I'm a beginner in cryptography, currently focusing on AES GCM, specifically the GF(2^128) multiplier which employs the irreducible polynomial x^128 + x^7 + x^2 + x + 1. I try to explore the transformation of GF(2^128) into composite fields, like GF((2^64)^2) or GF(((2^32)^2)^2), through isomorphic matrices.
However, I'm finding it challenging to understand the practical steps involved in constructing these matrices, within the context of composite fields. I would greatly appreciate guidance on how to approach this matrix construction.
Also, I'm seeking recommendations for keywords, papers, textbooks, or any resources that could deepen my understanding in this area.
Thank you for your time and assistance!
