Advertisement

Building a Collision-Resistant Compression Function from Non-compressing Primitives

(Extended Abstract)
  • Thomas Shrimpton
  • Martijn Stam
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5126)

Abstract

We consider how to build an efficient compression function from a small number of random, non-compressing primitives. Our main goal is to achieve a level of collision resistance as close as possible to the optimal birthday bound. We present a 2n-to-n bit compression function based on three independent n-to-n bit random functions, each called only once. We show that if the three random functions are treated as black boxes then finding collisions requires Θ(2n/2/n c ) queries for c ≈ 1. This result remains valid if two of the three random functions are replaced by a fixed-key ideal cipher in Davies-Meyer mode (i.e., E K (x) ⊕ x for permutation E K ). We also give a heuristic, backed by experimental results, suggesting that the security loss is at most four bits for block sizes up to 256 bits. We believe this is the best result to date on the matter of building a collision-resistant compression function from non-compressing functions. It also relates to an open question from Black et al. (Eurocrypt’05), who showed that compression functions that invoke a single non-compressing random function cannot suffice.

Keywords

Hash Functions Random Oracle Model Compression Functions Collision Resistance 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Bellare, M., Micciancio, D.: A new paradigm for collision-free hashing: incrementality at reduced cost. In: Fumy, W. (ed.) EUROCRYPT 1997. LNCS, vol. 1233, pp. 163–192. Springer, Heidelberg (1997)Google Scholar
  2. 2.
    Bellare, M., Ristenpart, T.: Multi-property-preserving hash domain extension and the EMD transform. In: Lai, X., Chen, K. (eds.) ASIACRYPT 2006. LNCS, vol. 4284, pp. 299–314. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  3. 3.
    Bernstein, D.: The Rumba20 compression function (2007), http://cr.yp.to/rumba20.html
  4. 4.
    Black, J., Cochran, M., Shrimpton, T.: On the impossibility of highly efficient blockcipher-based hash functions. In: Cramer, R.J.F. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 526–541. Springer, Heidelberg (2005)Google Scholar
  5. 5.
    Black, J., Rogaway, P., Shrimpton, T.: Black-box analysis of the block-cipher-based hash-function constructions from PGV. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol. 2442. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  6. 6.
    Damgård, I.: A design principle for hash functions. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435. Springer, Heidelberg (1990)Google Scholar
  7. 7.
    Gauravaram, P., Millan, W., Dawson, E., Viswanathan, K.: Constructing secure hash functions by enhancing Merkle-Damgård construction. In: Batten, L.M., Safavi-Naini, R. (eds.) ACISP 2006. LNCS, vol. 4058, pp. 407–420. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  8. 8.
    Gladman, B.: Implementation experience with AES candidate algorithms. In: Second AES Conference (1999)Google Scholar
  9. 9.
    Hirose, S.: Provably secure double-block-length hash functions in a black-box model. In: Park, C.-s., Chee, S. (eds.) ICISC 2004. LNCS, vol. 3506, pp. 330–342. Springer, Heidelberg (2005)Google Scholar
  10. 10.
    Joux, A.: Multicollisions in iterated hash functions. Application to cascaded constructions. In: Franklin, M.K. (ed.) Advances in Cryptology – CRYPTO 2004. LNCS, vol. 3621, pp. 306–316. Springer, Heidelberg (2004)Google Scholar
  11. 11.
    Matyas, S., Meyer, C., Oseas, J.: Generating strong one-way functions with cryptographic algorithms. IBM Technical Disclosure Bulletin 27(10a), 5658–5659 (1985)Google Scholar
  12. 12.
    Maurer, U., Tessaro, S.: Domain extension of public random functions: Beyond the birthday barrier. In: Menezes, A. (ed.) CRYPTO 2007. LNCS, vol. 4622, pp. 187–204. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  13. 13.
    Menezes, A., van Oorschot, P., Vanstone, S.: Handbook of Applied Cryptography. CRC Press, Boca Raton (1996)Google Scholar
  14. 14.
    Merkle, R.: One way hash functions and DES. In: Brassard, G. (ed.) Advances in Cryptology – CRYPTO 1989. LNCS, vol. 435, pp. 428–466. Springer, Heidelberg (1990)Google Scholar
  15. 15.
    Miyaguchi, S., Iwata, M., Ohta, K.: New 128-bit hash function. In: Proceedings 4th International Joint Workshop on Computer Communications, pp. 279–288 (1989)Google Scholar
  16. 16.
    Peyrin, T., Gilbert, H., Muller, F., Robshaw, M.: Combining compression functions and block cipher-based hash functions. In: Lai, X., Chen, K. (eds.) ASIACRYPT 2006. LNCS, vol. 4284, pp. 315–331. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  17. 17.
    Preneel, B., Govaerts, R., Vandewalle, J.: On the power of memory in the design of collision resistant hash functions. In: Seberry, J., Zheng, Y. (eds.) AUSCRYPT 1992. LNCS, vol. 718, pp. 105–121. Springer, Heidelberg (1993)Google Scholar
  18. 18.
    Preneel, B., Govaerts, R., Vandewalle, J.: Hash functions based on block ciphers: A synthetic approach. In: Stinson, D.R. (ed.) CRYPTO 1993. LNCS, vol. 773, pp. 368–378. Springer, Heidelberg (1994)Google Scholar
  19. 19.
    Rogaway, P., Steinberger, J.: How to build a permutation-based hash function (manuscript, 2008)Google Scholar
  20. 20.
    Rogaway, P., Steinberger, J.: Security/efficiency tradeoffs for permutation-based hashing. In: Smart, N. (ed.) EUROCRYPT 2008. LNCS, vol. 4965, pp. 220–236. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  21. 21.
    Shrimpton, T., Stam, M.: Building a collision-resistant compression function from non-compressing primitives. Technical Report 409, IACR e-print (2007)Google Scholar
  22. 22.
    Wagner, D.: A generalized birthday problem. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol. 2442, pp. 288–303. Springer, Heidelberg (2002)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Thomas Shrimpton
    • 1
  • Martijn Stam
    • 2
  1. 1.University of Lugano and Portland State University 
  2. 2.EPFL 

Personalised recommendations