(Difficult)
When looking at the laws associated with GF(4), I was unsure on how they determined the relationships between each element in GF(4). Are these laws derived from the structure of the field? That is, can we construct these laws for any GF(2^n) knowing how the field is structured?
(Reflective)
I was amazed at the end of the section that they talked about using fields of GF(2^n) with n around 150 for cryptographic purposes. Every other system we have studied is severely weakened when we place limitations on the field, like when we reduce n in RSA, or reduce p in ElGamal. This left me wondering why this does not leave elliptic systems vulnerable to such attacks like brute force attacks or birthday attacks.
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