩|\mathrm{r}⟩|\mathrm{h}⟩|\mathrm{x}⟩$$ (Equation 12)

The quantum cost required to represent a text containing $l_w\times l_s$ characters in the GQTR is no more than $a+b+10$ qubits.

MPQTW details

There can be various forms of watermark in text watermarking based on quantum representation, such as image, text, quantum key, etc. Among them, image is the option that deserves attention mainly for the following reasons. First of all, quantum image processing is an emerging research field that utilizes the power of quantum computing to process image data. Quantum image representation can be essentially interpreted as a quantum information matrix, which is more suitable for quantum watermarking algorithms than one-dimensional text or random secret key information. Second, embedding images as watermarks in text can utilize the richness and visual impact of images to enhance the copyright protection and authentication of text content. In addition, research on using binary information and text as watermarks is common, but embedding images as watermarks in text still needs to be explored. The combination of image and text is also an innovative watermarking technique. Thirdly, quantum text watermarking technology faces many technical challenges, such as the accurate representation of quantum information, the embedding and extraction of quantum watermarks, the design of quantum watermarking circuits, etc. Quantum image technology has achieved remarkable results, choosing images as watermarks can promote the solution of these technical problems and the development of quantum information processing technology.

Based on the proposed GQTR, we propose the MPQTW scheme using multi-scale watermarks. It can embed multiple watermark patterns into quantum text. It also allows embedding watermarks with different sizes in any suitable region of the text to enhance security and robustness. Based on proposed GQTR-CE, we embed the watermark information into the last 4 quantum least significant bit (QLSB) of the color qubits of each character. The effect of last 4 QLSBs change for the grayscale value on the color cannot be recognized by the human eye, thus ensuring the imperceptibility of the watermark while increasing the embedding capacity. Figure 4 illustrates the detailed MPQTW flowchart including the embedding and extraction processes.

Figure 4.

Flowchart of the proposed Multi-scale Pattern-based Quantum Text Watermarking (MPQTW) scheme, including embedding and extraction processes

It is worth emphasizing that the proposed MPQTW scheme can be used to embed watermarks into important or main parts of the text, or even into specified areas. Therefore, we declare that the text prepared quantitatively in the MPQTW scheme is cleaned. In other words, we have removed meaningless prepositions of less than 4 characters, as well as articles a, an, and the from the original English text.

First, we start by stating that the quantum representation model of the preparation of watermark images with size of $2^m\times 2^n$ can be done using a variety of quantum image representation models, such as INEQR.⁴² In order to make watermark embedding easy to implement, we prepare the classical watermark as a quantum image using INEQR quantum preparation circuits and grayscale depth q is 1. There are three steps in the embedding process, described in the further text.

• •Step 1. Assume that we have a prepared English text, and one or more watermarks of different sizes. We need to first select the appropriate watermarking area based on the size of the watermark $m\times n$, the length of the text and the words. Each watermark has its own text area for embedding. The embedding region selection strategy is explained in the further text. Assume we have a text consisting of words $W_0$, $W_1$, $W_2$, …, $W_{k-1}$, where the region suitable for embedding a watermark is $W_i$, $W_{i+1}$, $W_{i+2}$, …, $W_{i+\delta }$. The size of the watermark is $m\times n$, m and n are both integer powers of 2. Note that the watermark embedding region in the text has to satisfy the following relationship with the watermark.

$$\{\begin{array}{ll}& L\left(W_{em}\right)\ge \lceil \frac{n}{4}\rceil \\ & \delta +1\ge m\end{array}$$ (Equation 13)

• •Step 2. As illustrated in Figure 4, we need to perform quantum state preparation of the information {$i,j,\dots$} from selected text region for each watermark. We individually prepare the quantum information of the corresponding embedding position in the quantum text representation, which facilitates us to implement accurate watermark embedding.
• •Step 3. Finally, we need to prepare the quantum text using the proposed GQTR-CE. Then, the embedding is implemented. There are two implementations, the first one is to prepare the quantum text and quantum watermark first, then implement the quantum watermarking process. The other one is more concise, i.e., the watermarking information is directly embedded in the quantum text during the preparation process, eliminating the need for an independent embedding process. The former process is not difficult to understand, in order to explain the preparation and watermarking process of the latter, we give the explanation as follows. Since both processes perform quantum gate operations on the same target qubits, we merge preparation and watermarking processes to realize quantum state evolution together. This reduces the number of quantum gates. The English text, the watermark, the quantum information of the watermarking region are used as inputs, then the quantum watermarked text can be obtained after the GQTR preparation with internal watermarking process. The classical text content can be accurately retrieved using a finite number of quantum measurements.

There are two steps in the extraction process, described in the further text.

• •Step 1. The classical watermarked text is represented into quantum form using the GQTR-CE in order to facilitate the watermark extraction in the quantum system.
• •Step 2. Then, watermark extraction is done on the whole text by quantum extraction algorithm. Note that since the extraction is blind, no additional information is needed except the watermarked text. Therefore, we directly perform global extraction without distinguishing whether it is a watermarked region or not. Note that the extracted global watermark size $m^{\prime }\times n^{\prime }$ satisfies the following relation.

$$\{\begin{array}{cc}& m^{\prime }=2^{\lceil {\log }_2{l}_s\rceil }\\ & n^{\prime }=2^{\lceil {\log }_2{l}_w\rceil +2}\end{array}$$ (Equation 14)

where $l_s$ is the number of words in the text and $l_w$ is the number of characters in the longest word. Therefore, we need to prepare beforehand a quantum binary image of the same size $m^{\prime }\times n^{\prime }$ using the INEQR⁴² method with all pixel values of $|0⟩$. With a finite number of quantum measurements, the extracted watermark image can be accurately retrieved.

