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A Construction for One Way Hash Functions and Pseudorandom Bit Generators

  • Babak Sadeghiyan
  • Josef Pieprzyk
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 547)

Abstract

We prove that if f is a n-bit one-way permutation, i.e., it has some hard bits, a one-way permutation with n − k provably simultaneous hard bits can be constructed with it. We apply this construction to improve the efficiency of Blum-Micali pseudo-random bit generator. Then, we apply the construction to propose a new approach for building universal one-way hash functions. This approach merges Damgard’s design principle (or Merkle’s meta-method) and the method proposed by Zheng, Matsumoto and Imai for the construction of hash functions for long messages.

Keywords

Hash Function Signature Scheme Input String Probabilistic Algorithm Output String 
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]
    Selim G. Akl. On the security of compressed encoding. In Advances in Cryptology-CRYPTO’ 83, pages 209–230. Plenum Publishing Corporation, 1983.Google Scholar
  2. [2]
    W. Alexi, B. Chor, O. Goldreich, and C. P. Schnorr. RSA and Rabin functions: Certain parts are as hard as the whole. SIAM Journal on Computing, 17(2):194–209, 1988.zbMATHCrossRefMathSciNetGoogle Scholar
  3. [3]
    M. Blum and S. Micali. How to generate cryptographically strong sequences of pseudo-random bits. SIAM Journal on Computing, 13(4):850–864, 1984.zbMATHCrossRefMathSciNetGoogle Scholar
  4. [4]
    L. Brown. A proposed design for an extended DES. In Computer Security in the Age of Information. North-Holland, 1989. Proceedings of the Fifth IFIP International Conference on computer Security, IFIP/Sec’ 88.Google Scholar
  5. [5]
    J. L. Carter and M. N. Wegman. Universal classes of hash functions. Journal of Computer and System Sciences, 18:143–154, 1979.zbMATHCrossRefMathSciNetGoogle Scholar
  6. [6]
    D. Coppersmith. Analysis of ISO/CCITT Document X.509 Annex D, 1989.Google Scholar
  7. [7]
    I. B. Damgard. Collision free hash functions and public key signature schemes. In Advances in Cryptology-EUROCRYPT’ 87, volume 304 of Lecture Notes in Computer Science, pages 203–216. Springer-Verlag, 1987.Google Scholar
  8. [8]
    I. B. Damgard. A design principle for hash functions. In Advances in Cryptology-CRYPTO’ 89, volume 435 of Lecture Notes in Computer Science, pages 416–427. Springer-Verlag, 1989.Google Scholar
  9. [9]
    D. E. Denning. Digital signatures with RSA and other public-key cryptosystems. Communications of the ACM, 27(4):388–392, 1984.CrossRefMathSciNetGoogle Scholar
  10. [10]
    M. Girault. Hash-functions using modulo-n operations. In Advances in Cryptology-EUROCRYPT’ 87, volume 304 of Lecture Notes in Computer Science, pages 218–226. Springer-Verlag, 1987.Google Scholar
  11. [11]
    O. Goldreich, S. Goldwasser, and S. Micali. How to construct random functions. Journal of the ACM, 33(4):792–807, 1986.CrossRefMathSciNetGoogle Scholar
  12. [12]
    O. Goldreich and L. A. Levin. A hard-core predicate for all one-way functions. In the 21st ACM Symposium on Theory of Computing, pages 25–32, 1989.Google Scholar
  13. [13]
    R. Impagliazzo, L. A. Levin, and M. Luby. Pseudo-random generation from one-way functions. In the 21st ACM Symposium on Theory of Computing, pages 12–24, 1989.Google Scholar
  14. [14]
    W. De Jonge and D. Chaum. Attacks on some RSA signatures. In Advances in Cryptology-CRYPTO’ 85, volume 218 of Lecture Notes in Computer Science, pages 18–27. Springer-Verlag, 1985.CrossRefGoogle Scholar
