Chenchen Tu
Li Niu3*- 1College of Textile Science and Engineering, Jiangnan University, Wuxi, Jiangsu, China
- 2School of Fashion, Dalian Polytechnic University, Dalian, Liaoning, China
- 3School of Digital Technology & Innovation Design, Jiangnan University, Wuxi, Jiangsu, China
- 4School of Fashion Design and Engineering, Zhejiang Sci-Tech University, Hangzhou, Zhejiang, China
This paper proposes an encryption scheme based on hyperchaotic mapping for child information protection. First, phase diagrams of the hyperchaotic mapping are plotted under different parameter combinations, and the variation in phase trajectories confirms the sensitivity of the hyperchaotic mapping to control parameters. Then, the hyperchaotic mapping is iterated to obtain chaotic sequences, and the chaotic sequences are quantized to obtain pseudo-random sequences. Finally, based on those, a scrambling algorithm and a diffusion algorithm are designed to encrypt and protect the images. The original images are scrambled and diffused to obtain the ciphertext images and used to protect the information of missing children, which can effectively protect the safety of children’s information and assist the public security bureaus to quickly contact the parents of missing children.
1 Introduction
In the digital era, data are increasingly becoming an important part of personal life and economic development [1, 2]. Among various data formats, images are widely used as information carriers for Internet transmission as they can carry large amounts of information and have high visibility [3, 4]. Due to the dependence of work life on the Internet, the rich information contained in images is at risk of being leaked [5–7]. Among these, the secure transmission and storage of image data face significant challenges as they contain sensitive information such as biometrics and geographic locations [8, 9]. Especially in the field of social welfare, such as missing children tracking, images need to be widely disseminated to expand the search scope, but they also must be prevented from being maliciously utilized to cause secondary damage [10, 11]. Image encryption can be used to encrypt an image into a noise-like ciphertext image by various means [12–15].
As an effective method to protect image information, image encryption techniques, especially those based on chaos theory, have been a hot topic of research in recent years [16]. This is because many inherent properties of chaotic systems, including ergodicity, acyclicity, high sensitivity to initial conditions and control parameters, and pseudo-randomness, meet the needs of cryptography and have an irreplaceable advantage in image encryption [17–21]. Meanwhile, some scholars have pointed out that hyperchaotic systems can provide higher security to encryption algorithms [22, 23]. In the context of information protection and verification of missing children, hyperchaotic mapping is preferred in view of the need for real-time performance. In this study, hyperchaotic mapping [24–30] is used in the design of the missing child information encryption scheme.
In the previous image encryption scheme design and application, usually, the image is compressed and encrypted to realize the fast transmission and protection of the image on the Internet [31–33]; another method includes encoding and encryption of the image to realize the safe storage of the information and prevent leakage or tampering [31, 34–36]; there is also the encryption and steganography of the image to realize the double-layer protection of the image [37–39]. However, information protection and verification of missing children are different from the previous image encryption protection processes, where the main idea is to encrypt children’s information to obtain ciphertext images and apply the ciphertext images to children’s products as stickers, such as on children’s school bags, water cups, and clothes. In the process of children getting lost or being found, the children’s information is verified, and it is convenient to get in touch with the children’s parents quickly. In view of this application idea, this paper designs a missing child information protection and verification scheme based on hyperchaotic mapping. The information protection scheme is divided into two steps: image scrambling and diffusion, which when combined with chaotic sequences can effectively hide the original information of children, and the reversible encryption scheme ensures that the information of children can be decrypted and verified quickly.
This paper carries out the following tasks:
1. Memristor-coupled hyperchaotic mapping (MCHM) is presented in this paper, and its phase diagram is analyzed.
2. The image or photo containing a child’s information is encrypted with a confusion algorithm and a diffusion algorithm.