Quantum circuits

A quantum circuit⁵⁰ is a fundamental tool for realizing quantum computation and consists of a series of quantum logic gates⁵¹ that operate on qubits. This section provides quantum text preparation circuits for the proposed GQTR, and quantum watermarking circuits including embedding and extraction for the proposed MPQTW. Quantum circuit complexity is also analyzed. Note that the quantum circuit of Figure 5 is for the GQTR-CE. The quantum circuit that ignores the circuit module in the blue area is for the GQTR-PE.

Figure 5.

The quantum preparation circuit of the proposed GQTR

Figure 5 illustrates the quantum text preparation circuit. In addition to the single qubit H gate, we define two single quantum gates as follows. where I and X are the single qubit gate.

$$\{\begin{array}{cc}& U_r=\left(1-c\left(r,h\right)\right)\times I+c\left(r,h\right)\times X\\ & U_x=\left(1-g\left(x\right)\right)\times I+g\left(x\right)\times X\end{array}$$ (Equation 15)

Figure 6 shows the GQTR preparation quantum circuit with internal watermarking for the proposed MPQTW scheme. We define the single quantum gate $U_w$ in quantum preparation and watermarking circuit of Figure 6 as follows, where $x_w\in \left\{0,1,2,3\right\}$ corresponds to the last four QuLSBs of character color qubits. As mentioned earlier, h is the order of the words in the text and r is the order of the characters in the words. The quantum equal (QE)³⁹ module is used to compare two qubits sequences for equality. It utilizes a single qubit to indicate the result, with quantum state $|1⟩$ indicating that they are equal. Otherwise it indicates unequal. The 1-Adder is used to perform an add-one operation on a qubits sequence, e.g., a sequence of qubits $|100⟩$, the output of which after the 1-Adder results in $|101⟩$. Quantum circuit implementation similar to 1-Adder has also been studied in other related work,⁵² with similar complexity.

$$\{\begin{array}{cc}& U_w=P_w\times X+\left(1-P_w\right)\times I\\ & P_w=V_w\left(h-i+1,4r+x_w\right)\end{array}$$ (Equation 16)

Figure 6.

The quantum circuits of the GQTR preparation with internal watermarking for the proposed MPQTW scheme

Figure 7 shows the quantum watermark extraction circuit for implementing watermark extraction. The complexity of a quantum circuit⁵³ is a key metric for evaluating the efficiency of a quantum algorithm, and it is directly related to the running time and resources required for a quantum algorithm. Different types of quantum gates have different complexities. The complexity of a quantum circuit is usually the total number of quantum gates required to construct a particular quantum algorithm. The three quantum circuits in this paper are Figure 5 for quantum text preparation, and Figures 6 and 7 for quantum text watermarking algorithms.

Figure 7.

The quantum circuit of the MPQTW watermark extraction

A complex quantum circuit in quantum computing can be implemented by a series of elementary unitary quantum gates.^53,54 Thus, the complexity of a quantum circuit depends on the number of universal quantum gates required. An n-CNOT gate $\left(n\ge 3\right)$ is equivalent to $2\left(n-1\right)$ Toffoli gates and one CNOT gate, while a Toffoli gate can be realized by six CNOT gates, the complexity of a quantum circuit of n-CNOT gate can be calculated as $12n-11$. An extreme case when all control bits are $|0⟩$, the circuit complexity is no more than $14n-11$. Subsequently, the complexity of the quantum circuits in this paper is analyzed. In GQTR, we use a definite number of H gates with complexity $O\left(1\right)$. The rest are multi-qubit controlled gates, since the single quantum gate $U_r$ ($U_x$) is an I or Pauli X gate, so it is sufficient to consider only the total complexity of multi-qubit controlled X-gates. As the complexity of a multi-qubit controlled X-gate is $O\left(n\right)$, and the number depends on a and b, i.e., $2^{a+b}$ multi-qubit controlled X-gates. Thus the total complexity is $O\left(2^{a+b}\right)$. Moreover, in the proposed GQTR, the preparation circuit complexity of text grayscale values is also considered. Three quantum H-gates as well as eight CCCNOTs are required for each character’s grayscale preparation, because the complexity of each CCCNOT is 25, thus the complexity of quantum preparation of a character’s grayscale value is considered as $O\left(1\right)$. Together with the complexity of $O\left(\left(a+b\right)2^{a+b}\right)$ for the quantum preparation of the plain text analyzed earlier. Consequently, the quantum complexity of GQTR does not exceed $O\left(\left(a+b\right)2^{a+b}\right)$. Similarly, the preparation of the desired watermark image with size of $m\times n$ can be done using INEQR, with a complexity of no more than $O\left(q\left({\log }_{2}m+{\log }_{2}n\right)·2^{{\log }_{2}m+{\log }_{2}n}\right)$.

In addition, we compute the quantum watermarking complexity of the proposed MPQTW. In the embedding process, we use a QE module for constraint sequences and a 1-Adder module for positioning, as well as a CCNOT gate. We use only one CCNOT gate for embedding the prepared INEQR watermark into the gray scale quantum bits of a quantum text character. The complexity of the QE is $O\left(a+b\right)$. The 1-Adder module is composed of quantum X gates controlled by b quantum bits with a total complexity not exceeding $O\left(b^2\right)$. A CCNOT gate can be implemented by 6 base quantum gates. Finally, the quantum watermark embedding complexity does not exceed $O\left(b^2\right)$. The quantum watermark extraction process is faster and more efficient because only one QE is needed to determine the position and one CCNOT to extract the quantum bit information. Therefore, the total complexity of quantum watermark extraction can be considered as $O\left(a+b\right)$.

