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Keywords = lossless recovery

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22 pages, 437 KiB  
Article
ApproximateSecret Sharing in Field of Real Numbers
by Jiaqi Wan, Ziyue Wang, Yongqiang Yu and Xuehu Yan
Entropy 2025, 27(7), 769; https://doi.org/10.3390/e27070769 - 20 Jul 2025
Viewed by 194
Abstract
In the era of big data, the security of information encryption systems has garnered extensive attention, particularly in critical domains such as financial transactions and medical data management. While traditional Shamir’s Secret Sharing (SSS) ensures secure integer sharing through threshold cryptography, it exhibits [...] Read more.
In the era of big data, the security of information encryption systems has garnered extensive attention, particularly in critical domains such as financial transactions and medical data management. While traditional Shamir’s Secret Sharing (SSS) ensures secure integer sharing through threshold cryptography, it exhibits inherent limitations when applied to floating-point domains and high-precision numerical scenarios. To address these issues, this paper proposes an innovative algorithm to optimize SSS via type-specific coding for real numbers. By categorizing real numbers into four types—rational numbers, special irrationals, common irrationals, and general irrationals—our approach achieves lossless transmission for rational numbers, special irrationals, and common irrationals, while enabling low-loss recovery for general irrationals. The scheme leverages a type-coding system to embed data category identifiers in polynomial coefficients, combined with Bernoulli-distributed random bit injection to enhance security. The experimental results validate its effectiveness in balancing precision and security across various real-number types. Full article
(This article belongs to the Section Information Theory, Probability and Statistics)
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23 pages, 2184 KiB  
Article
Lossless Compression of Malaria-Infected Erythrocyte Images Using Vision Transformer and Deep Autoencoders
by Md Firoz Mahmud, Zerin Nusrat and W. David Pan
Computers 2025, 14(4), 127; https://doi.org/10.3390/computers14040127 - 1 Apr 2025
Viewed by 680
Abstract
Lossless compression of medical images allows for rapid image data exchange and faithful recovery of the compressed data for medical image assessment. There are many useful telemedicine applications, for example in diagnosing conditions such as malaria in resource-limited regions. This paper presents a [...] Read more.
Lossless compression of medical images allows for rapid image data exchange and faithful recovery of the compressed data for medical image assessment. There are many useful telemedicine applications, for example in diagnosing conditions such as malaria in resource-limited regions. This paper presents a novel machine learning-based approach where lossless compression of malaria-infected erythrocyte images is assisted by cutting-edge classifiers. To this end, we first use a Vision Transformer to classify images into two categories: those cells that are infected with malaria and those that are not. We then employ distinct deep autoencoders for each category, which not only reduces the dimensions of the image data but also preserves crucial diagnostic information. To ensure no loss in reconstructed image quality, we further compress the residuals produced by these autoencoders using the Huffman code. Simulation results show that the proposed method achieves lower overall bit rates and thus higher compression ratios than traditional compression schemes such as JPEG 2000, JPEG-LS, and CALIC. This strategy holds significant potential for effective telemedicine applications and can improve diagnostic capabilities in regions impacted by malaria. Full article
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22 pages, 24537 KiB  
Article
Recovery-Enhanced Image Steganography Framework with Auxiliary Model Based on Invertible Neural Networks
by Lin Huo, Kai Wang and Jie Wei
Symmetry 2025, 17(3), 456; https://doi.org/10.3390/sym17030456 - 18 Mar 2025
Viewed by 631
Abstract
With the advancement of technology, the information hiding capacity has significantly increased, allowing a cover image to conceal one or more secret images. However, this high hiding capacity often leads to contour shadows and color distortions, making the high-quality recovery of secret images [...] Read more.
