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Annual International Conference on the Theory and Applications of Cryptographic Techniques

EUROCRYPT 2022: Advances in Cryptology – EUROCRYPT 2022 pp 37–64Cite as

Garbled Circuits with Sublinear Evaluator

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13275))

Abstract

A recent line of work, Stacked Garbled Circuit (SGC), showed that Garbled Circuit (GC) can be improved for functions that include conditional behavior. SGC relieves the communication bottleneck of 2PC by only sending enough garbled material for a single branch out of the b total branches. Hence, communication is sublinear in the circuit size. However, both the evaluator and the generator pay in computation and perform at least factor \(\log b\) extra work as compared to standard GC.

We extend the sublinearity of SGC to also include the work performed by the GC evaluator \(E\); thus we achieve a fully sublinear \(E\), which is essential when optimizing for the online phase. We formalize our approach as a garbling scheme called \(\mathsf {GCWise}\): GC WIth Sublinear Evaluator.

We show one attractive and immediate application, Garbled PIR, a primitive that marries GC with Private Information Retrieval. Garbled PIR allows the GC to non-interactively and sublinearly access a privately indexed element from a publicly known database, and then use this element in continued GC evaluation.

A. Shah—Work partially done while at Microsoft Research, India.

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Notes

  1. 1.

    [HK20b] use oblivious transfer to convey these seeds, but they can also be encrypted according to the active branch GC labels in a GC gadget.

References

  1. Bellare, M., Hoang, V.T., Rogaway, P.: Foundations of garbled circuits. In: Yu, T., Danezis, G., Gligor, V.D. (eds.) ACM CCS 2012, pp. 784–796. ACM Press, October 2012

    Google Scholar 

  2. Ben-Efraim, A., Nielsen, M., Omri, E.: Turbospeedz: double your online SPDZ! improving SPDZ using function dependent preprocessing. In: Deng, R.H., Gauthier-Umaña, V., Ochoa, M., Yung, M. (eds.) ACNS 2019. LNCS, vol. 11464, pp. 530–549. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-21568-2_26

    Chapter  Google Scholar 

  3. Brakerski, Z., Vaikuntanathan, V.: Efficient fully homomorphic encryption from (standard) LWE. In: Ostrovsky, R. (ed.) 52nd FOCS, pp. 97–106. IEEE Computer Society Press, October 2011

    Google Scholar 

  4. Chor, B., Goldreich, O., Kushilevitz, E., Sudan, M.: Private information retrieval. In: 36th Annual Symposium on Foundations of Computer Science, Milwaukee, Wisconsin, USA, 23–25 October 1995, pp. 41–50. IEEE Computer Society (1995)

    Google Scholar 

  5. Corrigan-Gibbs, H., Kogan, D.: Private information retrieval with sublinear online time. In: Canteaut, A., Ishai, Y. (eds.) EUROCRYPT 2020, Part I. LNCS, vol. 12105, pp. 44–75. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-45721-1_3

    Chapter  Google Scholar 

  6. Chor, B., Kushilevitz, E., Goldreich, O., Sudan, M.: Private information retrieval. J. ACM 45(6), 965–981 (1998)

    Article  MathSciNet  Google Scholar 

  7. Choi, S.G., Katz, J., Kumaresan, R., Zhou, H.-S.: On the security of the “Free-XOR’’ technique. In: Cramer, R. (ed.) TCC 2012. LNCS, vol. 7194, pp. 39–53. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-28914-9_3

    Chapter  MATH  Google Scholar 

  8. Damgård, I., Pastro, V., Smart, N., 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). https://doi.org/10.1007/978-3-642-32009-5_38

    Chapter  Google Scholar 

  9. Frederiksen, T.K., Nielsen, J.B., Orlandi, C.: Privacy-free garbled circuits with applications to efficient zero-knowledge. In: Oswald, E., Fischlin, M. (eds.) EUROCRYPT 2015, Part II. LNCS, vol. 9057, pp. 191–219. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-46803-6_7

    Chapter  Google Scholar 

  10. Gentry, C.: Fully homomorphic encryption using ideal lattices. In: Mitzenmacher, M. (ed.) 41st ACM STOC, pp. 169–178. ACM Press, May/June 2009

