## Choosing n and m for composite field

Referring to “Efficient Normal Basis Multipliers in Composite Fields” – Sangho Oh, Chang Han Kim, Jongin Lim, and Dong Hyeon Cheon, there is classification of hardware-applicable composite fields:

1. Type I composite field where a subfield $GF(2^n)$ in ONB2 and an extension field $GF(2^{nm})$ in ONB1
2. Type II composite field where a subfield $GF(2^n)$ in ONB1 and an extension field $GF(2^{nm})$ in ONB2
3. Type III composite field where a subfield $GF(2^n)$ in ONB2 and an extension field $GF(2^{nm})$ in ONB2

This is different with composite fields presented in “Efficient Methods for Composite Field Arithmetic” – E. Sava ̧s and C ̧. K. Koc, where the selection of $n$ and $m$  does not put their normal basis types (ONB1 or ONB2) into consideration.

Now the questions are:

1. Would it be better if we choose $n$, $m$ and $nm$ in ONB1/ONB2?
2. Which polynomial irreducible to be used? With degree = $n$, or degree = $m$ or degree = $nm$?

[pounding headache, and without answering these questions i wouldnt be able to start the hw design.]