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UC-Secure OT from LWE, Revisited

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Security and Cryptography for Networks (SCN 2020)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 12238))

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Abstract

We build a two-round, UC-secure oblivious transfer protocol (OT) in the common reference string (CRS) model under the Learning with Errors assumption (LWE) with super-polynomial modulus-to-noise ratio. We do so by instantiating the dual-mode encryption framework of Peikert, Vaikuntanathan and Waters (CRYPTO’08). The resulting OT can be instantiated in either one of two modes: one providing statistical sender security, and the other statistical receiver security. Furthermore, our scheme allows the sender and the receiver to reuse the CRS across arbitrarily many executions of the protocol. To our knowledge, this is the first construction of an UC-secure OT from LWE that achieves either statistical receiver security or unbounded reusability of the CRS. For comparison, the construction of UC-secure OT from LWE of Peikert, Vaikuntanathan and Waters only provides computational receiver security and bounded reusability of the CRS.

Our main technical contribution is a public-key encryption scheme from LWE where messy public keys (under which encryptions hide the underlying message statistically) can be tested in time essentially independent of the LWE modulus q.

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Notes

  1. 1.

    One such setup is necessary to achieve simulation-based security.

  2. 2.

    Our construction essentially computes \(\lambda \) Regev ciphertexts. In comparison,  [DGH+20] uses (among others) a generic zero-knowledge proof (for all \(\mathsf {NP}\)) to ensure honest evaluation of a garbled circuit encoding an encryption procedure.

  3. 3.

    More precisely, the counting argument of [PVW08] actually shows that for all pair of public keys, such a test exhibits (at least) one messy public key.

  4. 4.

    Looking more closely at Lemma 2.4, \(\epsilon \) can be exponentially small if \(\tau \ge m\).

References

  1. Asharov, G., Jain, A., López-Alt, A., Tromer, E., Vaikuntanathan, V., Wichs, D.: Multiparty computation with low communication, computation and interaction via threshold FHE. In: Pointcheval and Johansson [PJ12], pp. 483–501

    Google Scholar 

  2. Aharonov, D., Regev, O.: A lattice problem in quantum NP. In: 44th FOCS, pp. 210–219. IEEE Computer Society Press, October 2003

    Google Scholar 

  3. Benhamouda, F., Blazy, O., Ducas, L., Quach, W.: Hash proof systems over lattices revisited. In: Abdalla, M., Dahab, R. (eds.) PKC 2018. LNCS, vol. 10770, pp. 644–674. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-76581-5_22

    Chapter  Google Scholar 

  4. Brakerski, Z., Döttling, N.: Two-message statistically sender-private OT from LWE. In: Beimel, A., Dziembowski, S. (eds.) TCC 2018. LNCS, vol. 11240, pp. 370–390. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-03810-6_14

    Chapter  Google Scholar 

  5. Canetti, R.: Universally composable security: a new paradigm for cryptographic protocols. In: 42nd FOCS, pp. 136–145. IEEE Computer Society Press, October 2001

    Google Scholar 

  6. Canetti, R., et al.: Fiat-Shamir: from practice to theory. In: 51st ACM STOC, pp. 1082–1090. ACM Press (2019)

    Google Scholar 

  7. Canetti, R., Rabin, T.: Universal composition with joint state. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol. 2729, pp. 265–281. Springer, Heidelberg (2003). https://doi.org/10.1007/978-3-540-45146-4_16

    Chapter  Google Scholar 

  8. Cramer, R., Shoup, V.: A practical public key cryptosystem provably secure against adaptive chosen ciphertext attack. In: Krawczyk, H. (ed.) CRYPTO 1998. LNCS, vol. 1462, pp. 13–25. Springer, Heidelberg (1998). https://doi.org/10.1007/BFb0055717

    Chapter  Google Scholar 

  9. Cramer, R., Shoup, V.: Universal hash proofs and a paradigm for adaptive chosen ciphertext secure public-key encryption. In: Knudsen, L.R. (ed.) EUROCRYPT 2002. LNCS, vol. 2332, pp. 45–64. Springer, Heidelberg (2002). https://doi.org/10.1007/3-540-46035-7_4

