New CPUs have special instructions that can do 64 bit binary field operations efficiently (the main requirement for this is to have a carryless multiplication). This gets rid of the logarithm lookup tables to compute field multiplications. This benchmark written by @kilic and @saitima shows that this is 4x faster than the 16 bit lookup table approach (it can do a 64 bit operation in the same time it takes to do 16 bit operations using lookup tables)

https://github.com/kilic/gf

This indicates we should switch to 64 bit field elements to improve performance.