Advertisement

Secure Two-Party Computation: A Visual Way

  • Paolo D’Arco
  • Roberto De PriscoEmail author
Conference paper
First Online:
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8317)

Abstract

In this paper we propose a novel method for performing secure two-party computation. By merging together in a suitable way two beautiful ideas of the 80’s and the 90’s, Yao’s garbled circuit construction and Naor and Shamir’s visual cryptography, respectively, we enable Alice and Bob to securely evaluate a function \(f(\cdot ,\cdot )\) of their inputs, \(x\) and \(y\), through a pure physical process. Indeed, once Alice has prepared a set of properly constructed transparencies, Bob computes the function value \(f(x,y)\) by applying a sequence of simple steps which require the use of a pair of scissors, superposing transparencies, and the human visual system. A crypto-device for the function evaluation process is not needed any more.

Keywords

Yao’s construction Visual cryptography Secure computation 
This is a preview of subscription content, log in to check access.

Notes

Acknowledgment

We would like to thank Alfredo De Santis for discussions and for pointing out to our attention [29], Carlo Blundo for comments on a preliminary version of this paper, and an anonymous referee for hints and suggestions.

References

  1. 1.
    Ateniese, G., Blundo, C., De Santis, A., Stinson, D.R.: Visual cryptography for general access structures. Inf. Comput. 129(2), 86–106 (1996)CrossRefzbMATHGoogle Scholar
  2. 2.
    Beaver, D., Micali, S., Rogaway, P.: The round complexity of secure protocols. In: Proceedings of 22nd ACM Symposium on Theory of Computing, pp. 503–513 (1990)Google Scholar
  3. 3.
    Beimel, A.: Secret-sharing schemes: a survey. In: Chee, Y.M., Guo, Z., Ling, S., Shao, F., Tang, Y., Wang, H., Xing, C. (eds.) IWCC 2011. LNCS, vol. 6639, pp. 11–46. Springer, Heidelberg (2011)Google Scholar
  4. 4.
    Bellare, M., Hoang, V.T., Rogaway, P.: Garbling schemes. Cryptology ePrint archive, report 2012/265 (2012)Google Scholar
  5. 5.
    Bellare, M., Rogaway, P.: Robust computational secret sharing and a unified account of classical secret-sharing goals. In: Proceedings of the 14th ACM Conference on Computer and Communications Security (ACM CCS), ACM (2007)Google Scholar
  6. 6.
    Blundo, C., D’Arco, P., De Santis, A., Stinson, D.R.: Contrast optimal threshold visual cryptography schemes. SIAM J. Discrete Math. 16, 224–261 (2003)CrossRefzbMATHMathSciNetGoogle Scholar
  7. 7.
    Boneh, D., Sahai, A., Waters, B.: Functional encryption: definitions and challenges. In: Ishai, Y. (ed.) TCC 2011. LNCS, vol. 6597, pp. 253–273. Springer, Heidelberg (2011)Google Scholar
  8. 8.
    Capocelli, R.M., De Santis, A., Gargano, L., Vaccaro, U.: On the size of shares for secret sharing schemes. In: Feigenbaum, J. (ed.) CRYPTO 1991. LNCS, vol. 576, pp. 101–113. Springer, Heidelberg (1992)Google Scholar
  9. 9.
    Canetti, R.: Security and composition of multiparty cryptographic protocols. J. Cryptol. 13, 143–202 (2000)CrossRefzbMATHMathSciNetGoogle Scholar
  10. 10.
    Chaum, D.: Secret-Ballot receipts and transparent integrity. http://www.vreceipt.com/article.pdf
  11. 11.
    Cimato, S., De Prisco, R., De Santis, A.: Colored visual cryptography without color darkening. In: Blundo, C., Cimato, S. (eds.) SCN 2004. LNCS, vol. 3352, pp. 235–248. Springer, Heidelberg (2005)Google Scholar
  12. 12.
    Cimato, S., De Prisco, R., De Santis, A.: Optimal colored threshold visual cryptography schemes. Des. Codes. Crypt. 35, 311–335 (2005)CrossRefzbMATHGoogle Scholar
  13. 13.
