Advertisement

A Three-Property-Secure Hash Function

  • Elena Andreeva
  • Bart Preneel
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5381)

Abstract

This paper proposes a new hash construction based on the widely used Merkle-Damgård (MD) iteration [13,9]. It achieves the three basic properties required from a cryptographic hash function: collision (Coll), second preimage (Sec) and preimage (Pre) security. We show property preservation for the first two properties in the standard security model and the third Pre security property is proved in the random oracle model. Similar to earlier known hash constructions that achieve a form of Sec (eSec [16]) property preservation [4,17], we make use of fixed key material in the iteration. But while these hashes employ keys of size at least logarithmic in the message length (in blocks), we only need a small constant key size. Another advantage of our construction is that the underlying compression function is instantiated as a keyless primitive.

The Sec security of our hash scheme, however, relies heavily on the standard definitional assumption that the target messages are sufficiently random. An example of a practical application that requires Sec security and satisfies this definitional premise on the message inputs is the popular Cramer-Shoup encryption scheme [8]. Still, in practice we have other hashing applications where the target messages are not sampled from spaces with uniform distribution. And while our scheme is Sec preserving for uniform message distributions, we show that this is not always the case for other distributions.

Keywords

Hash Function Random Oracle Compression Function Message Length Random Oracle Model 
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.
    Andreeva, E., Bouillaguet, C., Fouque, P.-A., Hoch, J.J., Kelsey, J., Shamir, A., Zimmer, S.: Second preimage attacks on dithered hash functions. In: Smart, N.P. (ed.) EUROCRYPT 2008. LNCS, vol. 4965, pp. 270–288. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  2. 2.
    Andreeva, E., Neven, G., Preneel, B., Shrimpton, T.: Seven-property-preserving iterated hashing: ROX. In: Kurosawa, K. (ed.) ASIACRYPT 2007. LNCS, vol. 4833, pp. 130–146. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  3. 3.
    Andreeva, E., Neven, G., Preneel, B., Shrimpton, T.: Seven-property-preserving iterated hashing: ROX. Cryptology ePrint Archive, Report 2007/176 (2007)Google Scholar
  4. 4.
    Bellare, M., Rogaway, P.: Collision-resistant hashing: Towards making uOWHFs practical. In: Kaliski Jr., B.S. (ed.) CRYPTO 1997. LNCS, vol. 1294, pp. 470–484. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  5. 5.
    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
  6. 6.
    Bellare, M., Ristenpart, T.: Hash functions in the dedicated-key setting: Design choices and MPP transforms. In: Arge, L., Cachin, C., Jurdziński, T., Tarlecki, A. (eds.) ICALP 2007. LNCS, vol. 4596, pp. 399–410. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  7. 7.
    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)CrossRefGoogle Scholar
  8. 8.
    Cramer, R., Shoup, V.: Design and analysis of practical public-key encryption schemes secure against adaptive chosen ciphertext attack. SIAM Journal on Computing 33(1), 167–226 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Damgård, I.B.: A design principle for hash functions. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 416–427. Springer, Heidelberg (1990)Google Scholar
  10. 10.
    Halevi, S., Krawczyk, H.: Strengthening digital signatures via randomized hashing. In: Dwork, C. (ed.) CRYPTO 2006. LNCS, vol. 4117, pp. 41–59. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  11. 11.
    Kelsey, J., Schneier, B.: Second preimages on n-bit hash functions for much less than 2n work. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 474–490. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  12. 12.
    Lai, X., Massey, J.L.: Hash functions based on block ciphers. In: Rueppel, R.A. (ed.) EUROCRYPT 1992. LNCS, vol. 658, pp. 55–70. Springer, Heidelberg (1993)CrossRefGoogle Scholar
  13. 13.
    Merkle, R.C.: One way hash functions and DES. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 428–446. Springer, Heidelberg (1990)Google Scholar
  14. 14.
    NIST. Announcing request for candidate algorithm nominations for a new cryptographic hash algorithm (sha–3) family (2007), http://csrc.nist.gov/groups/ST/hash
  15. 15.
    Rogaway, P.: Formalizing human ignorance. In: Nguyên, P.Q. (ed.) VIETCRYPT 2006. LNCS, vol. 4341, pp. 211–228. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  16. 16.
    Rogaway, P., Shrimpton, T.: Cryptographic hash-function basics: Definitions, implications, and separations for preimage resistance, second-preimage resistance, and collision resistance. In: Roy, B., Meier, W. (eds.) FSE 2004. LNCS, vol. 3017, pp. 371–388. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  17. 17.
    Shoup, V.: A composition theorem for universal one-way hash functions. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 445–452. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  18. 18.
    Wang, X., Yu, H.: How to break MD5 and other hash functions. In: Cramer, R. (ed.) EUROCRYPT 2005, vol. 3494, pp. 19–35. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  19. 19.
    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)CrossRefGoogle Scholar
  20. 20.
    Wang, X., Yu, H., Yin, Y.L.: Efficient collision search attacks on SHA-0. In: Shoup, V. (ed.) CRYPTO 2005. LNCS, vol. 3621, pp. 1–16. Springer, Heidelberg (2005)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Elena Andreeva
    • 1
  • Bart Preneel
    • 1
  1. 1.SCD-COSIC, Dept. of Electrical EngineeringKatholieke UniversiteitLeuven

Personalised recommendations