Secure Deterministic Automata Evaluation: Completeness and Efficient 2-party Protocols

  • Giovanni Di CrescenzoEmail author
  • Brian Coan
  • Jonathan Kirsch
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 12001)


Secure computation (i.e., performing computation while keeping privacy of the inputs) is a fundamental research area in cryptography and a fundamental capability in the theory of computing. Deterministic automata evaluation is a fundamental computation problem, with numerous application areas, including regular expressions, string matching, constant-space computations.

In this paper, we investigate the complexity of achieving secure 2-party deterministic automata evaluation protocols. We show black-box reductions between this problem and the problem of constructing secure 2-party information retrieval protocols, and viceversa. Using previous results, this implies various interesting consequences: completeness of secure deterministic automata evaluation in the class of problems having 2-party and multi-party secure function evaluation protocols (previously, only 2 less natural problems were showed to be complete, or non-constructive characterizations of complete problems were given), and, under standard cryptographic assumptions, a communication-efficient secure protocol for automata evaluation (no such problem was given in the literature) and a time-efficient secure protocol faster than applying Yao’s benchmark general solution.


  1. 1.
    Aiello, B., Ishai, Y., Reingold, O.: Priced oblivious transfer: how to sell digital goods. In: Pfitzmann, B. (ed.) EUROCRYPT 2001. LNCS, vol. 2045, pp. 119–135. Springer, Heidelberg (2001). Scholar
  2. 2.
    Bogetoft, P., et al.: Secure multiparty computation goes live. In: Dingledine, R., Golle, P. (eds.) FC 2009. LNCS, vol. 5628, pp. 325–343. Springer, Heidelberg (2009). Scholar
  3. 3.
    Di Crescenzo, G., Cook, D.L., McIntosh, A., Panagos, E.: Practical and privacy-preserving information retrieval from a database table. J. Comput. Secur. 24(4), 479–506 (2016)CrossRefGoogle Scholar
  4. 4.
    Di Crescenzo, G., Malkin, T., Ostrovsky, R.: Single database private information retrieval implies oblivious transfer. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 122–138. Springer, Heidelberg (2000). Scholar
  5. 5.
    Even, S., Goldreich, O., Lempel, A.: A randomized protocol for signing contracts. Commun. ACM 28(6), 637–647 (1985)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Freedman, M.J., Ishai, Y., Pinkas, B., Reingold, O.: Keyword search and oblivious pseudorandom functions. In: Kilian, J. (ed.) TCC 2005. LNCS, vol. 3378, pp. 303–324. Springer, Heidelberg (2005). Scholar
  7. 7.
    Goldreich, O., Micali, S., Wigderson, A.: Proofs that yield nothing but their validity or all languages in NP have zero-knowledge proof systems. J. ACM 38(1), 691–729 (1991)MathSciNetzbMATHGoogle Scholar
  8. 8.
    Goldreich, O.: The Foundations of Cryptography: Volume 2, Basic Applications. Cambridge University Press, Cambridge (2004)CrossRefGoogle Scholar
  9. 9.
    Goldwasser, S., Micali, S.: Probabilistic encryption. J. Comput. Syst. Sci. 28(2), 270–299 (1984)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Harnik, D., Naor, M., Reingold, O., Rosen, A.: Completeness in two-party secure computation: a computational view. J. Cryptol. 19(4), 521–552 (2006)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Huang, Y., Evans, D., Katz, J., Malka, L.: Faster secure two-party computation using garbled circuits. In: Proceedings of the 20th USENIX Security Symposium, San Francisco, CA, USA, 8–12 August 2011 (2011)Google Scholar
  12. 12.
    Ishai, Y., Paskin, A.: Evaluating branching programs on encrypted data. In: Vadhan, S.P. (ed.) TCC 2007. LNCS, vol. 4392, pp. 575–594. Springer, Heidelberg (2007). Scholar
  13. 13.
    Ishai, Y., Prabhakaran, M., Sahai, A.: Founding cryptography on oblivious transfer – efficiently. In: Wagner, D. (ed.) CRYPTO 2008. LNCS, vol. 5157, pp. 572–591. Springer, Heidelberg (2008). Scholar
  14. 14.
    Kilian, J.: A note on efficient proofs and arguments. In: Proceedings of ACM STOC 1992 (1992)Google Scholar
  15. 15.
    Kilian, J.: Founding cryptography on oblivious transfer. In: Proceedings of the 20th Annual ACM Symposium on Theory of Computing, Chicago, Illinois, USA, 2–4 May 1988, pp. 20–31 (1988)Google Scholar
  16. 16.
    Kilian, J., Kushilevitz, E., Micali, S., Ostrovsky, R.: Reducibility and completeness in private computations. SIAM J. Comput. 29(4), 1189–1208 (2000)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Kushilevitz, E., Ostrovsky, R.: Replication is NOT needed: SINGLE database, computationally-private information retrieval. In: 38th Annual Symposium on Foundations of Computer Science, FOCS 1997, Miami Beach, Florida, USA, 19–22 October 1997, pp. 364–373 (1997)Google Scholar
  18. 18.
    Malkhi, D., Nisan, N., Pinkas, B., Sella, Y.: Fairplay - secure two-party computation system. In: Proceedings of the 13th USENIX Security Symposium, San Diego, CA, USA, 9–13 August 2004, pp. 287–302 (2004)Google Scholar
  19. 19.
    Mohassel, P., Niksefat, S., Sadeghian, S., Sadeghiyan, B.: An efficient protocol for oblivious DFA evaluation and applications. In: Dunkelman, O. (ed.) CT-RSA 2012. LNCS, vol. 7178, pp. 398–415. Springer, Heidelberg (2012). Scholar
  20. 20.
    Rabin, M.O.: How to exchange secrets with oblivious transfer. IACR Cryptology ePrint Archive 2005:187 (2005)Google Scholar
  21. 21.
    Yao, A.C.-C.: How to generate and exchange secrets (extended abstract). In: FOCS, pp. 162–167 (1986)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Giovanni Di Crescenzo
    • 1
    Email author
  • Brian Coan
    • 1
  • Jonathan Kirsch
    • 1
  1. 1.Perspecta LabsBasking RidgeUSA

Personalised recommendations