With the advancement of technology, the information hiding capacity has significantly increased, allowing a cover image to conceal one or more secret images. However, this high hiding capacity often leads to contour shadows and color distortions, making the high-quality recovery of secret images extremely challenging. Existing image hiding algorithms based on Invertible Neural Networks (INNs) often discard useful information during the hiding process, resulting in poor quality of the recovered secret images, especially in multi-image hiding scenarios. The theoretical symmetry of INNs ensures the lossless reversibility of the embedder and decoder, but the lost information generated in practical image steganography disrupts this symmetry. To address this issue, we propose an INN-based image steganography framework that overcomes the limitations of current INN methods in image steganography applications. Our framework can embed multiple full-size secret images into cover images of the same size and utilize the correlation between the lost information and the secret and cover images to generate the lost information by combining the auxiliary model of the Dense–Channel–Spatial Attention Module to restore the symmetry of reversible neural networks, thereby improving the quality of the recovered images. In addition, we employ a multi-stage progressive training strategy to improve the recovery of lost information, thereby achieving high-quality secret image recovery. To further enhance the security of the hiding process, we introduced a multi-scale wavelet loss function into the loss function. Our method significantly improves the quality of image recovery in single-image steganography tasks across multiple datasets (DIV2K, COCO, ImageNet), with a PSNR reaching up to 50.37 dB (an improvement of over 3 dB compared to other methods). The results show that our method outperforms other state-of-the-art (SOTA) image hiding techniques on different datasets and achieves strong performance in multi-image hiding as well. Full article
(This article belongs to the Section Computer)
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21 pages, 7107 KiB  
Article
Data Hiding and Authentication Scheme for Medical Images Using Double POB
by Fang Ren, Xuan Shi, Enya Tang and Mengmeng Zeng
Appl. Sci. 2024, 14(6), 2664; https://doi.org/10.3390/app14062664 - 21 Mar 2024
Cited by 3 | Viewed by 1630
Abstract
To protect the security of medical images and to improve the embedding ability of data in encrypted medical images, this paper proposes a permutation ordered binary (POB) number system-based hiding and authentication scheme for medical images, which includes three parts: image preprocessing, double [...] Read more.
To protect the security of medical images and to improve the embedding ability of data in encrypted medical images, this paper proposes a permutation ordered binary (POB) number system-based hiding and authentication scheme for medical images, which includes three parts: image preprocessing, double hiding, and information extraction and lossless recovery. In the image preprocessing and double hiding phase, firstly, the region of significance (ROS) of the original medical image is segmented into a region of interest (ROI) and a region of non-interest (RONI). Then, the bit plane of the ROI and RONI are separated and cross-reorganization to obtain two new Share images. After the two new Share images are compressed, the images are encrypted to generate two encrypted shares. Finally, the embedding of secret data and attaching of authentication bits in each of these two encrypted shares was performed using the POB algorithm. In the information extraction and lossless recovery phase, the POBN algorithm is first used to extract the authentication bits to realize image tamper detection; then, the embedded secret message is extracted, and the original medical image is recovered. The method proposed in this research performs better in data embedding and lossless recovery, as demonstrated by experiments. Full article
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19 pages, 2571 KiB  
Article
Reversible Data Hiding in Encrypted Image Based on Bit-Plane Redundancy of Prediction Error
by Fang Ren, Ziyi Wu, Yaqi Xue and Yanli Hao
Mathematics 2023, 11(11), 2537; https://doi.org/10.3390/math11112537 - 31 May 2023
Cited by 6 | Viewed by 1830
Abstract
In this paper, we propose a reversible data hiding scheme in an encrypted image based on bit-plane redundancy of prediction error. The scheme greatly improves the embedding capacity while maintaining lossless image recovery and error-free secret data extraction. Firstly, the original image is [...] Read more.
In this paper, we propose a reversible data hiding scheme in an encrypted image based on bit-plane redundancy of prediction error. The scheme greatly improves the embedding capacity while maintaining lossless image recovery and error-free secret data extraction. Firstly, the original image is preprocessed to obtain the prediction error image. After the error matrix is divided into blocks, the corresponding block type is obtained. Secondly, the predicted error image is encrypted with stream cipher and the encryption matrix blocks are scrambled to ensure the security of the scheme. Finally, after embedding the block type value into the encrypted image, the spare room corresponding to each block was obtained, which was used to embed the secret data. The scheme makes full use of the spatial correlation of the pixels in the block, so it improves the embedding rate. By selecting 100 images in each dataset of BOSSbase and BOWS-2, when the block size is 3×3, the average embedding rate of our scheme can reach 3.56 bpp and 3.81 bpp, respectively. The performance of the proposed method is better than the other schemes with similar properties. Full article
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18 pages, 4092 KiB  
Article
Reversible Data Hiding in Encrypted Images Based on the Mixed Multi-Bit Layer Embedding Strategy
by Rui-Hua Liu and Quan Zhou
Appl. Sci. 2023, 13(9), 5696; https://doi.org/10.3390/app13095696 - 5 May 2023
Cited by 3 | Viewed by 2146
Abstract
With the increasing requirements for the security of medical data, military data, and other data transmission, data hiding technology has gradually developed from only protecting the security of secret data to all transmission data. As a necessary technical means, reversible data hiding in [...] Read more.
