Comparison of Hardware Complexity of Multipliers $GF(p^{m})$

The article discusses the use of Galois field (GF) multipliers for cryptographic data protection based on elliptical curves. It recommends using extended Galois fields with characteristics$\mathrm{d} > 2$for digital signatures. The article proposes a criterion for determining the best field to use for data protection. It also describes methods for creating cryptoprocessors cores, including a VHDL generator for extended Galois field multipliers. However, generating field multipliers with large characteristics can be time-consuming. To improve efficiency, the article suggests simplifying the design and minimizing logic gates in an FPGA. The article determines the best fields for data protection based on the selected criterion and a certain algorithm.