Changing the Threshold in a Bivariate Polynomial Based Secret Image Sharing Scheme
Secret image sharing (SIS) is an important application of the traditional secret sharing scheme, which has become popular in recent years. In an SIS scheme, a confidential image is encrypted into a group of shadows. Any set of shadows that reaches the threshold can reconstruct the image; otherwise,...
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MDPI AG
2022-02-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/5/710 |
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| author | Qindong Sun Han Cao Shancang Li Houbing Song Yanxiao Liu |
| author_facet | Qindong Sun Han Cao Shancang Li Houbing Song Yanxiao Liu |
| author_sort | Qindong Sun |
| collection | DOAJ |
| description | Secret image sharing (SIS) is an important application of the traditional secret sharing scheme, which has become popular in recent years. In an SIS scheme, a confidential image is encrypted into a group of shadows. Any set of shadows that reaches the threshold can reconstruct the image; otherwise, nothing can be recovered at all. In most existing SIS schemes, the threshold on shadows for image reconstruction is fixed. However, in this work, we consider more complicated cases of SIS, such that the threshold is changeable according to the security environment. In this paper, we construct a <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>k</mi><mo>↔</mo><mi>h</mi><mo>,</mo><mi>n</mi><mo>)</mo></mrow></semantics></math></inline-formula> threshold-changeable SIS (TCSIS) scheme using a bivariate polynomial, which provides <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>h</mi><mo>−</mo><mi>k</mi><mo>+</mo><mn>1</mn></mrow></semantics></math></inline-formula> possible thresholds, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>k</mi><mo>,</mo><mi>k</mi><mo>+</mo><mn>1</mn><mo>,</mo><mo>…</mo><mo>,</mo><mi>h</mi></mrow></semantics></math></inline-formula>. During image reconstruction, each participant can update their shadow according to the current threshold <i>T</i> based only on their initial shadow. Unlike previous TCSIS schemes, the proposed scheme achieves unconditional security and can overcome the information disclosure problem caused by homomorphism. |
| first_indexed | 2024-03-09T20:31:29Z |
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| language | English |
| last_indexed | 2024-03-09T20:31:29Z |
| publishDate | 2022-02-01 |
| publisher | MDPI AG |
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| series | Mathematics |
| spelling | doaj.art-d2c50aa3b67c4a2b864076fcfc0c165f2023-11-23T23:22:28ZengMDPI AGMathematics2227-73902022-02-0110571010.3390/math10050710Changing the Threshold in a Bivariate Polynomial Based Secret Image Sharing SchemeQindong Sun0Han Cao1Shancang Li2Houbing Song3Yanxiao Liu4School of Cyber Science and Engineering, Xi’an Jiaotong University, Xi’an 710049, ChinaShaanxi Key Laboratory of Network Computing and Security, Xi’an University of Technology, Xi’an 710048, ChinaDepartment of Computer Science and Creative Technologies, University of the West of England, Bristol BS16 1QY, UKDepartment of Electrical, Computer, Software and Systems Engineering, Embry-Riddle Aeronautical University, Daytona Beach, FL 32114, USADepartment of Computer Science and Engineering, Xi’an University of Technology, Xi’an 710048, ChinaSecret image sharing (SIS) is an important application of the traditional secret sharing scheme, which has become popular in recent years. In an SIS scheme, a confidential image is encrypted into a group of shadows. Any set of shadows that reaches the threshold can reconstruct the image; otherwise, nothing can be recovered at all. In most existing SIS schemes, the threshold on shadows for image reconstruction is fixed. However, in this work, we consider more complicated cases of SIS, such that the threshold is changeable according to the security environment. In this paper, we construct a <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>k</mi><mo>↔</mo><mi>h</mi><mo>,</mo><mi>n</mi><mo>)</mo></mrow></semantics></math></inline-formula> threshold-changeable SIS (TCSIS) scheme using a bivariate polynomial, which provides <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>h</mi><mo>−</mo><mi>k</mi><mo>+</mo><mn>1</mn></mrow></semantics></math></inline-formula> possible thresholds, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>k</mi><mo>,</mo><mi>k</mi><mo>+</mo><mn>1</mn><mo>,</mo><mo>…</mo><mo>,</mo><mi>h</mi></mrow></semantics></math></inline-formula>. During image reconstruction, each participant can update their shadow according to the current threshold <i>T</i> based only on their initial shadow. Unlike previous TCSIS schemes, the proposed scheme achieves unconditional security and can overcome the information disclosure problem caused by homomorphism.https://www.mdpi.com/2227-7390/10/5/710secret sharing schemesecret image sharingthreshold changeablebivariate polynomial |
| spellingShingle | Qindong Sun Han Cao Shancang Li Houbing Song Yanxiao Liu Changing the Threshold in a Bivariate Polynomial Based Secret Image Sharing Scheme Mathematics secret sharing scheme secret image sharing threshold changeable bivariate polynomial |
| title | Changing the Threshold in a Bivariate Polynomial Based Secret Image Sharing Scheme |
| title_full | Changing the Threshold in a Bivariate Polynomial Based Secret Image Sharing Scheme |
| title_fullStr | Changing the Threshold in a Bivariate Polynomial Based Secret Image Sharing Scheme |
| title_full_unstemmed | Changing the Threshold in a Bivariate Polynomial Based Secret Image Sharing Scheme |
| title_short | Changing the Threshold in a Bivariate Polynomial Based Secret Image Sharing Scheme |
| title_sort | changing the threshold in a bivariate polynomial based secret image sharing scheme |
| topic | secret sharing scheme secret image sharing threshold changeable bivariate polynomial |
| url | https://www.mdpi.com/2227-7390/10/5/710 |
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