Remove FieldExt::{RESCUE_ALPHA, RESCUE_INVALPHA}

CHANGELOG.md

@@ -17,6 +17,7 @@ and this project adheres to Rust's notion of
   - `FieldExt::ROOT_OF_UNITY` (use `ff::PrimeField::root_of_unity` instead).
   - `FieldExt::{T_MINUS1_OVER2, pow_by_t_minus1_over2, sqrt_alt, sqrt_ratio}`
     (moved to `SqrtRatio` trait).
+  - `FieldExt::{RESCUE_ALPHA, RESCUE_INVALPHA}`
 
 ## [0.2.1] - 2021-09-17
 ### Changed

src/arithmetic/fields.rs

@@ -74,13 +74,6 @@ pub trait FieldExt: SqrtRatio + From<bool> + Ord + Group<Scalar = Self> {
     /// Inverse of $2$ in the field.
     const TWO_INV: Self;
 
-    /// Ideally the smallest prime $\alpha$ such that gcd($p - 1$, $\alpha$) = $1$
-    const RESCUE_ALPHA: u64;
-
-    /// $RESCUE_INVALPHA \cdot RESCUE_ALPHA = 1 \mod p - 1$ such that
-    /// `(a^RESCUE_ALPHA)^RESCUE_INVALPHA = a`.
-    const RESCUE_INVALPHA: [u64; 4];
-
     /// Element of multiplicative order $3$.
     const ZETA: Self;
 

src/fields/fp.rs

@@ -730,13 +730,6 @@ impl FieldExt for Fp {
         0x0000000000000000,
         0x2000000000000000,
     ]);
-    const RESCUE_ALPHA: u64 = 5;
-    const RESCUE_INVALPHA: [u64; 4] = [
-        0xe0f0f3f0cccccccd,
-        0x4e9ee0c9a10a60e2,
-        0x3333333333333333,
-        0x3333333333333333,
-    ];
     const ZETA: Self = Fp::from_raw([
         0x1dad5ebdfdfe4ab9,
         0x1d1f8bd237ad3149,
@@ -807,18 +800,6 @@ fn test_inv() {
     assert_eq!(inv, INV);
 }
 
-#[cfg(feature = "std")]
-#[test]
-fn test_rescue() {
-    // NB: TWO_INV is standing in as a "random" field element
-    assert_eq!(
-        Fp::TWO_INV
-            .pow_vartime(&[Fp::RESCUE_ALPHA, 0, 0, 0])
-            .pow_vartime(&Fp::RESCUE_INVALPHA),
-        Fp::TWO_INV
-    );
-}
-
 #[cfg(feature = "std")]
 #[test]
 fn test_sqrt() {

src/fields/fq.rs

@@ -730,13 +730,6 @@ impl FieldExt for Fq {
         0x0000000000000000,
         0x2000000000000000,
     ]);
-    const RESCUE_ALPHA: u64 = 5;
-    const RESCUE_INVALPHA: [u64; 4] = [
-        0xd69f2280cccccccd,
-        0x4e9ee0c9a143ba4a,
-        0x3333333333333333,
-        0x3333333333333333,
-    ];
     const ZETA: Self = Fq::from_raw([
         0x2aa9d2e050aa0e4f,
         0x0fed467d47c033af,
@@ -807,18 +800,6 @@ fn test_inv() {
     assert_eq!(inv, INV);
 }
 
-#[cfg(feature = "std")]
-#[test]
-fn test_rescue() {
-    // NB: TWO_INV is standing in as a "random" field element
-    assert_eq!(
-        Fq::TWO_INV
-            .pow_vartime(&[Fq::RESCUE_ALPHA, 0, 0, 0])
-            .pow_vartime(&Fq::RESCUE_INVALPHA),
-        Fq::TWO_INV
-    );
-}
-
 #[cfg(feature = "std")]
 #[test]
 fn test_sqrt() {