When developing algorithms for Galois field computation on small Galois fields, a common performance optimization approach is to find a generator g and use the identity:
to implement multiplication as a sequence of table look ups for the logg(x) and g(x) functions and an integer addition operation[1]. This exploits the property that all finite fields contain generators. In the Rijndael field example, the polynomial x + 1 (or {03}) is one such generator, since it is irreducible.
