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).
Chapter PDF
Similar content being viewed by others
Keywords
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
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)
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)
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)
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)
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)
Even, S., Goldreich, O.: On the power of cascade ciphers. ACM Trans. Comput. Syst. 3(2), 108–116 (1985)
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)
Herzberg, A.: On tolerant cryptographic constructions. In: Menezes, A. (ed.) CT-RSA 2005. LNCS, vol. 3376, pp. 172–190. Springer, Heidelberg (2005)
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)
Katz, J., Koo, C.-Y.: On constructing universal one-way hash functions from arbitrary one-way functions. Cryptology ePrint Archive: Report 2005/328 (2005)
Maurer, U.M., Massey, J.L.: Cascade ciphers: The importance of being first. J. Cryptology 6(1), 55–61 (1993)
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)
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)
Naor, M., Yung, M.: Universal one-way hash functions and their cryptographic applications. In: STOC, pp. 33–43 (1989)
Rogaway, P.: Formalizing human ignorance: Collision-resistant hashing without the keys. Cryptology ePrint Archive: Report 2006/281 (2006)
Rompel, J.: One-way functions are necessary and sufficient for secure signatures. In: STOC, pp. 387–394 (1990)
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)
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)
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)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Pietrzak, K. (2007). Non-trivial Black-Box Combiners for Collision-Resistant Hash-Functions Don’t Exist. In: Naor, M. (eds) Advances in Cryptology - EUROCRYPT 2007. EUROCRYPT 2007. Lecture Notes in Computer Science, vol 4515. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72540-4_2
Download citation
DOI: https://doi.org/10.1007/978-3-540-72540-4_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-72539-8
Online ISBN: 978-3-540-72540-4
eBook Packages: Computer ScienceComputer Science (R0)