An OBDD-Based Technique for the Efficient Synthesis of Garbled Circuits

  • Stelvio CimatoEmail author
  • Valentina Ciriani
  • Ernesto Damiani
  • Maryam Ehsanpour
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11738)


Secure Multi-party Computation (SMC) protocols are exploited to perform collaborative computation of a function between two or more parties while keeping the privacy of the private inputs and sharing the computed result only. The Garbled Circuit (GC) protocol, proposed by Yao, is one of the possible approaches to solve the SMC problem, based on the evaluation of the Boolean Circuit representing the given function.

Recently, the question to improve efficiency in secure multi-party computation has gained much interest. One of the proposed techniques to increase the efficiency of the GC protocol is based on the reduction of the number of non-XOR gates in the Boolean circuit, since the evaluation of XOR gates have no cost for the execution of the whole protocol.

The aim of this work is to define a post-processing procedure that, given an optimized GC, decreases the number of non-XOR gates by transforming some parts of the circuit. The strategy is based on the fact that some gates behave as XORs apart from one output and then, if that input never occurs, those gates can be replaced by a XOR without changing the output of the overall network. The technique we propose is based on the analysis of the GC by using Ordered Binary Decision Diagrams (OBDD) representation. We present the application of our technique to some standard circuits to show the effectiveness of our proposal.


  1. 1.
    Barni, M., Droandi, G., Lazzeretti, R.: Privacy protection in biometric-based recognition systems: a marriage between cryptography and signal processing. IEEE Signal Process. Mag. 32(5), 66–76 (2015)CrossRefGoogle Scholar
  2. 2.
    Barni, M., Failla, P., Kolesnikov, V., Lazzeretti, R., Sadeghi, A.-R., Schneider, T.: Secure evaluation of private linear branching programs with medical applications. In: Backes, M., Ning, P. (eds.) ESORICS 2009. LNCS, vol. 5789, pp. 424–439. Springer, Heidelberg (2009). Scholar
  3. 3.
    Bogdanov, D., Kamm, L., Kubo, B., Rebane, R., Sokk, V., Talviste, R.: Students and taxes: a privacy-preserving study using secure computation. PoPETs 2016(3), 117–135 (2016)Google Scholar
  4. 4.
    Brickell, J., Porter, D.E., Shmatikov, V., Witchel, E.: Privacy-preserving remote diagnostics. In: Proceedings of the 14th ACM Conference on Computer and Communications Security, pp. 498–507. ACM (2007)Google Scholar
  5. 5.
    Cimato, S., Ciriani, V., Damiani, E., Ehsanpour, M.: A multiple valued logic approach for the synthesis of garbled circuits. In: IFIP/IEEE 25th International Conference on Very Large Scale Integration, VLSI-SoC, pp. 232–236 (2017)Google Scholar
  6. 6.
    Ehsanpour, M., Cimato, S., Ciriani, V., Damiani, E.: Exploiting quantum gates in secure computation. In: Kubátová, H., Novotný, M., Skavhaug, A. (eds.) Euromicro Conference on Digital System Design, DSD 2017, Vienna, Austria, 30 August–1 September 2017, pp. 291–294. IEEE Computer Society (2017)Google Scholar
  7. 7.
    Kerschbaum, F., Strüker, J., Koslowski, T.G.: Confidential information-sharing for automated sustainability benchmarks. In: Galletta, D.F., Liang, T.-P. (eds.) Proceedings of the International Conference on Information Systems, ICIS 2011, Shanghai, China, 4–7 December 2011. Association for Information Systems (2011)Google Scholar
  8. 8.
    Kolesnikov, V., Schneider, T.: Improved garbled circuit: free XOR gates and applications. In: Automata, Languages and Programming, pp. 486–498 (2008)Google Scholar
  9. 9.
    Lindell, Y., Pinkas, B.: Secure multiparty computation for privacy-preserving data mining. J. Privacy Confid. 1(1), 5 (2009)CrossRefGoogle Scholar
  10. 10.
    Naor, M., Pinkas, B., Sumner, R.: Privacy preserving auctions and mechanism design. In: Proceedings of the 1st ACM Conference on Electronic Commerce, pp. 129–139. ACM (1999)Google Scholar
  11. 11.
    Tuchman, W.: A brief history of the data encryption standard. In: Internet Besieged, pp. 275–280. ACM Press/Addison-Wesley Publishing Co., New York (1998)Google Scholar
  12. 12.
    Yao, A.C.-C.: How to generate and exchange secrets. In: 27th Annual Symposium on Foundations of Computer Science, pp. 162–167. IEEE (1986)Google Scholar

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Stelvio Cimato
    • 1
    Email author
  • Valentina Ciriani
    • 1
  • Ernesto Damiani
    • 1
    • 2
  • Maryam Ehsanpour
    • 1
  1. 1.Dipartimento di InformaticaUniversità degli Studi di MilanoMilanItaly
  2. 2.EBTIC - Khalifa University of Science and TechnologyAbu DhabiUAE

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