A compact realisation of the multiplicative inverse function in the finite field $\mathbb F_{2^{16}}$

In the paper, the well-known method for compact realization of the multiplicative inverse function in the field $\mathbb F_{2^8}$ is researched and expanded to the $\mathbb F_{2^{16}}$ field. We have got a size estimation for the multiplicative inverse function in the $\mathbb F_{2^{16}}$ field and proved a theorem showing that there exists a compact realization of the multiplicative inverse function in the field $\mathbb F_{2^{16}}$ that uses for its calculations at most 336 XORs and 189 ANDs, or 777 GE.