With the increasing requirements for the security of medical data, military data, and other data transmission, data hiding technology has gradually developed from only protecting the security of secret data to all transmission data. As a necessary technical means, reversible data hiding in encrypted images (RDH-EIs) provides superior performance in terms of security. To simultaneously improve the effectiveness of RDH-EIs, this work proposes a mixed multi-bit layer embedding strategy in encrypted images. The cover image is processed into two categories: available hidden blocks (AHBs) and unavailable hidden blocks (UHBs) at the sender. Then, all data are embedded in the multi-bit layer of the encrypted pixels in AHBs through two embedding strategies to obtain the transmission image. At the receiver, the user can extract the needed data separably according to different keys to achieve error-free extraction of the secret data and lossless recovery of the cover image. The experimental results show that the proposed scheme has the advantages of superior embedding capacity and high decryption quality over the current state-of-the-art works. Full article
(This article belongs to the Special Issue Digital Image Security and Privacy Protection)
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15 pages, 1448 KiB  
Article
A Lossless-Recovery Secret Distribution Scheme Based on QR Codes
by Jeng-Shyang Pan, Tao Liu, Bin Yan , Hong-Mei Yang  and Shu-Chuan Chu
Entropy 2023, 25(4), 653; https://doi.org/10.3390/e25040653 - 13 Apr 2023
Cited by 1 | Viewed by 2086
Abstract
The visual cryptography scheme (VCS) distributes a secret to several images that can enhance the secure transmission of that secret. Quick response (QR) codes are widespread. VCS can be used to improve their secure transmission. Some schemes recover QR codes with many errors. [...] Read more.
The visual cryptography scheme (VCS) distributes a secret to several images that can enhance the secure transmission of that secret. Quick response (QR) codes are widespread. VCS can be used to improve their secure transmission. Some schemes recover QR codes with many errors. This paper uses a distribution mechanism to achieve the error-free recovery of QR codes. An error-correction codeword (ECC) is used to divide the QR code into different areas. Every area is a key, and they are distributed to n shares. The loss of any share will make the reconstructed QR code impossible to decode normally. Stacking all shares can recover the secret QR code losslessly. Based on some experiments, the proposed scheme is relatively safe. The proposed scheme can restore a secret QR code without errors, and it is effective and feasible. Full article
(This article belongs to the Section Multidisciplinary Applications)
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26 pages, 11319 KiB  
Article
Reversible Data Hiding in Encrypted Images Based on an Adaptive Recognition Strategy for Blocks
by Zhi Pang, Han Li, Zhaolin Xiao and Liansheng Sui
Symmetry 2023, 15(2), 524; https://doi.org/10.3390/sym15020524 - 15 Feb 2023
Cited by 6 | Viewed by 2076
Abstract
As the rapid development of third-party storage and homomorphic encryption have profoundly stimulated the desire for secure communication, reversible data hiding in encrypted images has received widespread attention, since it allows lossless data conveying and perfect image recovery. In order to obtain secure [...] Read more.
As the rapid development of third-party storage and homomorphic encryption have profoundly stimulated the desire for secure communication, reversible data hiding in encrypted images has received widespread attention, since it allows lossless data conveying and perfect image recovery. In order to obtain secure reversible data hiding with high embedding capacity, a novel block embedding method is proposed, based on an adaptive recognition strategy for combined blocks in the binary image, with which the adjacent identical blocks can be integrated into a combination to reserve more spare bits for data accommodation. Furthermore, a fully reversible data hiding method for grayscale images in the encryption domain is designed. The secret data is hidden into lower bit-planes of the image while the original bits of those embedded lower pixels are recorded into the vacated space of higher bit-planes. The original image can be reconstructed flawlessly as well as the secret data being extracted without errors. To reinforce security, the original image and the secret data are encrypted and scrambled based on sequences generated with the high-dimension chaotic system. Due to its high sensitivity of initial values, the performance such as security and robustness is guaranteed. By comparing the PSNR value of the marked decrypted image and evaluating the quality of the extracted secret image, experimental results demonstrate that the proposed method can obtain higher embedding capacity, achieving 0.2700–0.3924 bpp increment over the state-of-the-art methods, and recover the marked decrypted image with high visual symmetry/quality, and efficiently resist against potential attacks, such as the histogram analysis, differential, brute-force, JPEG attacks, and so on. Full article
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17 pages, 4913 KiB  
Article
IEF-CSNET: Information Enhancement and Fusion Network for Compressed Sensing Reconstruction
by Ziqun Zhou, Fengyin Liu and Haibin Shen
Sensors 2023, 23(4), 1886; https://doi.org/10.3390/s23041886 - 8 Feb 2023
Cited by 4 | Viewed by 2203
Abstract
The rapidly growing requirement for data has put forward Compressed Sensing (CS) to realize low-ratio sampling and to reconstruct complete signals. With the intensive development of Deep Neural Network (DNN) methods, performance in image reconstruction from CS measurements is constantly increasing. Currently, many [...] Read more.
