Definition of the extended Galois field GF(dm) with minimal hardware complexity multiplier

Abstract

The paper compared the modern FPGA hardware cost to reduce hardware complexity implement multipliers for Galois field GF(dm) with approximately the same number of elements. Totally the hardware cost increases while basics of the field increase. Local minimums for odd d correspond to d = 2i -1 and the global minimum corresponds to the value d = 7.