Add extension_degree() method to Field (#108)

* Add extension_degree() method to Field

* Update ff/src/fields/mod.rs

Co-authored-by: Pratyush Mishra <pratyushmishra@berkeley.edu>

CHANGELOG.md

@@ -12,6 +12,7 @@
     replacing `x.unitary_inverse()` with `let mut tmp = x.clone(); tmp.conjugate()`
 - #53 (ark-poly) Add `Zero` trait bound to `Polynomial`.
 - #106 (ark-ff, ark-ec) Add `Zeroize` trait bound to `Field, ProjectiveGroup, AffineGroup` traits.
+- #108 (ark-ff) Add `extension_degree()` method to `Field`.
 
 ### Features
 - #20 (ark-poly) Add structs/traits for multivariate polynomials

ff/src/fields/macros.rs

@@ -158,6 +158,10 @@ macro_rules! impl_Fp {
         impl<P: $FpParameters> Field for $Fp<P> {
             type BasePrimeField = Self;
 
+            fn extension_degree() -> u64 {
+                1
+            }
+
             #[inline]
             fn double(&self) -> Self {
                 let mut temp = *self;

ff/src/fields/mod.rs

@@ -115,6 +115,10 @@ pub trait Field:
         Self::BasePrimeField::characteristic()
     }
 
+    /// Returns the extension degree of this field with respect
+    /// to `Self::BasePrimeField`.
+    fn extension_degree() -> u64;
+
     /// Returns `self + self`.
     #[must_use]
     fn double(&self) -> Self;

ff/src/fields/models/cubic_extension.rs

@@ -140,6 +140,10 @@ impl<P: CubicExtParameters> One for CubicExtField<P> {
 impl<P: CubicExtParameters> Field for CubicExtField<P> {
     type BasePrimeField = P::BasePrimeField;
 
+    fn extension_degree() -> u64 {
+        3 * P::BaseField::extension_degree()
+    }
+
     fn double(&self) -> Self {
         let mut result = *self;
         result.double_in_place();

ff/src/fields/models/quadratic_extension.rs

@@ -164,6 +164,10 @@ impl<P: QuadExtParameters> One for QuadExtField<P> {
 impl<P: QuadExtParameters> Field for QuadExtField<P> {
     type BasePrimeField = P::BasePrimeField;
 
+    fn extension_degree() -> u64 {
+        2 * P::BaseField::extension_degree()
+    }
+
     fn double(&self) -> Self {
         let mut result = *self;
         result.double_in_place();