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Annual International Cryptology Conference

CRYPTO 2019: Advances in Cryptology – CRYPTO 2019 pp 462–488Cite as

Reusable Non-Interactive Secure Computation

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Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 11694))

Abstract

We consider the problem of Non-Interactive Two-Party Secure Computation (NISC), where Rachel wishes to publish an encryption of her input x, in such a way that any other party, who holds an input y, can send her a single message which conveys to her the value f(x, y), and nothing more. We demand security against malicious parties. While such protocols are easy to construct using garbled circuits and general non-interactive zero-knowledge proofs, this approach inherently makes a non-black-box use of the underlying cryptographic primitives and is infeasible in practice.

Ishai et al. (Eurocrypt 2011) showed how to construct NISC protocols that only use parallel calls to an ideal oblivious transfer (OT) oracle, and additionally make only a black-box use of any pseudorandom generator. Combined with the efficient 2-message OT protocol of Peikert et al. (Crypto 2008), this leads to a practical approach to NISC that has been implemented in subsequent works. However, a major limitation of all known OT-based NISC protocols is that they are subject to selective failure attacks that allows a malicious sender to entirely compromise the security of the protocol when the receiver’s first message is reused.

Motivated by the failure of the OT-based approach, we consider the problem of basing reusable NISC on parallel invocations of a standard arithmetic generalization of OT known as oblivious linear-function evaluation (OLE). We obtain the following results:

  • We construct an information-theoretically secure reusable NISC protocol for arithmetic branching programs and general zero-knowledge functionalities in the OLE-hybrid model. Our zero-knowledge protocol only makes an absolute constant number of OLE calls per gate in an arithmetic circuit whose satisfiability is being proved. We also get reusable NISC in the OLE-hybrid model for general Boolean circuits using any one-way function.

  • We complement this by a negative result, showing that reusable NISC is impossible to achieve in the OT-hybrid model. This provides a formal justification for the need to replace OT by OLE.

  • We build a universally composable 2-message reusable OLE protocol in the CRS model that can be based on the security of Paillier encryption and requires only a constant number of modular exponentiations. This provides the first arithmetic analogue of the 2-message OT protocols of Peikert et al. (Crypto 2008).

  • By combining our NISC protocol in the OLE-hybrid model and the 2-message OLE protocol, we get protocols with new attractive asymptotic and concrete efficiency features. In particular, we get the first (designated-verifier) NIZK protocols for NP where following a statement-independent preprocessing, both proving and verifying are entirely “non-cryptographic” and involve only a constant computational overhead. Furthermore, we get the first statistical designated-verifier NIZK argument for NP under an assumption related to factoring.

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Notes

  1. 1.

    Alternatively, settling for computational security, one can replace a field by a “pseudo-field,” namely a ring whose description hides all zero-divisors. A useful example is the ring \(\mathbb {Z}_N\) for an RSA modulus N with an unknown factorization.

  2. 2.

    The actual roadmap is somewhat different, and will be gradually revealed in this overview. An impatient reader is referred to Fig. 1 at the end of the overview.

  3. 3.

    In the main body, we do not need to assume that y is random. Moreover, we will consider more general arithmetic conditions beyond \(z=xy\).

  4. 4.

    This is because the first component of the ciphertext, \(b^r\) contains no information about \(r\mod N\).

  5. 5.

    There is a minor subtlety here, where because \(G_{2p'q'}\) has an order 2 subgroup an extra component in this subgroup might not be detected; to prevent this, we actually square all the elements during decryption to eliminate this subgroup, and then decrypt the final result divided by 2.

References

  1. Afshar, A., Mohassel, P., Pinkas, B., Riva, B.: Non-interactive secure computation based on cut-and-choose. In: Nguyen, P.Q., Oswald, E. (eds.) EUROCRYPT 2014. LNCS, vol. 8441, pp. 387–404. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-642-55220-5_22

    Chapter  Google Scholar 

  2. Aiello, B., Ishai, Y., Reingold, O.: Priced oblivious transfer: how to sell digital goods. In: Pfitzmann, B. (ed.) EUROCRYPT 2001. LNCS, vol. 2045, pp. 119–135. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-44987-6_8

    Chapter  Google Scholar 

  3. Applebaum, B., Damgård, I., Ishai, Y., Nielsen, M., Zichron, L.: Secure arithmetic computation with constant computational overhead. In: Katz, J., Shacham, H. (eds.) CRYPTO 2017, Part I. LNCS, vol. 10401, pp. 223–254. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-63688-7_8

    Chapter  Google Scholar 

  4. Applebaum, B., Ishai, Y., Kushilevitz, E.: How to garble arithmetic circuits. SIAM J. Comput. 43(2), 905–929 (2014)

    Article  MathSciNet  Google Scholar 

  5. Bellare, M., Micali, S., Ostrovsky, R.: The (true) complexity of statistical zero knowledge. In: Ortiz, H. (ed.) Proceedings of the 22nd Annual ACM Symposium on Theory of Computing, Baltimore, Maryland, USA, 13–17 May 1990 (1990)

