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

  • Deepak Kumar Dalai
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5203)

Abstract

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.

Keywords

S-box Power Function APN Function Differential Cryptanalysis 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Berger, T.P., Canteaut, A., Charpin, P., Laigle-Chapuy, Y.: Almost Perfect Nonlinear functions. IEEE Trans. Inform. Theory 52(9), 4160–4170 (2006)CrossRefMathSciNetGoogle Scholar
  2. 2.
    Biham, E., Shamir, A.: Differential Cryptanalysis of DES-like Cryptosystem. Journal of Cryptology 4(1), 3–72 (1991)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Budaghyan, L., Carlet, C., Leander, G.: Constructing new APN functions from known ones. Cryptology ePrint Archive: report 2007/063Google Scholar
  4. 4.
    Carlet, C., Charpin, P., Zinoviev, V.: Codes, Bent Functions and Permutations Suitable For DES-like Cryptosystems. Des. Codes Cryptogr. 15(2), 125–156 (1998)MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Charpin, P., Tietävämen, A., Zinoviev, V.: On binary cyclic codes with minimum distance d = 3. Problems Inform. Transmission 33(4), 287–296 (1997)MATHMathSciNetGoogle Scholar
  6. 6.
    Comtet, L.: Advanced combinatorics. Reidel Publication (1974)Google Scholar
  7. 7.
    Nyberg, K., Knudsen, L.R.: Provable security against differential cryptanalysis. In: Brickell, E.F. (ed.) CRYPTO 1992. LNCS, vol. 740, pp. 566–574. Springer, Heidelberg (1993)Google Scholar
  8. 8.
    Nyberg, K.: Differentially uniform mappings for cryptography. In: Helleseth, T. (ed.) EUROCRYPT 1993. LNCS, vol. 765, pp. 55–64. Springer, Heidelberg (1994)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

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

Personalised recommendations