Binary Finite Field Extensions for Diffusion Matrices over the Finite Field F2m
Meltem Kurt Pehli̇vanoğlu, Fatma Büyüksaraçoğlu Sakallı, Sedat Akleylek, Muharrem Tolga Sakallı · 2021
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.