12.5. The field wrappers🔗

Fixing an irreducible modulus turns the packed polynomial ring into a field. Hex.GF2n is the single-word wrapper for GF(2ⁿ) with n < 64: an element is one UInt64 of coefficients, reduced modulo a monic degree-n modulus, and the type carries the irreducibility proof of that modulus so only genuine fields can be formed. Hex.GF2nPoly is the arbitrary-degree counterpart, backed by a full GF2Poly rather than a single word. Both expose the field operations (addition, multiplication, inverse, division) and a square-and-multiply exponentiation Hex.GF2n.pow.