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:
- Type I composite field where a subfield in ONB2 and an extension field in ONB1
- Type II composite field where a subfield in ONB1 and an extension field in ONB2
- Type III composite field where a subfield in ONB2 and an extension field 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 and does not put their normal basis types (ONB1 or ONB2) into consideration.
Now the questions are:
- Would it be better if we choose , and in ONB1/ONB2?
- Which polynomial irreducible to be used? With degree = , or degree = or degree = ?
[pounding headache, and without answering these questions i wouldnt be able to start the hw design.]