    Google Scholar 

  11. Dov Gordon, S., et al.: Secure two-party computation in sublinear (amortized) time. In: Yu, T., Danezis, G., Gligor, V.D. (eds.) ACM CCS 2012, pp. 513–524. ACM Press, October 2012

    Google Scholar 

  12. Goldwasser, S., Kalai, Y.T., Popa, R.A., Vaikuntanathan, V., Zeldovich, N.: How to run turing machines on encrypted data. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013, Part II. LNCS, vol. 8043, pp. 536–553. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-40084-1_30

    Chapter  Google Scholar 

  13. Gentry, C., Sahai, A., Waters, B.: Homomorphic encryption from learning with errors: conceptually-simpler, asymptotically-faster, attribute-based. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013, Part I. LNCS, vol. 8042, pp. 75–92. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-40041-4_5

    Chapter  Google Scholar 

  14. Heath, D., Kolesnikov, V.: Stacked garbling. In: Micciancio, D., Ristenpart, T. (eds.) CRYPTO 2020, Part II. LNCS, vol. 12171, pp. 763–792. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-56880-1_27

    Chapter  Google Scholar 

  15. Heath, D., Kolesnikov, V.: Stacked garbling for disjunctive zero-knowledge proofs. In: Canteaut, A., Ishai, Y. (eds.) EUROCRYPT 2020, Part III. LNCS, vol. 12107, pp. 569–598. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-45727-3_19

    Chapter  Google Scholar 

  16. Heath, D., Kolesnikov, V.: LogStack: stacked garbling with \(O(b \log b)\) computation. In: Canteaut, A., Standaert, F.-X. (eds.) EUROCRYPT 2021. LNCS, vol. 12698, pp. 3–32. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-77883-5_1

    Chapter  Google Scholar 

  17. Jawurek, M., Kerschbaum, F., Orlandi, C.: Zero-knowledge using garbled circuits: how to prove non-algebraic statements efficiently. In: Sadeghi, A.-R., Gligor, V.D., Yung, M. (eds.) ACM CCS 2013, pp. 955–966. ACM Press, November 2013

    Google Scholar 

  18. Kennedy, W.S., Kolesnikov, V., Wilfong, G.: Overlaying conditional circuit clauses for secure computation. In: Takagi, T., Peyrin, T. (eds.) ASIACRYPT 2017, Part II. LNCS, vol. 10625, pp. 499–528. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-70697-9_18

    Chapter  Google Scholar 

  19. Kolesnikov, V., Mohassel, P., Rosulek, M.: FleXOR: flexible garbling for XOR gates that beats free-XOR. In: Garay, J.A., Gennaro, R. (eds.) CRYPTO 2014, Part II. LNCS, vol. 8617, pp. 440–457. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-662-44381-1_25

    Chapter  Google Scholar 

  20. Kushilevitz, E., Ostrovsky, R.: Replication is NOT needed: SINGLE database, computationally-private information retrieval. In: 38th FOCS, pp. 364–373. IEEE Computer Society Press, October 1997

    Google Scholar 

  21. Kolesnikov, V.: \({\sf Free}\)\(\mathtt{IF}\): how to omit inactive branches and implement \(\cal{S}\)-universal garbled circuit (almost) for free. In: Peyrin, T., Galbraith, S. (eds.) ASIACRYPT 2018, Part III. LNCS, vol. 11274, pp. 34–58. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-03332-3_2

    Chapter  Google Scholar 

  22. Kolesnikov, V., Schneider, T.: Improved garbled circuit: free XOR gates and applications. In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds.) ICALP 2008, Part II. LNCS, vol. 5126, pp. 486–498. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-70583-3_40

    Chapter  MATH  Google Scholar 

  23. Kolesnikov, V., Schneider, T.: A practical universal circuit construction and secure evaluation of private functions. In: Tsudik, G. (ed.) FC 2008. LNCS, vol. 5143, pp. 83–97. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-85230-8_7

    Chapter  MATH  Google Scholar 

  24. Lu, S., Ostrovsky, R.: How to garble RAM programs? In: Johansson, T., Nguyen, P.Q. (eds.) EUROCRYPT 2013. LNCS, vol. 7881, pp. 719–734. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-38348-9_42