    Chapter  Google Scholar 

  10. Döttling, N., Garg, S., Hajiabadi, M., Masny, D., Wichs, D.: Two-round oblivious transfer from CDH or LPN. In: Canteaut, A., Ishai, Y. (eds.) EUROCRYPT 2020. LNCS, vol. 12106, pp. 768–797. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-45724-2_26

    Chapter  Google Scholar 

  11. Goldreich, O., Micali, S., Wigderson, A.: How to play any mental game or a completeness theorem for protocols with honest majority. In: Aho, A. (ed.) 19th ACM STOC, pp. 218–229. ACM Press, May 1987

    Google Scholar 

  12. Gentry, C., Peikert, C., Vaikuntanathan, V.: Trapdoors for hard lattices and new cryptographic constructions. In: Ladner, R.E., Dwork, C. (eds.) 40th ACM STOC, pp. 197–206. ACM Press, May 2008

    Google Scholar 

  13. Kalai, Y.T.: Smooth projective hashing and two-message oblivious transfer. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 78–95. Springer, Heidelberg (2005). https://doi.org/10.1007/11426639_5

    Chapter  Google Scholar 

  14. Micciancio, D., Peikert, C.: Trapdoors for lattices: simpler, tighter, faster, smaller. In: Pointcheval and Johansson [PJ12], pp. 700–718

    Google Scholar 

  15. Micciancio, D., Regev, O.: Worst-case to average-case reductions based on Gaussian measures. In: 45th FOCS, pp. 372–381. IEEE Computer Society Press, October 2004

    Google Scholar 

  16. Pass, R.: Unprovable security of perfect NIZK and non-interactive non-malleable commitments. In: Sahai, A. (ed.) TCC 2013. LNCS, vol. 7785, pp. 334–354. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-36594-2_19

    Chapter  MATH  Google Scholar 

  17. Peikert, C.: Limits on the hardness of lattice problems in LP norms. Comput. Complex. 17(2), 300–351 (2008)

    Article  Google Scholar 

  18. Pointcheval, D., Johansson, T. (eds.): EUROCRYPT 2012. LNCS, vol. 7237. Springer, Heidelberg (2012)

    MATH  Google Scholar 

  19. Peikert, C., Shiehian, S.: Noninteractive zero knowledge for NP from (Plain) learning with errors. In: Boldyreva, A., Micciancio, D. (eds.) CRYPTO 2019. LNCS, vol. 11692, pp. 89–114. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-26948-7_4

    Chapter  Google Scholar 

  20. 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 

  21. Rabin, M.O.: How to Exchange Secrets with Oblivious Transfer, 1981. Harvard Aiken Computational Laboratory TR-81

    Google Scholar 

  22. Regev, O.: On lattices, learning with errors, random linear codes, and cryptography. In: Gabow, H.N., Fagin, R. (eds.) 37th ACM STOC, pp. 84–93. ACM Press, May 2005

    Google Scholar 

  23. Schnorr, C.P.: A hierarchy of polynomial time lattice basis reduction algorithms. Theor. Comput. Sci. 53(2), 201–224 (1987)

    Article  MathSciNet  Google Scholar 

  24. 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 

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Acknowledgements

We thank Vinod Vaikuntanathan and Daniel Wichs for helpful discussions and comments about this work. Part of this work was done while the author was visiting the Simons Institute for the Theory of Computing for the Spring 2020 program “Lattices: Algorithms, Complexity, and Cryptography”.

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Authors and Affiliations

  1. Northeastern University, Boston, USA

    Willy Quach

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  1. Willy Quach
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Correspondence to Willy Quach .

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Editors and Affiliations

  1. Università degli Studi di Salerno, Fisciano, Italy

    Clemente Galdi

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

    Vladimir Kolesnikov

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Quach, W. (2020). UC-Secure OT from LWE, Revisited. In: Galdi, C., Kolesnikov, V. (eds) Security and Cryptography for Networks. SCN 2020. Lecture Notes in Computer Science(), vol 12238. Springer, Cham. https://doi.org/10.1007/978-3-030-57990-6_10

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  • DOI: https://doi.org/10.1007/978-3-030-57990-6_10

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