The rapidly growing requirement for data has put forward Compressed Sensing (CS) to realize low-ratio sampling and to reconstruct complete signals. With the intensive development of Deep Neural Network (DNN) methods, performance in image reconstruction from CS measurements is constantly increasing. Currently, many network structures pay less attention to the relevance of before- and after-stage results and fail to make full use of relevant information in the compressed domain to achieve interblock information fusion and a great receptive field. Additionally, due to multiple resamplings and several forced compressions of information flow, information loss and network structure redundancy inevitably result. Therefore, an Information Enhancement and Fusion Network for CS reconstruction (IEF-CSNET) is proposed in this work, and a Compressed Information Extension (CIE) module is designed to fuse the compressed information in the compressed domain and greatly expand the receptive field. The Error Comprehensive Consideration Enhancement (ECCE) module enhances the error image by incorporating the previous recovered error so that the interlink among the iterations can be utilized for better recovery. In addition, an Iterative Information Flow Enhancement (IIFE) module is further proposed to complete the progressive recovery with loss-less information transmission during the iteration. In summary, the proposed method achieves the best effect, exhibits high robustness at this stage, with the peak signal-to-noise ratio (PSNR) improved by 0.59 dB on average under all test sets and sampling rates, and presents a greatly improved speed compared with the best algorithm. Full article
(This article belongs to the Special Issue Compressed Sensing and Imaging Processing)
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14 pages, 2528 KiB  
Article
Lossless Image Steganography Based on Invertible Neural Networks
by Lianshan Liu, Li Tang and Weimin Zheng
Entropy 2022, 24(12), 1762; https://doi.org/10.3390/e24121762 - 1 Dec 2022
Cited by 14 | Viewed by 4726
Abstract
Image steganography is a scheme that hides secret information in a cover image without being perceived. Most of the existing steganography methods are more concerned about the visual similarity between the stego image and the cover image, and they ignore the recovery accuracy [...] Read more.
Image steganography is a scheme that hides secret information in a cover image without being perceived. Most of the existing steganography methods are more concerned about the visual similarity between the stego image and the cover image, and they ignore the recovery accuracy of secret information. In this paper, the steganography method based on invertible neural networks is proposed, which can generate stego images with high invisibility and security and can achieve lossless recovery for secret information. In addition, this paper introduces a mapping module that can compress information actually embedded to improve the quality of the stego image and its antidetection ability. In order to restore message and prevent loss, the secret information is converted into a binary sequence and then embedded in the cover image through the forward operation of the invertible neural networks. This information will then be recovered from the stego image through the inverse operation of the invertible neural networks. Experimental results show that the proposed method in this paper has achieved competitive results in the visual quality and safety of stego images and achieved 100% accuracy in information extraction. Full article
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15 pages, 5191 KiB  
Article
Reversible Data Hiding Using an Improved Pixel Value Ordering and Complementary Strategy
by Rajeev Kumar, Neeraj Kumar and Ki-Hyun Jung
Symmetry 2022, 14(12), 2477; https://doi.org/10.3390/sym14122477 - 22 Nov 2022
Cited by 2 | Viewed by 1867
Abstract
Reversible data hiding (RDH) schemes based on pixel value ordering have gained significant popularity due to their unique capability of providing high-quality marked images with a decent embedding capacity, while also enabling secret information extraction and the lossless recovery of the original images [...] Read more.
