Arithmetic Walsh Transform of Quadratic Boolean Functions

(Extended Abstract)
  • Andrew Klapper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7280)


Recently an arithmetic or “with carry” analog of the Walsh-Hadamard transform of Boolean functions was defined. In this paper we compute the arithmetic Walsh transforms of quadratic functions. We find that, as with traditional Walsh-Hadamard transform, the arithmetic Walsh spectrum of quadratic functions is very flat.


Boolean function Walsh transform block cipher stream cipher 2-adic 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Cusick, T., Stănică, P.: Bounds on the number of functions satisfying the strict avalanche criterion. Inf. Proc. Lett. 60, 215–219 (1996)CrossRefGoogle Scholar
  2. 2.
    Klapper, A.: Cross-Correlations of Geometric Sequences in Characteristic Two. Designs, Codes, and Cryptography 3, 347–377 (1993)MathSciNetMATHCrossRefGoogle Scholar
  3. 3.
    Klapper, A., Goresky, M.: A With-Carry Walsh Transform (Extended Abstract). In: Carlet, C., Pott, A. (eds.) SETA 2010. LNCS, vol. 6338, pp. 217–228. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  4. 4.
    Klapper, A., Goresky, M.: Arithmetic Correlations and Walsh Transforms. IEEE Trans. Info. Theory 58, 479–492 (2012)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Lidl, R., Niederreiter, H.: Finite Fields. Encyclopedia of Mathematics, vol. 20. Cambridge University Press, Cambridge (1983)MATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Andrew Klapper
    • 1
  1. 1.Dept. of Computer ScienceUniversity of KentuckyUSA

Personalised recommendations