ff: Remove frobenius_map from Field trait

It is only used internally in the bls12_381 crate, and field extensions
aren't exposed anywhere in the Zcash stack.

bellman/src/groth16/tests/dummy_engine.rs

@@ -214,10 +214,6 @@ impl Field for Fr {
         }
     }
 
-    fn frobenius_map(&mut self, _: usize) {
-        // identity
-    }
-
     fn sqrt(&self) -> CtOption<Self> {
         // Tonelli-Shank's algorithm for q mod 16 = 1
         // https://eprint.iacr.org/2012/685.pdf (page 12, algorithm 5)

ff/ff_derive/src/lib.rs

@@ -1266,11 +1266,6 @@ fn prime_field_impl(
                 #invert_impl
             }
 
-            #[inline(always)]
-            fn frobenius_map(&mut self, _: usize) {
-                // This has no effect in a prime field.
-            }
-
             #[inline]
             fn square(&self) -> Self
             {

ff/src/lib.rs

@@ -72,10 +72,6 @@ pub trait Field:
     /// failing if the element is zero.
     fn invert(&self) -> CtOption<Self>;
 
-    /// Exponentiates this element by a power of the base prime modulus via
-    /// the Frobenius automorphism.
-    fn frobenius_map(&mut self, power: usize);
-
     /// Returns the square root of the field element, if it is
     /// quadratic residue.
     fn sqrt(&self) -> CtOption<Self>;

pairing/src/bls12_381/fq.rs

@@ -1865,7 +1865,6 @@ fn test_fq_root_of_unity() {
 fn fq_field_tests() {
     crate::tests::field::random_field_tests::<Fq>();
     crate::tests::field::random_sqrt_tests::<Fq>();
-    crate::tests::field::random_frobenius_tests::<Fq, _>(Fq::char(), 13);
     crate::tests::field::from_str_tests::<Fq>();
 }
 

pairing/src/bls12_381/fq12.rs

@@ -39,6 +39,15 @@ impl Fq12 {
         self.c0.mul_by_nonresidue();
         self.c0.add_assign(&aa);
     }
+
+    pub fn frobenius_map(&mut self, power: usize) {
+        self.c0.frobenius_map(power);
+        self.c1.frobenius_map(power);
+
+        self.c1.c0.mul_assign(&FROBENIUS_COEFF_FQ12_C1[power % 12]);
+        self.c1.c1.mul_assign(&FROBENIUS_COEFF_FQ12_C1[power % 12]);
+        self.c1.c2.mul_assign(&FROBENIUS_COEFF_FQ12_C1[power % 12]);
+    }
 }
 
 impl ConditionallySelectable for Fq12 {
@@ -200,15 +209,6 @@ impl Field for Fq12 {
         }
     }
 
-    fn frobenius_map(&mut self, power: usize) {
-        self.c0.frobenius_map(power);
-        self.c1.frobenius_map(power);
-
-        self.c1.c0.mul_assign(&FROBENIUS_COEFF_FQ12_C1[power % 12]);
-        self.c1.c1.mul_assign(&FROBENIUS_COEFF_FQ12_C1[power % 12]);
-        self.c1.c2.mul_assign(&FROBENIUS_COEFF_FQ12_C1[power % 12]);
-    }
-
     fn square(&self) -> Self {
         let mut ab = self.c0;
         ab.mul_assign(&self.c1);
@@ -282,8 +282,5 @@ fn test_fq12_mul_by_014() {
 
 #[test]
 fn fq12_field_tests() {
-    use ff::PrimeField;
-
     crate::tests::field::random_field_tests::<Fq12>();
-    crate::tests::field::random_frobenius_tests::<Fq12, _>(super::fq::Fq::char(), 13);
 }

pairing/src/bls12_381/fq2.rs

@@ -53,6 +53,10 @@ impl Fq2 {
 
         t1
     }
+
+    pub fn frobenius_map(&mut self, power: usize) {
+        self.c1.mul_assign(&FROBENIUS_COEFF_FQ2_C1[power % 2]);
+    }
 }
 
 impl ConditionallySelectable for Fq2 {
@@ -238,10 +242,6 @@ impl Field for Fq2 {
         })
     }
 
-    fn frobenius_map(&mut self, power: usize) {
-        self.c1.mul_assign(&FROBENIUS_COEFF_FQ2_C1[power % 2]);
-    }
-
     /// WARNING: THIS IS NOT ACTUALLY CONSTANT TIME YET!
     /// THIS WILL BE REPLACED BY THE bls12_381 CRATE, WHICH IS CONSTANT TIME!
     fn sqrt(&self) -> CtOption<Self> {
@@ -920,9 +920,6 @@ fn test_fq2_mul_nonresidue() {
 
