Research hardware complexity of multipliers of extended Galois field GF(dm)

Abstract

The paper analyzes the hardware costs of multipliers of extended Galois fields GF(dm). There are compared realised on modern FPGA Galois fields multipliers hardware cost to select Galois field GF(dm) with approximately the same number of elements and the lowest multiplier hardware complexity. 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 for analisys based on Guild cell with realization like single unit corresponds to the value d = 3 and based on Guild cell with its multiplier and adder separate realization – the value d=7.