Sufficient Conditions for Collision-Resistant Hashing

  • Yuval Ishai
  • Eyal Kushilevitz
  • Rafail Ostrovsky
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3378)

Abstract

We present several new constructions of collision-resistant hash-functions (CRHFs) from general assumptions. We start with a simple construction of CRHF from any homomorphic encryption. Then, we strengthen this result by presenting constructions of CRHF from two other primitives that are implied by homomorphic-encryption: one-round private information retrieval (PIR) protocols and homomorphic one-way commitments.

Keywords

Collision-resistant hash functions homomorphic encryption private information-retrieval 

References

  1. 1.
    Barak, B.: How to Go Beyond the Black-Box Simulation Barrier. In: Proc. of 42nd FOCS, pp. 106–115 (2001)Google Scholar
  2. 2.
    Barak, B., Goldreich, O.: Universal Arguments and their Applications. In: Proc. of 17th Conference on Computational Complexity, pp. 194–203 (2002)Google Scholar
  3. 3.
    Beimel, A., Ishai, Y., Kushilevitz, E., Malkin, T.: One-Way Functions Are Essential for Single-Server Private Information Retrieval. In: Proc. of 31st STOC, pp. 89–98 (1999)Google Scholar
  4. 4.
    Cachin, C., Micali, S., Stadler, M.A.: Computationally private information retrieval with polylogarithmic communication. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, p. 402. Springer, Heidelberg (1999)Google Scholar
  5. 5.
    Damgård, I.B.: Collision free hash functions and public key signature schemes. In: Price, W.L., Chaum, D. (eds.) EUROCRYPT 1987. LNCS, vol. 304, pp. 203–216. Springer, Heidelberg (1988)Google Scholar
  6. 6.
    Damgård, I.B., Pedersen, T.P., Pfitzmann, B.: On the existence of statistically hiding bit commitment schemes and fail-stop sigantures. In: Stinson, D.R. (ed.) CRYPTO 1993. LNCS, vol. 773, pp. 250–265. Springer, Heidelberg (1994)Google Scholar
  7. 7.
    Fischlin, M.: On the Impossibility of Constructing Non-interactive Statistically-Secret Protocols from Any Trapdoor One-Way Function. In: Proc. of CT-RSA, pp. 79–95 (2002)Google Scholar
  8. 8.
    Goldreich, O.: Foundations of Cryptography. Basic Tools, vol. I. Cambridge University Press, Cambridge (2001)MATHCrossRefGoogle Scholar
  9. 9.
    Goldreich, O.: Foundations of Cryptography. Basic Applications, vol. II. Cambridge University Press, Cambridge (2004)Google Scholar
  10. 10.
    Goldreich, O., Goldwasser, S., Halevi, S.: Collision-Free Hashing from Lattice Problems. ECCC TR-42 (1996)Google Scholar
  11. 11.
    Goldwasser, S., Micali, S.: Probabilistic Encryption. Journal of Computer and systems sciences 28, 270–299 (1984)MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Halevi, S., Micali, S.: Practical and provably-secure commitment schemes from collision-free hashing. In: Koblitz, N. (ed.) CRYPTO 1996. LNCS, vol. 1109, pp. 201–215. Springer, Heidelberg (1996)Google Scholar
  13. 13.
    Hsiao, C.-Y., Reyzin, L.: Finding collisions on a public road, or do secure hash functions need secret coins? In: Franklin, M. (ed.) CRYPTO 2004. LNCS, vol. 3152, pp. 92–105. Springer, Heidelberg (2004)Google Scholar
  14. 14.
    Kilian, J.: A Note on Efficient Zero-Knowledge Proofs and Arguments. In: Proc. of 24th STOC, pp. 723–732 (1992)Google Scholar
  15. 15.
    Kushilevitz, E., Ostrovsky, R.: Replication is Not Needed: Single Database, Computationally-Private Information Retrieval. In: Proc. of 38th FOCS, pp. 364–373 (1997)Google Scholar
  16. 16.
    Mann, E.: Private access to distributed information. Master’s thesis, Technion – Israel Institute of Technology, Haifa (1998)Google Scholar
  17. 17.
    Micali, S.: CS Proofs. SIAM J. Computing 30(4), 1253–1298 (2000); Early version appeared in FOCS 1994MATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    Ogata, W., Kurosawa, K.: On Claw Free Families. IEICE Trans. E77-A(1), 72–80 (1994); Matsumoto, T., Imai, H., Rivest, R.L. (eds.): ASIACRYPT 1991. LNCS, vol. 739, pp. 72–80. Springer, Heidelberg (1993)Google Scholar
  19. 19.
    Russell, A.: Necessary and Sufficient Conditions for Collision-Free Hashing. J. Cryptology 8(2), 87–100 (1995); Brickell, E.F. (ed.) CRYPTO 1992. LNCS, vol. 740, pp. 433–441. Springer, Heidelberg (1993)Google Scholar
  20. 20.
    Simon, D.R.: Findings 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
  21. 21.
    Stern, J.P.: A new and efficient all-or-nothing disclosure of secrets protocol. In: Ohta, K., Pei, D. (eds.) ASIACRYPT 1998. LNCS, vol. 1514, pp. 357–371. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  22. 22.
    Wang, X., Feng, D., Lai, X., Yu, H.: Collisions for Hash Functions MD4, MD5, HAVAL-128 and RIPEMD. Cryptology ePrint Archive TR-199 (2004)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Yuval Ishai
    • 1
  • Eyal Kushilevitz
    • 1
  • Rafail Ostrovsky
    • 2
  1. 1.Computer Science DepartmentTechnionHaifaIsrael
  2. 2.Computer Science DepartmentUCLA 

Personalised recommendations