Abstract
In this paper, we consider a new visual cryptography scheme that allows for sharing of multiple secret images on graphs: we are given an arbitrary graph (V,E) where every node and every edge are assigned an arbitrary image. Images on the vertices are “public” and images on the edges are “secret”. The problem that we are considering is how to make a construction such that when the encoded images of two adjacent vertices are printed on transparencies and overlapped, the secret image corresponding to the edge is revealed. We define the most stringent security guarantees for this problem (perfect secrecy) and show a general construction for all graphs where the cost (in terms of pixel expansion and contrast of the images) is proportional to the chromatic number of the cube of the underlying graph. For the case of bounded degree graphs, this gives us constant-factor pixel expansion and contrast. This compares favorably to previous works, where pixel expansion and contrast are proportional to the number of images.
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Work of S. Lu done in part while visiting IPAM. Partially supported by Xerox Innovation Group Award, NSF grants 0430254, 0716835, 0716389, and NSF VIGRE grant DMS-0502315.
Work of D. Manchala done while a member of research and technical staff at Xerox’s Innovation Group.
Work of R. Ostrovsky done in part while visiting IPAM. Partially supported by Xerox Innovation Group Award, IBM Faculty Award, NSF grants 0430254, 0716835, 0716389 and U.C. MICRO grant.
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Lu, S., Manchala, D. & Ostrovsky, R. Visual cryptography on graphs. J Comb Optim 21, 47–66 (2011). https://doi.org/10.1007/s10878-009-9241-x
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DOI: https://doi.org/10.1007/s10878-009-9241-x