Secure and scalable match: overcoming the universal circuit bottleneck using group programs

Open access


Confidential Content-Based Publish/Subscribe (C-CBPS) is an interaction model that allows parties to exchange content while protecting their security and privacy interests. In this paper we advance the state of the art in C-CBPS by showing how all predicate circuits in NC1 (logarithmic-depth, bounded fan-in) can be confidentially computed by a broker while guaranteeing perfect information-theoretic security. Previous work could handle only strictly shallower circuits (e.g. those with depth O(ℑ)). We present three protocols—UGP-Match, FSGP-Match and OFSGP-Match—based on 2-decomposable randomized encodings of group programs for circuits in NC1. UGP-Match is conceptually simple and has a clean proof of correctness but its running time is a polynomial with a high exponent and hence impractical. FSGP-Match uses a “fixed structure” construction that reduces the exponent drastically and achieves efficiency and scalability. OFSGP-Match optimizes the group programs further to shave off a linear factor.

If the inline PDF is not rendering correctly, you can download the PDF file here.

  • [1] B. Applebaum. Randomly encoding functions: A new cryptographic paradigm - (invited talk). In ICITS pages 25–31 2011.

  • [2] B. Applebaum Y. Ishai and E. Kushilevitz. Cryptography in NC0. In FOCS pages 166–175 2004.

  • [3] B. Applebaum Y. Ishai and E. Kushilevitz. Computationally private randomizing polynomials and their applications. In IEEE Conference on Computational Complexity pages 260–274 2005.

  • [4] S. Arora and B. Barak. Computational Complexity - A Modern Approach. Cambridge University Press 2009.

  • [5] G. Banavar T. D. Chandra B. Mukherjee J. Nagarajarao R. E. Strom and D. C. Sturman. An efficient multicast protocol for content-based publish-subscribe systems. In ICDCS pages 262–272 1999.

  • [6] D. A. M. Barrington. Bounded-width polynomial-size branching programs recognize exactly those languages in NC1. J. Comput. Syst. Sci. 38(1):150–164 1989.

  • [7] A. Ben-David N. Nisan and B. Pinkas. Fairplaymp: a system for secure multi-party computation. In ACM Conference on Computer and Communications Security pages 257–266 2008.

  • [8] M. Ben-Or S. Goldwasser and A. Wigderson. Completeness theorems for non-cryptographic fault-tolerant distributed computation (extended abstract). In STOC pages 1–10 1988.

  • [9] A. Carzaniga D. S. Rosenblum and A. L. Wolf. Design and evaluation of a wide-area event notification service. ACM Trans. Comput. Syst. 19(3):332–383 2001.

  • [10] D. Chaum C. Crépeau and I. Damgård. Multiparty unconditionally secure protocols (extended abstract). In STOC pages 11–19 1988.

  • [11] I. Damgård and J. B. Nielsen. Scalable and unconditionally secure multiparty computation. In CRYPTO pages 572–590 2007.

  • [12] A. K. Datta M. Gradinariu M. Raynal and G. Simon. Anonymous publish/subscribe in p2p networks. In IPDPS page 74 2003.

  • [13] U. Feige J. Kilian and M. Naor. A minimal model for secure computation (extended abstract). In STOC pages 554–563 1994.

  • [14] C. Gentry. Fully homomorphic encryption using ideal lattices. In STOC pages 169–178 2009.

  • [15] O. Goldreich. The Foundations of Cryptography - Volume 1 Basic Techniques. Cambridge University Press 2001.

  • [16] O. Goldreich. The Foundations of Cryptography - Volume 2 Basic Applications. Cambridge University Press 2004.

  • [17] O. Goldreich S. Micali and A. Wigderson. How to play any mental game or a completeness theorem for protocols with honest majority. In STOC pages 218–229 1987.

  • [18] W. Henecka S. Kögl A.-R. Sadeghi T. Schneider and I. Wehrenberg. Tasty: tool for automating secure two-party computations. In ACM Conference on Computer and Communications Security pages 451–462 2010.

  • [19] Y. Ishai and E. Kushilevitz. Randomizing polynomials: A new representation with applications to round-efficient secure computation. In FOCS pages 294–304 2000.

  • [20] Y. Ishai E. Kushilevitz R. Ostrovsky and A. Sahai. Cryptography with constant computational overhead. In STOC pages 433–442 2008.

  • [21] Y. Ishai E. Kushilevitz R. Ostrovsky and A. Sahai. Extracting correlations. In FOCS pages 261–270 2009.

  • [22] J. Katz and Y. Lindell. Introduction to Modern Cryptography. Chapman and Hall/CRC Press 2007.

  • [23] A. Kerckhoffs. Kerckhoffs’s principle.’s_principle 1883.

  • [24] V. Kolesnikov. Advances and impact of secure function evaluation. Bell Labs Technical Journal 14(3):187–192 2009.

  • [25] V. Kolesnikov and T. Schneider. A practical universal circuit construction and secure evaluation of private functions. In Financial Cryptography pages 83–97 2008.

  • [26] R. Krishnan. Illustration of OFSGP-match using Javascript and Scheme for Web delivery. 2013.

  • [27] R. Krishnan. Decision Evaluation in Encrypted Domains— OFSGP-Match Implementation in Java. 2014.

  • [28] L. Malka. Vmcrypt: modular software architecture for scalable secure computation. In ACM Conference on Computer and Communications Security pages 715–724 2011.

  • [29] C. H. Papadimitriou. Computational complexity. Addison-Wesley 1994.

  • [30] C. Raiciu and D. S. Rosenblum. Enabling confidentiality in content-based publish/subscribe infrastructures. In SecureComm pages 1–11 2006.

  • [31] T. Sander A. L. Young and M. Yung. Non-interactive cryptocomputing for NC1. In FOCS pages 554–567 1999.

  • [32] M. Srivatsa and L. Liu. Securing publish-subscribe overlay services with EventGuard. In ACM Conference on Computer and Communications Security pages 289–298 2005.

  • [33] L. G. Valiant. Universal circuits (preliminary report). In STOC pages 196–203 1976.

  • [34] E. Viola. Gems of theoretical computer science. Lecture no. 11. Barrington’s theorem. 2009.

  • [35] Wikipedia. NC1 - barrington’s theorem. 2012.

  • [36] Wikipedia. NC - complexity class. 2012.

  • [37] Wikipedia. Multiplexer. 2012.

  • [38] Wikipedia. Notation for representing permutations. 2012.

  • [39] Wikipedia. Solvable group. 2012.

  • [40] A. C.-C. Yao. Protocols for secure computations (extended abstract). In FOCS pages 160–164 1982.

Journal information
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 207 71 0
PDF Downloads 94 36 0