Add conversion from base prime field to field

CHANGELOG.md

@@ -44,6 +44,7 @@
     - `SWModelParameters` → `SWCurveConfig`
     - `TEModelParameters` → `TECurveConfig`
     - `MontgomeryModelParameters` → `MontCurveConfig`
+- [\#440](https://github.com/arkworks-rs/algebra/pull/440) (`ark-ff`) Add a method to construct a field element from an element of the underlying base prime field.
 
 ### Features
 

ff/src/fields/mod.rs

@@ -153,6 +153,16 @@ pub trait Field:
     /// If the slice length != Self::extension_degree(), must return None.
     fn from_base_prime_field_elems(elems: &[Self::BasePrimeField]) -> Option<Self>;
 
+    /// Constructs a field element from a single base prime field elements.
+    /// ```
+    /// # use ark_ff::Field;
+    /// # use ark_test_curves::bls12_381::Fq as F;
+    /// # use ark_test_curves::bls12_381::Fq2 as F2;
+    /// # use ark_std::One;
+    /// assert_eq!(F2::from_base_prime_field(F::one()), F2::one());
+    /// ```
+    fn from_base_prime_field(elem: Self::BasePrimeField) -> Self;
+
     /// Returns `self + self`.
     #[must_use]
     fn double(&self) -> Self;

ff/src/fields/models/cubic_extension.rs

@@ -134,11 +134,7 @@ impl<P: CubicExtConfig> CubicExtField<P> {
 
 impl<P: CubicExtConfig> Zero for CubicExtField<P> {
     fn zero() -> Self {
-        Self::new(
-            P::BaseField::zero(),
-            P::BaseField::zero(),
-            P::BaseField::zero(),
-        )
+        Self::new(P::BaseField::ZERO, P::BaseField::ZERO, P::BaseField::ZERO)
     }
 
     fn is_zero(&self) -> bool {
@@ -148,11 +144,7 @@ impl<P: CubicExtConfig> Zero for CubicExtField<P> {
 
 impl<P: CubicExtConfig> One for CubicExtField<P> {
     fn one() -> Self {
-        Self::new(
-            P::BaseField::one(),
-            P::BaseField::zero(),
-            P::BaseField::zero(),
-        )
+        Self::new(P::BaseField::ONE, P::BaseField::ZERO, P::BaseField::ZERO)
     }
 
     fn is_one(&self) -> bool {
@@ -172,6 +164,11 @@ impl<P: CubicExtConfig> Field for CubicExtField<P> {
         3 * P::BaseField::extension_degree()
     }
 
+    fn from_base_prime_field(elem: Self::BasePrimeField) -> Self {
+        let fe = P::BaseField::from_base_prime_field(elem);
+        Self::new(fe, P::BaseField::ZERO, P::BaseField::ZERO)
+    }
+
     fn to_base_prime_field_elements(&self) -> Self::BasePrimeFieldIter {
         self.c0.to_base_prime_field_elements().chain(
             self.c1
@@ -344,7 +341,7 @@ impl<P: CubicExtConfig> Zeroize for CubicExtField<P> {
 impl<P: CubicExtConfig> From<u128> for CubicExtField<P> {
     fn from(other: u128) -> Self {
         let fe: P::BaseField = other.into();
-        Self::new(fe, P::BaseField::zero(), P::BaseField::zero())
+        Self::new(fe, P::BaseField::ZERO, P::BaseField::ZERO)
     }
 }
 
@@ -363,7 +360,7 @@ impl<P: CubicExtConfig> From<i128> for CubicExtField<P> {
 impl<P: CubicExtConfig> From<u64> for CubicExtField<P> {
     fn from(other: u64) -> Self {
         let fe: P::BaseField = other.into();
-        Self::new(fe, P::BaseField::zero(), P::BaseField::zero())
+        Self::new(fe, P::BaseField::ZERO, P::BaseField::ZERO)
     }
 }
 
@@ -382,7 +379,7 @@ impl<P: CubicExtConfig> From<i64> for CubicExtField<P> {
 impl<P: CubicExtConfig> From<u32> for CubicExtField<P> {
     fn from(other: u32) -> Self {
         let fe: P::BaseField = other.into();
-        Self::new(fe, P::BaseField::zero(), P::BaseField::zero())
+        Self::new(fe, P::BaseField::ZERO, P::BaseField::ZERO)
     }
 }
 
@@ -401,7 +398,7 @@ impl<P: CubicExtConfig> From<i32> for CubicExtField<P> {
 impl<P: CubicExtConfig> From<u16> for CubicExtField<P> {
     fn from(other: u16) -> Self {
         let fe: P::BaseField = other.into();
-        Self::new(fe, P::BaseField::zero(), P::BaseField::zero())
+        Self::new(fe, P::BaseField::ZERO, P::BaseField::ZERO)
     }
 }
 
@@ -420,7 +417,7 @@ impl<P: CubicExtConfig> From<i16> for CubicExtField<P> {
 impl<P: CubicExtConfig> From<u8> for CubicExtField<P> {
     fn from(other: u8) -> Self {
         let fe: P::BaseField = other.into();
-        Self::new(fe, P::BaseField::zero(), P::BaseField::zero())
+        Self::new(fe, P::BaseField::ZERO, P::BaseField::ZERO)
     }
 }
 