3. Security analysis of encrypted images to highlight the superiority of the scheme.
2 Chaotic mapping
MCHM is obtained by coupling the memristor and the iterative chaotic map with infinite collapse (ICMIC), and its mathematical model is described as Equation 1:
When the initial value is (x0, y0) = [0.3, 0.5] and the system parameters a, b, c, d, and e are [−1, 1.5, −1, 1, 0.5], [−1, 1.5, −1.1, 1, 0.5], and [−1, 1.5, −1, 1.2, 0.5], the phase diagrams of MCHM are as shown in Figure 1. Comparing Figures 1a–c, the trajectory of the MCHM clearly changes when the control parameters are changed. That is, when the key changes slightly during the operation of the encryption scheme, the chaotic sequences generated by the MCHM also change, which changes the cipher images. This means that the mapping can provide great security for the design and operation of the encryption scheme.
Figure 1. Phase diagrams of MCHM, (x0, y0) = [0.3, 0.5]: (a) (a, b, c, d, and e) = [-1, 1.5, −1, 1, 0.5]; (b) (a, b, c, d, and e) = [-1, 1.5, −1.1, 1, 0.5]; (c) (a, b, c, d, and e) = [-1, 1.5, −1, 1.2, 0.5].
The chaotic range of the system parameters is decided by analyzing the Lyapunov exponent (LE) response. If one of the LEs is greater than 0, it is in a chaotic state, and if two LEs are greater than 0, it is in a hyperchaotic state. Encryption is carried out in the chaotic state situation by selecting the parameters. As shown in Figure 2, the range case of each parameter in a chaotic state is a∈[-1.1,-0.75], b∈[1.35,1.5], c∈[-1,-0.9], d∈[0.7,1.1], and e∈[0.4,0.54]. When parameter a is at [-1.1, -0.875] or [-0.87, -0.747], parameter b is at [1.43, 1.5], parameter c is at [-1, -0.975] or [-0.96, -0.92], parameter d is at [0.85, 1.1], and parameter e is at [0.47, 0.54], the system is in a hyperchaotic state. More complex dynamic characteristics are shown in this state, and the pseudo-random sequence generated by the system through iteration has higher randomness.
Figure 2. Distribution of LEs with different parameters. (a) Parameter a; (b) parameter b; (c) parameter c; (d) parameter d; (e) parameter e.
To test the randomness of the chaotic sequences, an NIST test (NIST SP800-22) is performed. It includes 15 tests. When the p-value is greater than or equal to 0.01 and the pass rate is greater than 96%, the sequence passes the randomness test. The specific test results are shown in Table 1. It can be seen from the results that this random sequence exhibits good randomness characteristics in statistical tests. It is shown that it is suitable for the proposed encryption scheme.
Table 1. NIST test results for MCHM.
3 Encryption scheme
The encryption process includes three stages: parameter setting, image confusion, and diffusion. The encryption schematic is shown in Figure 3. The detailed steps are described as follows:
Step 1: The image containing the child’s information and photo is imported, and the size of the ith image is recorded as mi × ni × li.
Step 2: All images are converted into column vectors, and all column vectors are stitched into a whole, which is denoted as vector A, with length vl.
Step 3: Column vector A is converted to cube B with dimensions M × N × L, where M and N are the height and width of each plane of the cube, respectively, and L is the height of the cube. M and N can be set as desired, and L is obtained by Equation 2.
Step 4: Based on the input image, the parameters associated with the plaintext hi are obtained.
where Pj stands for the pixel value and Hm stands for information entropy.
Step 5: All the keys are inputted, and the MCHM is iterated based on the total image data volume vl to obtain the chaotic sequences of length 2×vl, and they are quantized to finally obtain two pseudo-random sequences x and y. The pseudo-random sequences q1–q12 used in the algorithm are obtained by Equations 4–8.
Step 6: The sequences q1 and q2 are processed and used to control the length of the permutation sequence, and q1 and q2 can be obtained by Equations 9, 10.
Step 7: Each row vector of cube B is split into two parts of random length, and the positions are swapped with the row vectors at random locations.
Step 8: Each column vector of cube B is split into two parts of random length, and the positions are swapped with the column vectors at random locations. The cube with the completed column swap is noted as C. It can be obtained by Equations 13, 14.
