Advertisement

On the construction of highly nonlinear permutations

  • Kaisa Nyberg
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 658)

Abstract

Highly nonlinear permutations play an important role in the design of cryptographic transformations such as block ciphers, hash functions and stream ciphers. The substitution boxes of DES are relatively small in dimension and they can be generated by testing randomly chosen functions for required design criteria. Security may be increased by the use of substitution transformations of higher dimensions. But when the dimensions grow larger, analytic construction methods become necessary.

Keywords

Quadratic Form Hash Function Finite Field Linear Structure Coordinate Function 
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.
    C. Carlet, Partially-bent functions, Codes, Designs and Cryptography (to appear).Google Scholar
  2. 2.
    X. Lai, Linear structures of functions over prime fields, Unpublished preprint (1990).Google Scholar
  3. 3.
    R. Lidl and H. Niederreiter, “Finite fields,” Encyclopedia of Mathematics and its applications, Vol. 20. Addison-Wesley, Reading, Massachusetts, 1983.Google Scholar
  4. 4.
    T. Matsumoto and H. Imai, Public quadratic polynomial-tuples for efficient signature-verification and message-encryption, Advances in Cryptology Eurocrypt’ 88. Lecture Notes in Computer Science, Springer-Verlag, 1989.Google Scholar
  5. 5.
    K. Nyberg, Constructions of bent functions and difference sets, Advances in Cryptology — Proceedings of Eurocrypt’ 90. Lecture Notes in Computer Science 473, Springer-Verlag, 1991.Google Scholar
  6. 6.
    J. Pieprzyk, On bent permutations, Technical Report CS91/11; The University of New South Wales, Department of Computer Science. Presented at the International Conference on Finite Fields, Coding Theory and Advances in Communications and Computing, Las Vegas, 1991.Google Scholar
  7. 7.
    B. Preneel et al., Cryptographic properties of quadratic Boolean functions, International Conference on Finite Fields, Coding Theory and advances in Communications and Computing, Las Vegas, 1991; Boolean functions satisfying higher order propagation criteria, Advances in Cryptology — Eurocrypt’ 91. Lecture Notes in Computer Science 547, Springer-Verlag, 1991.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Kaisa Nyberg
    • 1
  1. 1.Finnish Defence ForcesUniversity of HelsinkiFinland

Personalised recommendations