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Visual Cryptography on Graphs

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Computing and Combinatorics (COCOON 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5092))

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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 in which every vertex image is encoded and printed on a transparency, such that if two adjacent vertices’ transparencies are overlapped, the secret image of their 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 dependent on 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.

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References

  1. Ateniese, G., Blundo, C., De Santis, A., Stinson, D.R.: Constructions and Bounds for Visual Cryptography. In: auf der Heide, F.M., Monien, B. (eds.) ICALP 1996. LNCS, vol. 1099, pp. 416–428. Springer, Heidelberg (1996)

    Google Scholar 

  2. Ateniese, G., Blundo, C., De Santis, A., Stinson, D.R.: Visual Cryptography for General Access Structures. Electronic Colloquium on Computational Complexity 3(12) (1996)

    Google Scholar 

  3. Ateniese, G., Blundo, C., De Santis, A., Stinson, D.R.: Extended Capabilities for Visual Cryptography. heor. Comput. Sci. 250(1-2), 143–161 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  4. Blundo, C., Cimato, S., De Santis, A.: De: Visual Cryptography Schemes with Optimal Pixel Expansion. Theor. Comput. Sci. 369(1–3), 169–182 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  5. Benaloh, J.C., Leichter, J.: Generalized Secret Sharing and Monotone Functions. In: Goldwasser, S. (ed.) CRYPTO 1988. LNCS, vol. 403, pp. 27–35. Springer, Heidelberg (1990)

    Google Scholar 

  6. Blakley, G.: Safeguarding Cryptographic Keys. In: Proc. Am. Federation of Information Processing Soc., pp. 313–317 (1979)

    Google Scholar 

  7. Blundo, C., De Santis, A., Di Crescenzo, G., Gaggia, A.G., Vaccaro, U.: Multi-secret Sharing Schemes. In: Desmedt, Y.G. (ed.) CRYPTO 1994. LNCS, vol. 839, pp. 150–163. Springer, Heidelberg (1994)

    Google Scholar 

  8. Blundo, C., De Santis, A., Stinson, D.R., Vaccaro, U.: Graph Decompositions and Secret Sharing Schemes. J. Cryptology 8(1), 39–64 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  9. Blundo, C., De Santis, A., De Simone, R., Vaccaro, U.: Tight Bounds on the Information Rate of Secret Sharing Schemes. Des. Codes Cryptography 11(2), 107–110 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  10. Blundo, C., De Santis, A., Vaccaro, U.: Efficient Sharing of Many Secrets. In: Enjalbert, P., Wagner, K.W., Finkel, A. (eds.) STACS 1993. LNCS, vol. 665, pp. 692–703. Springer, Heidelberg (1993)

    Google Scholar 

  11. Di Crescenzo, G.: Sharing One Secret vs. Sharing Many Secrets. Theor. Comput. Sci. 295(1-3), 123–140 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  12. Csirmaz, L.: Secret Sharing Schemes on Graphs. Cryptology ePrint Archive, Report 2005/059 (2005), http://eprint.iacr.org/

  13. Chen, K.Y., Wu, W.P., Laih, C.S.: On the (2,2) Visual Multi-secret Sharing Schemes (2006)

    Google Scholar 

  14. Itoh, M., Saito, A., Nishizeki, T.: Secret Sharing Scheme Realizing General Access Structure. In: Proc. of IEEE Globecom, pp. 99–102 (1987)

    Google Scholar 

  15. Iwamoto, M., Yamamoto, H.: A Construction Method of Visual Secret Sharing Schemes for Plural Secret Images. IEICE Trans. on Fundamentals E86.A(10), 2577–2588 (2003)

    Google Scholar 

  16. Katoh, T., Imai, H.: An Extended Construction Method for Visual Secret Sharing Schemes. Electronics and Communications in Japan (Part III: Fundamental Electronic Science) 81(7), 55–63 (1998)

    Article  Google Scholar 

  17. Luby, M.: A Simple Parallel Algorithm for the Maximal Independent Set Problem. SIAM J. Comput. 15(4), 1036–1055 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  18. Manchala, D., Lu, S., Ostrovsky, R.: Visual Cryptography on Graphs. Cryptology ePrint Archive (2008), http://eprint.iacr.org/

  19. Naor, M., Shamir, A.: Visual Cryptography. In: De Santis, A. (ed.) EUROCRYPT 1994. LNCS, vol. 950, pp. 1–12. Springer, Heidelberg (1995)

    Chapter  Google Scholar 

  20. Shamir, A.: How to Share a Secret. Commun. ACM 22(11), 612–613 (1979)

    Article  MATH  MathSciNet  Google Scholar 

  21. Stinson, D.: Decomposition Constructions for Secret Sharing Schemes. IEEE Transactions on Information Theory 40(1), 118–125 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  22. Wang, D., Yi, F., Li, X., Luo, P., Dai, Y.: On the Analysis and Generalization of Extended Visual Cryptography Schemes (2006)

    Google Scholar 

  23. Yi, F., Wang, D., Luo, P., Huang, L., Dai, Y.: Multi Secret Image Color Visual Cryptography Schemes for General Access Structures. Progress in Natural Science 16(4), 431–436 (2006)

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. University of California, Los Angeles,  

    Steve Lu & Rafail Ostrovsky

  2. Xerox Corporation,  

    Daniel Manchala

Authors
  1. Steve Lu
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  2. Daniel Manchala
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  3. Rafail Ostrovsky
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Xiaodong Hu Jie Wang

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Lu, S., Manchala, D., Ostrovsky, R. (2008). Visual Cryptography on Graphs. In: Hu, X., Wang, J. (eds) Computing and Combinatorics. COCOON 2008. Lecture Notes in Computer Science, vol 5092. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69733-6_23

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  • DOI: https://doi.org/10.1007/978-3-540-69733-6_23

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-69732-9

  • Online ISBN: 978-3-540-69733-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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