Results

To evaluate the effectiveness, imperceptibility, and robustness of the proposed MPQTW scheme. We implement a series of simulation evaluation experiments. Since quantum computing still faces challenges at this stage, quantum computers are not yet widely available. Therefore, we simulate the proposed quantum approach using MATLAB 2020b on a conventional computer with an Intel(R) Core(TM) i7 CPU 2.30GHz 16.00-GB RAM. The MATLAB simplifies the representation and processing of matrices as well as vectors. Quantum text representation can be regarded as a matrix form, thus making MATLAB suitable for the simulation. The English text samples used in our experiments are from the publicly available news article dataset BBC News Summary,⁵⁵ downloaded from Kaggle: https://www.kaggle.com/datasets/pariza/bbc-news-summary. We randomly select 6 texts from the dataset for the evaluation experiments. The watermarks are multiple binary images of sizes $8\times 8$, $8\times 16$, $16\times 8$ and $16\times 16$. Visually, these watermarks consist of patterns such as “MPU”, “copy”, “1101C1”, “EL”. We conduct two sets of evaluation experiments for assessing the proposed MPQTW, i.e., effectiveness and performance evaluation experiments. The effectiveness experiments are conducted to embed image watermarks on two randomly selected texts according to the actual requirements in a real situation. The imperceptibility of the watermarks is evaluated first and then the watermarks are extracted after attacking them on demand to evaluate the robustness. Performance experiments are conducted by embedding the same multiple watermarks in five texts of similar size and then evaluate the imperceptibility and robustness. In addition, to quantify the experimental results, we design various metrics for evaluating the performance of text watermarking algorithms for multiple watermark images. Next, we first introduce the definition and meaning of these evaluation metrics, and then describe the experimental results.

Evaluation metrics

Due to the randomness of the scale of text information, common evaluation metrics are not applicable to quantitatively evaluate non-matrixed text. To evaluate the imperceptibility of text with embedded watermark information, we first extract the color information of the text. It is then transformed into matrix form to use common evaluation metrics. In order to evaluate the imperceptibility, the degree of visual difference between the original text and the watermarked text needs to be quantified. It is clear that peak signal-to-noise ratio (PSNR), structural similarity index (SSIM)²⁴ and mean absolute error (MAE) are appropriate. Specifically, as shown in Figure 3, we only extract color information from the matrixed text. Thus, the color matrix of the text is obtained. We define the evaluation metrics on the text visualization including text peak signal-to-noise ratio (TPSNR), text structural similarity index (TSSIM) and the text mean absolute error (TMAE) for assessing text visual quality. The calculation expressions are as follows.

$$\{\begin{array}{cc}TPSNR=PSNR\left(A,B\right)& \\ TSSIM=SSIM\left(A,B\right)& \\ TMAE=MAE\left(A,B\right)& \end{array}$$ (Equation 17)

where A is the color matrix of the original text and B is the color information matrix of the watermarked text. Note that a higher TPSNR and TSSIM mean that the visual quality of the watermarked text is closer to the original text. And the lower the TMAE value, the better the watermark is hidden.

Furthermore, to evaluate the quality of the extracted watermark, we define the quantum image accuracy (QIA) as follows. The value of QIA ranges from 0 to 1, the larger the value the better the quality of the extracted watermark.

$$QIA=\left(1-\frac{N_{eq}}{N_{tq}}\right)\times 100\%$$ (Equation 18)

where $N_{eq}$ is the number of qubits in the quantum image where the error occurred, $N_{tq}$ is the total number of qubits. We also used Jaccard similarity coefficient (JSC)⁵⁶ to measure the performance of the proposed method in extracting the watermark correctly. JSC takes a value in the range of 0–1, the closer the value is to 1 means that the extracted watermark is closer to the original watermark with high fidelity.

In evaluating the capability of watermark extraction, we depend on the watermark extraction rate (ER) as well as the watermark accuracy rate. We first intuitively determine the number of recognizable watermarks in the extracted global watermark, where a higher number of recognizable watermarks indicate better performance, while noting that we only need to extract one clearly recognizable watermark to indicate copyright. For this purpose, we define the ER and extraction accuracy (EA). The ER is the ratio of the number of successfully extracted watermarks to the total number of embedded watermarks. The EA is the ratio of correctly extracted watermarks to the total number of successfully extracted watermarks. The meaning of a correctly extracted watermark is an image with copyright information that is recognizable to the human eye. They are expressed as follows.

$$\{\begin{array}{cc}ER=\frac{N_e}{N_t}& \\ EA=\frac{N_c}{N_e}& \end{array}$$ (Equation 19)

where $N_e$ is number of extracted watermarks, $N_t$ is the total number of watermarks, $N_c$ is the number of recognizable watermarks. Recognizable watermarks can be judged by visual and image accuracy. If the extracted watermark is visually clear pattern, then it can be considered as recognizable. In addition, the QIA value of the extracted watermark can also be calculated to assist in the judgment. We can set a threshold value and only the watermarks whose QIA reaches the threshold value is considered recognizable. In this paper we set the threshold to 80%. Note that Equation 19 works when $N_e\ne 0$. Otherwise, both $ER$ and $EA$ are 0.

To comprehensively evaluate the extraction performance of the proposed quantum text multiple watermarks, we also define the metric watermark efficiency index (WEI) for evaluating the efficiency. The expression is as follows.

$$WEI=\frac{2\times ER\times EA}{ER+EA}$$ (Equation 20)

The range of values for WEI is (0, 1). Specifically, a WEI of 1 indicates perfect performance. The closer the WEI is to 1, it indicates a good performance of the watermarking system. If WEI is close to 0, it indicates poor performance. In addition, we can set a threshold to evaluate the comprehensive performance of quantum text watermarking, i.e., the balance between the number of extracted and recognizable watermarks. In this paper, we set 0.5 as the threshold value, higher than 0.5 indicates a good watermark extraction performance and balance.

