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Visual cryptography on graphs

Author

Listed:
  • Steve Lu

    (University of California)

  • Daniel Manchala

    (Xerox Corporation)

  • Rafail Ostrovsky

    (University of California)

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.

Suggested Citation

  • Steve Lu & Daniel Manchala & Rafail Ostrovsky, 2011. "Visual cryptography on graphs," Journal of Combinatorial Optimization, Springer, vol. 21(1), pages 47-66, January.
    • Handle: RePEc:spr:jcomop:v:21:y:2011:i:1:d:10.1007_s10878-009-9241-x
    DOI: 10.1007/s10878-009-9241-x
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