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On ELFs, Deterministic Encryption, and Correlated-Input Security

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Advances in Cryptology – EUROCRYPT 2019 (EUROCRYPT 2019)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 11478))

Abstract

We construct deterministic public key encryption secure for any constant number of arbitrarily correlated computationally unpredictable messages. Prior works required either random oracles or non-standard knowledge assumptions. In contrast, our constructions are based on the exponential hardness of DDH, which is plausible in elliptic curve groups. Our central tool is a new trapdoored extremely lossy function, which modifies extremely lossy functions by adding a trapdoor.

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References

  1. Alwen, J., Dodis, Y., Wichs, D.: Survey: leakage resilience and the bounded retrieval model. In: Kurosawa, K. (ed.) ICITS 2009. LNCS, vol. 5973, pp. 1–18. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-14496-7_1

    Chapter  Google Scholar 

  2. Barak, B., et al.: On the (im)possibility of obfuscating programs. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 1–18. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-44647-8_1

    Chapter  Google Scholar 

  3. Bellare, M., Boldyreva, A., O’Neill, A.: Deterministic and efficiently searchable encryption. In: Menezes, A. (ed.) CRYPTO 2007. LNCS, vol. 4622, pp. 535–552. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-74143-5_30

    Chapter  Google Scholar 

  4. Bellare, M., Cash, D., Miller, R.: Cryptography secure against related-key attacks and tampering. In: Lee, D.H., Wang, X. (eds.) ASIACRYPT 2011. LNCS, vol. 7073, pp. 486–503. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-25385-0_26

    Chapter  Google Scholar 

  5. Bellare, M., Fischlin, M., O’Neill, A., Ristenpart, T.: Deterministic encryption: definitional equivalences and constructions without random oracles. In: Wagner, D. (ed.) CRYPTO 2008. LNCS, vol. 5157, pp. 360–378. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-85174-5_20

    Chapter  Google Scholar 

  6. Bellare, M., Hoang, V.T.: Resisting randomness subversion: fast deterministic and hedged public-key encryption in the standard model. In: Oswald, E., Fischlin, M. (eds.) EUROCRYPT 2015, Part II. LNCS, vol. 9057, pp. 627–656. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-46803-6_21

    Chapter  MATH  Google Scholar 

  7. Bellare, M., Rogaway, P.: Random oracles are practical: a paradigm for designing efficient protocols. In: Ashby, V. (ed.) ACM CCS 1993, pp. 62–73. ACM Press, November 1993

    Google Scholar 

  8. Boldyreva, A., Fehr, S., O’Neill, A.: On notions of security for deterministic encryption, and efficient constructions without random oracles. In: Wagner, D. (ed.) CRYPTO 2008. LNCS, vol. 5157, pp. 335–359. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-85174-5_19

    Chapter  Google Scholar 

  9. Brakerski, Z., Segev, G.: Better security for deterministic public-key encryption: the auxiliary-input setting. In: Rogaway, P. (ed.) CRYPTO 2011. LNCS, vol. 6841, pp. 543–560. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-22792-9_31

    Chapter  Google Scholar 

  10. Brzuska, C., Farshim, P., Mittelbach, A.: Indistinguishability obfuscation and UCEs: the case of computationally unpredictable sources. In: Garay, J.A., Gennaro, R. (eds.) CRYPTO 2014, Part I. LNCS, vol. 8616, pp. 188–205. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-662-44371-2_11

    Chapter  Google Scholar 

  11. Canetti, R., Goldreich, O., Halevi, S.: The random oracle methodology, revisited (preliminary version). In: 30th ACM STOC, pp. 209–218. ACM Press, May 1998

    Google Scholar 

  12. Chung, K.-M., Lin, H., Mahmoody, M., Pass, R.: On the power of nonuniformity in proofs of security. In: Kleinberg, R.D. (ed.) ITCS 2013, pp. 389–400. ACM, January 2013

    Google Scholar 

  13. Freeman, D.M., Goldreich, O., Kiltz, E., Rosen, A., Segev, G.: More constructions of lossy and correlation-secure trapdoor functions. In: Nguyen, P.Q., Pointcheval, D. (eds.) PKC 2010. LNCS, vol. 6056, pp. 279–295. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-13013-7_17

    Chapter  Google Scholar 

  14. Fuller, B., O’Neill, A., Reyzin, L.: A unified approach to deterministic encryption: new constructions and a connection to computational entropy. In: Cramer, R. (ed.) TCC 2012. LNCS, vol. 7194, pp. 582–599. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-28914-9_33

    Chapter  Google Scholar 

  15. Goldreich, O., Levin, L.A.: A hard-core predicate for all one-way functions. In: 21st ACM STOC, pp. 25–32. ACM Press, May 1989

    Google Scholar 

  16. Goyal, V., O’Neill, A., Rao, V.: Correlated-input secure hash functions. In: Ishai, Y. (ed.) TCC 2011. LNCS, vol. 6597, pp. 182–200. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-19571-6_12

    Chapter  Google Scholar 

  17. Matsuda, T., Hanaoka, G.: Chosen ciphertext security via UCE. In: Krawczyk, H. (ed.) PKC 2014. LNCS, vol. 8383, pp. 56–76. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-642-54631-0_4

    Chapter  Google Scholar 

  18. Peikert, C., Waters, B.: Lossy trapdoor functions and their applications. In: Ladner, R.E., Dwork, C. (eds.) 40th ACM STOC, pp. 187–196. ACM Press, May 2008

    Google Scholar 

  19. Raghunathan, A., Segev, G., Vadhan, S.P.: Deterministic public-key encryption for adaptively chosen plaintext distributions. In: Johansson, T., Nguyen, P.Q. (eds.) EUROCRYPT 2013. LNCS, vol. 7881, pp. 93–110. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-38348-9_6

    Chapter  Google Scholar 

  20. Villar, J.L.: Optimal reductions of some decisional problems to the rank problem. In: Wang, X., Sako, K. (eds.) ASIACRYPT 2012. LNCS, vol. 7658, pp. 80–97. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-34961-4_7

    Chapter  Google Scholar 

  21. Wichs, D.: Barriers in cryptography with weak, correlated and leaky sources. In: Kleinberg, R.D. (ed.) ITCS 2013, pp. 111–126. ACM, January 2013

    Google Scholar 

  22. Zhandry, M.: The magic of ELFs. In: Robshaw, M., Katz, J. (eds.) CRYPTO 2016, Part I. LNCS, vol. 9814, pp. 479–508. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53018-4_18

    Chapter  Google Scholar 

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Correspondence to Mark Zhandry .

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Zhandry, M. (2019). On ELFs, Deterministic Encryption, and Correlated-Input Security. In: Ishai, Y., Rijmen, V. (eds) Advances in Cryptology – EUROCRYPT 2019. EUROCRYPT 2019. Lecture Notes in Computer Science(), vol 11478. Springer, Cham. https://doi.org/10.1007/978-3-030-17659-4_1

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  • DOI: https://doi.org/10.1007/978-3-030-17659-4_1

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