On 3-to-1 and Power APN S-Boxes

  • Deepak Kumar Dalai
Conference paper

DOI: 10.1007/978-3-540-85912-3_33

Part of the Lecture Notes in Computer Science book series (LNCS, volume 5203)
Cite this paper as:
Dalai D.K. (2008) On 3-to-1 and Power APN S-Boxes. In: Golomb S.W., Parker M.G., Pott A., Winterhof A. (eds) Sequences and Their Applications - SETA 2008. SETA 2008. Lecture Notes in Computer Science, vol 5203. Springer, Berlin, Heidelberg


Almost Perfect Nonlinear (APN) S-boxes are used in block ciphers to prevent differential attacks. The non-evidence of permutation APN S-box on even number of variables and the efficiency of power functions bring the importance of power APN S-boxes to use in block ciphers. We present a special class of 3-to-1 S-box (named as S3-to-1 S-box) on even number of variables. The power APN S-boxes on even number of variables fall in this class. Further, another important class of APN functions X3 + tr(X9) too falls in this class. We study some results of S3-to-1 S-boxes. In another section we present a necessary condition for power functions to be APN. Using this necessary condition we can filter out some non-APN power functions. Specifically, if the number of variables is multiple of small primes, then one can filter out many non-APN functions.


S-box Power Function APN Function Differential Cryptanalysis 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Deepak Kumar Dalai
    • 1
  1. 1.Applied Statistics Unit, Indian Statistical InstituteCalcuttaIndia

Personalised recommendations