Characterizing the Cryptographic Properties of Reactive 2-Party Functionalities

  • R. Amzi Jeffs
  • Mike Rosulek
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7785)


In secure multi-party computation, a reactive functionality is one which maintains persistent state, takes inputs, and gives outputs over many rounds of interaction with its parties. Reactive functionalities are fundamental and model many interesting and natural cryptographic tasks; yet their security properties are not nearly as well-understood as in the non-reactive case (known as secure function evaluation).

We present new combinatorial characterizations for 2-party reactive functionalities, which we model as finite automata. We characterize the functionalities that have passive-secure protocols, and those which are complete with respect to passive adversaries. Both characterizations are in the information-theoretic setting.


  1. 1.
    Beaver, D.: Perfect privacy for two-party protocols. In: Feigenbaum, J., Merritt, M. (eds.) Proceedings of DIMACS Workshop on Distributed Computing and Cryptography, vol. 2, pp. 65–77. American Mathematical Society (1989)Google Scholar
  2. 2.
    Canetti, R.: Universally composable security: A new paradigm for cryptographic protocols. In: Naor, M. (ed.) FOCS, pp. 136–145. IEEE Computer Society Press (2001); Revised version (2005) on Cryptology ePrint Archive,
  3. 3.
    Canetti, R., Fischlin, M.: Universally Composable Commitments. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 19–40. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  4. 4.
    Chor, B., Kushilevitz, E.: A zero-one law for boolean privacy. SIAM J. Discrete Math. 4(1), 36–47 (1991)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Goldreich, O., Micali, S., Wigderson, A.: How to play any mental game or a completeness theorem for protocols with honest majority. In: STOC, pp. 218–229. ACM (1987)Google Scholar
  6. 6.
    Kilian, J.: A general completeness theorem for two-party games. In: STOC, pp. 553–560. ACM (1991)Google Scholar
  7. 7.
    Kilian, J.: More general completeness theorems for secure two-party computation. In: STOC, pp. 316–324. ACM (2000)Google Scholar
  8. 8.
    Kilian, J., Kushilevitz, E., Micali, S., Ostrovsky, R.: Reducibility and completeness in private computations. SIAM J. Comput. 29(4), 1189–1208 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Kraschewski, D., Müller-Quade, J.: Completeness Theorems with Constructive Proofs for Finite Deterministic 2-Party Functions. In: Ishai, Y. (ed.) TCC 2011. LNCS, vol. 6597, pp. 364–381. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  10. 10.
    Kreitz, G.: A Zero-One Law for Secure Multi-party Computation with Ternary Outputs. In: Ishai, Y. (ed.) TCC 2011. LNCS, vol. 6597, pp. 382–399. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  11. 11.
    Künzler, R., Müller-Quade, J., Raub, D.: Secure Computability of Functions in the IT Setting with Dishonest Majority and Applications to Long-Term Security. In: Reingold, O. (ed.) TCC 2009. LNCS, vol. 5444, pp. 238–255. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  12. 12.
    Kushilevitz, E.: Privacy and communication complexity. In: FOCS, pp. 416–421. IEEE (1989)Google Scholar
  13. 13.
    Maji, H.K., Prabhakaran, M., Rosulek, M.: Complexity of Multi-party Computation Problems: The Case of 2-Party Symmetric Secure Function Evaluation. In: Reingold, O. (ed.) TCC 2009. LNCS, vol. 5444, pp. 256–273. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  14. 14.
    Maji, H.K., Prabhakaran, M., Rosulek, M.: A Zero-One Law for Cryptographic Complexity with Respect to Computational UC Security. In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol. 6223, pp. 595–612. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  15. 15.
    Prabhakaran, M., Rosulek, M.: Cryptographic Complexity of Multi-Party Computation Problems: Classifications and Separations. In: Wagner, D. (ed.) CRYPTO 2008. LNCS, vol. 5157, pp. 262–279. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  16. 16.
    Rosulek, M.: Universal Composability from Essentially Any Trusted Setup. In: Safavi-Naini, R., Canetti, R. (eds.) CRYPTO 2012. LNCS, vol. 7417, pp. 406–423. Springer, Heidelberg (2012)Google Scholar
  17. 17.
    Yao, A.C.: Protocols for secure computations (extended abstract). In: FOCS, pp. 160–164. IEEE (1982)Google Scholar

Copyright information

© International Association for Cryptologic Research 2013

Authors and Affiliations

  • R. Amzi Jeffs
    • 1
  • Mike Rosulek
    • 2
  1. 1.Department of Computer ScienceHarvey Mudd CollegeUSA
  2. 2.Department of Computer ScienceUniversity of MontanaUSA

Personalised recommendations