Reversible data hiding (RDH) schemes based on pixel value ordering have gained significant popularity due to their unique capability of providing high-quality marked images with a decent embedding capacity, while also enabling secret information extraction and the lossless recovery of the original images at the receiving side. However, the marked image quality may be distorted severely when the pixel value ordering (PVO) method is employed in a layer-wise manner to increase the embedding capacity. In this paper, a new high-capacity RDH scheme using a complementary strategy is introduced to overcome the limitation of the image quality in the case of layer-wise embedding. The proposed RDH scheme first divides the cover image into non-overlapping blocks of 2 × 2 pixels uniformly and then sorts the pixels of each block according to their intensity values. The secret data are then embedded into two layers. In the first layer, the minimum value of the block is decreased and the maximum value is increased by either 1 or 2 to embed the secret data bits. The second layer is used as a complement to the first layer and is in symmetry with the first layer. In the second layer, the proposed RDH scheme increases the minimum valued pixel and decreases the maximum valued pixel in order to minimize the distortion resulting from the first layer embedding and to embed an additional amount of the secret data. As a result, the proposed RDH scheme significantly increases the embedding capacity, which is clearly evident from the conducted experimental results. Full article
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22 pages, 7087 KiB  
Article
A High-Capacity Reversible Data-Hiding Scheme for Medical Image Transmission Using Modified Elias Gamma Encoding
by V. M. Manikandan, Kandala Sree Rama Murthy, Bhavana Siddineni, Nancy Victor, Praveen Kumar Reddy Maddikunta and Saqib Hakak
Electronics 2022, 11(19), 3101; https://doi.org/10.3390/electronics11193101 - 28 Sep 2022
Cited by 4 | Viewed by 2354
Abstract
Reversible data hiding (RDH) is a recently emerged research domain in the field of information security domain with broad applications in medical images and meta-data handling in the cloud. The amount of data required to handle the healthcare sector has exponentially increased due [...] Read more.
Reversible data hiding (RDH) is a recently emerged research domain in the field of information security domain with broad applications in medical images and meta-data handling in the cloud. The amount of data required to handle the healthcare sector has exponentially increased due to the increase in the population. Medical images and various reports such as discharge summaries and diagnosis reports are the most common data in the healthcare sector. The RDH schemes are widely explored to embed the medical reports in the medical image instead of sending them as separate files. The receiver can extract the clinical reports and recover the original medical image for further diagnosis. This manuscript proposes an approach that uses a new lossless compression-based RDH scheme that creates vacant room for data hiding. The proposed scheme uses run-length encoding and a modified Elias gamma encoding scheme on higher-order bit planes for lossless compression. The conventional Elias gamma encoding process is modified in the proposed method to embed some additional data bits during the encoding process itself. The revised approach ensures a high embedding rate and lossless recovery of medical images at the receiver side. The experimental study is conducted on both natural images and medical images. The average embedding rate from the proposed scheme for the medical images is 0.75 bits per pixel. The scheme achieved a 0 bit error rate during image recovery and data extraction. The experimental study shows that the newly introduced scheme performs better when compared with the existing RDH schemes. Full article
(This article belongs to the Section Computer Science & Engineering)
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33 pages, 9029 KiB  
Article
Serial Decoders-Based Auto-Encoders for Image Reconstruction
by Honggui Li, Maria Trocan, Mohamad Sawan and Dimitri Galayko
Appl. Sci. 2022, 12(16), 8256; https://doi.org/10.3390/app12168256 - 18 Aug 2022
Cited by 4 | Viewed by 2643
Abstract
Auto-encoders are composed of coding and decoding units; hence, they hold an inherent potential of being used for high-performance data compression and signal-compressed sensing. The main disadvantages of current auto-encoders comprise the following aspects: the research objective is not to achieve lossless data [...] Read more.
