Practical Secret Image Sharing Based on the Chinese Remainder Theorem

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 ra...
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Autor*in:	Longlong Li [verfasserIn] Yuliang Lu [verfasserIn] Lintao Liu [verfasserIn] Yuyuan Sun [verfasserIn] Jiayu Wang [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2022

Schlagwörter:	secret image sharing Chinese remainder theorem ( practical lossless

Übergeordnetes Werk:	In: Mathematics - MDPI AG, 2013, 10(2022), 12, p 1959
Übergeordnetes Werk:	volume:10 ; year:2022 ; number:12, p 1959

Links:	Link aufrufen Link aufrufen Link aufrufen Journal toc

DOI / URN:	10.3390/math10121959

Katalog-ID:	DOAJ042515874

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spelling	10.3390/math10121959 doi (DE-627)DOAJ042515874 (DE-599)DOAJ2eb6dd58f8ae4250acdea7490f47f36a DE-627 ger DE-627 rakwb eng QA1-939 Longlong Li verfasserin aut Practical Secret Image Sharing Based on the Chinese Remainder Theorem 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier 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 <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<(</mo<<mi<k</mi<<mo<,</mo<<mi<n</mi<<mo<)</mo<</mrow<</semantics<</math<</inline-formula< 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. secret image sharing Chinese remainder theorem (<i<k</i<, <i<n</i<) threshold practical lossless Mathematics Yuliang Lu verfasserin aut Lintao Liu verfasserin aut Yuyuan Sun verfasserin aut Jiayu Wang verfasserin aut In Mathematics MDPI AG, 2013 10(2022), 12, p 1959 (DE-627)737287764 (DE-600)2704244-3 22277390 nnns volume:10 year:2022 number:12, p 1959 https://doi.org/10.3390/math10121959 kostenfrei https://doaj.org/article/2eb6dd58f8ae4250acdea7490f47f36a kostenfrei https://www.mdpi.com/2227-7390/10/12/1959 kostenfrei https://doaj.org/toc/2227-7390 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 10 2022 12, p 1959
allfields_unstemmed	10.3390/math10121959 doi (DE-627)DOAJ042515874 (DE-599)DOAJ2eb6dd58f8ae4250acdea7490f47f36a DE-627 ger DE-627 rakwb eng QA1-939 Longlong Li verfasserin aut Practical Secret Image Sharing Based on the Chinese Remainder Theorem 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier 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 <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<(</mo<<mi<k</mi<<mo<,</mo<<mi<n</mi<<mo<)</mo<</mrow<</semantics<</math<</inline-formula< 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. secret image sharing Chinese remainder theorem (<i<k</i<, <i<n</i<) threshold practical lossless Mathematics Yuliang Lu verfasserin aut Lintao Liu verfasserin aut Yuyuan Sun verfasserin aut Jiayu Wang verfasserin aut In Mathematics MDPI AG, 2013 10(2022), 12, p 1959 (DE-627)737287764 (DE-600)2704244-3 22277390 nnns volume:10 year:2022 number:12, p 1959 https://doi.org/10.3390/math10121959 kostenfrei https://doaj.org/article/2eb6dd58f8ae4250acdea7490f47f36a kostenfrei https://www.mdpi.com/2227-7390/10/12/1959 kostenfrei https://doaj.org/toc/2227-7390 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 10 2022 12, p 1959
allfieldsGer	10.3390/math10121959 doi (DE-627)DOAJ042515874 (DE-599)DOAJ2eb6dd58f8ae4250acdea7490f47f36a DE-627 ger DE-627 rakwb eng QA1-939 Longlong Li verfasserin aut Practical Secret Image Sharing Based on the Chinese Remainder Theorem 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier 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 <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<(</mo<<mi<k</mi<<mo<,</mo<<mi<n</mi<<mo<)</mo<</mrow<</semantics<</math<</inline-formula< 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. secret image sharing Chinese remainder theorem (<i<k</i<, <i<n</i<) threshold practical lossless Mathematics Yuliang Lu verfasserin aut Lintao Liu verfasserin aut Yuyuan Sun verfasserin aut Jiayu Wang verfasserin aut In Mathematics MDPI AG, 2013 10(2022), 12, p 1959 (DE-627)737287764 (DE-600)2704244-3 22277390 nnns volume:10 year:2022 number:12, p 1959 https://doi.org/10.3390/math10121959 kostenfrei https://doaj.org/article/2eb6dd58f8ae4250acdea7490f47f36a kostenfrei https://www.mdpi.com/2227-7390/10/12/1959 kostenfrei https://doaj.org/toc/2227-7390 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 10 2022 12, p 1959
