Advertisement

Verifiable Outsourcing of Computations Using Garbled Onions

  • Tahsin C. M. Dönmez
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11091)

Abstract

Solutions to the verifiable outsourcing problem based on Yao’s Garbled Circuit (GC) construction have been investigated in previous works. A major obstacle to the practicality of these solutions is the single-use nature of the GC construction. This work introduces the novel technique onion garbling, which circumvents this obstacle by using only a symmetric-key cipher as its cryptographic machinery. This work also proposes a non-interactive protocol for verifiable outsourcing which utilizes the onion garbling technique. The protocol works in a 3-party setting, and consists of a preprocessing phase and an online phase. The cost of a preprocessing phase which can support up to N computations is independent of N for the outsourcing party. For the other two parties, the memory and communication cost of N-reusability is proportional to \(N \cdot m\), where m is the bit-length of the input. The cost of input preparation and verification is \(\mathcal {O}(m+n)\) symmetric-key cipher operations, where n is the bit-length of the output. The overall costs associated with the outsourcing party are low enough to allow verifiable outsourcing of arbitrary computations by resource-constrained devices on constrained networks. Finally, this work reports on a proof-of-concept implementation of the proposed verifiable outsourcing protocol.

Keywords

Verifiable computation Outsourcing Garbled onion 

Notes

Acknowledgements

This work is supported in part by Tekes under the project Wireless for Verticals (WIVE). WIVE is a part of 5G Test Network Finland (5GTNF). We thank Ethiopia Nigussie for encouraging us to think about applications of secure multiparty computation in the context of the Internet of Things and Edge Computing. Finally, the author would like to thank the anonymous reviewers for their valuable comments.

References

  1. 1.
    Applebaum, B., Ishai, Y., Kushilevitz, E.: From secrecy to soundness: efficient verification via secure computation. In: Abramsky, S., Gavoille, C., Kirchner, C., Meyer auf der Heide, F., Spirakis, P.G. (eds.) ICALP 2010. LNCS, vol. 6198, pp. 152–163. Springer, Heidelberg (2010).  https://doi.org/10.1007/978-3-642-14165-2_14CrossRefGoogle Scholar
  2. 2.
    Beaver, D., Micali, S., Rogaway, P.: The round complexity of secure protocols. In: Proceedings of the Twenty-Second Annual ACM Symposium on Theory of Computing, STOC 1990, pp. 503–513. ACM, New York (1990).  https://doi.org/10.1145/100216.100287
  3. 3.
    Bellare, M., Hoang, V.T., Rogaway, P.: Foundations of garbled circuits. In: Proceedings of the 2012 ACM Conference on Computer and Communications Security, CCS 2012, pp. 784–796. ACM, New York (2012).  https://doi.org/10.1145/2382196.2382279
  4. 4.
    Dönmez, T.C.M.: Fairenough, July 2018. https://gitlab.utu.fi/tcmdon/Fairenough
  5. 5.
    Dworkin, M.: Recommendation for block cipher modes of operation. Methods and techniques. Technical report, National Institute of Standards and Technology, Gaithersburg, MD. Computer Security Division, December 2001. http://www.dtic.mil/docs/citations/ADA400014
  6. 6.
    Gennaro, R., Gentry, C., Parno, B.: Non-interactive verifiable computing: outsourcing computation to untrusted workers. Cryptology ePrint Archive, Report 2009/547 (2009). https://eprint.iacr.org/2009/547
  7. 7.
    Gennaro, R., Gentry, C., Parno, B.: Non-interactive verifiable computing: outsourcing computation to untrusted workers. In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol. 6223, pp. 465–482. Springer, Heidelberg (2010).  https://doi.org/10.1007/978-3-642-14623-7_25CrossRefGoogle Scholar
  8. 8.
    Goldwasser, S., Kalai, Y., Popa, R.A., Vaikuntanathan, V., Zeldovich, N.: Reusable garbled circuits and succinct functional encryption. In: Proceedings of the Forty-Fifth Annual ACM Symposium on Theory of Computing, STOC 2013, pp. 555–564. ACM, New York (2013).  https://doi.org/10.1145/2488608.2488678
  9. 9.
    Huang, Y., Shen, C., Evans, D., Katz, J., Shelat, A.: Efficient secure computation with garbled circuits. In: Jajodia, S., Mazumdar, C. (eds.) ICISS 2011. LNCS, vol. 7093, pp. 28–48. Springer, Heidelberg (2011).  https://doi.org/10.1007/978-3-642-25560-1_2CrossRefGoogle Scholar
  10. 10.
    Ishai, Y., Wee, H.: Partial garbling schemes and their applications. In: Esparza, J., Fraigniaud, P., Husfeldt, T., Koutsoupias, E. (eds.) ICALP 2014. LNCS, vol. 8572, pp. 650–662. Springer, Heidelberg (2014).  https://doi.org/10.1007/978-3-662-43948-7_54CrossRefzbMATHGoogle Scholar
  11. 11.
    Keranen, A., Ersue, M., Bormann, C.: Terminology for constrained-node networks. RFC 7228, RFC Editor, May 2014.  https://doi.org/10.17487/RFC7228, http://www.rfc-editor.org/info/rfc7228
  12. 12.
    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. LNCS, vol. 8617, pp. 440–457. Springer, Heidelberg (2014).  https://doi.org/10.1007/978-3-662-44381-1_25CrossRefGoogle Scholar
  13. 13.
    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. LNCS, vol. 5126, pp. 486–498. Springer, Heidelberg (2008).  https://doi.org/10.1007/978-3-540-70583-3_40CrossRefzbMATHGoogle Scholar
  14. 14.
    Malkhi, D., Nisan, N., Pinkas, B., Sella, Y.: Fairplay–a secure two-party computation system. In: Proceedings of the 13th Conference on USENIX Security Symposium, SSYM 2004, vol. 13, p. 20. USENIX Association, Berkeley (2004). http://dl.acm.org/citation.cfm?id=1251375.1251395
  15. 15.
    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. ACM, New York (1999).  https://doi.org/10.1145/336992.337028
  16. 16.
    Parno, B., Howell, J., Gentry, C., Raykova, M.: Pinocchio: nearly practical verifiable computation. In: 2013 IEEE Symposium on Security and Privacy, pp. 238–252, May 2013.  https://doi.org/10.1109/SP.2013.47
  17. 17.
    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_15CrossRefGoogle Scholar
  18. 18.
    Yao, A.C.: Protocols for secure computations. In: 23rd Annual Symposium on Foundations of Computer Science (SFCS 1982), pp. 160–164, November 1982.  https://doi.org/10.1109/SFCS.1982.38
  19. 19.
    Yao, A.C.C.: How to generate and exchange secrets. In: 27th Annual Symposium on Foundations of Computer Science (SFCS 1986), pp. 162–167, October 1986.  https://doi.org/10.1109/SFCS.1986.25
  20. 20.
    Zahur, S., Rosulek, M., Evans, D.: Two halves make a whole. In: Oswald, E., Fischlin, M. (eds.) EUROCRYPT 2015. LNCS, vol. 9057, pp. 220–250. Springer, Heidelberg (2015).  https://doi.org/10.1007/978-3-662-46803-6_8CrossRefzbMATHGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Department of Future TechnologiesUniversity of TurkuTurkuFinland

Personalised recommendations