 #[test]
 fn fq2_field_tests() {
-    use ff::PrimeField;
-
     crate::tests::field::random_field_tests::<Fq2>();
     crate::tests::field::random_sqrt_tests::<Fq2>();
-    crate::tests::field::random_frobenius_tests::<Fq2, _>(super::fq::Fq::char(), 13);
 }

pairing/src/bls12_381/fq6.rs

@@ -99,6 +99,15 @@ impl Fq6 {
         self.c1 = t2;
         self.c2 = t3;
     }
+
+    pub fn frobenius_map(&mut self, power: usize) {
+        self.c0.frobenius_map(power);
+        self.c1.frobenius_map(power);
+        self.c2.frobenius_map(power);
+
+        self.c1.mul_assign(&FROBENIUS_COEFF_FQ6_C1[power % 6]);
+        self.c2.mul_assign(&FROBENIUS_COEFF_FQ6_C2[power % 6]);
+    }
 }
 
 impl ConditionallySelectable for Fq6 {
@@ -305,15 +314,6 @@ impl Field for Fq6 {
         }
     }
 
-    fn frobenius_map(&mut self, power: usize) {
-        self.c0.frobenius_map(power);
-        self.c1.frobenius_map(power);
-        self.c2.frobenius_map(power);
-
-        self.c1.mul_assign(&FROBENIUS_COEFF_FQ6_C1[power % 6]);
-        self.c2.mul_assign(&FROBENIUS_COEFF_FQ6_C2[power % 6]);
-    }
-
     fn square(&self) -> Self {
         let s0 = self.c0.square();
         let mut ab = self.c0;
@@ -474,8 +474,5 @@ fn test_fq6_mul_by_01() {
 
 #[test]
 fn fq6_field_tests() {
-    use ff::PrimeField;
-
     crate::tests::field::random_field_tests::<Fq6>();
-    crate::tests::field::random_frobenius_tests::<Fq6, _>(super::fq::Fq::char(), 13);
 }

pairing/src/bls12_381/fr.rs

@@ -645,7 +645,6 @@ fn test_fr_root_of_unity() {
 fn fr_field_tests() {
     crate::tests::field::random_field_tests::<Fr>();
     crate::tests::field::random_sqrt_tests::<Fr>();
-    crate::tests::field::random_frobenius_tests::<Fr, _>(Fr::char(), 13);
     crate::tests::field::from_str_tests::<Fr>();
 }
 

pairing/src/tests/field.rs

@@ -1,28 +1,7 @@
-use ff::{Field, PowVartime, PrimeField};
+use ff::{Field, PrimeField};
 use rand_core::{RngCore, SeedableRng};
 use rand_xorshift::XorShiftRng;
 
-pub fn random_frobenius_tests<F: Field, C: AsRef<[u8]>>(characteristic: C, maxpower: usize) {
-    let mut rng = XorShiftRng::from_seed([
-        0x59, 0x62, 0xbe, 0x5d, 0x76, 0x3d, 0x31, 0x8d, 0x17, 0xdb, 0x37, 0x32, 0x54, 0x06, 0xbc,
-        0xe5,
-    ]);
-
-    for _ in 0..100 {
-        for i in 0..=maxpower {
-            let mut a = F::random(&mut rng);
-            let mut b = a;
-
-            for _ in 0..i {
-                a = a.pow_vartime(&characteristic);
-            }
-            b.frobenius_map(i);
-
-            assert_eq!(a, b);
-        }
-    }
-}
-
 pub fn random_sqrt_tests<F: Field>() {
     let mut rng = XorShiftRng::from_seed([
         0x59, 0x62, 0xbe, 0x5d, 0x76, 0x3d, 0x31, 0x8d, 0x17, 0xdb, 0x37, 0x32, 0x54, 0x06, 0xbc,

zcash_primitives/src/jubjub/fs.rs

@@ -499,11 +499,6 @@ impl Field for Fs {
         CtOption::new(inverse, Choice::from(if self.is_zero() { 0 } else { 1 }))
     }
 
-    #[inline(always)]
-    fn frobenius_map(&mut self, _: usize) {
-        // This has no effect in a prime field.
-    }
-
     #[inline]
     fn square(&self) -> Self {
         let mut carry = 0;