Binary finite field extensions for diffusion matrices over the finite field F2m F2msonlu cismi üzerindeki yayilim matrisleri için ikili sonlu cisim genişlemeleri

KURT PEHLİVANOĞLU M., Buyuksaracoglu Sakalli F., Akleylek S., Sakalli M. T.

29th IEEE Conference on Signal Processing and Communications Applications, SIU 2021, Virtual, Istanbul, Turkey, 9 - 11 June 2021 identifier

  • Publication Type: Conference Paper / Full Text
  • Doi Number: 10.1109/siu53274.2021.9477916
  • City: Virtual, Istanbul
  • Country: Turkey
  • Keywords: Binary fields, Diffusion layer, Extension tool, Lightweight cryptography, XOR count
  • Ondokuz Mayıs University Affiliated: Yes

Abstract

In this paper, a new software tool has been developed that computes the corresponding m× m binary matrix over the finite field F2 of each element which is defined over 2m F (where 3 = m = 8 ) generated by different primitive irreducible polynomials. This extension process is necessary for the optimization of XOR (exclusive OR) counts of diffusion matrices whose elements are defined over the finite field, which are used especially in the diffusion layers of block ciphers. Therefore, the corresponding binary matrices given in this study can be used directly for the construction of new diffusion matrices.