    Cimato, S., De Prisco, R., De Santis, A.: Probabilistic visual cryptography schemes. Comput. J. 49(1), 97–107 (2006)CrossRefGoogle Scholar
  14. 14.
    Cimato, S., De Prisco, R., De Santis, A.: Colored visual cryptography without color darkening. Theor. Comput. Sci. 374(1–3), 261–276 (2007)CrossRefzbMATHGoogle Scholar
  15. 15.
    Cimato, S., Yang, C.-N. (eds.): Visual Cryptography and Secret Image Sharing. CRC Press, Boca Raton (2012). ISBN: 978-1-4398-3721-4Google Scholar
  16. 16.
    De Prisco, R., De Santis, A.: Using colors to improve visual cryptography for black and white images. In: Fehr, S. (ed.) ICITS 2011. LNCS, vol. 6673, pp. 182–201. Springer, Heidelberg (2011)Google Scholar
  17. 17.
    De Prisco, R., De Santis, A.: Color visual cryptography schemes for black and white secret image. Theoretical Computer Science. http://dx.doi.org/10.1016/j.tcs.2013.09.005 (to appear)
  18. 18.
    Even, S., Goldreich, O., Lempel, A.: A randomized protocol for signing contracts. Commun. ACM. 28(6), 637–647 (1985)CrossRefMathSciNetGoogle Scholar
  19. 19.
    Eisen, P.A., Stinson, D.R.: Threshold visual cryptography schemes with specified whiteness levels of reconstructed pixels. Des. Codes. Crypt. 25, 15–61 (2002)CrossRefzbMATHMathSciNetGoogle Scholar
  20. 20.
    Goldreich, O.: Foundation Cryptography, vol. II. MIT Press, Cambridge (2004)CrossRefGoogle Scholar
  21. 21.
    Goldreich, O., Micali, S., Wigderson, A.: How to play any mental game. In: STOC, pp. 218–229 (1987)Google Scholar
  22. 22.
    Gennaro, R., Gentry, C., Parno, B.: Non-interactive verifiable computing: outsourcing computation to untrusted workers. In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol. 6223, pp. 465–482. Springer, Heidelberg (2010)Google Scholar
  23. 23.
    Hofmeister, T., Krause, M., Simon, H.U.: Contrast-optimal \(k\) out of \(n\) secret sharing schemes in visual cryptography. Theor. Comput. Sci. 240, 471–485 (2000)CrossRefzbMATHMathSciNetGoogle Scholar
  24. 24.
    Kafri, O., Keren, E.: Encryption of pictures and shapes by random grids. Opt. Lett. 12(6), 377–379 (1987)CrossRefGoogle Scholar
  25. 25.
    Karnin, E., Greene, J., Hellman, M.: On secret sharing systems. IEEE Trans. Inf. Theor. 29(1), 3551 (1983)MathSciNetGoogle Scholar
  26. 26.
    Kolesnikov, V.: Gate evaluation secret sharing and secure one-round two-party computation. In: Roy, B. (ed.) ASIACRYPT 2005. LNCS, vol. 3788, pp. 136–155. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  27. 27.
    Naor, M., Shamir, A.: Visual cryptography. In: De Santis, A. (ed.) EUROCRYPT 1994. LNCS, vol. 950, pp. 1–12. Springer, Heidelberg (1995)Google Scholar
  28. 28.
    Lindell, Y., Pinkas, B.: A proof of security of Yao’s protocol for two-party computation. J. Cryptology 22, 161–188 (2009)CrossRefzbMATHMathSciNetGoogle Scholar
  29. 29.
    Moran, T., Naor, M.: Basing cryptographic protocols on tamper-evident seals. Theor. Comput. Sci. 411, 1283–1310 (2010)CrossRefzbMATHMathSciNetGoogle Scholar
  30. 30.
    Yang, C.-N.: New visual secret sharing schemes using probabilistic method. Pattern Recogn. Lett. 25, 481–494 (2004)CrossRefGoogle Scholar
  31. 31.
    Yao, A.C.: Protocols for secure computations. In: Proceedings of 23rd IEEE Symposium on Foundations of Computational Science, pp. 160–164 (1982)Google Scholar
  32. 32.
    Yao, A.C.: How to generate and exchange secrets (extended abstract). In: Proceedings of 27th IEEE Symposium on Foundations of Computational Science, pp. 162–167 (1986)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Dipartimento di InformaticaUniversity of SalernoFiscianoItaly

Personalised recommendations

Cite paper

Buy options