The embedding capacity and embedding rate of text watermarking is an important parameter to measure the effectiveness of text watermarking algorithms. It reflects the size of the information embedded by the text watermarking algorithm relative to the original text. Embedding capacity usually refers to the maximum length of watermark information that can be embedded in the text. The factors that affect the embedding capacity are mainly the size of the original text, watermarking algorithm, imperceptibility, and robustness requirements. A simplified way to calculate the embedding capacity is the total amount of embedded watermark information. Therefore, assuming an embedded λ watermarks, the embedding capacity $C_w$ is calculated as follows.

$$C_w=\sum _{i=1}^{\lambda }{m}_i\times n_i$$ (Equation 21)

The embedding ratio is the ratio of the total amount of embedded watermark information to the text size. It can be expressed in bits per character or percentage. We denote the total number of characters in the text as $C_t$. The embedding ratio R is usually calculated as:

$$R=\frac{C_w}{C_t}qubits/character$$ (Equation 22)

Imperceptibility and effectiveness results

Figure 8 illustrates randomly selected English text samples T1, T2, and multi-scale watermarks. The scale bar is 16 mm, which represents an actual size of 2 mm. Imperceptibility means that the watermark cannot be perceived by the human eye. This is generally achieved by keeping a high similarity between the original samples and the watermarked samples. In other words, the original data should remain almost unchanged after embedding.

Figure 8.

Results of MPQTW imperceptibility and effectiveness

Embedding areas for different watermark sizes ($8\times 16$, $16\times 16$, $16\times 8$, $8\times 8$) are located in orange, blue, yellow, green regions, respectively. The watermark extracted from watermarked text T1 measures 32 $\times$ 64 pixels, comprising the complete set of original watermark patterns. Similarly, the watermark from watermarked text T2, measuring 64$\times$ 64 pixels, also contains the full complement of original watermark patterns.

To evaluate validity and imperceptibility, we conduct two experiments. The first experiment is used to evaluate the scenario of multiple embedding of the same watermark, which can be used to backup the watermark to improve the resistance to attacks. The second experiment is used to evaluate the application scenario of embedding different watermarks. First, we take T1 as a carrier sample and embed two watermarks of size $8\times 16$ to simulate a repeated embedding scenario. Then, we take T2 as a carrier sample and embed three watermarks of size $16\times 16$, $16\times 8$, and $8\times 8$ to simulate a multi-scale watermarking scenario. Moreover, in the Figure 8, the areas of the text used to embed the watermarks are highlighted in different colors due to the different watermarks. As can be seen from the watermarked text results, they are almost indistinguishable from the original text, which proves the good imperceptibility of our MPQTW method. In addition, the extracted global watermark from the whole watermarked text is shown in the bottom right part of Figure 8. All the visual contents are clearly and accurately extracted. It indicates that our MPQTW method is correct and effective.

We evaluate the imperceptibility of watermarks. Table 2 illustrates the experimental results of TPSNR, TMAE, and TSSIM for the visual quality of watermarked text. Based on the experimental results, it can be seen that higher TPSNR and TSSIM indicate that the visual difference between the watermarked text and the original text is minimal. This is also confirmed by the TMAE, which is just around 0.5. As a result, the proposed MPQTW has good imperceptibility.

Table 2.

The experiment results of visual quality of watermarked text in terms of TPSNR (dB), TMAE, and TSSIM

A	B	TPSNR(A,B)	TSSIM(A,B)	TMAE(A,B)
T1	Watermarked T1	42.45	0.9073	0.47
T2	Watermarked T2	41.28	0.8985	0.52

Robustness results

The robustness of text watermarking refers to the ability of the watermark to be successfully detected or extracted when subjected to various intentional or unintentional attacks. Even when the watermarked text is modified or changed, the original watermark information can be effectively detected and extracted from the attacked text. A robust text watermarking system is able to maintain the recognizability of the extracted watermark even after the content has been inserted, deleted, replaced, and other operations. To evaluate the robustness of the proposed MPQTW, we carry out a series of simulation experiments including insertion/addition attack, deletion attack, and synonym substitution attack. Finally the syntax transformation attack is also analyzed. Table 3 collects all the results of the robustness experiments in terms of ER, EA, WEI, QIA, and JSC. From the results, it can be seen that the results of extracting the watermark are satisfactory. The WEI values are above 0.5 and the best result is 1, which indicates that the robustness of the proposed MPQTW is well balanced. In terms of image quality of extracted watermarks, QIA is between 96% and 100%. JSC is between 0.9 and 1. This indicates the high quality of the extracted watermark. Thus, our method can be feasible in practical applications and resistant to a certain level of common attacks. In addition, it is noted that there are some gaps in the experimental results of T1 and T2, although they both meet the expectations. The reasons are analyzed in the further text. For T1, since it is a repeated embedding of the same watermark, the embedding area is related to the watermark size, and how many watermarks can be embedded in the text depends on the text structure. This leads to a relatively limited embedding process in some cases. If the text structure is complex or irregular, it may not be possible to fully utilize all the space for embedding watermarks, thus making the distribution of watermarks less flexible. Moreover, as it is the same watermark, once the watermark is destroyed, due to its repetitive nature, it may have a greater impact on the overall watermark effect. As for T2, it has unique advantages. Although its embedding area is also related to the watermark size, it can be flexibly embedded with the right size watermark according to the text structure. This flexibility allows us to maximize the size and coverage of the watermark embedding. For example, in the text of some complex long words in the region, can be embedded in the large size of the watermark, while in some details of the short text area, can be embedded in a small size of the watermark. This can make fuller use of the text space and improve the overall coverage of the watermark. Moreover, the different sizes of watermarks mean that it is difficult for an attacker to destroy all watermarks at the same time through one attack, thus showing better stability and robustness in performance than T1.

