Wuhan University Journal of Natural Sciences

, Volume 11, Issue 6, pp 1862–1864 | Cite as

Walsh spectrum properties of rotation symmetric boolean function

  • Wang Yongjuan
  • Han Wenbao
  • Li Shiqu
Applications of Information Security


Rotation symmetric function was presented by Pieprzyk. The algebraic configuration of rotation symmetric(RotS) function is special. For a RotSn variables functionf(x 1,x2,···,xn) we havef(π n k (x1,x2,···,xn)=f(x 1,x2,···,xn) fork=0,1,…n−1. In this paper, useing probability method we find that when the parameters of RotS function is under circular translation of indices, its walsh spectrum is invariant. And we prove the result is both sufficient and necessary.

Key words

rotation symmetric function rotation shift Walsh spectra 

CLC number

TN 918 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Pieprzyk J, Qu C X. Fast Hashing and Rotation Symmetric Function[J].Journal Universal Computer Science, 1999 (1):20–31.MathSciNetGoogle Scholar
  2. [2]
    Cusick W, Stanica P, Maitra S. Fast Evaluation, Weight and Nonlinearity of Rotation-Symmetric Function[J].Discrete Mathematics, 2002,258(1–3):289–301.MATHCrossRefMathSciNetGoogle Scholar
  3. [3]
    Dailai D K, Gupta K C, Maitra S. Results on Algebraic Immunity for Cryptographically Significant Boolean Functions [C]//5th International Corference on Cryptology in India. Chennai, India, Dec. 20–22, 2004.Google Scholar
  4. [4]
    Hell M, Maximov A, Maitra S. On Efficient Implementation of Search Strategy for Rotation Symmetric Boolean Functions [C]//Ninth International Workshop on Algebraic and Combinatoral Coding Theory, ACCT 2004, Black Sea Coast, Bulgaria, June 19–25, 2004.Google Scholar
  5. [5]
    Maximov A, Hell M, Maitra S. Plateaued Rotation Symmetric Boolean Functions on Odd Number of Variables[EB/OL]. [2005-12-20]. Google Scholar
  6. [6]
    Maximov A. Classes of Plateaued Rotation Symmetric Boolean Functions under Transformation of Walsh Spectra[EB/OL]. [2005-12-29]. Google Scholar
  7. [7]
    Clark J, Jacob J, Maitra S,et al. Almost Boolean Functions: The Design of Boolean Functions By Spectral Inversion [J].Computational intelligence, 2004, (3):450–462.CrossRefMathSciNetGoogle Scholar
  8. [8]
    Moriai S, Shinmoyama T, Kaneko T. Higher Order Differential Attack Using Chosen Higher Order Differences. In Selected Areas in Cryptography-SAC'98 (LNCS 1556), Berlin: Springer Verlag, 1999:106–117.CrossRefGoogle Scholar
  9. [9]
    Stanica, maitra. S. Rotation Symmetric Boolean function Count and Cryptographic Properties[EB/OL]. [2005-10-11]. Scholar
  10. [10]
    Li Shiqu, Zeng Bensheng,et al. Logic Functions in Cryptography[M]. Beijing: Zhongruan Electric Publishing Company 2003(Ch).Google Scholar

Copyright information

© Springer 2006

Authors and Affiliations

  1. 1.Institute of Information EngineeringInformation Engineering UniversityZhengzhou, HenanChina

Personalised recommendations