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.]

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