Step 9: Cube C is converted into column vector D, and the first pixel value is combined with the pseudo-random sequence to get the new pixel value. It can be obtained by Equations 15, 16.
Step 10: The vector E is segmented and shaped according to the dimensions of the original images to obtain the corresponding ciphertext images.
Figure 3. Encryption schematics.
4 Simulation result
Being able to completely encrypt and decrypt children’s information and photos is the first requirement for practical applications. In the simulation experiment, three sets of images are used (“kid” with size 200 × 289 × 3, “information1” with size 300 × 152 × 3; “girl” with size 768 × 512 × 3, “information2” with size 300 × 174 × 3; and “boy” with size 768 × 512 × 3, “information3” with size 300 × 138 × 3), and they are encrypted and decrypted separately and in a hybrid manner. The simulation results are shown in Figures 4–7. From Figures 4–6, it can be seen that the scheme can successfully encrypt and decrypt children’s information and photographs. As shown in Figure 7, it is also possible to securely encrypt and decrypt a large number of children’s information and photographs if necessary. In other words, the proposed encryption and decryption scheme can perform both individual processing and batch protection of children’s information and photographs.
Figure 4. Simulation results: (a) original images, “kid” and “information1”; (b) encryption images; (c) decryption images.
Figure 5. Simulation results: (a) original images, “girl” and “information2”; (b) encryption images; (c) decryption images.
Figure 6. Simulation results: (a) original images, “boy” and “information3”; (b) encryption images; (c) decryption images.
Figure 7. Simulation results: (a) original images; (b) encryption images; (c) decryption images.
5 Performance tests
5.1 Key security
5.1.1 Key space
The size of the key space determines whether the encryption scheme can resist exhaustive attacks. Generally, when the key space reaches 2100, it is considered to be capable of resisting exhaustive attacks, and the more the key space is, the better the scheme. In this encryption scheme, the key comprises two components: parameters related to the original images and those associated with hyperchaotic mapping. All the keys are tested one by one; the key space of parameters b and d is 1015, and the key space of the remaining parameters is 1016, so the total key space is 10 (15 × 2 + 16 × 7) = 10142 ≈ 2471. The key space of different algorithms is shown in Table 2 [16, 40–42]. The key space test and comparison results indicate that the proposed encryption scheme has adequate capability to resist brute-force attacks.
5.1.2 Key sensitivity
The encryption scheme can be considered key-sensitive when a small error in the key can cause decryption failure on the decryption side. In the key sensitivity test, “kid” and “information1” are used as the test images. During the test, each key on the encryption side is kept constant, and the key a = a + 10-16 on the decryption side. The decryption results are shown in Figure 8. The ciphertext image cannot be decrypted successfully with smaller parameter variations. As shown in Figure 8, a small error in the key causes the decryption to fail, verifying the key sensitivity of this scheme.
Figure 8. Key sensitivity test results, a = a+10−16.
5.2 Statistical characterization
5.2.1 Histogram
A histogram can visually depict the strength of the pixels in the image. By comparing the histograms of the original image and the encrypted image, the ability of the encryption scheme to change the pixel values of the image can be verified. The histograms of “kid” and “information1” are shown in Figure 9. The histograms of the original images have distinct crests and varying distributions at each pixel level. The histograms of the encrypted images show an undifferentiated uniform distribution, which means that the pixel-level distribution of the original images is effectively changed and hidden by the encryption scheme.
Figure 9. Histogram of “kid” and “information1”: (a) original images and (b) encryption images.
5.2.2 Correlation
The property of local smoothing of the image determines a strong correlation between the adjacent pixels of the image, and the intensity of the correlation is measured by both the coordinate plot and the coefficient, which are shown in Figure 9 and Table 2, respectively. As shown in Figure 10, neighboring pixels of “kid” and “information1” are compactly distributed on a straight line with slope 1, which means that the neighboring pixels have the same or similar values. The adjacent pixels of the corresponding encrypted images are distributed throughout the coordinate space, and the values of the adjacent pixels are not correlated. As shown in Table 3, the correlation coefficients of the original images are large, while the correlation coefficients of the encrypted images are close to 0. The change in the correlation between the adjacent pixels of the image indicates that the encryption scheme effectively swaps the location and changes the values of the pixels, thus hiding the correlation characteristics of the original images.