    Chapter  Google Scholar 

  25. Lindell, Y., Pinkas, B.: A proof of security of Yao’s protocol for two-party computation. J. Cryptol. 22(2), 161–188 (2009)

    Article  MathSciNet  Google Scholar 

  26. Liu, H., Yu, Y., Zhao, S., Zhang, J., Liu, W.: Pushing the limits of valiant’s universal circuits: simpler, tighter and more compact. Cryptology ePrint Archive, Report 2020/161 (2020). https://eprint.iacr.org/2020/161

  27. Naor, M., Pinkas, B., Sumner, R.: Privacy preserving auctions and mechanism design. In: Proceedings of the 1st ACM Conference on Electronic Commerce, EC 1999, pp. 129–139, 1999. Association for Computing Machinery, New York (1999)

    Google Scholar 

  28. Pinkas, B., Schneider, T., Smart, N.P., Williams, S.C.: Secure two-party computation is practical. In: Matsui, M. (ed.) ASIACRYPT 2009. LNCS, vol. 5912, pp. 250–267. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-10366-7_15

    Chapter  Google Scholar 

  29. Rosulek, M., Roy, L.: Three halves make a whole? beating the half-gates lower bound for garbled circuits. In: Malkin, T., Peikert, C. (eds.) CRYPTO 2021. LNCS, vol. 12825, pp. 94–124. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-84242-0_5

    Chapter  Google Scholar 

  30. Valiant, L.G.: Universal circuits (preliminary report). In: STOC, pp. 196–203. ACM Press, New York (1976)

    Google Scholar 

  31. Wang, X., Ranellucci, S., Katz, J.: Authenticated garbling and efficient maliciously secure two-party computation. In: Thuraisingham, B.M., Evans, D., Malkin, T., Xu, D. (eds.) ACM CCS 2017, pp. 21–37. ACM Press, October/November 2017

    Google Scholar 

  32. Yao, A.C.-C.: How to generate and exchange secrets (extended abstract). In: 27th FOCS, pp. 162–167. IEEE Computer Society Press, October 1986

    Google Scholar 

  33. Zahur, S., Rosulek, M., Evans, D.: Two halves make a whole. In: Oswald, E., Fischlin, M. (eds.) EUROCRYPT 2015, Part II. LNCS, vol. 9057, pp. 220–250. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-46803-6_8

    Chapter  MATH  Google Scholar 

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Acknowledgements

This work was supported in part by NSF award #1909769, by a Facebook research award, a Cisco research award, and by Georgia Tech’s IISP cybersecurity seed funding (CSF) award. This material is also based upon work supported in part by DARPA under Contract No. HR001120C0087. This work is also supported by DARPA under Cooperative Agreement HR0011-20-2-0025, NSF grant CNS-2001096, CNS-1764025, CNS-1718074, US-Israel BSF grant 2015782, Google Faculty Award, JP Morgan Faculty Award, IBM Faculty Research Award, Xerox Faculty Research Award, OKAWA Foundation Research Award, B. John Garrick Foundation Award, Teradata Research Award, Lockheed-Martin Research Award and Sunday Group. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies, either expressed or implied, of DARPA, the Department of Defense, or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for governmental purposes not withstanding any copyright annotation therein.

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Authors and Affiliations

  1. NC State, Raleigh, USA

    Abida Haque

  2. Georgia Tech, Atlanta, USA

    David Heath & Vladimir Kolesnikov

  3. Stealth Software Technologies, Inc., Los Angeles, USA

    Steve Lu

  4. UCLA, Los Angeles, USA

    Rafail Ostrovsky & Akash Shah

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  1. Abida Haque
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Correspondence to David Heath .

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Editors and Affiliations

  1. University of Haifa, Haifa, Haifa, Israel

    Orr Dunkelman

  2. University of Warsaw, Warsaw, Poland

    Stefan Dziembowski

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Haque, A., Heath, D., Kolesnikov, V., Lu, S., Ostrovsky, R., Shah, A. (2022). Garbled Circuits with Sublinear Evaluator. In: Dunkelman, O., Dziembowski, S. (eds) Advances in Cryptology – EUROCRYPT 2022. EUROCRYPT 2022. Lecture Notes in Computer Science, vol 13275. Springer, Cham. https://doi.org/10.1007/978-3-031-06944-4_2

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