On the algebraic expression of the AES S-box like S-boxes

SAKALLI M. T., Aslan B., Buluş E., Mesut A., Büyüksaraçoǧlu F., Karaahmetoǧlu O.

2nd International Conference on 'Networked Digital Technologies', NDT 2010, Prague, Çek Cumhuriyeti, 7 - 09 Temmuz 2010, cilt.87 CCIS, ss.213-227, (Tam Metin Bildiri) identifier

  • Yayın Türü: Bildiri / Tam Metin Bildiri
  • Cilt numarası: 87 CCIS
  • Doi Numarası: 10.1007/978-3-642-14292-5_23
  • Basıldığı Şehir: Prague
  • Basıldığı Ülke: Çek Cumhuriyeti
  • Sayfa Sayıları: ss.213-227
  • Anahtar Kelimeler: Algebraic Expression, Finite Fields, Power Mappings, S-boxes
  • Trakya Üniversitesi Adresli: Evet

Özet

In the literature, there are several proposed block ciphers like AES, Square, Shark and Hierocrypt which use S-boxes that are based on inversion mapping over a finite field. Because of the simple algebraic structure of S-boxes generated in this way, these ciphers usually use a bitwise affine transformation after the inversion mapping. In some ciphers like Camellia, an additional affine transformation is used before the input of the S-box as well. In this paper, we study algebraic expressions of S-boxes based on power mappings with the aid of finite field theory and show that the number of terms in the algebraic expression of an S-box based on power mappings changes according to the place an affine transformation is added. Moreover, a new method is presented to resolve the algebraic expression of the AES S-box like S-boxes according to the given three probable cases. © 2010 Springer-Verlag.