Table 3.

Experiment results of extracted watermarks under different attacks in terms of ER, EA, WEI, QIA and JSC

Text	T1			T2
Attacks	Insertion	Deletion	Synonym	Insertion	Deletion	Synonym
Watermark extraction efficiency
ER	100%	50%	100%	100%	67%	100%
EA	100%	100%	50%	100%	100%	100%
WEI	1	0.67	0.67	1	0.80	1
Average watermark quality
QIA	100%	100%	100%	100%	96.88%	99.74%
JSC	1	1	1	1	0.9149	0.9912

Figure 9 shows the detailed simulation experimental results including the attack type, the attacked text, the global extracted watermark, and a description of the test results. The scale bar is 32 mm, which represents an actual size of 4 mm. Next, we provide a detailed description and explanation of each robustness experiment. Figure 9A illustrates the experimental details of the text insertion attack including words and phrases insertion. We provide the experimental process, results, and analysis as follows.

• •Insertion attack: the insertion attack involves inserting new words or phrases at certain locations in the text, thereby altering the original structure of the text. This may make the watermark information corrupted or difficult to detect and extract.
• •Experimental method: we randomly selected some appropriate words to insert into the text based on the semantics of T1 and T2. The red font is the insertion part.
• •Extracted watermark: the size of the watermark we extracted from the attacked text T1 is $64\times 64$, the size of the watermark we extracted from the attacked text T2 is $64\times 64$. In terms of visual content, the global watermark of the attacked T1 contains a stretched “MPU” logo, and a clear “MPU” logo. The global watermark of the attacked T2 contains a stretched “MPU” logo, a clear “copy” mark, a string of characters “1101C1”, as well as a clear vertical “MPU” logo and “EL” logo.
• •Result analysis: the size of the extracted watermark conforms to the definition of Equation 14. Each extracted watermark contains clear and recognizable visual information.
• •Conclusion: the proposed MPQTW is resistant to insertion attacks. In addition, it is well suited for watermarking large-size texts. Because in the proposed MPQTW, the effect of the insertion attack on the watermark is only the visual effect of stretching, it does not affect the recognition and correctness of the watermark information.

Figure 9.

Results of MPQTW robustness

(A) Insertion attack results (red text indicates insertion).

(B) Deletion attacks results (localized and dispersed deletion, where struckthrough portion represents deleted text).

(C) Synonym substitution attack results (purple italics indicate substituted words).

Figure 9B illustrates the experimental details of the text deletion attack including localized and dispersed deletion. We provide the experimental process, results, and analysis as follows.

• •Deletion attack: an attacker removes some words or characters from the text to reduce the risk of plagiarism. This deletion may result in the loss of watermark information. In particular, if the deletion happens to contain a critical part of the watermark, it can lead to failure of watermark recognition.
• •Experimental method: we randomly selected some content for deletion in T1 and T2. Note that T1 text is used for localized sequential deletion while T2 is used for dispersed deletion.

• Extracted watermark: the size of the watermark we extracted from the attacked text T1 is $16\times 64$, and the size of the watermarks we extracted from the attacked text T2 is $64\times 64$. In terms of visual content, the global watermark of the attacked T1 contains a clear “MPU” logo. And the global watermark of the attacked T2 contains a clear “MPU” logo, a clear “copy” mark, and a clear vertical “MPU” logo.

• •Result analysis: the size of the extracted watermark conforms to the definition of Equation 14. Each extracted watermark contains clear and recognizable visual information.
• •Conclusion: the proposed MPQTW is resistant to deletion attacks and is well suited for long text protection scenarios. Because it allows repeated embedding to increase watermark redundancy and also allows embedding multi-scale watermarks, which improves the robustness against deletion attacks.

Figure 9C illustrates the experimental details of the synonym substitution. We provide the experimental process, results, and analysis as follows.

• •Synonym substitution attack: the attacker replaces certain words in the text with synonyms or similar expressions, a substitution that may not significantly change the meaning of the text but destroys the integrity of the watermark.
• •Experimental method: we randomly selected some words from T1 and T2 for substituting its synonyms according to its semantics. The purple part in the text is the replaced content.
• •Extracted watermark: the size of the watermark we extracted from the attacked text T1 is $32\times 64$, the size of the watermarks we extracted from the attacked text T2 is $64\times 64$. In terms of visual content, the global watermark of the attacked T1 contains a clear “MPU” logo. The global watermark of the attacked T2 contains a clear “MPU” logo, a clear “copy” mark, a string of characters “1101C1”, as well as a recognizable vertical “MPU” logo and an “EL” logo.
• •Result analysis: the size of the extracted watermark conforms to the definition of Equation 14. Each extracted watermark contains clear and recognizable visual information
• •Conclusion: the proposed MPQTW is resistant to synonym substitution attack and is well suited for multi-scale watermark embedding scenarios. This is because the effect of synonym substitution on MPQTW extracted watermarks is manifested as a row of the watermark image becomes black. Multi-scale watermark embedding not only disperses this effect, but also reduces the scope of interference with the visual information of each watermark.

