From 24b32ea66c4510f443d8fabebf89f7a77e4baccb Mon Sep 17 00:00:00 2001
From: Supragya Raj <supragyaraj@gmail.com>
Date: Mon, 1 Jul 2024 23:31:42 +0530
Subject: [PATCH] cleaner: reuse .pow() code

---
 src/field/prime/mod.rs | 19 ++++++-------------
 1 file changed, 6 insertions(+), 13 deletions(-)

diff --git a/src/field/prime/mod.rs b/src/field/prime/mod.rs
index b524002..745f68c 100644
--- a/src/field/prime/mod.rs
+++ b/src/field/prime/mod.rs
@@ -114,19 +114,12 @@ impl<const P: usize> const FiniteField for PrimeField<P> {
     if self.value == 0 {
       return None;
     }
-    let exponent = Self::ORDER - 2;
-    let mut result = Self::ONE;
-    let mut base = *self;
-    let mut power = exponent;
-
-    while power > 0 {
-      if power & 1 == 1 {
-        result *= base;
-      }
-      base = base * base;
-      power >>= 1;
-    }
-    Some(result)
+
+    // By fermat's little theorem, in any prime field P, for any elem:
+    //    e^(P-1) = 1 mod P
+    // So,
+    //    e^(P-2) = e^-1 mod P
+    Some(self.pow(Self::ORDER - 2))
   }
 
   fn pow(self, power: usize) -> Self {