Yes. These sorts of fields are quite useful for crypto, so I believe there is even some hardware support for them in many CPUs, IIRC?
https://en.wikipedia.org/wiki/CLMUL_instruction_set might be the closest to what you meant?
I just did some Google Scholar searches, and found a lot about FPGAs etc, but not too much about stock CPUs. But that might reflect more on my search skills than on availability of material.
Some standard CPUs now have instructions to specifically run eg AES.
https://www.snia.org/sites/default/files/files2/files2/SDC20... was probably the most interesting of the bunch I found. It's about error correcting codes, not crypto. (Though interestingly, the holy trinity of error correcting codes, information theory and cryptography all flew once through the common conduit of Claude Shannon.)
Technically you can get fields with p^n elements, too; but they are constructed in a more complicated way than just taking a modulo.