Advertisement

Constant-Overhead Secure Computation of Boolean Circuits using Preprocessing

  • Ivan Damgård
  • Sarah Zakarias
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7785)

Abstract

We present a protocol for securely computing a Boolean circuit C in presence of a dishonest and malicious majority. The protocol is unconditionally secure, assuming a preprocessing functionality that is not given the inputs. For a large number of players the work for each player is the same as computing the circuit in the clear, up to a constant factor. Our protocol is the first to obtain these properties for Boolean circuits. On the technical side, we develop new homomorphic authentication schemes based on asymptotically good codes with an additional multiplication property. We also show a new algorithm for verifying the product of Boolean matrices in quadratic time with exponentially small error probability, where previous methods only achieved constant error.

Keywords

Linear Code Communication Overhead Authentication Scheme Message Authentication Code Ideal Functionality 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. [BDOZ11]
    Bendlin, R., Damgård, I., Orlandi, C., Zakarias, S.: Semi-homomorphic Encryption and Multiparty Computation. In: Paterson, K.G. (ed.) EUROCRYPT 2011. LNCS, vol. 6632, pp. 169–188. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  2. [Can01]
    Canetti, R.: Universally composable security: A new paradigm for cryptographic protocols. In: FOCS, pp. 136–145 (2001)Google Scholar
  3. [CCX11]
    Cascudo, I., Cramer, R., Xing, C.: The Torsion-Limit for Algebraic Function Fields and Its Application to Arithmetic Secret Sharing. In: Rogaway, P. (ed.) CRYPTO 2011. LNCS, vol. 6841, pp. 685–705. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  4. [CLOS02]
    Canetti, R., Lindell, Y., Ostrovsky, R., Sahai, A.: Universally composable two-party and multi-party secure computation. In: STOC, pp. 494–503 (2002)Google Scholar
  5. [DIK10]
    Damgård, I., Ishai, Y., Krøigaard, M.: Perfectly Secure Multiparty Computation and the Computational Overhead of Cryptography. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 445–465. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  6. [DPSZ12]
    Damgård, I., Pastro, V., Smart, N.P., Zakarias, S.: Multiparty Computation from Somewhat Homomorphic Encryption. In: Safavi-Naini, R., Canetti, R. (eds.) CRYPTO 2012. LNCS, vol. 7417, pp. 643–662. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  7. [DZ12]
    Damgård, I., Zakarias, S.: Constant-overhead secure computation for boolean circuits in the preprocessing model. Cryptology ePrint Archive, Report 2012/512, full version (2012), http://eprint.iacr.org/
  8. [Fre77]
    Freivalds, R.: Probabilistic machines can use less running time. In: IFIP Congress, pp. 839–842 (1977)Google Scholar
  9. [GHS12]
    Gentry, C., Halevi, S., Smart, N.P.: Fully Homomorphic Encryption with Polylog Overhead. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 465–482. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  10. [Hoe63]
    Hoeffding, W.: Probability inequalities for sums of bounded random variables. Journal of the American Statistical Association 58(301), 13–30 (1963)MathSciNetCrossRefzbMATHGoogle Scholar
  11. [IKM+13]
    Ishai, Y., Kushilevitz, E., Meldgaard, S., Orlandi, C., Paskin-Cherniavsky, A.: On the Power of Correlated Randomness in Secure Computation. In: Sahai, A. (ed.) TCC 2013. LNCS, vol. 7785, pp. 600–620. Springer, Heidelberg (2013)Google Scholar
  12. [IKOS08]
    Ishai, Y., Kushilevitz, E., Ostrovsky, R., Sahai, A.: Cryptography with constant computational overhead. In: Dwork, C. (ed.) STOC, pp. 433–442. ACM (2008)Google Scholar
  13. [NN93]
    Naor, J., Naor, M.: Small-bias probability spaces: Efficient constructions and applications. SIAM J. Comput. 22(4), 838–856 (1993)MathSciNetCrossRefzbMATHGoogle Scholar
  14. [NNOB12]
    Nielsen, J.B., Nordholt, P.S., Orlandi, C., Burra, S.S.: A New Approach to Practical Active-Secure Two-Party Computation. In: Safavi-Naini, R., Canetti, R. (eds.) CRYPTO 2012. LNCS, vol. 7417, pp. 681–700. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  15. [Spi96]
    Spielman, D.A.: Linear-time encodable and decodable error-correcting codes. IEEE Transactions on Information Theory 42(6), 1723–1731 (1996)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© International Association for Cryptologic Research 2013

Authors and Affiliations

  • Ivan Damgård
    • 1
  • Sarah Zakarias
    • 1
  1. 1.Dept. of Computer ScienceAarhus UniversityDenmark

Personalised recommendations