allfieldsSound	10.3390/math10121959 doi (DE-627)DOAJ042515874 (DE-599)DOAJ2eb6dd58f8ae4250acdea7490f47f36a DE-627 ger DE-627 rakwb eng QA1-939 Longlong Li verfasserin aut Practical Secret Image Sharing Based on the Chinese Remainder Theorem 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier 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 <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<(</mo<<mi<k</mi<<mo<,</mo<<mi<n</mi<<mo<)</mo<</mrow<</semantics<</math<</inline-formula< 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. secret image sharing Chinese remainder theorem (<i<k</i<, <i<n</i<) threshold practical lossless Mathematics Yuliang Lu verfasserin aut Lintao Liu verfasserin aut Yuyuan Sun verfasserin aut Jiayu Wang verfasserin aut In Mathematics MDPI AG, 2013 10(2022), 12, p 1959 (DE-627)737287764 (DE-600)2704244-3 22277390 nnns volume:10 year:2022 number:12, p 1959 https://doi.org/10.3390/math10121959 kostenfrei https://doaj.org/article/2eb6dd58f8ae4250acdea7490f47f36a kostenfrei https://www.mdpi.com/2227-7390/10/12/1959 kostenfrei https://doaj.org/toc/2227-7390 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 10 2022 12, p 1959
language	English
source	In Mathematics 10(2022), 12, p 1959 volume:10 year:2022 number:12, p 1959
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authorswithroles_txt_mv	Longlong Li @@aut@@ Yuliang Lu @@aut@@ Lintao Liu @@aut@@ Yuyuan Sun @@aut@@ Jiayu Wang @@aut@@
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callnumber-first	Q - Science
author	Longlong Li
spellingShingle	Longlong Li misc QA1-939 misc secret image sharing misc Chinese remainder theorem misc (<i<k</i<, <i<n</i<) threshold misc practical misc lossless misc Mathematics Practical Secret Image Sharing Based on the Chinese Remainder Theorem
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topic_title	QA1-939 Practical Secret Image Sharing Based on the Chinese Remainder Theorem secret image sharing Chinese remainder theorem (<i<k</i<, <i<n</i<) threshold practical lossless
topic	misc QA1-939 misc secret image sharing misc Chinese remainder theorem misc (<i<k</i<, <i<n</i<) threshold misc practical misc lossless misc Mathematics
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title	Practical Secret Image Sharing Based on the Chinese Remainder Theorem
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title_sort	practical secret image sharing based on the chinese remainder theorem
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title_auth	Practical Secret Image Sharing Based on the Chinese Remainder Theorem
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 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 <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<(</mo<<mi<k</mi<<mo<,</mo<<mi<n</mi<<mo<)</mo<</mrow<</semantics<</math<</inline-formula< 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.
abstractGer	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 <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<(</mo<<mi<k</mi<<mo<,</mo<<mi<n</mi<<mo<)</mo<</mrow<</semantics<</math<</inline-formula< 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.
abstract_unstemmed	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 <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<(</mo<<mi<k</mi<<mo<,</mo<<mi<n</mi<<mo<)</mo<</mrow<</semantics<</math<</inline-formula< 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.
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container_issue	12, p 1959
title_short	Practical Secret Image Sharing Based on the Chinese Remainder Theorem
url	https://doi.org/10.3390/math10121959 https://doaj.org/article/2eb6dd58f8ae4250acdea7490f47f36a https://www.mdpi.com/2227-7390/10/12/1959 https://doaj.org/toc/2227-7390
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Practical Secret Image Sharing Based on the Chinese Remainder Theorem

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