Advertisement

Reproducible Circularly-Secure Bit Encryption: Applications and Realizations

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9215)

Abstract

We give generic constructions of several fundamental cryptographic primitives based on a new encryption primitive that combines circular security for bit encryption with the so-called reproducibility property (Bellare et al. PKC 2003). At the heart of our constructions is a novel technique which gives a way of de-randomizing reproducible public-key bit-encryption schemes and also a way of reducing one-wayness conditions of a constructed trapdoor-function family (TDF) to circular security of the base scheme. The main primitives that we build from our encryption primitive include k-wise one-way TDFs (Rosen and Segev TCC 2009), CCA2-secure encryption and deterministic encryption. Our results demonstrate a new set of applications of circularly-secure encryption beyond fully-homomorphic encryption and symbolic soundness. Finally, we show the plausibility of our assumptions by showing that the DDH-based circularly-secure scheme of Boneh et al. (Crypto 2008) and the subgroup indistinguishability based scheme of Brakerski and Goldwasser (Crypto 2010) are both reproducible.

Keywords

Circular security Correlated-input security Trapdoor functions (non-)shielding CCA construction Deterministic encryption 

References

  1. 1.
    Applebaum, B.: Key-dependent message security: generic amplification and completeness. In: Paterson, K.G. (ed.) EUROCRYPT 2011. LNCS, vol. 6632, pp. 527–546. Springer, Heidelberg (2011) CrossRefGoogle Scholar
  2. 2.
    Applebaum, B., Cash, D., Peikert, C., Sahai, A.: Fast cryptographic primitives and circular-secure encryption based on hard learning problems. In: Halevi, S. (ed.) CRYPTO 2009. LNCS, vol. 5677, pp. 595–618. Springer, Heidelberg (2009) CrossRefGoogle Scholar
  3. 3.
    Barak, B., Haitner, I., Hofheinz, D., Ishai, Y.: Bounded key-dependent message security. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 423–444. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  4. 4.
    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) CrossRefGoogle Scholar
  5. 5.
    Bellare, M., Boldyreva, A., Staddon, J.: Randomness re-use in multi-recipient encryption schemeas. In: Desmedt, Y.G. (ed.) PKC 2003. LNCS, vol. 2567, pp. 85–99. Springer, Heidelberg (2003) CrossRefGoogle Scholar
  6. 6.
    Bellare, M., Fischlin, M., O’Neill, A., Ristenpart, T.: Deterministic encryption: definitional equivalences and constructions without random oracles. In: Wagner [31], pp. 360–378Google Scholar
  7. 7.
    Birrell, E., Chung, K.-M., Pass, R., Telang, S.: Randomness-dependent message security. In: Sahai, A. (ed.) TCC 2013. LNCS, vol. 7785, pp. 700–720. Springer, Heidelberg (2013) CrossRefGoogle Scholar
  8. 8.
    Black, J., Rogaway, P., Shrimpton, T.: Encryption-scheme security in the presence of key-dependent messages. In: Nyberg, K., Heys, H. (eds.) SAC 2002. LNCS, vol. 2595, pp. 62–75. Springer, Heidelberg (2003) CrossRefGoogle Scholar
  9. 9.
    Boldyreva, A., Fehr, S., O’Neill, A.: On notions of security for deterministic encryption, and efficient constructions without random oracles. In: Wagner [31], pp. 335–359Google Scholar
  10. 10.
    Boneh, D., Canetti, R., Halevi, S., Katz, J.: Chosen-ciphertext security from identity-based encryption. SIAM J. Comput. 36(5), 1301–1328 (2007)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Boneh, D., Halevi, S., Hamburg, M., Ostrovsky, R.: Circular-secure encryption from decision Diffie-Hellman. In: Wagner [31], pp. 108–125Google Scholar
  12. 12.
    Brakerski, Z., Goldwasser, S.: Circular and leakage resilient public-key encryption under subgroup indistinguishability. In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol. 6223, pp. 1–20. Springer, Heidelberg (2010) CrossRefGoogle Scholar
  13. 13.
