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Weaknesses in the SL2(\( \mathbb{F}_{2^n } \)) Hashing Scheme

  • Rainer Steinwandt
  • Markus Grassl
  • Willi Geiselmann
  • Thomas Beth
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1880)

Abstract

We show that for various choices of the parameters in the SL2(\( \mathbb{F}_{2^n } \)) hashing scheme, suggested by Tillich and Zémor, messages can be modified without changing the hash value. Moreover, examples of hash functions “with a trapdoor” within this family are given. Due to these weaknesses one should impose at least certain restrictions on the allowed parameter values when using the SL2(\( \mathbb{F}_{2^n } \)) hashing scheme for cryptographic purposes.

Keywords

Hash Function Computer Algebra System Small Order Functional Decomposition Jordan Normal Form 
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.
    K. S. Abdukhalikov and C. Kim, On the Security of the Hashing Scheme Based on SL2, in Fast Software Encryption-FSE’ 98, S. Vaudenay, ed., vol. 1372 of Lecture Notes in Computer Science, Springer, 1998, pp. 93–102.CrossRefGoogle Scholar
  2. 2.
    M. Bellare and D. Micciancio, A New Paradigm for Collision-Free Hashing: Incrementality at Reduced Cost, in Advances in Cryptology-EUROCRYPT’ 97, W. Fumy, ed., vol. 1233 of Lecture Notes in Computer Science, Springer, 1997, pp. 163–192.Google Scholar
  3. 3.
    C. Charnes and J. Pieprzyk, Attacking the SL2 hashing scheme, in Advances in Cryptology-ASIACRYPT’ 94, J. Pieprzyk and R. Safavi-Naini, eds., vol. 917 of Lecture Notes in Computer Science, Springer, 1995, pp. 322–330.CrossRefGoogle Scholar
  4. 4.
    I. B. Damgård, A Design Principle for Hash Functions, in Advances in Cryptology-CRYPTO’ 89, G. Brassard, ed., vol. 435 of Lecture Notes in Computer Science, Springer, 1989, pp. 416–427.Google Scholar
  5. 5.
    W. Geiselmann, A Note on the Hash Function of Tillich and Zemor, in Cryptography and Coding, C. Boyd, ed., vol. 1025 of Lecture Notes in Computer Science, Springer, 1995, pp. 257–263.Google Scholar
  6. 6.
    J. Gutiérrez, T. Recio, and C. Ruiz de Velasco, Polynomial decomposition algorithm of almost quadratic complexity, in Applied Algebra, Algebraic Algorithms and Error-Correcting Codes (AAECC-6), Rome, Italy, 1988, T. Mora, ed., vol. 357 of Lecture Notes in Computer Science, Springer, 1989, pp. 471–475.Google Scholar
  7. 7.
    B. Huppert, Endliche Gruppen I, vol. 134 of Grundlehren der mathematischen Wissenschaften, Springer, 1967. Zweiter Nachdruck der ersten Auflage.Google Scholar
  8. 8.
    D. Kozen and S. Landau, Polynomial Decomposition Algorithms, Journal of Symbolic Computation, 7 (1989), pp. 445–456.zbMATHMathSciNetCrossRefGoogle Scholar
  9. 9.
    B. Preneel, Design principles for dedicated hash functions, in Fast Software Encryption, R. Anderson, ed., vol. 809 of Lecture Notes in Computer Science, Springer, 1994, pp. 71–82.Google Scholar
  10. 10.
    J.-J. Quisquater and M. Joye, Authentication of sequences with the SL2 hash function: Application to video sequences., Journal of Computer Security, 5 (1997), pp. 213–223.Google Scholar
  11. 11.
    J.-P. Tillich and G. Zémor, Hashing with SL2, in Advances in Cryptology-CRYPTO’ 94, Y. Desmedt, ed., vol. 839 of Lecture Notes in Computer Science, Springer, 1994, pp. 40–49.Google Scholar
  12. 12.
    S. Vaudenay, Hidden Collisions on DSS, in Advances in Cryptology-CRYPTO’ 96, N. Koblitz, ed., vol. 1109 of Lecture Notes in Computer Science, Springer, 1996, pp. 83–88.CrossRefGoogle Scholar
  13. 13.
    J. Von zur Gathen, Functional Decomposition of Polynomials: The Tame Case, Journal of Symbolic Computation, 9 (1990), pp. 281–300.zbMATHMathSciNetCrossRefGoogle Scholar
  14. 14.
    -, Functional Decomposition of Polynomials: The Wild Case, Journal of Symbolic Computation, 10 (1990), pp. 437–452.zbMATHMathSciNetCrossRefGoogle Scholar
  15. 15.
    G. Zémor, Hash Functions and Graphs With Large Girths, in Advances in Cryptology-EUROCRYPT’ 91, D. W. Davies, ed., vol. 547 of Lecture Notes in Computer Science, Springer, 1991, pp. 508–511.Google Scholar
  16. 16.
    -, Hash Functions and Cayley Graphs, Designs, Codes and Cryptography, 4 (1994), pp. 381–394.zbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Rainer Steinwandt
    • 1
  • Markus Grassl
    • 1
  • Willi Geiselmann
    • 1
  • Thomas Beth
    • 1
  1. 1.Institut für Algorithmen und Kognitive Systeme, Fakultät für InformatikUniversität KarlsruheKarlsruheGermany

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