  15. [15]
    W. De Jonge and D. Chaum. Some variations on RSA signatures and their security. In Advances in Cryptology-CRYPTO’ 86, volume 263 of Lecture Notes in Computer Science, pages 49–59. Springer-Verlag, 1986.Google Scholar
  16. [16]
    R. R. Jueneman. Electronic document authentication. IEEE Network Magazine, 1(2):17–23, 1987.Google Scholar
  17. [17]
    J. B. Kam and G. I. Davida. Structured design of substitution-permutation encryption networks. IEEE Transactions on Computers, 28(10):747–753, 1979.zbMATHCrossRefMathSciNetGoogle Scholar
  18. [18]
    S. M. Matyas, C. H. Meyer, and J. Oseas. Generating strong one-way functions with cryptographic algorithm. IBM Technical Disclosure Bulletin, 27(10A):5658–5659, 1985.Google Scholar
  19. [19]
    R. C. Merkle. One way hash functions and DES. In Advances in Cryptology-CRYPTO’ 89, volume 435 of Lecture Notes in Computer Science, pages 428–446. Springer-Verlag, 1989.Google Scholar
  20. [20]
    S. Miyaguchi, K. Ohta, and M. Iwata. Confirmation that some hash functions are not collision free. In Abstracts of EUROCRYPT’ 90, pages 293–308, 1990.Google Scholar
  21. [21]
    J. H. Moore. Protocol failures in cryptosystems. Proceedings of the IEEE, 76(5):594–601, 1988.CrossRefGoogle Scholar
  22. [22]
    Moni Naor and Moti Yung. Universal one-way hash functions and their cryptographic applications. In the 21st ACM Symposium on Theory of Computing, pages 33–43, 1989.Google Scholar
  23. [23]
    J. Quisquater and M. Girault. 2n-bit hash functions using n-bit symmetric block cipher algorithms. In Abstracts of EUROCRYPT’ 89, 1989.Google Scholar
  24. [24]
    J. Rompel. One-way functions are necessary and sufficient for secure signatures. In the 22nd ACM Symposium on Theory of Computing, pages 387–394, 1990.Google Scholar
  25. [25]
    A. De Santis and M. Yung. On the design of provably-secure cryptographic hash functions. In Abstracts of EUROCRYPT’ 90, pages 377–397, 1990.Google Scholar
  26. [26]
    A. F. Webster and S. E. Tavares. On the design of S-boxes. In Advances in Cryptology-CRYPTO’ 85, Lecture Notes in Computer Science, pages 523–534. Springer-Verlag, 1985.Google Scholar
  27. [27]
    M. N. Wegman and J. L. Carter. New hash functions and their use in authentication and set equality. Journal of Computer and System Sciences, 22:265–279, 1981.zbMATHCrossRefMathSciNetGoogle Scholar
  28. [28]
    R. S. Winternitz. Producing a one-way hash function from DES. In Advances in Cryptology-CRYPTO’ 83, pages 203–207. Plenum Publishing Corporation, 1983.Google Scholar
  29. [29]
    R. S. Winternitz. A secure one-way hash function built from DES. In the 1984 IEEE Symposium on Security and Privacy, 1984.Google Scholar
  30. [30]
    A. C. Yao. Theory and applications of trapdoor functions. In the 23rd IEEE Symposium on the Foundations of Computer Science, pages 80–91, 1982.Google Scholar
  31. [31]
    Y. Zheng, T. Matsumoto, and H. Imai. Duality between Two Cryptographic Primitives. In the 8th International Conference on Applied Algebra, Algebraic Algorithms and Error Correcting Codes, page 15, 1990.Google Scholar
  32. [32]
    Y. Zheng, T. Matsumoto, and H. Imai. Structural properties of one-way hash-functions. In CRYPTO’ 90, pages 263–280, 1990.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Babak Sadeghiyan
    • 1
  • Josef Pieprzyk
    • 1
  1. 1.Department of Computer Science, University College, University of New South WalesAustralian Defence Force AcademyCanberraAustralia

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