    Brakerski, Z., Goldwasser, S., Kalai, Y.T.: Black-box circular-secure encryption beyond affine functions. In: Ishai, Y. (ed.) TCC 2011. LNCS, vol. 6597, pp. 201–218. Springer, Heidelberg (2011) CrossRefGoogle Scholar
  14. 14.
    Choi, S.G., Wee, H.: Lossy trapdoor functions from homomorphic reproducible encryption. Inf. Process. Lett. 112(20), 794–798 (2012)MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    Dodis, Y., Ostrovsky, R., Reyzin, L., Smith, A.: Fuzzy extractors: How to generate strong keys from biometrics and other noisy data. SIAM J. Comput. 38(1), 97–139 (2008)MathSciNetCrossRefMATHGoogle Scholar
  16. 16.
    Freeman, D.M., Goldreich, O., Kiltz, E., Rosen, A., Segev, G.: More constructions of lossy and correlation-secure trapdoor functions. J. Cryptology 26(1), 39–74 (2013)MathSciNetCrossRefMATHGoogle Scholar
  17. 17.
    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) CrossRefGoogle Scholar
  18. 18.
    Gertner, Y., Malkin, T., Myers, S.: Towards a separation of semantic and CCA security for public key encryption. In: Vadhan, S.P. (ed.) TCC 2007. LNCS, vol. 4392, pp. 434–455. Springer, Heidelberg (2007) CrossRefGoogle Scholar
  19. 19.
    Gertner, Y., Malkin, T., Reingold, O.: On the impossibility of basing trapdoor functions on trapdoor predicates. In: 42nd Annual Symposium on Foundations of Computer Science, FOCS 2001, 14–17 October 2001, Las Vegas, Nevada, USA, pp. 126–135. IEEE Computer Society (2001)Google Scholar
  20. 20.
    Goldreich, O., Levin, L.A.: A hard-core predicate for all one-way functions. In: Johnson [22], pp. 25–32Google Scholar
  21. 21.
    Impagliazzo, R., Rudich, S.: Limits on the provable consequences of one-way permutations. In: Johnson [22], pp. 44–61Google Scholar
  22. 22.
    Johnson, D.S. (ed.): Proceedings of the 21st Annual ACM Symposium on Theory of Computing. ACM, New York (1989)Google Scholar
  23. 23.
    Malkin, T., Teranishi, I., Yung, M.: Efficient circuit-size independent public key encryption with KDM security. In: Paterson, K.G. (ed.) EUROCRYPT 2011. LNCS, vol. 6632, pp. 507–526. Springer, Heidelberg (2011) CrossRefGoogle Scholar
  24. 24.
    Myers, S., Shelat, A.: Bit encryption is complete. In: 50th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2009, 25–27 October 2009, Atlanta, Georgia, USA, pp. 607–616. IEEE Computer Society (2009)Google Scholar
  25. 25.
    Nisan, N., Zuckerman, D.: Randomness is linear in space. J. Comput. Syst. Sci. 52(1), 43–52 (1996)MathSciNetCrossRefMATHGoogle Scholar
  26. 26.
    Peikert, C., Waters, B.: Lossy trapdoor functions and their applications. In: Dwork, C. (ed.) STOC, pp. 187–196. ACM (2008)Google Scholar
  27. 27.
    Reingold, O., Trevisan, L., Vadhan, S.P.: Notions of reducibility between cryptographic primitives. In: Naor, M. (ed.) TCC 2004. LNCS, vol. 2951, pp. 1–20. Springer, Heidelberg (2004) CrossRefGoogle Scholar
  28. 28.
    Rosen, A., Segev, G.: Chosen-ciphertext security via correlated products. SIAM J. Comput. 39(7), 3058–3088 (2010)MathSciNetCrossRefMATHGoogle Scholar
  29. 29.
    Rothblum, R.D.: On the circular security of bit-encryption. In: Sahai, A. (ed.) TCC 2013. LNCS, vol. 7785, pp. 579–598. Springer, Heidelberg (2013) CrossRefGoogle Scholar
  30. 30.
    Vahlis, Y.: Two is a crowd? A black-box separation of one-wayness and security under correlated inputs. In: Micciancio, D. (ed.) TCC 2010. LNCS, vol. 5978, pp. 165–182. Springer, Heidelberg (2010) CrossRefGoogle Scholar
  31. 31.
    Wagner, D.: Advances in Cryptology - CRYPTO 2008. LNCS, vol. 5157. Springer, Heidelberg (2008) CrossRefMATHGoogle Scholar
  32. 32.
    Wee, H.: Dual projective hashing and its applications — lossy trapdoor functions and more. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 246–262. Springer, Heidelberg (2012) CrossRefGoogle Scholar

Copyright information

© International Association for Cryptologic Research 2015

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of VictoriaVictoriaCanada

Personalised recommendations