@@ -440,8 +437,8 @@ impl<P: CubicExtConfig> From<bool> for CubicExtField<P> {
     fn from(other: bool) -> Self {
         Self::new(
             u8::from(other).into(),
-            P::BaseField::zero(),
-            P::BaseField::zero(),
+            P::BaseField::ZERO,
+            P::BaseField::ZERO,
         )
     }
 }
@@ -699,4 +696,20 @@ mod cube_ext_tests {
             assert_eq!(actual, expected);
         }
     }
+
+    #[test]
+    fn test_from_base_prime_field_element() {
+        let ext_degree = Fq6::extension_degree() as usize;
+        let max_num_elems_to_test = 10;
+        for _ in 0..max_num_elems_to_test {
+            let mut random_coeffs = vec![Fq::zero(); ext_degree];
+            let random_coeff = Fq::rand(&mut test_rng());
+            let res = Fq6::from_base_prime_field(random_coeff);
+            random_coeffs[0] = random_coeff;
+            assert_eq!(
+                res,
+                Fq6::from_base_prime_field_elems(&random_coeffs).unwrap()
+            );
+        }
+    }
 }

ff/src/fields/models/fp/mod.rs

@@ -240,6 +240,10 @@ impl<P: FpConfig<N>, const N: usize> Field for Fp<P, N> {
         1
     }
 
+    fn from_base_prime_field(elem: Self::BasePrimeField) -> Self {
+        elem
+    }
+
     fn to_base_prime_field_elements(&self) -> Self::BasePrimeFieldIter {
         iter::once(*self)
     }

ff/src/fields/models/quadratic_extension.rs

@@ -244,6 +244,11 @@ impl<P: QuadExtConfig> Field for QuadExtField<P> {
         2 * P::BaseField::extension_degree()
     }
 
+    fn from_base_prime_field(elem: Self::BasePrimeField) -> Self {
+        let fe = P::BaseField::from_base_prime_field(elem);
+        Self::new(fe, P::BaseField::ZERO)
+    }
+
     fn to_base_prime_field_elements(&self) -> Self::BasePrimeFieldIter {
         self.c0
             .to_base_prime_field_elements()
@@ -410,12 +415,12 @@ where
             // so either a0 = sqrt(c0) or a1 = sqrt(c0/P::NONRESIDUE)
             if self.c0.legendre().is_qr() {
                 // either c0 is a valid sqrt in the base field
-                return self.c0.sqrt().map(|c0| Self::new(c0, P::BaseField::zero()));
+                return self.c0.sqrt().map(|c0| Self::new(c0, P::BaseField::ZERO));
             } else {
                 // or we need to compute sqrt(c0/P::NONRESIDUE)
                 return (self.c0.div(P::NONRESIDUE))
                     .sqrt()
-                    .map(|res| Self::new(P::BaseField::zero(), res));
+                    .map(|res| Self::new(P::BaseField::ZERO, res));
             }
         }
         // Try computing the square root
@@ -497,7 +502,7 @@ impl<P: QuadExtConfig> Zeroize for QuadExtField<P> {
 
 impl<P: QuadExtConfig> From<u128> for QuadExtField<P> {
     fn from(other: u128) -> Self {
-        Self::new(other.into(), P::BaseField::zero())
+        Self::new(other.into(), P::BaseField::ZERO)
     }
 }
 
@@ -515,7 +520,7 @@ impl<P: QuadExtConfig> From<i128> for QuadExtField<P> {
 
 impl<P: QuadExtConfig> From<u64> for QuadExtField<P> {
     fn from(other: u64) -> Self {
-        Self::new(other.into(), P::BaseField::zero())
+        Self::new(other.into(), P::BaseField::ZERO)
     }
 }
 
@@ -533,7 +538,7 @@ impl<P: QuadExtConfig> From<i64> for QuadExtField<P> {
 
 impl<P: QuadExtConfig> From<u32> for QuadExtField<P> {
     fn from(other: u32) -> Self {
-        Self::new(other.into(), P::BaseField::zero())
+        Self::new(other.into(), P::BaseField::ZERO)
     }
 }
 
@@ -551,7 +556,7 @@ impl<P: QuadExtConfig> From<i32> for QuadExtField<P> {
 
 impl<P: QuadExtConfig> From<u16> for QuadExtField<P> {
     fn from(other: u16) -> Self {
-        Self::new(other.into(), P::BaseField::zero())
+        Self::new(other.into(), P::BaseField::ZERO)
     }
 }
 
@@ -569,7 +574,7 @@ impl<P: QuadExtConfig> From<i16> for QuadExtField<P> {
 
 impl<P: QuadExtConfig> From<u8> for QuadExtField<P> {
     fn from(other: u8) -> Self {
-        Self::new(other.into(), P::BaseField::zero())
+        Self::new(other.into(), P::BaseField::ZERO)
     }
 }
 
@@ -587,7 +592,7 @@ impl<P: QuadExtConfig> From<i8> for QuadExtField<P> {
 
 impl<P: QuadExtConfig> From<bool> for QuadExtField<P> {
     fn from(other: bool) -> Self {
-        Self::new(u8::from(other).into(), P::BaseField::zero())
+        Self::new(u8::from(other).into(), P::BaseField::ZERO)
     }
 }
 
@@ -802,4 +807,20 @@ mod quad_ext_tests {
             assert_eq!(actual, expected);
         }
     }
+
+    #[test]
+    fn test_from_base_prime_field_element() {
+        let ext_degree = Fq2::extension_degree() as usize;
+        let max_num_elems_to_test = 10;
+        for _ in 0..max_num_elems_to_test {
+            let mut random_coeffs = vec![Fq::zero(); ext_degree];
+            let random_coeff = Fq::rand(&mut test_rng());
+            let res = Fq2::from_base_prime_field(random_coeff);
+            random_coeffs[0] = random_coeff;
+            assert_eq!(
+                res,
+                Fq2::from_base_prime_field_elems(&random_coeffs).unwrap()
+            );
+        }
+    }
 }