Auto-encoders are composed of coding and decoding units; hence, they hold an inherent potential of being used for high-performance data compression and signal-compressed sensing. The main disadvantages of current auto-encoders comprise the following aspects: the research objective is not to achieve lossless data reconstruction but efficient feature representation; the evaluation of data recovery performance is neglected; it is difficult to achieve lossless data reconstruction using pure auto-encoders, even with pure deep learning. This paper aims at performing image reconstruction using auto-encoders, employs cascade decoders-based auto-encoders, perfects the performance of image reconstruction, approaches gradually lossless image recovery, and provides a solid theoretical and applicational basis for auto-encoders-based image compression and compressed sensing. The proposed serial decoders-based auto-encoders include the architectures of multi-level decoders and their related progressive optimization sub-problems. The cascade decoders consist of general decoders, residual decoders, adversarial decoders, and their combinations. The effectiveness of residual cascade decoders for image reconstruction is proven in mathematics. Progressive training can efficiently enhance the quality, stability, and variation of image reconstruction. It has been shown by the experimental results that the proposed auto-encoders outperform classical auto-encoders in the performance of image reconstruction. Full article
(This article belongs to the Special Issue Deep Neural Network: Algorithms and Applications)
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21 pages, 8000 KiB  
Article
A Multi-Domain Embedding Framework for Robust Reversible Data Hiding Scheme in Encrypted Videos
by Pei Chen, Zhuo Zhang, Yang Lei, Ke Niu and Xiaoyuan Yang
Electronics 2022, 11(16), 2552; https://doi.org/10.3390/electronics11162552 - 15 Aug 2022
Cited by 3 | Viewed by 1998
Abstract
For easier cloud management, reversible data hiding is performed in an encrypted domain to embed label information. However, the existing schemes are not robust and may cause the loss of label information during transmission. Enhancing robustness while maintaining reversibility in data hiding is [...] Read more.
For easier cloud management, reversible data hiding is performed in an encrypted domain to embed label information. However, the existing schemes are not robust and may cause the loss of label information during transmission. Enhancing robustness while maintaining reversibility in data hiding is a challenge. In this paper, a multi-domain embedding framework in encrypted videos is proposed to achieve both robustness and reversibility. In the framework, the multi-domain characteristic of encrypted video is fully used. The element for robust embedding is encrypted through Logistic chaotic scrambling, which is marked as element-I. To further improve robustness, the label information will be encoded with the Bose–Chaudhuri–Hocquenghem code. Then, the label information will be robustly embedded into element-I by modulating the amplitude of element-I, in which the auxiliary information is generated for lossless recovery of the element-I. The element for reversible embedding is marked as element-II, the sign of which will be encrypted by stream cipher. The auxiliary information will be reversibly embedded into element-Ⅱ through traditional histogram shifting. To verity the feasibility of the framework, an anti-recompression RDH-EV based on the framework is proposed. The experimental results show that the proposed scheme outperforms the current representative ones in terms of robustness, while achieving reversibility. In the proposed scheme, video encryption and data hiding are commutative and the original video bitstream can be recovered fully. These demonstrate the feasibility of the multi-domain embedding framework in encrypted videos. Full article
(This article belongs to the Topic Computer Vision and Image Processing)
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18 pages, 21988 KiB  
Article
Practical Secret Image Sharing Based on the Chinese Remainder Theorem
by Longlong Li, Yuliang Lu, Lintao Liu, Yuyuan Sun and Jiayu Wang
Mathematics 2022, 10(12), 1959; https://doi.org/10.3390/math10121959 - 7 Jun 2022
Cited by 8 | Viewed by 2636
Abstract
Compared with Shamir’s original secret image sharing (SIS), the Chinese-remainder-theorem-based SIS (CRTSIS) generally has the advantages of a lower computation complexity, lossless recovery and no auxiliary encryption. However, general CRTSIS is neither perfect nor ideal, resulting in a narrower range of share pixels [...] Read more.
Compared with Shamir’s original secret image sharing (SIS), the Chinese-remainder-theorem-based SIS (CRTSIS) generally has the advantages of a lower computation complexity, lossless recovery and no auxiliary encryption. However, general CRTSIS is neither perfect nor ideal, resulting in a narrower range of share pixels than that of secret pixels. In this paper, we propose a practical and lossless CRTSIS based on Asmuth and Bloom’s threshold algorithm. To adapt the original scheme for grayscale images, our scheme shares the high seven bits of each pixel and utilizes the least significant bit (LSB) matching technique to embed the LSBs into the random integer that is generated in the sharing phase. The chosen moduli are all greater than 255 and the share pixels are in the range of [0, 255] by a screening operation. The generated share pixel values are evenly distributed in the range of [0, 255] and the selection of (k,n) threshold is much more flexible, which significantly improves the practicality of CRTSIS. Since color images in RGB mode are made up of three channels, it is easy to extend the scheme to color images. Theoretical analysis and experiments are given to validate the effectiveness of the proposed scheme. Full article
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