Two Is a Crowd? A Black-Box Separation of One-Wayness and Security under Correlated Inputs

  • Yevgeniy Vahlis
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5978)

Abstract

A family of trapdoor functions is one-way under correlated inputs if no efficient adversary can invert it even when given the value of the function on multiple correlated inputs. This powerful primitive was introduced at TCC 2009 by Rosen and Segev, who use it in an elegant black box construction of a chosen ciphertext secure public key encryption. In this work we continue the study of security under correlated inputs, and prove that there is no black box construction of correlation secure injective trapdoor functions from classic trapdoor permutations, even if the latter is assumed to be one-way for inputs from high entropy, rather than uniform distributions. Our negative result holds for all input distributions where each x i is determined by the remaining n − 1 coordinates. The techniques we employ for proving lower bounds about trapdoor permutations are new and quite general, and we believe that they will find other applications in the area of black-box separations.

References

  1. 1.
    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)CrossRefGoogle Scholar
  2. 2.
    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
  3. 3.
    Boneh, D., Canetti, R., Halevi, S., Katz, J.: Chosen-ciphertext security from identity-based encryption. SIAM J. Comput. 36(5), 1301–1328 (2006)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Boneh, D., Franklin, M.K.: Identity-based encryption from the weil pairing. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 213–229. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  5. 5.
    Boneh, D., Papakonstantinou, P., Rackoff, C., Vahlis, Y., Waters, B.: On the impossibility of basing identity based encryption on trapdoor permutations. In: FOCS 2008: Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science, Washington, DC, USA, pp. 283–292. IEEE Computer Society, Los Alamitos (2008)CrossRefGoogle Scholar
  6. 6.
    Canetti, R., Goldreich, O., Goldwasser, S., Micali, S.: Resettable zero-knowledge (extended abstract). In: STOC 2000: Proceedings of the thirty-second annual ACM symposium on Theory of computing, pp. 235–244. ACM, New York (2000)CrossRefGoogle Scholar
  7. 7.
    Diffie, W., Hellman, M.: New directions in cryptography. IEEE Transactions on Information Theory 22(6), 644–654 (1976)MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Dolev, D., Dwork, C., Naor, M.: Non-malleable cryptography. In: STOC 1991: Proceedings of the twenty-third annual ACM symposium on Theory of computing, pp. 542–552. ACM, New York (1991)CrossRefGoogle Scholar
  9. 9.
    Dolev, D., Dwork, C., Naor, M.: Nonmalleable cryptography. SIAM Review 45(4), 727–784 (2003)MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Gennaro, R., Gertner, Y., Katz, J., Trevisan, L.: Bounds on the efficiency of generic cryptographic constructions. SIAM J. Comput. 35(1), 217–246 (2005)MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Gertner, Y., Kannan, S., Malkin, T., Reingold, O., Viswanathan, M.: The relationship between public key encryption and oblivious transfer. In: FOCS 2000: Proceedings of the 41st Annual Symposium on Foundations of Computer Science, Washington, DC, USA, p. 325. IEEE Computer Society, Los Alamitos (2000)Google Scholar
  12. 12.
    Gertner, Y., Malkin, T., Reingold, O.: On the impossibility of basing trapdoor functions on trapdoor predicates. In: FOCS 2001: Proceedings of the 42nd IEEE symposium on Foundations of Computer Science, Washington, DC, USA, p. 126. IEEE Computer Society, Los Alamitos (2001)Google Scholar
  13. 13.
    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
  14. 14.
    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
  15. 15.
    Impagliazzo, R., Rudich, S.: Limits on the provable consequences of one-way permutations. In: STOC 1989: Proceedings of the twenty-first annual ACM symposium on Theory of computing, pp. 44–61. ACM, New York (1989)CrossRefGoogle Scholar
  16. 16.
    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
  17. 17.
    Rosen, A., Segev, G.: Chosen-ciphertext security via correlated products. In: Reingold, O. (ed.) TCC 2009. LNCS, vol. 5444, pp. 419–436. Springer, Heidelberg (2009)Google Scholar
  18. 18.
    Simon, D.R.: Finding collisions on a one-way street: Can secure hash functions be based on general assumptions? In: Nyberg, K. (ed.) EUROCRYPT 1998. LNCS, vol. 1403, pp. 334–345. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  19. 19.
    Vahlis, Y.: Two is a crowd? a black-box separation of one-wayness and security under correlated inputs (2009), http://www.cs.toronto.edu/~evahlis

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Yevgeniy Vahlis
    • 1
  1. 1.University of TorontoCanada

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