Our method is actually also effective in resisting syntax transformation attacks. Syntax transformation attack refers to the attacker’s ability to destroy the watermark information by modifying the grammatical structure of the text, such as changing the use of tense, morphology, or clauses. In the proposed MPQTW scheme, because the meaningless prepositions, articles, etc. have been removed from the classical English text used for quantum representation. Similarly these are also removed in the preparation of the quantum watermarked text before extraction. Therefore, modification of prepositions etc. will not affect the watermark extraction. In addition, in terms of tense changes such as changing the present tense to past or future tense, the impact of these transformations does not exceed the insertion attack shown in Figure 9A. In the case of tense transformation, such as changing an active sentence to passive, the impact of these transformations does not exceed that of the synonym substitution attack shown in Figure 9C.

In terms of embedding capacity and rate, it can be calculated based on the previous definitions. We calculate the embedding capacity of texts T1, T2 to be 256 qubits and 448 qubits, respectively. Correspondingly, according to Equation 22, their embedding ratios are calculated to be 1.5 qubits/character and 1.9 qubits/character, respectively.

General performance results

To quantitatively evaluate the general performance of the proposed MPQTW method, we randomly selected five texts with similar sizes (77 words on average), then embedded the same four watermark images at appropriate positions in the texts, respectively. The imperceptibility of the five watermarked texts is evaluated first, then different extent of attacks are implemented separately before extracting the watermarks. Robustness is evaluated by calculating the metrics for the extracted watermarks. Figure 10 shows the selected text and the four watermarks to be embedded. The scale bar is 16 mm, which represents an actual size of 2 mm. Note that the four watermarks selected cover both cases of embedding of different watermarks and repeated embedding of the same watermark.

Figure 10.

Five randomly selected five texts of the similar size and four watermark images to be embedded

Each text has all four watermarks embedded in the appropriate region.

In terms of watermarking imperceptibility, we evaluate it by comparing the visual difference between the original text and the watermarked text. The five watermarked texts are first converted into matrix form, and then their gray value information is compared with the original quantum text gray value matrix to calculate the related metrics TPSNR, TSSIM, and TMAE. Since these five texts have similar sizes, their converted quantum matrices are of the same size. The embedded watermark information is the same, so their TPSNR, TSSIM, and TMAE are similar, which are 43.91 dB, 0.9273 and 0.34, respectively. Based on the results, it can be seen that the higher TPSNR and TSSIM indicate that the proposed MPQTW possesses good imperceptibility and the watermark is difficult to be detected by the human eye. The low TMAE also confirms that the embedded watermark has minimal effect on the original text visually.

For robustness performance evaluation, we implement the same attack on five watermarked texts separately, then extract the watermarks and compute the average of their experimental results. First, since the insertion attack affects the watermark extraction in the proposed MPQTW method only as a visual stretch of the watermark image without losing the watermark information, the extracted watermark can be considered to contain all the original information and be recognizable. Therefore the robustness evaluation experiments include deletion and synonym substitution attacks that will affect the watermark. For the purpose of evaluation, we simulate successive deletion attacks with different degrees. Different extents of synonym substitution attacks, which are decentralized and random, are also simulated. Figure 11 shows the experimental results of watermarks extracted under both attacks. Figure 11A shows the average results for different degrees of successive deletion attacks. The average ER, EA, WEI under 10% deletion are 0.75,1 and 0.86, respectively; the results under 30% deletion are 0.6, 0.93, and 0.67; and those under 50% deletion are 0.45, 0.8, and 0.55. Figure 11B shows the average results for different degrees of substitution attacks. The average ER, EA, WEI under 5% random substitution are 1, 0.95, and 0.97, respectively; under 10% the results are 0.85, 0.90, and 0.86, respectively; and under 15% they are 0.75, 0.77, and 0.72. Their average WEI results are all above 0.5, indicating a satisfactory and balanced extraction performance for multiple watermarks.

Figure 11.

Results of MPQTW general performance in terms of EA, ER, and WEI

(A) Deletion attacks results (10%, 30%, and 50%) on five watermarked texts.

(B) Substitution attacks results (5%, 10%, and 15%) on five watermarked texts. Data are represented as mean.

Even though deletion attacks can eliminate or destroy watermark information, benefiting from our multiple watermark embedding mechanism, successive deletion attacks on the watermarked text do not affect the watermark information in other parts. There are always unaffected watermarks that can be extracted. Therefore, all watermarks extracted in the successive deletion evaluation experiments have error-free watermark versions, and their corresponding QIA and JCR averages are all 1. The synonym substitution attack is the replacement of suitable words based on the context and it is a random and decentralized attack. As a result, multiple watermarks embedded in the text may be affected and corrupted at the same time. In the extracted watermarks, we evaluate the image quality of the recognizable watermarks and compute the average QIA and JCR results of the extracted watermarks under different extent of substitution attacks. The average QIA and JCR results are 98.22% and 0.9422 when the range of replacement is 5%, 98.18%, and 0.9386 when the range is 10%, and 95.57% and 0.8426 when the range is 15%. The experimental results show that the average quality of the extracted watermarks is satisfactory and identical or have high similarity with the original watermarks.

Discussion

In this paper, we have shown a new model for quantum text representation GQTR. This lays an important foundation for the processing of text information in quantum systems, and it also is an important prerequisite for utilizing powerful quantum computing and communication capabilities. Subsequently, based on the proposed GQTR, we elaborate a quantum text watermarking scheme MPQTW that realizes multi-scale watermark images embedded in text, which is a new exploration in text watermarking research utilizing quantum capabilities. The quantum text representation model advances the processing of text information itself utilizing the emerging quantum computing and quantum communication in the future quantum era, and also quantum text watermarking opens up a higher level of security for copyright protection of the text information.