    Google Scholar 

  6. Blum, M., Feldman, P., Micali, S.: Non-interactive zero-knowledge and its applications (extended abstract). In: Simon, J. (ed.) Proceedings of the 20th Annual ACM Symposium on Theory of Computing, Chicago, Illinois, USA, 2–4 May 1988 (1988)

    Google Scholar 

  7. Bootle, J., Cerulli, A., Ghadafi, E., Groth, J., Hajiabadi, M., Jakobsen, S.K.: Linear-time zero-knowledge proofs for arithmetic circuit satisfiability. In: Takagi, T., Peyrin, T. (eds.) ASIACRYPT 2017, Part III. LNCS, vol. 10626, pp. 336–365. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-70700-6_12

    Chapter  Google Scholar 

  8. Boyle, E., Couteau, G., Gilboa, N., Ishai, Y.: Compressing vector OLE. In: Proceedings of the 2018 ACM SIGSAC Conference on Computer and Communications Security, CCS 2018, Toronto, ON, Canada, 15–19 October 2018 (2018)

    Google Scholar 

  9. Brakerski, Z., Vaikuntanathan, V.: Efficient fully homomorphic encryption from (standard) LWE. In: IEEE 52nd Annual Symposium on Foundations of Computer Science, FOCS 2011, Palm Springs, CA, USA, 22–25 October 2011 (2011)

    Google Scholar 

  10. Canetti, R., Chen, Y., Holmgren, J., Lombardi, A., Rothblum, G.N., Rothblum, R.D.: Fiat-Shamir from simpler assumptions. Cryptology ePrint Archive, Report 2018/1004 (2018)

    Google Scholar 

  11. Chaidos, P., Couteau, G.: Efficient designated-verifier non-interactive zero-knowledge proofs of knowledge. In: Nielsen, J.B., Rijmen, V. (eds.) EUROCRYPT 2018, Part III. LNCS, vol. 10822, pp. 193–221. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-78372-7_7

    Chapter  Google Scholar 

  12. Döttling, N., Ghosh, S., Nielsen, J.B., Nilges, T., Trifiletti, R.: TinyOLE: efficient actively secure two-party computation from oblivious linear function evaluation. In: CCS 2017 (2017)

    Google Scholar 

  13. Döttling, N., Kraschewski, D., Müller-Quade, J.: Statistically secure linear-rate dimension extension for oblivious affine function evaluation. In: Smith, A. (ed.) ICITS 2012. LNCS, vol. 7412, pp. 111–128. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-32284-6_7

    Chapter  MATH  Google Scholar 

  14. Genkin, D., Ishai, Y., Prabhakaran, M., Sahai, A., Tromer, E.: Circuits resilient to additive attacks with applications to secure computation. In: STOC 2014 (2014)

    Google Scholar 

  15. 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_25

    Chapter  Google Scholar 

  16. Gentry, C.: Fully homomorphic encryption using ideal lattices. In: Proceedings of the 41st Annual ACM Symposium on Theory of Computing, STOC 2009, Bethesda, MD, USA, 31 May–2 June 2009 (2009)

    Google Scholar 

  17. Ghosh, S., Nielsen, J.B., Nilges, T.: Maliciously secure oblivious linear function evaluation with constant overhead. In: Takagi, T., Peyrin, T. (eds.) ASIACRYPT 2017. LNCS, vol. 10624, pp. 629–659. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-70694-8_22

    Chapter  Google Scholar 

  18. Ishai, Y., Kushilevitz, E.: Perfect constant-round secure computation via perfect randomizing polynomials. In: Widmayer, P., Eidenbenz, S., Triguero, F., Morales, R., Conejo, R., Hennessy, M. (eds.) ICALP 2002. LNCS, vol. 2380, pp. 244–256. Springer, Heidelberg (2002). https://doi.org/10.1007/3-540-45465-9_22

    Chapter  Google Scholar 

  19. Ishai, Y., Kushilevitz, E., Ostrovsky, R., Prabhakaran, M., Sahai, A.: Efficient non-interactive secure computation. In: Paterson, K.G. (ed.) EUROCRYPT 2011. LNCS, vol. 6632, pp. 406–425. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-20465-4_23

    Chapter  Google Scholar 

  20. Ishai, Y., Kushilevitz, E., Ostrovsky, R., Sahai, A.: Zero-knowledge proofs from secure multiparty computation. SIAM J. Comput. 39(3), 1121–1152 (2009)

