The field of prime order:

has some nice properties for ZK proofs, notably STARKs.

The order of is , which is equal to:

This means that the field has a th root of unity, which is very useful.

is generated by:

And taking gives us our root of unity:

Extensions

is an irreducible polynomial of degree 2 in

is an irreducible polynomial of degree 3 in

We can use these to define and , respectively, giving us fields of size and bits.

Addendum

Shotouts to @mjos_crypto for finding a smaller root of unity:

(https://twitter.com/mjos_crypto/status/1565438293717786625)