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The extended visual cryptography scheme (EVCS) proposed by Ateniese et al. is one of variations of the visual cryptography scheme such that a secret image is recovered by superimposition of certain qualified collections of shares, where cover images are visible on respective shares. In this paper, we give a new definition of the EVCS for improving visibility of the recovered secret image as well as the cover images. We formulate the problem to construct the basis matrices of the EVCS with the minimum pixel expansion as an integer programming problem. We solve the integer programming problem for general access structures with less than or equal to five participants and show that basis matrices with a smaller pixel expansion can be obtained for certain cases. We also analyze security of the EVCS meeting the new definition from an information-theoretic viewpoint. We give a condition under which any forbidden collection of shares does not reveal any additional information on not only a secret image but also the cover images that are not visible on the other shares.

- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E104-A No.9 pp.1235-1244

- Publication Date
- 2021/09/01

- Publicized
- 2021/03/16

- Online ISSN
- 1745-1337

- DOI
- 10.1587/transfun.2020DMP0010

- Type of Manuscript
- Special Section PAPER (Special Section on Discrete Mathematics and Its Applications)

- Category
- Cryptography and Information Security

Kyohei SEKINE

University of Tsukuba

Hiroki KOGA

University of Tsukuba

The copyright of the original papers published on this site belongs to IEICE. Unauthorized use of the original or translated papers is prohibited. See IEICE Provisions on Copyright for details.

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Kyohei SEKINE, Hiroki KOGA, "Optimal Basis Matrices of a Visual Cryptography Scheme with Meaningful Shares and Analysis of Its Security" in IEICE TRANSACTIONS on Fundamentals,
vol. E104-A, no. 9, pp. 1235-1244, September 2021, doi: 10.1587/transfun.2020DMP0010.

Abstract: The extended visual cryptography scheme (EVCS) proposed by Ateniese et al. is one of variations of the visual cryptography scheme such that a secret image is recovered by superimposition of certain qualified collections of shares, where cover images are visible on respective shares. In this paper, we give a new definition of the EVCS for improving visibility of the recovered secret image as well as the cover images. We formulate the problem to construct the basis matrices of the EVCS with the minimum pixel expansion as an integer programming problem. We solve the integer programming problem for general access structures with less than or equal to five participants and show that basis matrices with a smaller pixel expansion can be obtained for certain cases. We also analyze security of the EVCS meeting the new definition from an information-theoretic viewpoint. We give a condition under which any forbidden collection of shares does not reveal any additional information on not only a secret image but also the cover images that are not visible on the other shares.

URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.2020DMP0010/_p

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@ARTICLE{e104-a_9_1235,

author={Kyohei SEKINE, Hiroki KOGA, },

journal={IEICE TRANSACTIONS on Fundamentals},

title={Optimal Basis Matrices of a Visual Cryptography Scheme with Meaningful Shares and Analysis of Its Security},

year={2021},

volume={E104-A},

number={9},

pages={1235-1244},

abstract={The extended visual cryptography scheme (EVCS) proposed by Ateniese et al. is one of variations of the visual cryptography scheme such that a secret image is recovered by superimposition of certain qualified collections of shares, where cover images are visible on respective shares. In this paper, we give a new definition of the EVCS for improving visibility of the recovered secret image as well as the cover images. We formulate the problem to construct the basis matrices of the EVCS with the minimum pixel expansion as an integer programming problem. We solve the integer programming problem for general access structures with less than or equal to five participants and show that basis matrices with a smaller pixel expansion can be obtained for certain cases. We also analyze security of the EVCS meeting the new definition from an information-theoretic viewpoint. We give a condition under which any forbidden collection of shares does not reveal any additional information on not only a secret image but also the cover images that are not visible on the other shares.},

keywords={},

doi={10.1587/transfun.2020DMP0010},

ISSN={1745-1337},

month={September},}

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TY - JOUR

TI - Optimal Basis Matrices of a Visual Cryptography Scheme with Meaningful Shares and Analysis of Its Security

T2 - IEICE TRANSACTIONS on Fundamentals

SP - 1235

EP - 1244

AU - Kyohei SEKINE

AU - Hiroki KOGA

PY - 2021

DO - 10.1587/transfun.2020DMP0010

JO - IEICE TRANSACTIONS on Fundamentals

SN - 1745-1337

VL - E104-A

IS - 9

JA - IEICE TRANSACTIONS on Fundamentals

Y1 - September 2021

AB - The extended visual cryptography scheme (EVCS) proposed by Ateniese et al. is one of variations of the visual cryptography scheme such that a secret image is recovered by superimposition of certain qualified collections of shares, where cover images are visible on respective shares. In this paper, we give a new definition of the EVCS for improving visibility of the recovered secret image as well as the cover images. We formulate the problem to construct the basis matrices of the EVCS with the minimum pixel expansion as an integer programming problem. We solve the integer programming problem for general access structures with less than or equal to five participants and show that basis matrices with a smaller pixel expansion can be obtained for certain cases. We also analyze security of the EVCS meeting the new definition from an information-theoretic viewpoint. We give a condition under which any forbidden collection of shares does not reveal any additional information on not only a secret image but also the cover images that are not visible on the other shares.

ER -