    Article  MathSciNet  Google Scholar 

  21. Ishai, Y., Prabhakaran, M., Sahai, A.: Founding cryptography on oblivious transfer – efficiently. In: Wagner, D.A. (ed.) CRYPTO 2008. LNCS, vol. 5157, pp. 572–591. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-85174-5_32

    Chapter  Google Scholar 

  22. Kim, S., Wu, D.J.: Multi-theorem preprocessing NIZKs from lattices. In: Shacham, H., Boldyreva, A. (eds.) CRYPTO 2018, Part II. LNCS, vol. 10992, pp. 733–765. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-96881-0_25

    Chapter  Google Scholar 

  23. 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 

  24. Naor, M., Pinkas, B.: Efficient oblivious transfer protocols. In: Proceedings of the Twelfth Annual Symposium on Discrete Algorithms, Washington, DC, USA, 7–9 January 2001 (2001)

    Google Scholar 

  25. Paillier, P.: Public-key cryptosystems based on composite degree residuosity classes. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 223–238. Springer, Heidelberg (1999). https://doi.org/10.1007/3-540-48910-X_16

    Chapter  Google Scholar 

  26. Peikert, C., Vaikuntanathan, V., Waters, B.: A framework for efficient and composable oblivious transfer. In: Wagner, D. (ed.) CRYPTO 2008. LNCS, vol. 5157, pp. 554–571. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-85174-5_31

    Chapter  Google Scholar 

  27. Rivest, R.L., Adleman, L., Dertouzos, M.L.: On data banks and privacy homomorphisms. In: DeMillo, R.A., Dobkin, D.P., Jones, A.K., Lipton, R.J. (eds.) Foundations of Secure Computation (1978)

    Google Scholar 

  28. Rothblum, R.D., Sealfon, A., Sotiraki, K.: Towards non-interactive zero-knowledge for NP from LWE. IACR Cryptology ePrint Archive 2018, 240 (2018)

    Google Scholar 

  29. Yao, A.C.C.: How to generate and exchange secrets (extended abstract). In: Proceedings of FOCS 1986 (1986)

    Google Scholar 

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Acknowledgements

Y. Dodis was supported in part by gifts from VMware Labs, Facebook and Google, and NSF grants 1314568, 1619158, 1815546. Y. Ishai was supported by ERC Project NTSC (742754), ISF grant 1709/14, NSF-BSF grant 2015782, and a grant from the Ministry of Science and Technology, Israel and Department of Science and Technology, Government of India. D. Kraschewski Supported by the European Union’s Tenth Framework Programme (FP10/2010-2016) under grant agreement no. 259426 - ERC Cryptography and Complexity. Work mostly done while at the Technion. T. Liu was supported in part by NSF Grants CNS-1350619, CNS-1414119 and CNS-1718161, an MIT-IBM grant and a DARPA Young Faculty Award. R. Ostrovsky was supported by NSF grant 1619348, BSF grant 2015782, DARPA SafeWare subcontract to Galois Inc., DARPA SPAWAR contract N66001-15-C-4065, JP Morgan Faculty Research Award, OKAWA Foundation Research Award, IBM Faculty Research Award, Xerox Faculty Research Award, B. John Garrick Foundation Award, Teradata Research Award, and Lockheed-Martin Corporation Research Award. The views expressed are those of the authors and do not reflect position of the Department of Defense or the U.S. Government. V. Vaikuntanathan was supported in part by NSF Grants CNS-1350619, CNS-1414119 and CNS-1718161, an MIT-IBM grant and a DARPA Young Faculty Award.

Author information

Authors and Affiliations

  1. Microsoft Research, Redmond, USA

    Melissa Chase

  2. New York University, New York, USA

    Yevgeniy Dodis

  3. Technion, Haifa, Israel

    Yuval Ishai

  4. TNG Technology Consulting GmbH, Unterföhring, Germany

    Daniel Kraschewski

  5. MIT, Cambridge, USA

    Tianren Liu & Vinod Vaikuntanathan

  6. UCLA, Los Angeles, USA

    Rafail Ostrovsky

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  1. Melissa Chase
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  2. Yevgeniy Dodis
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  7. Vinod Vaikuntanathan
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Correspondence to Yuval Ishai or Tianren Liu .

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Editors and Affiliations

  1. Georgia Institute of Technology, Atlanta, GA, USA

    Alexandra Boldyreva

  2. University of California at San Diego, La Jolla, CA, USA

    Daniele Micciancio

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Chase, M. et al. (2019). Reusable Non-Interactive Secure Computation. In: Boldyreva, A., Micciancio, D. (eds) Advances in Cryptology – CRYPTO 2019. CRYPTO 2019. Lecture Notes in Computer Science(), vol 11694. Springer, Cham. https://doi.org/10.1007/978-3-030-26954-8_15

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  • DOI: https://doi.org/10.1007/978-3-030-26954-8_15

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