Table 2. Comparison of key spaces
Figure 10. Correlation coordinate diagram of “kid” and “information1”: (a) original images and (b) encryption images.
Table 3. Correlation coefficients of different images.
5.2.3 Information entropy
Information entropy is used to test the statistical characteristics of an image. For an image, the higher the information entropy is, the more information it contains, and the more confusing the image is. The original images contain a certain amount of visual information, and their information entropy is a constant value. The information of the encrypted images is confusing, and the information entropy increases with a theoretical maximum value of 8 [43]. The information entropy test results for different images are shown in Table 4, and the information entropy test results for different algorithms are shown in Table 5 [35, 42, 44–46]. As shown in Table 4, compared to the original images, the information entropy of the encrypted images increases significantly and is close to the theoretical maximum. As shown in Table 5, the designed encryption scheme has some advantages in hiding the statistical features of the image data.
Table 4. Information entropy of different images.
Table 5. Information entropy of different algorithms.
5.3 Anti-rolling edge test
The encrypted images containing children’s information are printed on the clothes, and if the edge of the image rolls up as the clothes are used, then the edge information may be invalidated. When the edge information of the images is invalidated, the decryption effects of the encrypted images are shown in Figure 11. The edge of the original images is cropped by one circle, and the invalidated information accounts for 23.44%; the cropping effects are shown in Figure 10a. The visual effects of the damaged ciphertext images after being decrypted on the decryption side are shown in Figure 10b. As shown in Figure 11, the original information can still be recovered even if the child’s information and photo edges are rolled up to some extent.
Figure 11. Anti-rolling edge test results: (a) cipher image and (b) restored image.
5.4 Noise test
The cipher image is usually acquired using the photographing method, which produces noise on the cipher image. Salt and pepper noise and Gaussian noise are chosen to model the effect of noise on image restoration. Figure 12 shows the cipher image subjected to salt and pepper (S&P) noise with 0.1, 0.01, and 0.001 intensity and Gaussian noise with 0.001 intensity. The content of the image can be clearly seen at the reduction end, which in turn illustrates the feasibility of the scheme.
Figure 12. Noise test results: (a) S&P 0.1; (b) S&P 0.01; (c) S&P 0.001; (d) Gaussian noise 0.001.
5.5 Differential attack
Differential attack is a common method used by attackers to crack algorithms. The attacker randomly changes one pixel point of the plaintext image to get the cipher image and analyzes the difference between the two cipher images to crack the scheme.
In the differential attack test, the plaintext image is encrypted twice; the first time is normal encryption, and the cipher image is T1; the second time, the attacker randomly changes one pixel point of the plaintext image to get the cipher image, and the cipher image is T2. Since the scheme plaintext information is associated with the initial value of the chaotic system, randomly changing one pixel value of the plaintext image will again result in a different initial value of the chaotic system, and its chaotic sequence also changes. Therefore, the encrypted structure and content are changed, and the resulting encrypted image is also changed.
The difference between T1 and T2 is evaluated by the number of pixels change rate (NPCR) and the unified average changing intensity (UACI). The test results are shown in Table 6.
where Sign (•) is a symbolic function.
Table 6. Test results of different images.
5.6 Comparison with other state-of-the-art encryption schemes
In conclusion, the various performance metrics mentioned above are discussed to compare the proposed encryption algorithm with other state-of-the-art chaotic and non-chaotic encryption algorithms. Reference [46] and Reference [47] proposed chaotic encryption schemes. Reference [48] used the advanced encryption standard (AES) scheme. The comparison results are shown in Table 7.
Table 7. Comparison with other encryption schemes.
6 Discussion and conclusion
6.1 Discussion
In recent years, significant progress has been made in visual information mapping techniques based on deep learning [49, 50]. The visual consistency of feature embedding has been optimized through the cascading attention mechanism, and the robustness of cross-modal information has been improved using adversarial generative networks [51, 52]. These techniques are better able to print child-protective cipher information on clothing in the future.
