TY - GEN
T1 - Color Visual Cryptography Schemes Using Linear Algebraic Techniques over Rings
AU - Dutta, Sabyasachi
AU - Sardar, Md Kutubuddin
AU - Adhikari, Avishek
AU - Ruj, Sushmita
AU - Sakurai, Kouichi
N1 - Funding Information:
S. Dutta—is grateful to the NICT, Japan for financial support under the NICT International Exchange Program during 2018-19 when the preliminary draft was prepared. Md K. Sardar—is thankful to the CSIR, Govt. of India for providing financial support (Award no. 09/028(0975)/2016-EMR-1). A. Adhikari—Research of A. Adhikari is partially supported by DST-SERB Project MATRICS vide Sanction Order: MTR/2019/001573.
Publisher Copyright:
© 2020, Springer Nature Switzerland AG.
PY - 2020
Y1 - 2020
N2 - The research on color Visual Cryptographic Scheme (VCS) is much more difficult than that of the black and white VCS. This is essentially because of the fact that in color VCS, the rule for superimposition of two colors is not that simple as in black and white VCS. It was a long standing open issue whether linear algebraic technique in constructing Black and White visual cryptographic schemes could also be extended for color images. It was thought that such an extension was impossible. However, we resolve this issue by providing color VCS in same color model for the threshold access structures by extending linear algebraic techniques from the binary field Z2 to finite ring Zc of integers modulo c. We first give a construction method based on linear algebra to share a color image for an (n, n)-threshold access structure. Then we give constructions for (2, n)-threshold access structures and in general (k, n)-threshold access structures. Existing methodology for constructing color VCS in same color model assumes the existence of black and white VCS, whereas our construction is a direct one. Moreover, we give closed form formulas for pixel expansion which is combinatorially a difficult task. Lastly, we give experimental results and propose a method to reduce pixel expansion.
AB - The research on color Visual Cryptographic Scheme (VCS) is much more difficult than that of the black and white VCS. This is essentially because of the fact that in color VCS, the rule for superimposition of two colors is not that simple as in black and white VCS. It was a long standing open issue whether linear algebraic technique in constructing Black and White visual cryptographic schemes could also be extended for color images. It was thought that such an extension was impossible. However, we resolve this issue by providing color VCS in same color model for the threshold access structures by extending linear algebraic techniques from the binary field Z2 to finite ring Zc of integers modulo c. We first give a construction method based on linear algebra to share a color image for an (n, n)-threshold access structure. Then we give constructions for (2, n)-threshold access structures and in general (k, n)-threshold access structures. Existing methodology for constructing color VCS in same color model assumes the existence of black and white VCS, whereas our construction is a direct one. Moreover, we give closed form formulas for pixel expansion which is combinatorially a difficult task. Lastly, we give experimental results and propose a method to reduce pixel expansion.
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U2 - 10.1007/978-3-030-65610-2_13
DO - 10.1007/978-3-030-65610-2_13
M3 - Conference contribution
AN - SCOPUS:85097823006
SN - 9783030656096
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 198
EP - 217
BT - Information Systems Security - 16th International Conference, ICISS 2020, Proceedings
A2 - Kanhere, Salil
A2 - Patil, Vishwas T
A2 - Sural, Shamik
A2 - Gaur, Manoj S
PB - Springer Science and Business Media Deutschland GmbH
T2 - 16th International Conference on Information Systems Security, ICISS 2020
Y2 - 16 December 2020 through 20 December 2020
ER -