Simple arithmetic operations (+, -, *, /) over prime/extended fields using polynomial basis. There is no distincion between prime- and extension fields and so no optimization has been done. Furthermore all calculations are done using standard elixir numbers. GF(2^e) will not use any binary operations. An eventual feature update may bring Nx like backends where such optimizations could take place.

Irreducible polynomials are automatically provided for GF(2), GF(3), GF(5), GF(7), GF(11), each with extensions from 1 to 4 (see GF.IrreduciblePolynomials). Custom ones can be provided via the Field contructor.

If available in Hex, the package can be installed by adding galois to your list of dependencies in mix.exs:

def deps do
  [
    {:galois, "~> 0.0.1"}
  ]
end