Add a few simplifications around Mont inverse (arkworks-rs#788)

* Add a few simplifications around Mont inverse * Update ff/src/biginteger/mod.rs Co-authored-by: Pratyush Mishra <pratyush795@gmail.com> --------- Co-authored-by: Pratyush Mishra <pratyush795@gmail.com>
PayneJoe · Feb 27, 2024 · 2a8f518 · 2a8f518
1 parent 80e7b5a
commit 2a8f518
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Showing 2 changed files with 46 additions and 48 deletions.
diff --git a/ff/src/biginteger/mod.rs b/ff/src/biginteger/mod.rs
@@ -427,8 +427,7 @@ impl<const N: usize> BigInteger for BigInt<N> {
     #[inline]
     fn div2(&mut self) {
         let mut t = 0;
-        for i in 0..N {
-            let a = &mut self.0[N - i - 1];
+        for a in self.0.iter_mut().rev() {
             let t2 = *a << 63;
             *a >>= 1;
             *a |= t;

diff --git a/ff/src/fields/models/fp/montgomery_backend.rs b/ff/src/fields/models/fp/montgomery_backend.rs
@@ -295,64 +295,63 @@ pub trait MontConfig<const N: usize>: 'static + Sync + Send + Sized {
 
     fn inverse(a: &Fp<MontBackend<Self, N>, N>) -> Option<Fp<MontBackend<Self, N>, N>> {
         if a.is_zero() {
-            None
-        } else {
-            // Guajardo Kumar Paar Pelzl
-            // Efficient Software-Implementation of Finite Fields with Applications to
-            // Cryptography
-            // Algorithm 16 (BEA for Inversion in Fp)
-
-            let one = BigInt::from(1u64);
-
-            let mut u = a.0;
-            let mut v = Self::MODULUS;
-            let mut b = Fp::new_unchecked(Self::R2); // Avoids unnecessary reduction step.
-            let mut c = Fp::zero();
-
-            while u != one && v != one {
-                while u.is_even() {
-                    u.div2();
-
-                    if b.0.is_even() {
-                        b.0.div2();
-                    } else {
-                        let carry = b.0.add_with_carry(&Self::MODULUS);
-                        b.0.div2();
-                        if !Self::MODULUS_HAS_SPARE_BIT && carry {
-                            (b.0).0[N - 1] |= 1 << 63;
-                        }
-                    }
-                }
+            return None;
+        }
+        // Guajardo Kumar Paar Pelzl
+        // Efficient Software-Implementation of Finite Fields with Applications to
+        // Cryptography
+        // Algorithm 16 (BEA for Inversion in Fp)
 
-                while v.is_even() {
-                    v.div2();
+        let one = BigInt::from(1u64);
 
-                    if c.0.is_even() {
-                        c.0.div2();
-                    } else {
-                        let carry = c.0.add_with_carry(&Self::MODULUS);
-                        c.0.div2();
-                        if !Self::MODULUS_HAS_SPARE_BIT && carry {
-                            (c.0).0[N - 1] |= 1 << 63;
-                        }
+        let mut u = a.0;
+        let mut v = Self::MODULUS;
+        let mut b = Fp::new_unchecked(Self::R2); // Avoids unnecessary reduction step.
+        let mut c = Fp::zero();
+
+        while u != one && v != one {
+            while u.is_even() {
+                u.div2();
+
+                if b.0.is_even() {
+                    b.0.div2();
+                } else {
+                    let carry = b.0.add_with_carry(&Self::MODULUS);
+                    b.0.div2();
+                    if !Self::MODULUS_HAS_SPARE_BIT && carry {
+                        (b.0).0[N - 1] |= 1 << 63;
                     }
                 }
+            }
+
+            while v.is_even() {
+                v.div2();
 
-                if v < u {
-                    u.sub_with_borrow(&v);
-                    b -= &c;
+                if c.0.is_even() {
+                    c.0.div2();
                 } else {
-                    v.sub_with_borrow(&u);
-                    c -= &b;
+                    let carry = c.0.add_with_carry(&Self::MODULUS);
+                    c.0.div2();
+                    if !Self::MODULUS_HAS_SPARE_BIT && carry {
+                        (c.0).0[N - 1] |= 1 << 63;
+                    }
                 }
             }
 
-            if u == one {
-                Some(b)
+            if v < u {
+                u.sub_with_borrow(&v);
+                b -= &c;
             } else {
-                Some(c)
+                v.sub_with_borrow(&u);
+                c -= &b;
             }
         }
+
+        if u == one {
+            Some(b)
+        } else {
+            Some(c)
+        }
     }
 
     fn from_bigint(r: BigInt<N>) -> Option<Fp<MontBackend<Self, N>, N>> {