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Non-trivial Black-Box Combiners for Collision-Resistant Hash-Functions Don’t Exist

  • Krzysztof Pietrzak
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4515)

Abstract

A (k,ℓ)-robust combiner for collision-resistant hash-functions is a construction which from ℓ hash-functions constructs a hash-function which is collision-resistant if at least k of the components are collision-resistant. One trivially gets a (k,ℓ)-robust combiner by concatenating the output of any ℓ− k + 1 of the components, unfortunately this is not very practical as the length of the output of the combiner is quite large. We show that this is unavoidable as no black-box (k,ℓ)-robust combiner whose output is significantly shorter than what can be achieved by concatenation exists. This answers a question of Boneh and Boyen (Crypto’06).

Keywords

Hash Function Oblivious Transfer Oracle Query Private Information Retrieval Output Length 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Asmuth, C.A., Blakley, G.R.: An efficient algorithm for constructing a cryptosystem which is harder to break than two other cryptosystems. Computers and Mathematics with Applications, 447–450 (1981)Google Scholar
  2. 2.
    Boneh, D., Boyen, X.: On the impossibility of efficiently combining collision resistant hash functions. In: Dwork, C. (ed.) CRYPTO 2006. LNCS, vol. 4117, pp. 570–583. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  3. 3.
    Contini, S., Lenstra, A.K., Steinfeld, R.: VSH, an efficient and provable collision-resistant hash function. In: Vaudenay, S. (ed.) EUROCRYPT 2006. LNCS, vol. 4004, pp. 165–182. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  4. 4.
    Coron, J.-S., Dodis, Y., Malinaud, C., Puniya, P.: Merkle-Damgård revisited: How to construct a hash function. In: Shoup, V. (ed.) CRYPTO 2005. LNCS, vol. 3621, pp. 430–448. Springer, Heidelberg (2005)Google Scholar
  5. 5.
    Dodis, Y., Katz, J.: Chosen-ciphertext security of multiple encryption. In: Kilian, J. (ed.) TCC 2005. LNCS, vol. 3378, pp. 188–209. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  6. 6.
    Even, S., Goldreich, O.: On the power of cascade ciphers. ACM Trans. Comput. Syst. 3(2), 108–116 (1985)CrossRefGoogle Scholar
  7. 7.
    Harnik, D., Kilian, J., Naor, M., Reingold, O., Rosen, A.: On robust combiners for oblivious transfer and other primitives. In: Cramer, R.J.F. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 96–113. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  8. 8.
    Herzberg, A.: On tolerant cryptographic constructions. In: Menezes, A. (ed.) CT-RSA 2005. LNCS, vol. 3376, pp. 172–190. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  9. 9.
    Joux, A.: Multicollisions in iterated hash functions. application to cascaded constructions. In: Franklin, M. (ed.) CRYPTO 2004. LNCS, vol. 3152, pp. 306–316. Springer, Heidelberg (2004)Google Scholar
  10. 10.
    Katz, J., Koo, C.-Y.: On constructing universal one-way hash functions from arbitrary one-way functions. Cryptology ePrint Archive: Report 2005/328 (2005)Google Scholar
  11. 11.
    Maurer, U.M., Massey, J.L.: Cascade ciphers: The importance of being first. J. Cryptology 6(1), 55–61 (1993)zbMATHCrossRefGoogle Scholar
  12. 12.
    Meier, R., Przydatek, B.: On robust combiners for private information retrieval and other primitives. In: Dwork, C. (ed.) CRYPTO 2006. LNCS, vol. 4117, pp. 555–569. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  13. 13.
    Meier, R., Przydatek, B., Wullschleger, J.: Robuster combiners for oblivious transfer. In: Vadhan, S.P. (ed.) TCC 2007. LNCS, vol. 4392, pp. 404–418. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  14. 14.
    Naor, M., Yung, M.: Universal one-way hash functions and their cryptographic applications. In: STOC, pp. 33–43 (1989)Google Scholar
  15. 15.
    Rogaway, P.: Formalizing human ignorance: Collision-resistant hashing without the keys. Cryptology ePrint Archive: Report 2006/281 (2006)Google Scholar
  16. 16.
    Rompel, J.: One-way functions are necessary and sufficient for secure signatures. In: STOC, pp. 387–394 (1990)Google Scholar
  17. 17.
    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
  18. 18.
    Wang, X., Yin, Y.L., Yu, H.: Finding collisions in the full sha-1. In: Shoup, V. (ed.) CRYPTO 2005. LNCS, vol. 3621, pp. 17–36. Springer, Heidelberg (2005)Google Scholar
  19. 19.
    Wang, X., Yu, H.: How to break md5 and other hash functions. In: Cramer, R.J.F. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 19–35. Springer, Heidelberg (2005)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Krzysztof Pietrzak
    • 1
  1. 1.CWIAmsterdam

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