The existing solutions mainly conduct anti-edge curling and noise tests for image encryption on carriers such as clothing and schoolbags. However, in practical applications, children’s information may be printed on more complex carriers (such as clothes with rough fabric textures and easily worn plastic labels). In the future, the decryption effect of encrypted images under extreme physical conditions (such as high temperature, water stains, and tensile deformation) can be further tested, and combined with image restoration algorithms (such as damaged area completion based on deep learning), the adaptability of the scheme to diverse carriers and environments can be enhanced.
6.2 Conclusion
An image encryption scheme is proposed in this paper for the protection and verification of missing children’s information. First, the dynamical behavior of the hyperchaotic mapping used in the design of the encryption scheme is analyzed, and the analysis results prove that the hyperchaotic mapping is suitable for image-encryption design. Then, the pseudo-random sequences are used to swap the missing child image information with random length random positions, divided into row swap and column swap. Next, a selective XOR is used between the image sequence and the pseudo-random sequences. Finally, the effectiveness of the encryption scheme is verified by simulation. Considering that the missing child’s information should be decrypted by a specific person, the security of the encryption scheme should also be guaranteed. The sensitivity to the key and the large key space guarantee the resistance of the encryption scheme to exhaustive attacks. Comparing the statistical characteristics of the data between the cipher images and the original images, the pixel-level distribution status of the original images, the correlation between the adjacent pixels, and the amount of information contained in the image are hidden or broken. Considering that children’s clothes will have curled edges in the process of use, the image encryption scheme is tested against curled edges. The test results show that even if the missing child information has a certain degree of curled edges, it can be recovered. In summary, this scheme provides technical support for the protection and verification of missing children’s information.
Moreover, this technique can be applied to prevent the missing of children. For example, the detailed information of children, along with those of their parents (Figure 13), can be encoded. The encrypted image will be attached to the clothes (Figure 14). In instances where children go missing, law enforcement agencies can employ specialized readers to decrypt the encrypted information, thereby facilitating accurate and expeditious contact with designated guardians. Moreover, the amalgamation of image encryption significantly amplifies the computational complexity faced by malicious entities attempting to breach the encryption, effectively impeding easy access to children’s information and mitigating concerns regarding privacy breaches. It can enhance the probability of successfully locating missing children.
Figure 13. Lost children information.
Figure 14. Encrypted image (represented by the blue labels) integrated into different areas of the garment.
Data availability statement
The data used in this study is available from the corresponding author upon reasonable request.
Ethics statement
Written informed consent was obtained from the minor(s)' legal guardian/next of kin for the publication of any potentially identifiable images or data included in this article.
Author contributions
CT: Conceptualization, Methodology, Software, Writing – original draft. LN: Funding acquisition, Supervision, Writing – review and editing. RC: Validation, Formal analysis, Writing – review and editing.
Funding
The author(s) declare that financial support was received for the research and/or publication of this article. The research was supported by the Scientific Research Project of Dalian Polytechnic University (KJ20250095) and the Liaoning Provincial Department of Education Scientific Research Project (JYTMS20230410).
Conflict of interest
The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
Generative AI statement
The author(s) declare that no Generative AI was used in the creation of this manuscript.
Publisher’s note
All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.
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Keywords: child information protection, hyperchaotic mapping, image encryption, children’s clothes, information security
Citation: Tu C, Niu L and Cui R (2025) A child information protection scheme based on hyperchaotic mapping. Front. Phys. 13:1655166. doi: 10.3389/fphy.2025.1655166
Received: 27 June 2025; Accepted: 17 July 2025;
Published: 14 October 2025.
Edited by:
Fei Yu, Changsha University of Science and Technology, ChinaReviewed by:
Huihai Wang, Central South University, ChinaBaoxiang Du, Heilongjiang University, China
Copyright © 2025 Tu, Niu and Cui. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
*Correspondence: Li Niu, ODIwMTUwMTAwOUBqaWFuZ25hbi5lZHUuY24=