Abstract
In (2,n) visual cryptographic schemes, a secret image(text or picture) is encrypted into n shares, which are distributed among n participants. The image cannot be decoded from any single share but any two participants can together decode it visually, without using any complex decoding mechanism. In this paper, we introduce three meaningful optimality criteria for evaluating different schemes and show that some classes of combinatorial designs, such as BIB designs, PBIB designs and regular graph designs, can yield a large number of black and white (2,n) schemes that are optimal with respect to all these criteria. For a practically useful range of n, we also obtain optimal schemes with the smallest possible pixel expansion.
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References
Adhikari A, Bose M (2004) A new visual cryptographic scheme using Latin squares. IEICE Trans Fund E87-A:1998–2002
Adhikari A, Bose M, Kumar D, Roy B (2005) Applications of partially balanced and balanced incomplete block designs in developing visual cryptographic schemes. Indian Statistical Institute Technical Report no. ASD/2005/11
G Ateniese C Blundo ADe Santis DR Stinson (1996) Constructions and bounds for visual cryptography ICALP ’96. Springer-Verlag Berlin 416–428
C Blundo ADe Santis DR Stinson (1999) ArticleTitleOn the contrast in visual cryptography schemes J Cryptol 12 261–289 Occurrence Handle0944.94010 Occurrence Handle10.1007/s001459900057
C Blundo ADe Santis M Naor (2001) ArticleTitleVisual cryptography for grey-level images Infor Processing Lett 75 255–259 Occurrence Handle10.1016/S0020-0190(00)00108-3
Bose M, Kumar D (2004) New Visual cryptographic schemes using PBIBD’s. Indian Statistical Technical Report no. ASD/2004/14
WH Clatworthy (1973) Tables of two-associate partially balanced designs National Bureau of Standards Washington D.C
A Dey (1986) Theory of block designs Wiley Eastern New Delhi Occurrence Handle0653.05010
A Dey R Mukerjee (1999) Fractional factorial plans John Wiley New York Occurrence Handle0930.62081
Droste S (1999) New results on visual cryptography. CRYPTO ’96. Springer-Verlag, Berlin 401–415
Ishihara T, Koga H (2002) New constructions of the Lattice-based visual secret sharing using mixture of colors. IEICE Trans Fund E85-A:158–166
Koga H, Iwamoto M, Yamamoto H (2001) An analytic construction of visual secret sharing scheme for color images. IEICE Trans Fund E84-A:262–272
Koga H, Yamamoto H (1998) Proposal of a Lattice-based visual secret sharing scheme for color and gray-scale images. IEICE Trans Fund E81-A:1262–1269
Naor M, Shamir A (1994) Visual cryptography. Eurocrypt ’94. Springer-Verlag, Berlin, 1–12
D Raghavarao (1971) Constructions and combinatorial problems in designs of experiments Wiley New York
KR Shah BK Sinha (1989) Theory of optimal designs Springer-Verlag Berlin Occurrence Handle0688.62043
CFJ Wu M Hamada (2000) Experiments planning, analysis and parameter design optimization Wiley New York Occurrence Handle0964.62065
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Bose, M., Mukerjee, R. Optimal (2, n) visual cryptographic schemes. Des Codes Crypt 40, 255–267 (2006). https://doi.org/10.1007/s10623-006-0011-9
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DOI: https://doi.org/10.1007/s10623-006-0011-9