Unlike the content-based text embedding commonly used in classical schemes,^57,58 in the proposed MPQTW, we embed the watermark information into the color qubits of the characters, and due to the quantum state superposition property we only need a small number of qubits to have a large embedding space. In addition, since insensitivity of the human eye to color changes, each character in the GQTR text has an embedding capacity of at least 4 qubits. It is worth emphasizing that MPQTW allows embedding multiple visual watermarks into English text of arbitrary length, however, most current watermarks in text watermarking are in the form of specific keys.⁵⁷ We randomly selected text samples of different lengths for simulation experiments to evaluate the imperceptibility, robustness, and embedding rate of MPQTW. The results show that the change of watermarked text is imperceptible to the human eye. In terms of robustness, it is resistant to common text attacks such as insertion, deletion, synonym replacement and syntax transformation attacks as we extract recognizable visual watermarks from them. Experimental results show that the proposed method allows flexible division of multiple embedding regions based on text length. Each embedding region can be embedded with different visual watermark patterns as well as support full-text watermark coverage. Therefore, when the watermarked text is attacked, the watermark information cannot be completely eliminated unless the content is completely altered. However, when this text is completely changed such as replacing all the words, there is no need to protect the copyright of the changed text. As a result, quantum text watermarking not only provides information security guaranteed by quantum properties, but also provides good robustness.

In order to show the advancement and value of the research in this paper, we compare the proposed MPQTW with the latest traditional text watermarking methods from several perspectives. Table 4 shows the comparison results with related classical methods in terms of principle, performance, watermark type, capacity, and robustness. Our method exploits the application of quantum technology in the direction of text watermarking with higher security and processing speed compared to conventional methods. In terms of innovativeness, unlike common binary information sequences or text watermarking, we investigate multiple image-based text watermarking mechanism. The proposed MPQTW has better robust performance since multiple independent watermarks unrelated to text semantics can be embedded simultaneously. In addition, the process of classical methods is more cumbersome and usually requires a preprocessing process.^59,60,61 The MPQTW can directly represent the selected embedding region into quantum form and then perform the quantum watermark embedding process, while the extraction is done directly from the quantum watermarked text through several CNOT gates. Since our approach is semantic-independent, the watermark embedding does not change the meaning of the original text. While classical methods⁵⁹ and⁶⁰ make the original content change. In terms of complexity, the quantum approach has a natural advantage as both the text information and the watermarks are represented as quantum states, and dealing with quantum superposition states allows for truly high-speed parallel processing, which usually requires only a small number of quantum gates for large-scale quantum state evolution. In contrast, classical requires progressive processing, which is theoretically slower and less efficient than quantum methods when dealing with large amounts of text data, such as deep learning-based methods⁵⁹ and.⁶⁰ In addition, the embedding capacity varies depending on the actual needs and text size. For direct comparison, we compare the maximum embedding capacity of different methods in a text with a size of 10000 characters. We consider spaces and set the average character number w of a word to 6. The larger w is, the higher our capacity is. The comparison is carried out by converting the number of embedded bits to the number of characters uniformly. From the data in the Table 4, it is clear that our maximum character capacity is much higher than other methods.

Table 4.

Comprehensive comparative results with related works

Methods	Main principle	Watermarking features			WaType	Extraction needs	Text invariance	MaxCapb	Robustness
		PreP	WN	WSS
20209	Markov model	Need	1	ACD	Feature numerical	Parameters, features	$\surd$	–	Insertion, reordering, deletion
202162	Instance-based learning algorithm	Need	1	ACD	Text	Hidden string	$\surd$	2500	Tampering, plagiarism
202361	Position and glyph	Need	n	ACD	Binary	Correction, segmentation, normalization	$\surd$	63	Print, scanning, shooting
202459	Deep learning	Need	1	ACD	Text	/	$\times$	–	Deletion, insertion, substitution
202460	Deep learning, neural network	Need	1	ACD	Text	Key information	$\times$	178	/
Ours	Quantum theory, Quantum circuit	No need	n	QMP	Image a(text, etc)	/	$\surd$	4285	Deletion, insertion, substitution

PreP stands for pre-processing, WN stands for the number of watermarks, WSS stands for watermark signal security. WaType stands for watermark type. ACD denotes the dependence on the algorithm complexity design, QMP denotes high security provided by quantum mechanical principles. MaxCap indicates the maximum capacity.

^aEmbedding pattern images as watermarks in text is the main way in MPQTW. Generally, any information that can be encoded as a matrix (like key, binary, text) can be embedded in text as a watermark.

^bFor direct comparison, we compare the maximum embedding capacity of different methods in a text of size 10000 characters.

In fact, there are still issues to be further considered in the research of quantum text watermarking algorithms, such as how to improve the robustness of text watermarking under quantum noise channels. Current quantum watermarking methods are mostly studied under the premise of reliable quantum computation and communication, i.e., ignoring quantum errors.⁶³ If we are to build on the current stage of quantum technology, we need to take quantum environmental interference into consideration to propose new research, such as quantum text watermarking with error tolerance.

Conclusions and Future work

In this study, we pioneer the exploration of quantum text watermarking technology as a cutting-edge solution for next-generation text security protection. We first establish the GQTR model, which lays the foundation for the accurate representation and retrieval of English text in quantum systems. The GQTR enables precise quantum representation and retrieval of textual information. On this basis, we propose MPQTW, an innovative quantum text watermarking method using multiple watermarks, which can effectively embed multi-scale images into quantum text for digital text copyright protection. In order to comprehensively evaluate the effectiveness of the MPQTW scheme, we design a variety of evaluation metrics and provide detailed quantum circuits for GQTR model and MPQTW watermarking. Through a series of simulation experiments, we evaluate the performance of the MPQTW scheme from multiple perspectives, such as imperceptibility, robustness, and embedding rate, and the results demonstrate its excellent performance. This research not only provides a new theoretical foundation and practical method for the field of quantum text processing, but also makes an important contribution to the field of cross-research between quantum computing and text watermarking, and promotes the development of text security technology.

