Advertisement

On Arithmetic Subtraction Linear Approximation

  • Krzysztof Chmiel
Conference paper

Abstract

In the paper two methods of linear approximation of n-bit arithmetic subtraction function are considered. In the first method, called the model of approximation of a single S-box, approximations are calculated for arbitrary m consecutive bits, where mn is limited by the size of so-called table of pairs TP, used during calculation. In the second method, called the model of exact composition of approximations, the subtraction approximations are calculated as a composition of k approximations of m-bit subtraction cells, where mn is limited by the size of the same table of pairs TP. In the first method, the set of nonzero approximations is limited to approximations in the range of m consecutive bits while in the second method is not limited. For n-bit arithmetic subtraction function however, the approximation probability can be calculated with use of the methods in time O(l) and O(k), respectively.

Key words

Cryptanalysis linear approximation arithmetic subtraction function 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Biham E., Shamir A. 1993. ‘Differential Cryptanalysis of the Data Encryption Standard’. Springer-Verlag, New York.Google Scholar
  2. [2]
    Chmiel K. 1998. ‘Principles of Differential Cryptanalysis through the Example of the DES Algorithm’. (In Polish). Technical Report No. 461. Poznań University of Technology, Chair of Control, Robotics and Computer Science, Poznań (Oct.).Google Scholar
  3. [3]
    Chmiel K. 1999. ‘Principles of Linear Cryptanalysis through the Example of the DES Algorithm’. (In Polish). Technical Report No. 471. Poznań University of Technology, Chair of Control, Robotics and Computer Science, Poznań (Oct.).Google Scholar
  4. [4]
    Chmiel K. 2000. ‘Linear Cryptanalysis of the Reduced DES Algorithms’. Proceedings of the Regional Conference on Military Communication and Information Systems’ 2000 (Zegrze, Oct. 4–6) WIŁ, Zegrze, vol. 1, pp. 111–118.Google Scholar
  5. [5]
    Chmiel K. 2000. ‘Differential Cryptanalysis of the Reduced DES Algorithms’. (In Polish). Studia z Automatyki i Informatyki, vol. 25, pp. 127–146.Google Scholar
  6. [6]
    Chmiel K. 2000. ‘Linear Approximation of S-box Functions’. (In Polish). Technical Report No. 471. Poznań University of Technology, Chair of Control, Robotics and Computer Science, Poznań (Oct.).Google Scholar
  7. [7]
    Chmiel K. 2001. ‘Linear Approximation of some S-box Functions’. Proceedings of the Regional Conference on Military Communication and Information Systems 2001 (Zegrze, Oct. 10–12) WIŁ, Zegrze, vol. 1, pp. 211–218.Google Scholar
  8. [8]
    Chmiel K. 2001. ‘Linear Approximation of Arithmetic Sum’. (In Polish). Technical Report No. 481. Poznań University of Technology, Chair of Control, Robotics and Computer Science, Poznań (Oct.).Google Scholar
  9. [9]
    Chmiel K. 2002. ‘On Some Models of Arithmetic Sum Function Linear Approximation’. Proceedings of NATO Regional Conference on Military Communications and Information Systems 2002 (Zegrze, Oct. 9–11) WIŁ, Zegrze, vol. 2, pp. 199–204.Google Scholar
  10. [10]
    Chmiel K. 2002. ‘Linear Approximation of Arithmetic Sum Function’. Proceedings of the 9-th International Conference on Advanced Computer Systems ACS’ 2002 (Międzyzdroje, Oct. 23–25), Szczecin, vol. 2, pp. 19–28.Google Scholar
  11. [11]
    Górska A., Górski K., Kotulski Z., Paszkiewicz A., Szczepański J. 2001. ‘New Experimental Results in Differential — Linear Cryptanalysis of Reduced Variants of DES’. Proceedings of the 8-th International Conference on Advanced Computer Systems ACS’2001, Mielno, vol. 1, pp. 333–346.Google Scholar
  12. [12]
    Matsui M. 1993. ‘Linear Cryptanalysis Method for DES Cipher’. Advances in Cryptology Eurocrypt’ 93.Google Scholar
  13. [13]
    Matsui M. 1998. ‘Linear Cryptanalysis Method for DES Cipher’. Springer-Verlag, New York.Google Scholar
  14. [14]
    Zugaj A., Górski K., Kotulski Z., Szczepański J., Paszkiewicz A. 1999. ‘Extending Linear Cryptanalysis-Theory and Experiments’. Proceedings of the Regional Conference on Military Communication and Information Systems’ 99 (Zegrze, Oct. 6–8) WIŁ, Zegrze, vol. 2, pp.77–84.Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • Krzysztof Chmiel
    • 1
  1. 1.Poznań University of TechnologyPoznańPoland

Personalised recommendations