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)