Quantum text watermarking technology, as a cutting-edge field of digital copyright protection, its future research will deeply explore algorithm optimization and innovation, extend the support of multi-language and multi-format text, strengthen the security, and promote the practicality and standardization. We will design more text processing algorithms and models, such as quantum text watermarking algorithms with fault-tolerance to improve the robustness of quantum text watermarking. Meanwhile, future research will focus on developing quantum-classical hybrid systems, such as integrating machine learning and artificial intelligence techniques, to explore the future of this technology in securing information and promoting quantum computing applications.

Limitations of the study

This study is a theoretical study of quantum watermarking while ignoring quantum errors. The work mainly focuses on the feasibility of quantum text watermarking and only common attacks are considered. However, it is also necessary to consider quantum environmental interference in a quantum perspective and introduce quantum errors to further optimize the robustness. Additionally, the samples used for evaluation experiments may need to be diversified.

Resource availability

Lead contact

Further information for resources and materials should be directed to and will be fulfilled by the lead contact, Dr. Xiaochen Yuan (xcyuan@mpu.edu.mo).

Materials availability

This study did not generate new unique materials.

Data and code availability

• •All experimental data are clearly explained in this paper. All data are generated in numerical form. All calculations can be performed using the formulas in the text and the software listed in the key resources table.
• •This paper does not report original code.
• •Any additional information required to reanalyze the data reported in this paper is available from the lead contact upon request.

Acknowledgments

This work was supported in part by the Science and Technology Development Fund of Macau SAR under grant 0045/2022/A, and Macao Polytechnic University under grant RP/FCA-12/2022.

Author contributions

Conceptualization, Z.X.; methodology, Z.X. and X.Y.; writing—original draft, Z.X.; validation, Z.X. and X.Y.; writing—review and editing, Z.X., X.Y., and C.-T.L.; supervision, X.Y. and C.-T.L.; funding acquisition, X.Y. and C.-T.L.

Declaration of interests

The authors declare no competing interests.

STAR★Methods

Key resources table

REAGENT or RESOURCE	SOURCE	IDENTIFIER
Software and algorithms
MATLAB 2020b	MathWorks Inc	https://ww2.mathworks.cn/products/matlab.html
BBC News Summary Dataset	Kaggle platform	https://www.kaggle.com/datasets/pariza/bbc-news-summary
Microsoft Visio	Microsoft Corporation	https://www.microsoft.com/microsoft-365/visio

Experimental model and study participant details

This study is a theoretical investigation and method design for quantum text watermarking. No experimental animals, human participants, plants, microbial strains, cell lines, or primary cell cultures are involved. Therefore, there are no experimental models or study participants to state. The study is based exclusively on theoretical analyses and computer simulations. It does not involve the collection and use of any biological samples or personal data.

Method details

In this study, we simulate a series of experiments using the software MATLAB 2020b on a conventional computer equipped with an Intel(R) Core(TM) i7 CPU 2.30GHz 16.00-GB RAM.MATLAB simplifies the representation and processing of matrices and vectors. The English text samples used in the experiments are from the publicly available news article dataset BBC News Summary, downloaded from Kaggle. All the software and data involved can be publicly available in the key resources table.

Quantification and statistical analysis

Visual quality analysis

In order to evaluate the impact on the visual quality of the text by watermarking, we define the evaluation metrics on the text visualization including Text Peak Signal-to-Noise Ratio (TPSNR), Text Structural Similarity Index (TSSIM) and the Text Mean Absolute Error (TMAE) for assessing text visual quality.

$$\{\begin{array}{cc}TPSNR=PSNR\left(A,B\right)& \\ TSSIM=SSIM\left(A,B\right)& \\ TMAE=MAE\left(A,B\right)& \end{array}$$ (Equation 23)

where A is the color matrix of the original text and B is the color information matrix of the watermarked text.

The imperceptibility performance of the watermarked image in terms of TPSNR, TSSIM, and TMAE respectively is given in Table 2.

Robustness analysis

In order to comprehensively evaluate the extraction performance as well as the attack resistance of the proposed method, we quantify the results using a variety of metrics. We define the Quantum Image Accuracy (QIA) as follows.

$$QIA=\left(1-\frac{N_{eq}}{N_{tq}}\right)\times 100\%$$ (Equation 24)

where $N_{eq}$ is the number of qubits in the quantum image where the error occurred, $N_{tq}$ is the total number of qubits. We also used Jaccard Similarity Coefficient (JSC) to measure the performance of the proposed method in extracting the watermark correctly.

The Extraction Rate (ER) and Extraction Accuracy (EA) are used. They are expressed as follows.

$$\{\begin{array}{cc}ER=\frac{N_e}{N_t}& \\ EA=\frac{N_c}{N_e}& \end{array}$$ (Equation 25)

where $N_e$ is number of extracted watermarks, $N_t$ is the total number of watermarks, $N_c$ is recognizable watermarks.

The metric Watermark Efficiency Index (WEI) for evaluating the efficiency is defined as follows.

$$WEI=\frac{2\times ER\times EA}{ER+EA}$$ (Equation 26)

The robustness performance of the proposed method is given in Figures 9 and 11 and Table 3.

Capacity analysis

To calculate the embedding capacity, the embedding capacity $C_w$ is calculated as follows.

$$C_w=\sum _{i=1}^{\lambda }{m}_i\times n_i$$ (Equation 27)

where λ is the number of watermarks. The embedding ratio is calculated as follows.

$$R=\frac{C_w}{C_t}qubits/character$$ (Equation 28)

where $C_t$ is the total number of characters.

Published: November 12, 2024