Secure Two-Party Computation: A Visual Way

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


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.


Yao’s construction Visual cryptography Secure computation 



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.


  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.
  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. (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

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