Advertisement

Duality between two cryptographic primitives

  • Yuliang Zheng
  • Tsutomu Matsumoto
  • Hideki Imai
Submitted Contributions Cryptography
Part of the Lecture Notes in Computer Science book series (LNCS, volume 508)

Abstract

This paper reveals a duality between constructions of two basic cryptographic primitives, pseudo-random string generators and one-way hash functions. Applying the duality, we present a construction for universal one-way hash functions assuming the existence of one-way permutations. Under a stronger assumption, the existence of distinction-intractable permutations, we prove that the construction constitutes a collision-intractable hash function. Using ideas behind the construction, we propose practical one-way hash functions, the fastest of which compress nearly 2n-bit long input into n-bit long output strings by applying only twice a one-way function.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [BM84]
    M. Blum and S. Micali, How to generate cryptographically strong sequences of pseudo-random bits, SIAM J. on Comp. 13 (1984) 850–864.Google Scholar
  2. [BH89]
    R. Boppana and R. Hirschfeld, Pseudorandom generations and complexity classes, in: S. Micali, ed., Randomness and Computation, (JAI Press Inc., 1989) 1–26.Google Scholar
  3. [Dam89]
    I. Damgård, A design principle for hash functions, Presented at Crypto'89 (1989).Google Scholar
  4. [GGM86]
    O. Goldreich, S. Goldwasser and S. Micali, How to construct random functions, J. of ACM 33 (1986) 792–807.Google Scholar
  5. [GM84]
    S. Goldwasser and S. Micali, Probabilistic encryption, J. of Comp. and Sys. Sci. 28 (1984) 270–299.Google Scholar
  6. [ILL89]
    R. Impagliazzo, L. Levin and M. Luby, Pseudo-random generation from one-way functions, Proc. of the 21-th ACM STOC (1989) 12–24.Google Scholar
  7. [IL89]
    R. Impagliazzo and M. Luby, One-way functions are essential for complexity based cryptography, Proc. of the 30-th IEEE FOCS (1989) 230–235.Google Scholar
  8. [Mer89]
    R. Merkle, One way hash functions and DES, Presented at Crypto'89 (1989).Google Scholar
  9. [MSc88]
    S. Micali and C.P. Schnorr, Super-efficient, perfect random number generators, in: S. Goldwasser, ed., Proc. of Crypto'88, (Springer-Verlag, 1990) 173–198.Google Scholar
  10. [NY89]
    M. Naor and M. Yung, Universal one-way hash functions and their cryptographic applications, Proc. of the 21-th ACM STOC (1989) 33–43.Google Scholar
  11. [NS90]
    K. Nishimura and M. Sibuya, Probability to meet in the middle, J. of Cryptology 2 (1990) 13–22.Google Scholar
  12. [WC81]
    M. Wegman and J. Carter, New hash functions and their use in authentication and set equality, J. of Comp. and Sys. Sci. 22 (1981) 265–279.Google Scholar
  13. [Yao82]
    A. Yao, Theory and applications of trapdoor functions, Proc. of the 23-th IEEE FOCS (1982) 80–91.Google Scholar
  14. [ZMI89]
    Y. Zheng, T. Matsumoto and H. Imai, On the construction of block ciphers provably secure and not relying on any unproved hypotheses, Presented at Crypto'89, (1989).Google Scholar
  15. [ZMI90a]
    Y. Zheng, T. Matsumoto and H. Imai, Connections among several versions of one-way hash functions, Proc. of IEICE of Japan E73 (July 1990).Google Scholar
  16. [ZMI90b]
    Y. Zheng, T. Matsumoto and H. Imai, Structural properties of one-way hash functions, Presented at Crypto'90, (1990).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Yuliang Zheng
    • 1
  • Tsutomu Matsumoto
    • 1
  • Hideki Imai
    • 1
  1. 1.Division of Electrical and Computer EngineeringYokohama National UniversityYokohamaJapan

Personalised recommendations